Merge branch 'delcypher-cmake_fix_enable_tracing_in_debug_mode'

CMakeLists.txt

@@ -289,12 +289,14 @@ endif()
 ################################################################################
 # Tracing
 ################################################################################
-option(ENABLE_TRACING OFF "Enable tracing")
-if (ENABLE_TRACING)
+option(ENABLE_TRACING_FOR_NON_DEBUG "Enable tracing in non-debug builds." OFF)
+if (ENABLE_TRACING_FOR_NON_DEBUG)
   list(APPEND Z3_COMPONENT_CXX_DEFINES "-D_TRACE")
+else()
+  # Tracing is always enabled in debug builds
+  list(APPEND Z3_COMPONENT_CXX_DEFINES $<$<CONFIG:Debug>:_TRACE>)
 endif()
 # Should we always enable tracing when doing a debug build?
-#list(APPEND Z3_COMPONENT_CXX_DEFINES $<$<CONFIG:Debug>:_TRACE>)
 
 ################################################################################
 # Postion indepdent code

README-CMake.md

@@ -265,7 +265,8 @@ The following useful options can be passed to CMake whilst configuring.
 * ``CMAKE_INSTALL_INCLUDEDIR`` - STRING. The path to install z3 include files (relative to ``CMAKE_INSTALL_PREFIX``), e.g. ``include``.
 * ``CMAKE_INSTALL_LIBDIR`` - STRING. The path to install z3 libraries (relative to ``CMAKE_INSTALL_PREFIX``), e.g. ``lib``.
 * ``CMAKE_INSTALL_PREFIX`` - STRING. The install prefix to use (e.g. ``/usr/local/``).
-* ``ENABLE_TRACING`` - BOOL. If set to ``TRUE`` enable tracing, if set to ``FALSE`` disable tracing.
+* ``CMAKE_INSTALL_PYTHON_PKG_DIR`` - STRING. The path to install the z3 python bindings. This can be relative (to ``CMAKE_INSTALL_PREFIX``) or absolute.
+* ``ENABLE_TRACING_FOR_NON_DEBUG`` - BOOL. If set to ``TRUE`` enable tracing in non-debug builds, if set to ``FALSE`` disable tracing in non-debug builds. Note in debug builds tracing is always enabled.
 * ``BUILD_LIBZ3_SHARED`` - BOOL. If set to ``TRUE`` build libz3 as a shared library otherwise build as a static library.
 * ``ENABLE_EXAMPLE_TARGETS`` - BOOL. If set to ``TRUE`` add the build targets for building the API examples.
 * ``USE_OPENMP`` - BOOL. If set to ``TRUE`` and OpenMP support is detected build with OpenMP support.

contrib/cmake/src/api/python/CMakeLists.txt

@@ -74,35 +74,50 @@ add_custom_target(build_z3_python_bindings
 ###############################################################################
 option(INSTALL_PYTHON_BINDINGS "Install Python bindings when invoking install target" ON)
 if (INSTALL_PYTHON_BINDINGS)
-  # Determine the installation path for the bindings
   message(STATUS "Emitting rules to install Z3 python bindings")
-  execute_process(
-    COMMAND "${PYTHON_EXECUTABLE}" "-c"
-      "import distutils.sysconfig; print(distutils.sysconfig.get_python_lib())"
-    RESULT_VARIABLE exit_code
-    OUTPUT_VARIABLE python_pkg_dir
-    OUTPUT_STRIP_TRAILING_WHITESPACE
-  )
+  # Try to guess the installation path for the bindings
+  if (NOT DEFINED CMAKE_INSTALL_PYTHON_PKG_DIR)
+    message(STATUS "CMAKE_INSTALL_PYTHON_PKG_DIR not set. Trying to guess")
+    execute_process(
+      COMMAND "${PYTHON_EXECUTABLE}" "-c"
+        "import distutils.sysconfig; print(distutils.sysconfig.get_python_lib())"
+      RESULT_VARIABLE exit_code
+      OUTPUT_VARIABLE CMAKE_INSTALL_PYTHON_PKG_DIR
+      OUTPUT_STRIP_TRAILING_WHITESPACE
+    )
 
-  if (NOT ("${exit_code}" EQUAL 0))
-    message(FATAL_ERROR "Failed to determine your Python package directory")
+    if (NOT ("${exit_code}" EQUAL 0))
+      message(FATAL_ERROR "Failed to determine your Python package directory")
+    endif()
+    message(STATUS "Detected Python package directory: \"${CMAKE_INSTALL_PYTHON_PKG_DIR}\"")
+    # Set a cache variable that the user can modify if needed
+    set(CMAKE_INSTALL_PYTHON_PKG_DIR
+      "${CMAKE_INSTALL_PYTHON_PKG_DIR}"
+      CACHE PATH
+      "Path to install python bindings. This can be relative or absolute.")
+    mark_as_advanced(CMAKE_INSTALL_PYTHON_PKG_DIR)
+  else()
+    message(STATUS "CMAKE_INSTALL_PYTHON_PKG_DIR already set (\"${CMAKE_INSTALL_PYTHON_PKG_DIR}\")"
+                   ". Not trying to guess.")
   endif()
-  message(STATUS "Detected Python package directory: \"${python_pkg_dir}\"")
 
-  # Check if path exists under the install prefix
-  set(python_install_dir "")
-  string(FIND "${python_pkg_dir}" "${CMAKE_INSTALL_PREFIX}" position)
-  if (NOT ("${position}" EQUAL 0))
-    message(WARNING "The detected Python package directory \"${python_pkg_dir}\" "
-            "does not exist under the install prefix \"${CMAKE_INSTALL_PREFIX}\"."
-            " Running the install target may lead to a broken installation."
-           )
+  # Check if path exists under the install prefix if it is absolute. If the
+  # path is relative it will be installed under the install prefix so there
+  # if nothing to check
+  if (IS_ABSOLUTE "${CMAKE_INSTALL_PYTHON_PKG_DIR}")
+    string(FIND "${CMAKE_INSTALL_PYTHON_PKG_DIR}" "${CMAKE_INSTALL_PREFIX}" position)
+    if (NOT ("${position}" EQUAL 0))
+      message(WARNING "The directory to install the python bindings \"${CMAKE_INSTALL_PYTHON_PKG_DIR}\" "
+              "is not under the install prefix \"${CMAKE_INSTALL_PREFIX}\"."
+              " Running the install target may lead to a broken installation. "
+              "To change the install directory modify the CMAKE_INSTALL_PYTHON_PKG_DIR cache variable."
+              )
+    endif()
   endif()
   # Using DESTDIR still seems to work even if we use an absolute path
-  set(python_install_dir "${python_pkg_dir}")
-  message(STATUS "Python bindings will be installed to \"${python_install_dir}\"")
+  message(STATUS "Python bindings will be installed to \"${CMAKE_INSTALL_PYTHON_PKG_DIR}\"")
   install(FILES ${build_z3_python_bindings_target_depends}
-    DESTINATION "${python_install_dir}"
+    DESTINATION "${CMAKE_INSTALL_PYTHON_PKG_DIR}"
   )
 else()
   message(STATUS "Not emitting rules to install Z3 python bindings")

contrib/cmake/src/ast/rewriter/CMakeLists.txt

@@ -12,6 +12,7 @@ z3_add_component(rewriter
     expr_safe_replace.cpp
     factor_rewriter.cpp
     fpa_rewriter.cpp
+    label_rewriter.cpp
     mk_simplified_app.cpp
     pb_rewriter.cpp
     quant_hoist.cpp

contrib/cmake/src/qe/CMakeLists.txt

@@ -1,21 +1,28 @@
 z3_add_component(qe
   SOURCES
     nlarith_util.cpp
+    nlqsat.cpp
     qe_arith.cpp
     qe_arith_plugin.cpp
     qe_array_plugin.cpp
+    qe_arrays.cpp
     qe_bool_plugin.cpp
     qe_bv_plugin.cpp
     qe_cmd.cpp
     qe.cpp
     qe_datatype_plugin.cpp
+    qe_datatypes.cpp
     qe_dl_plugin.cpp
     qe_lite.cpp
+    qe_mbp.cpp
     qe_sat_tactic.cpp
     qe_tactic.cpp
-    qe_util.cpp
+    qsat.cpp
     vsubst_tactic.cpp
   COMPONENT_DEPENDENCIES
+    nlsat_tactic
+    nlsat
     sat
-    smt
+    smt   
+    tactic 
 )

scripts/mk_genfile_common.py

@@ -57,7 +57,7 @@ def sorted_headers_by_component(l):
         _logger.debug("get_key({})".format(path))
         path_components = []
         stripped_path = path
-        assert 'src' in stripped_path.split(os.path.sep)
+        assert 'src' in stripped_path.split(os.path.sep) or 'src' in stripped_path.split('/')
         # Keep stripping off directory components until we hit ``src``
         while os.path.basename(stripped_path) != 'src':
             path_components.append(os.path.basename(stripped_path))
@@ -214,7 +214,7 @@ def mk_gparams_register_modules_internal(component_src_dirs, path):
     """
     assert isinstance(component_src_dirs, list)
     assert check_dir_exists(path)
-    cmds = []
+    cmds = []    
     mod_cmds = []
     mod_descrs = []
     fullname = os.path.join(path, 'gparams_register_modules.cpp')

scripts/mk_project.py

@@ -57,7 +57,7 @@ def init_project_def():
     add_lib('fuzzing', ['ast'], 'test/fuzzing')
     add_lib('smt_tactic', ['smt'], 'smt/tactic')
     add_lib('sls_tactic', ['tactic', 'normal_forms', 'core_tactics', 'bv_tactics'], 'tactic/sls')
-    add_lib('qe', ['smt','sat'], 'qe')
+    add_lib('qe', ['smt','sat','nlsat','tactic','nlsat_tactic'], 'qe')
     add_lib('duality', ['smt', 'interp', 'qe'])
     add_lib('muz', ['smt', 'sat', 'smt2parser', 'aig_tactic', 'qe'], 'muz/base')
     add_lib('dataflow', ['muz'], 'muz/dataflow')

src/api/c++/z3++.h

@@ -604,8 +604,16 @@ namespace z3 {
 
         /**
            \brief Return true if this expression is a numeral.
+           Specialized functions also return representations for the numerals as
+           small integers, 64 bit integers or rational or decimal strings.
         */
         bool is_numeral() const { return kind() == Z3_NUMERAL_AST; }
+        bool is_numeral_i64(__int64& i) const { bool r = 0 != Z3_get_numeral_int64(ctx(), m_ast, &i); check_error(); return r;}
+        bool is_numeral_u64(__uint64& i) const { bool r = 0 != Z3_get_numeral_uint64(ctx(), m_ast, &i); check_error(); return r;}
+        bool is_numeral_i(int& i) const { bool r = 0 != Z3_get_numeral_int(ctx(), m_ast, &i); check_error(); return r;}
+        bool is_numeral_u(unsigned& i) const { bool r = 0 != Z3_get_numeral_uint(ctx(), m_ast, &i); check_error(); return r;}
+        bool is_numeral(std::string& s) const { if (!is_numeral()) return false; s = Z3_get_numeral_string(ctx(), m_ast); check_error(); return true; }
+        bool is_numeral(std::string& s, unsigned precision) const { if (!is_numeral()) return false; s = Z3_get_numeral_decimal_string(ctx(), m_ast, precision); check_error(); return true; }
         /**
            \brief Return true if this expression is an application.
         */
@@ -625,7 +633,7 @@ namespace z3 {
         /**
            \brief Return true if expression is an algebraic number.
         */
-        bool is_algebraic() const { return Z3_is_algebraic_number(ctx(), m_ast); }
+        bool is_algebraic() const { return 0 != Z3_is_algebraic_number(ctx(), m_ast); }
 
         /**
            \brief Return true if this expression is well sorted (aka type correct).
@@ -649,12 +657,11 @@ namespace z3 {
            
            \pre is_numeral()
         */
-        int get_numeral_int() const {
-            assert(is_numeral());
+        int get_numeral_int() const {             
             int result;
-            Z3_bool state = Z3_get_numeral_int(ctx(), m_ast, &result);
-            if (state != Z3_TRUE)
+            if (!is_numeral_i(result)) {
                 throw exception("numeral does not fit in machine int");
+            }
             return result;
         }
         
@@ -667,9 +674,9 @@ namespace z3 {
         unsigned get_numeral_uint() const {
             assert(is_numeral());
             unsigned result;
-            Z3_bool state = Z3_get_numeral_uint(ctx(), m_ast, &result);
-            if (state != Z3_TRUE)
+            if (!is_numeral_u(result)) {
                 throw exception("numeral does not fit in machine uint");
+            }
             return result;
         }
         
@@ -682,9 +689,9 @@ namespace z3 {
         __int64 get_numeral_int64() const {
             assert(is_numeral());
             __int64 result;
-            Z3_bool state = Z3_get_numeral_int64(ctx(), m_ast, &result);
-            if (state != Z3_TRUE)
+            if (!is_numeral_i64(result)) {
                 throw exception("numeral does not fit in machine __int64");
+            }
             return result;
         }
         
@@ -697,9 +704,9 @@ namespace z3 {
         __uint64 get_numeral_uint64() const {
             assert(is_numeral());
             __uint64 result;
-            Z3_bool state = Z3_get_numeral_uint64(ctx(), m_ast, &result);
-            if (state != Z3_TRUE)
+            if (!is_numeral_u64(result)) {
                 throw exception("numeral does not fit in machine __uint64");
+            }
             return result;
         }
            

src/api/python/z3.py

@@ -3940,7 +3940,7 @@ class ArraySortRef(SortRef):
         >>> A.range()
         Bool
         """
-        return _to_sort_ref(Z3_get_array_sort_range(self.ctx_ref(), self.ast), self.ctx)
+        return _to_sort_ref(Z3_get_array_sort_range(self.ctx_ref(), self.ast), self.ctx)    
 
 class ArrayRef(ExprRef):
     """Array expressions. """
@@ -4162,6 +4162,7 @@ def Select(a, i):
         _z3_assert(is_array(a), "First argument must be a Z3 array expression")
     return a[i]
 
+    
 def Map(f, *args):
     """Return a Z3 map array expression.
 

src/ast/arith_decl_plugin.cpp

@@ -664,3 +664,45 @@ algebraic_numbers::anum const & arith_util::to_irrational_algebraic_numeral(expr
     SASSERT(is_irrational_algebraic_numeral(n));
     return plugin().aw().to_anum(to_app(n)->get_decl());
 }
+
+expr_ref arith_util::mk_mul_simplify(expr_ref_vector const& args) {
+    return mk_mul_simplify(args.size(), args.c_ptr());
+
+}
+expr_ref arith_util::mk_mul_simplify(unsigned sz, expr* const* args) {
+    expr_ref result(m_manager);
+    
+    switch (sz) {
+    case 0:
+        result = mk_numeral(rational(1), true);
+        break;
+    case 1:
+        result = args[0];
+        break;
+    default:
+        result = mk_mul(sz, args);
+        break;                    
+    }
+    return result;
+}
+
+expr_ref arith_util::mk_add_simplify(expr_ref_vector const& args) {
+    return mk_add_simplify(args.size(), args.c_ptr());
+
+}
+expr_ref arith_util::mk_add_simplify(unsigned sz, expr* const* args) {
+    expr_ref result(m_manager);
+    
+    switch (sz) {
+    case 0:
+        result = mk_numeral(rational(0), true);
+        break;
+    case 1:
+        result = args[0];
+        break;
+    default:
+        result = mk_add(sz, args);
+        break;                    
+    }
+    return result;
+}

src/ast/arith_decl_plugin.h

@@ -149,7 +149,6 @@ protected:
     func_decl * m_mod_0_decl;
     func_decl * m_u_asin_decl;
     func_decl * m_u_acos_decl;
-
     ptr_vector<app> m_small_ints;
     ptr_vector<app> m_small_reals;
 
@@ -416,6 +415,11 @@ public:
         return m_manager.mk_eq(lhs, rhs);
     }
 
+    expr_ref mk_mul_simplify(expr_ref_vector const& args);
+    expr_ref mk_mul_simplify(unsigned sz, expr* const* args);
+
+    expr_ref mk_add_simplify(expr_ref_vector const& args);
+    expr_ref mk_add_simplify(unsigned sz, expr* const* args);
 };
 
 #endif /* ARITH_DECL_PLUGIN_H_ */

src/ast/ast_smt2_pp.cpp

@@ -1200,6 +1200,14 @@ std::ostream& operator<<(std::ostream& out, app_ref const&  e) {
     return out << mk_ismt2_pp(e.get(), e.get_manager());
 }
 
+std::ostream& operator<<(std::ostream& out, func_decl_ref const&  e) {
+    return out << mk_ismt2_pp(e.get(), e.get_manager());
+}
+
+std::ostream& operator<<(std::ostream& out, sort_ref const&  e) {
+    return out << mk_ismt2_pp(e.get(), e.get_manager());
+}
+
 std::ostream& operator<<(std::ostream& out, expr_ref_vector const&  e) {
     for (unsigned i = 0; i < e.size(); ++i) {
         out << mk_ismt2_pp(e[i], e.get_manager());
@@ -1216,6 +1224,18 @@ std::ostream& operator<<(std::ostream& out, app_ref_vector const&  e) {
     return out;
 }
 
+std::ostream& operator<<(std::ostream& out, func_decl_ref_vector const&  e) {
+    for (unsigned i = 0; i < e.size(); ++i) 
+        out << mk_ismt2_pp(e[i], e.get_manager()) << "\n";
+    return out;
+}
+
+std::ostream& operator<<(std::ostream& out, sort_ref_vector const&  e) {
+    for (unsigned i = 0; i < e.size(); ++i) 
+        out << mk_ismt2_pp(e[i], e.get_manager()) << "\n";
+    return out;
+}
+
 #ifdef Z3DEBUG
 void pp(expr const * n, ast_manager & m) {
     std::cout << mk_ismt2_pp(const_cast<expr*>(n), m) << std::endl;

src/ast/ast_smt2_pp.h

@@ -117,8 +117,13 @@ std::ostream& operator<<(std::ostream& out, mk_ismt2_pp const & p);
 
 std::ostream& operator<<(std::ostream& out, expr_ref const& e);
 std::ostream& operator<<(std::ostream& out, app_ref const& e);
+std::ostream& operator<<(std::ostream& out, func_decl_ref const& e);
+std::ostream& operator<<(std::ostream& out, sort_ref const& e);
+
 
 std::ostream& operator<<(std::ostream& out, expr_ref_vector const& e);
 std::ostream& operator<<(std::ostream& out, app_ref_vector const& e);
+std::ostream& operator<<(std::ostream& out, func_decl_ref_vector const& e);
+std::ostream& operator<<(std::ostream& out, sort_ref_vector const& e);
 
 #endif

src/ast/ast_util.cpp

@@ -170,7 +170,6 @@ app* mk_and(ast_manager & m, unsigned num_args, app * const * args) {
     return to_app(mk_and(m, num_args, (expr* const*) args));
 }
 
-
 expr * mk_or(ast_manager & m, unsigned num_args, expr * const * args) {
     if (num_args == 0)
         return m.mk_false();
@@ -188,10 +187,43 @@ expr * mk_not(ast_manager & m, expr * arg) {
     expr * atom;
     if (m.is_not(arg, atom))
         return atom;
+    else if (m.is_true(arg)) 
+        return m.mk_false();
+    else if (m.is_false(arg))
+        return m.mk_true();
     else
         return m.mk_not(arg);
 }
 
+expr_ref push_not(const expr_ref& e) {
+    ast_manager& m = e.get_manager();
+    if (!is_app(e)) {
+        return expr_ref(m.mk_not(e), m);
+    }
+    app* a = to_app(e);
+    if (m.is_and(a)) {
+        if (a->get_num_args() == 0) {
+            return expr_ref(m.mk_false(), m);
+        }
+        expr_ref_vector args(m);
+        for (unsigned i = 0; i < a->get_num_args(); ++i) {
+            args.push_back(push_not(expr_ref(a->get_arg(i), m)));
+        }
+        return mk_or(args);
+    }
+    if (m.is_or(a)) {
+        if (a->get_num_args() == 0) {
+            return expr_ref(m.mk_true(), m);
+        }
+        expr_ref_vector args(m);
+        for (unsigned i = 0; i < a->get_num_args(); ++i) {
+            args.push_back(push_not(expr_ref(a->get_arg(i), m)));
+        }
+        return mk_and(args);
+    }
+    return expr_ref(mk_not(m, e), m);    
+}
+
 expr * expand_distinct(ast_manager & m, unsigned num_args, expr * const * args) {
     expr_ref_buffer new_diseqs(m);
     for (unsigned i = 0; i < num_args; i++) {
@@ -201,6 +233,24 @@ expr * expand_distinct(ast_manager & m, unsigned num_args, expr * const * args)
     return mk_and(m, new_diseqs.size(), new_diseqs.c_ptr());
 }
 
+expr* mk_distinct(ast_manager& m, unsigned num_args, expr * const * args) {
+    switch (num_args) {
+    case 0:
+    case 1:
+        return m.mk_true();
+    case 2:
+        return m.mk_not(m.mk_eq(args[0], args[1]));
+    default:
+        return m.mk_distinct(num_args, args);
+    }
+}
+
+expr_ref mk_distinct(expr_ref_vector const& args) {
+    ast_manager& m = args.get_manager();
+    return expr_ref(mk_distinct(m, args.size(), args.c_ptr()), m);
+}
+
+
 void flatten_and(expr_ref_vector& result) {
     ast_manager& m = result.get_manager();
     expr* e1, *e2, *e3;

src/ast/ast_util.h

@@ -121,18 +121,29 @@ app  * mk_or(ast_manager & m, unsigned num_args, app * const * args);
 inline app_ref mk_or(app_ref_vector const& args) { return app_ref(mk_or(args.get_manager(), args.size(), args.c_ptr()), args.get_manager()); }
 inline expr_ref mk_or(expr_ref_vector const& args) { return expr_ref(mk_or(args.get_manager(), args.size(), args.c_ptr()), args.get_manager()); }
 
-
 /**
    Return a          if arg = (not a)
    Retur (not arg)   otherwise
  */
 expr * mk_not(ast_manager & m, expr * arg);
 
+/**
+   Negate and push over conjunction or disjunction.
+ */
+expr_ref push_not(const expr_ref& arg);
+
 /**
    Return the expression (and (not (= args[0] args[1])) (not (= args[0] args[2])) ... (not (= args[num_args-2] args[num_args-1])))
 */
 expr * expand_distinct(ast_manager & m, unsigned num_args, expr * const * args);
 
+/**
+   Create simplified distinct term. Binary distinct becomes a single disequality.
+ */
+expr * mk_distinct(ast_manager& m, unsigned num_args, expr * const * args);
+
+expr_ref mk_distinct(expr_ref_vector const& args);
+
 /**
    \brief Collect top-level conjunctions and disjunctions.
 */

src/ast/bv_decl_plugin.cpp

@@ -865,6 +865,12 @@ sort * bv_util::mk_sort(unsigned bv_size) {
     return m_manager.mk_sort(get_fid(), BV_SORT, 1, p);
 }
 
+unsigned bv_util::get_int2bv_size(parameter const& p) {
+    int sz;
+    VERIFY(m_plugin->get_int2bv_size(1, &p, sz));
+    return static_cast<unsigned>(sz);
+}
+
 app * bv_util::mk_bv2int(expr* e) {
     sort* s = m_manager.mk_sort(m_manager.mk_family_id("arith"), INT_SORT);
     parameter p(s);

src/ast/bv_decl_plugin.h

@@ -234,7 +234,6 @@ protected:
 
     func_decl * mk_mkbv(unsigned arity, sort * const * domain);
 
-    bool get_int2bv_size(unsigned num_parameters, parameter const * parameters, int & result);
 
     func_decl * mk_num_decl(unsigned num_parameters, parameter const * parameters, unsigned arity);
 
@@ -267,6 +266,8 @@ public:
 
     virtual expr * get_some_value(sort * s);
 
+    bool get_int2bv_size(unsigned num_parameters, parameter const * parameters, int & result);
+
     virtual bool is_considered_uninterpreted(func_decl * f) {
         if (f->get_family_id() != get_family_id())
             return false;
@@ -390,6 +391,8 @@ public:
         return static_cast<unsigned>(s->get_parameter(0).get_int());
     }
     unsigned get_bv_size(expr const * n) const { return get_bv_size(m_manager.get_sort(n)); }
+    unsigned get_int2bv_size(parameter const& p);
+
 
     app * mk_ule(expr * arg1, expr * arg2) { return m_manager.mk_app(get_fid(), OP_ULEQ, arg1, arg2); }
     app * mk_sle(expr * arg1, expr * arg2) { return m_manager.mk_app(get_fid(), OP_SLEQ, arg1, arg2); }
@@ -427,6 +430,7 @@ public:
     app * mk_bvumul_no_ovfl(expr* m, expr* n) { return m_manager.mk_app(get_fid(), OP_BUMUL_NO_OVFL, n, m); }
 
     app * mk_bv(unsigned n, expr* const* es) { return m_manager.mk_app(get_fid(), OP_MKBV, n, es); }
+
 };
 
 #endif /* BV_DECL_PLUGIN_H_ */

src/ast/datatype_decl_plugin.cpp

@@ -1000,3 +1000,25 @@ void datatype_util::display_datatype(sort *s0, std::ostream& strm) {
     }
 
 }
+
+bool datatype_util::is_func_decl(datatype_op_kind k, unsigned num_params, parameter const* params, func_decl* f) {
+    bool eq = 
+        f->get_decl_kind() == k &&
+        f->get_family_id() == m_family_id &&
+        f->get_num_parameters() == num_params;
+    for (unsigned i = 0; eq && i < num_params; ++i) {
+        eq = params[i] == f->get_parameter(i);
+    }
+    return eq;
+}
+
+bool datatype_util::is_constructor_of(unsigned num_params, parameter const* params, func_decl* f) {
+    return 
+        num_params == 2 &&
+        m_family_id == f->get_family_id() &&
+        OP_DT_CONSTRUCTOR == f->get_decl_kind() &&
+        2 == f->get_num_parameters() &&
+        params[0] == f->get_parameter(0) &&
+        params[1] == f->get_parameter(1);
+}
+

src/ast/datatype_decl_plugin.h

@@ -209,6 +209,8 @@ public:
     func_decl * get_recognizer_constructor(func_decl * recognizer);
     family_id get_family_id() const { return m_family_id; }
     bool are_siblings(sort * s1, sort * s2);
+    bool is_func_decl(datatype_op_kind k, unsigned num_params, parameter const* params, func_decl* f);
+    bool is_constructor_of(unsigned num_params, parameter const* params, func_decl* f);
     void reset();
     void display_datatype(sort *s, std::ostream& strm);
 

src/ast/expr_abstract.cpp

@@ -22,6 +22,10 @@ Notes:
 
 void expr_abstractor::operator()(unsigned base, unsigned num_bound, expr* const* bound, expr* n, expr_ref& result) {
     
+    if (num_bound == 0) {
+        result = n;
+        return;
+    }
     expr * curr = 0, *b = 0;
     SASSERT(n->get_ref_count() > 0);
 
@@ -106,3 +110,27 @@ void expr_abstract(ast_manager& m, unsigned base, unsigned num_bound, expr* cons
     expr_abstractor abs(m);
     abs(base, num_bound, bound, n, result);
 }
+
+expr_ref mk_quantifier(bool is_forall, ast_manager& m, unsigned num_bound, app* const* bound, expr* n) {
+    expr_ref result(m);
+    expr_abstract(m, 0, num_bound, (expr* const*)bound, n, result);    
+    if (num_bound > 0) {
+        ptr_vector<sort> sorts;
+        svector<symbol> names;
+        for (unsigned i = 0; i < num_bound; ++i) {
+            sorts.push_back(m.get_sort(bound[i]));
+            names.push_back(bound[i]->get_decl()->get_name());
+        }
+        result = m.mk_quantifier(is_forall, num_bound, sorts.c_ptr(), names.c_ptr(), result);
+    }
+    return result;
+
+}
+
+expr_ref mk_forall(ast_manager& m, unsigned num_bound, app* const* bound, expr* n) {
+    return mk_quantifier(true, m, num_bound, bound, n);
+}
+
+expr_ref mk_exists(ast_manager& m, unsigned num_bound, app* const* bound, expr* n) {
+    return mk_quantifier(false, m, num_bound, bound, n);
+}

src/ast/expr_abstract.h

@@ -33,6 +33,8 @@ public:
 };
 
 void expr_abstract(ast_manager& m, unsigned base, unsigned num_bound, expr* const* bound, expr* n, expr_ref&  result);
+expr_ref mk_forall(ast_manager& m, unsigned num_bound, app* const* bound, expr* n);
+expr_ref mk_exists(ast_manager& m, unsigned num_bound, app* const* bound, expr* n);
 
 #endif
 

src/ast/rewriter/expr_safe_replace.cpp

@@ -30,6 +30,14 @@ void expr_safe_replace::insert(expr* src, expr* dst) {
     m_subst.insert(src, dst);
 }
 
+void expr_safe_replace::operator()(expr_ref_vector& es) {
+    expr_ref val(m);
+    for (unsigned i = 0; i < es.size(); ++i) {
+        (*this)(es[i].get(), val);
+        es[i] = val;
+    }
+}
+
 void expr_safe_replace::operator()(expr* e, expr_ref& res) {
     m_todo.push_back(e);
     expr* a, *b;

src/ast/rewriter/expr_safe_replace.h

@@ -42,6 +42,8 @@ public:
 
     void operator()(expr* src, expr_ref& e);
 
+    void operator()(expr_ref_vector& es);
+
     void apply_substitution(expr* s, expr* def, expr_ref& t);
 
     void reset();

src/ast/rewriter/label_rewriter.cpp

@@ -0,0 +1,53 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    label_rewriter.cpp
+
+Abstract:
+
+    Basic rewriting rules for removing labels.
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-19-10
+
+Notes:
+
+--*/
+
+#include"rewriter.h"
+#include"rewriter_def.h"
+#include"label_rewriter.h"
+
+
+label_rewriter::label_rewriter(ast_manager & m) : 
+    m_label_fid(m.get_label_family_id()),
+    m_rwr(m, false, *this) {}
+
+label_rewriter::~label_rewriter() {}
+
+br_status label_rewriter::reduce_app(
+    func_decl * f, unsigned num, expr * const * args, expr_ref & result, 
+    proof_ref & result_pr) {
+    if (is_decl_of(f, m_label_fid, OP_LABEL)) {
+        SASSERT(num == 1);
+        result = args[0];
+        return BR_DONE;
+    }
+    return BR_FAILED;
+}
+
+void label_rewriter::remove_labels(expr_ref& fml, proof_ref& pr) {
+    ast_manager& m = fml.get_manager();
+    expr_ref tmp(m);
+    m_rwr(fml, tmp);
+    if (pr && fml != tmp) {        
+        pr = m.mk_modus_ponens(pr, m.mk_rewrite(fml, tmp));
+    }
+    fml = tmp;
+}
+
+
+//template class rewriter_tpl<label_rewriter>;

src/ast/rewriter/label_rewriter.h

@@ -0,0 +1,41 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    label_rewriter.h
+
+Abstract:
+
+    Basic rewriting rules for labels.
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-19-10
+
+Notes:
+
+--*/
+#ifndef LABEL_REWRITER_H_
+#define LABEL_REWRITER_H_
+
+#include"ast.h"
+#include"rewriter_types.h"
+
+
+class label_rewriter : public default_rewriter_cfg {
+    family_id m_label_fid;
+    rewriter_tpl<label_rewriter> m_rwr;
+public:    
+    label_rewriter(ast_manager & m);
+    ~label_rewriter();
+
+    br_status reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, 
+                         proof_ref & result_pr);
+
+    
+    void remove_labels(expr_ref& fml, proof_ref& pr);
+    
+};
+
+#endif

src/ast/rewriter/quant_hoist.cpp

@@ -73,7 +73,7 @@ public:
         unsigned nd = q->get_num_decls();
         for (unsigned i = 0; i < nd; ++i) {
             sort* s = q->get_decl_sort(i);
-            app* a = m.mk_fresh_const("x", s);
+            app* a = m.mk_fresh_const(q->get_decl_name(i).str().c_str(), s);
             vars.push_back(a);
         }
         expr * const * exprs = (expr* const*) (vars.c_ptr() + vars.size()- nd);
@@ -154,9 +154,7 @@ private:
     }
     
     quantifier_type& negate(quantifier_type& qt) {
-        TRACE("qe", display(qt, tout); tout << "\n";);
         qt = static_cast<quantifier_type>(qt ^0x1);
-        TRACE("qe", display(qt, tout); tout << "\n";);
         return qt;
     }
     
@@ -205,6 +203,7 @@ private:
         case AST_APP: {
             expr_ref_vector args(m);
             expr_ref tmp(m);
+            expr* t1, *t2, *t3;
             unsigned num_args = 0;
             app* a = to_app(fml);
             if (m.is_and(fml)) {
@@ -228,16 +227,35 @@ private:
                 negate(qt);
                 result = m.mk_not(tmp);
             }
-            else if (m.is_implies(fml)) {
-                pull_quantifier(to_app(fml)->get_arg(0), negate(qt), vars, tmp);
+            else if (m.is_implies(fml, t1, t2)) {
+                pull_quantifier(t1, negate(qt), vars, tmp);
                 negate(qt);
-                pull_quantifier(to_app(fml)->get_arg(1), qt, vars, result);
+                pull_quantifier(t2, qt, vars, result);
                 result = m.mk_implies(tmp, result);
             }
-            else if (m.is_ite(fml)) {
-                pull_quantifier(to_app(fml)->get_arg(1), qt, vars, tmp);
-                pull_quantifier(to_app(fml)->get_arg(2), qt, vars, result);
-                result = m.mk_ite(to_app(fml)->get_arg(0), tmp, result);
+            else if (m.is_ite(fml, t1, t2, t3)) {
+                expr_ref tt1(m), tt2(m), tt3(m), ntt1(m), nt1(m);
+                pull_quantifier(t2, qt, vars, tt2);
+                pull_quantifier(t3, qt, vars, tt3);
+                if (has_quantifiers(t1)) {
+                    pull_quantifier(t1, qt, vars, tt1);
+                    nt1 = m.mk_not(t1);
+                    pull_quantifier(nt1, qt, vars, ntt1);
+                    result = m.mk_and(m.mk_or(ntt1, tt2), m.mk_or(tt1, tt3));
+                }
+                else {
+                    result = m.mk_ite(t1, tt2, tt3);
+                }
+            }
+            else if ((m.is_eq(fml, t1, t2) && m.is_bool(t1)) || m.is_iff(fml, t1, t2)) {
+                expr_ref tt1(m), tt2(m), ntt1(m), ntt2(m), nt1(m), nt2(m);
+                pull_quantifier(t1, qt, vars, tt1);
+                pull_quantifier(t2, qt, vars, tt2);
+                nt1 = m.mk_not(t1);
+                nt2 = m.mk_not(t2);
+                pull_quantifier(nt1, qt, vars, ntt1);
+                pull_quantifier(nt2, qt, vars, ntt2);
+                result = m.mk_and(m.mk_or(ntt1, tt2), m.mk_or(ntt2, tt1));
             }
             else {
                 // the formula contains a quantifier, but it is "inaccessible"

src/ast/rewriter/th_rewriter.cpp

@@ -578,6 +578,16 @@ struct th_rewriter_cfg : public default_rewriter_cfg {
         return st;
     }
 
+    expr_ref mk_app(func_decl* f, unsigned num_args, expr* const* args) {
+        expr_ref result(m());
+        proof_ref pr(m());
+        if (BR_FAILED == reduce_app(f, num_args, args, result, pr)) {
+            result = m().mk_app(f, num_args, args);
+        }
+        return result;
+    }
+
+
     bool reduce_quantifier(quantifier * old_q, 
                            expr * new_body, 
                            expr * const * new_patterns, 
@@ -695,6 +705,9 @@ struct th_rewriter::imp : public rewriter_tpl<th_rewriter_cfg> {
         rewriter_tpl<th_rewriter_cfg>(m, m.proofs_enabled(), m_cfg),
         m_cfg(m, p) {
     }
+    expr_ref mk_app(func_decl* f, unsigned sz, expr* const* args) {
+        return m_cfg.mk_app(f, sz, args);
+    }
 };
 
 th_rewriter::th_rewriter(ast_manager & m, params_ref const & p):
@@ -776,3 +789,7 @@ void th_rewriter::reset_used_dependencies() {
         m_imp->cfg().m_used_dependencies = 0;
     }
 }
+
+expr_ref th_rewriter::mk_app(func_decl* f, unsigned num_args, expr* const* args) {
+    return m_imp->mk_app(f, num_args, args);
+}

src/ast/rewriter/th_rewriter.h

@@ -45,6 +45,8 @@ public:
     void operator()(expr * t, expr_ref & result, proof_ref & result_pr);
     void operator()(expr * n, unsigned num_bindings, expr * const * bindings, expr_ref & result);
 
+    expr_ref mk_app(func_decl* f, unsigned num_args, expr* const* args);
+
     void cleanup();
     void reset();
 

src/cmd_context/tactic_cmds.cpp

@@ -303,8 +303,8 @@ public:
             goal_ref g = alloc(goal, m, ctx.produce_proofs(), ctx.produce_models(), ctx.produce_unsat_cores());
             assert_exprs_from(ctx, *g);
 
-            unsigned timeout   = p.get_uint("timeout", UINT_MAX);
-            unsigned rlimit  =   p.get_uint("rlimit", 0);
+            unsigned timeout   = p.get_uint("timeout", ctx.params().m_timeout);
+            unsigned rlimit  =   p.get_uint("rlimit", ctx.params().m_rlimit);
 
             goal_ref_buffer     result_goals;
             model_converter_ref mc;

src/math/polynomial/algebraic_numbers.cpp

@@ -539,7 +539,6 @@ namespace algebraic_numbers {
         }
 
         bool factor(scoped_upoly const & up, factors & r) {
-            // std::cout << "factor: "; upm().display(std::cout, up); std::cout << std::endl;
             if (m_factor) {
                 return upm().factor(up, r, m_factor_params);
             }
@@ -547,7 +546,7 @@ namespace algebraic_numbers {
                 scoped_upoly & up_sqf = m_isolate_tmp3;
                 up_sqf.reset();
                 upm().square_free(up.size(), up.c_ptr(), up_sqf);
-                TRACE("anum_bug", upm().display(tout, up_sqf.size(), up_sqf.c_ptr()); tout << "\n";);
+                TRACE("algebraic", upm().display(tout, up_sqf.size(), up_sqf.c_ptr()); tout << "\n";);
                 r.push_back(up_sqf, 1);
                 return false;
             }
@@ -566,6 +565,7 @@ namespace algebraic_numbers {
         }
 
         void isolate_roots(scoped_upoly const & up, numeral_vector & roots) {
+            TRACE("algebraic", upm().display(tout, up); tout << "\n";);
             if (up.empty())
                 return; // ignore the zero polynomial
             factors & fs = m_isolate_factors;
@@ -586,6 +586,7 @@ namespace algebraic_numbers {
                 upolynomial::numeral_vector const & f = fs[i];
                 // polynomial f contains the non zero roots
                 unsigned d = upm().degree(f);
+                TRACE("algebraic", tout << "factor " << i << " degree: " << d << "\n";);
                 if (d == 0)
                     continue; // found all roots of f
                 scoped_mpq r(qm());
@@ -601,8 +602,9 @@ namespace algebraic_numbers {
                 }
                 SASSERT(m_isolate_roots.empty() && m_isolate_lowers.empty() && m_isolate_uppers.empty());
                 upm().sqf_isolate_roots(f.size(), f.c_ptr(), bqm(), m_isolate_roots, m_isolate_lowers, m_isolate_uppers);
-                // collect rational/basic roots
+                // collect rational/basic roots                
                 unsigned sz = m_isolate_roots.size();
+                TRACE("algebraic", tout << "isolated roots: " << sz << "\n";);
                 for (unsigned i = 0; i < sz; i++) {
                     to_mpq(qm(), m_isolate_roots[i], r);
                     roots.push_back(numeral(mk_basic_cell(r)));

src/model/model_params.pyg

@@ -4,6 +4,5 @@ def_module_params('model',
                           ('v1', BOOL, False, 'use Z3 version 1.x pretty printer'),
                           ('v2', BOOL, False, 'use Z3 version 2.x (x <= 16) pretty printer'),
                           ('compact', BOOL, False, 'try to compact function graph (i.e., function interpretations that are lookup tables)'),
-                          ('new_eval', BOOL, True, 'use new evaluator (temporary parameter for testing)'),
                           ))
 

src/muz/base/dl_rule.cpp

@@ -55,8 +55,7 @@ namespace datalog {
           m_args(m),
           m_hnf(m),
           m_qe(m),
-          m_cfg(m),
-          m_rwr(m, false, m_cfg),
+          m_rwr(m),
           m_ufproc(m) {}
 
     void rule_manager::inc_ref(rule * r) {
@@ -76,28 +75,8 @@ namespace datalog {
         }
     }
 
-    rule_manager::remove_label_cfg::~remove_label_cfg() {}
-
-    br_status rule_manager::remove_label_cfg::reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, 
-                                                         proof_ref & result_pr)
-    {
-        if (is_decl_of(f, m_label_fid, OP_LABEL)) {
-            SASSERT(num == 1);
-            result = args[0];
-            return BR_DONE;
-        }
-        return BR_FAILED;
-    }
-
-
     void rule_manager::remove_labels(expr_ref& fml, proof_ref& pr) {
-        expr_ref tmp(m);
-        m_rwr(fml, tmp);
-        if (pr && fml != tmp) {
-            
-            pr = m.mk_modus_ponens(pr, m.mk_rewrite(fml, tmp));
-        }
-        fml = tmp;
+        m_rwr.remove_labels(fml, pr);
     }
 
     var_idx_set& rule_manager::collect_vars(expr* e) {
@@ -1092,5 +1071,4 @@ namespace datalog {
     
 };
 
-template class rewriter_tpl<datalog::rule_manager::remove_label_cfg>;
 

src/muz/base/dl_rule.h

@@ -32,6 +32,7 @@ Revision History:
 #include"qe_lite.h"
 #include"var_subst.h"
 #include"datatype_decl_plugin.h"
+#include"label_rewriter.h"
 
 namespace datalog {
 
@@ -102,16 +103,6 @@ namespace datalog {
     */
     class rule_manager
     {
-        class remove_label_cfg : public default_rewriter_cfg {
-            family_id m_label_fid;
-        public:        
-            remove_label_cfg(ast_manager& m): m_label_fid(m.get_label_family_id()) {}
-            virtual ~remove_label_cfg();
-            
-            br_status reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, 
-                                 proof_ref & result_pr);
-        };
-    
         ast_manager&         m;
         context&             m_ctx;
         rule_counter         m_counter;
@@ -124,8 +115,7 @@ namespace datalog {
         svector<bool>        m_neg;
         hnf                  m_hnf;
         qe_lite              m_qe;
-        remove_label_cfg               m_cfg;
-        rewriter_tpl<remove_label_cfg> m_rwr;
+        label_rewriter       m_rwr;
         mutable uninterpreted_function_finder_proc m_ufproc;
         mutable quantifier_finder_proc m_qproc;
         mutable expr_sparse_mark       m_visited;

src/muz/base/dl_util.h

@@ -29,7 +29,6 @@ Revision History:
 #include"ast_counter.h"
 #include"statistics.h"
 #include"lbool.h"
-#include"qe_util.h"
 
 namespace datalog {
 

src/muz/pdr/pdr_closure.cpp

@@ -20,6 +20,7 @@ Revision History:
 #include "pdr_closure.h"
 #include "pdr_context.h"
 #include "expr_safe_replace.h"
+#include "ast_util.h"
 
 namespace pdr {
 
@@ -147,7 +148,7 @@ namespace pdr {
         for (unsigned i = 0; i < fmls.size(); ++i) {
             fmls[i] = close_fml(fmls[i].get());            
         }
-        return qe::mk_and(fmls);
+        return expr_ref(mk_and(fmls), m);
     }
 
     expr_ref closure::relax(unsigned i, expr* fml) {
@@ -169,7 +170,7 @@ namespace pdr {
         for (unsigned i = 0; i < As.size(); ++i) {
             fmls.push_back(relax(i, As[i]));
         }
-        B = qe::mk_and(fmls);
+        B = mk_and(fmls);
         return B;
     }
 

src/muz/pdr/pdr_context.cpp

@@ -45,7 +45,6 @@ Notes:
 #include "smt_value_sort.h"
 #include "proof_utils.h"
 #include "dl_boogie_proof.h"
-#include "qe_util.h"
 #include "scoped_proof.h"
 #include "blast_term_ite_tactic.h"
 #include "model_implicant.h"

src/muz/pdr/pdr_farkas_learner.cpp

@@ -201,7 +201,7 @@ namespace pdr {
                 lits.push_back(extract_consequence(lo, hi));
                 lo = hi;
             }
-            res = qe::mk_or(lits);
+            res = mk_or(lits);
             IF_VERBOSE(2, { if (lits.size() > 1) { verbose_stream() << "combined lemma: " << mk_pp(res, m) << "\n"; } });
 #endif
         }
@@ -415,6 +415,7 @@ namespace pdr {
                 return false;
             }
         }
+
     };
 
     class collect_pure_proc {

src/muz/pdr/pdr_generalizers.cpp

@@ -117,7 +117,7 @@ namespace pdr {
     void core_farkas_generalizer::operator()(model_node& n, expr_ref_vector& core, bool& uses_level) {
         ast_manager& m  = n.pt().get_manager();
         if (core.empty()) return;
-        expr_ref A(m), B(qe::mk_and(core)), C(m);
+        expr_ref A(m), B(mk_and(core)), C(m);
         expr_ref_vector Bs(m);
         flatten_or(B, Bs);
         A = n.pt().get_propagation_formula(m_ctx.get_pred_transformers(), n.level());
@@ -129,13 +129,13 @@ namespace pdr {
             if (m_farkas_learner.get_lemma_guesses(A, B, lemmas)) {
                 TRACE("pdr", 
                       tout << "Old core:\n" << mk_pp(B, m) << "\n";
-                      tout << "New core:\n" << mk_pp(qe::mk_and(lemmas), m) << "\n";);            
-                Bs[i] = qe::mk_and(lemmas);
+                      tout << "New core:\n" << mk_and(lemmas) << "\n";);            
+                Bs[i] = mk_and(lemmas);
                 change = true;
             }
         }
         if (change) {
-            C = qe::mk_or(Bs);
+            C = mk_or(Bs);
             TRACE("pdr", tout << "prop:\n" << mk_pp(A,m) << "\ngen:" << mk_pp(B, m) << "\nto: " << mk_pp(C, m) << "\n";);
             core.reset();
             flatten_and(C, core);    
@@ -186,7 +186,7 @@ namespace pdr {
         }        
         closure cl(n.pt(), m_is_closure);
 
-        expr_ref fml1 = qe::mk_and(core);        
+        expr_ref fml1 = mk_and(core);        
         expr_ref fml2 = n.pt().get_formulas(n.level(), false);
         fml1_2.push_back(fml1);
         fml1_2.push_back(0);
@@ -205,7 +205,7 @@ namespace pdr {
             if (l_false == n.pt().is_reachable(nd, &conv2, uses_level1)) {
                 new_cores.push_back(std::make_pair(conv2, uses_level1));
                 change = true;
-                expr_ref state1 = qe::mk_and(conv2);
+                expr_ref state1 = mk_and(conv2);
                 TRACE("pdr", 
                       tout << mk_pp(state, m) << "\n";
                       tout << "Generalized to:\n" << mk_pp(state1, m) << "\n";);
@@ -593,7 +593,7 @@ namespace pdr {
             for (unsigned i = ut_size; i < t_size; i++) {
                 conj.push_back(rule.get_tail(i));
             }         
-            result = qe::mk_and(conj);
+            result = mk_and(conj);
             if (!sub.empty()) {
                 expr_ref tmp = result;
                 var_subst(m, false)(tmp, sub.size(), sub.c_ptr(), result);
@@ -685,7 +685,7 @@ namespace pdr {
             for (unsigned i = 0; i < rules.size(); ++i) {
                 fmls.push_back(m.mk_not(mk_transition_rule(reps, level, *rules[i])));           
             }
-            fml = qe::mk_and(fmls);
+            fml = mk_and(fmls);
             TRACE("pdr", tout << mk_pp(fml, m) << "\n";);
             return fml;
         }
@@ -741,7 +741,7 @@ namespace pdr {
                 }                
             }
 
-            expr_ref result = qe::mk_and(conjs);
+            expr_ref result = mk_and(conjs);
             TRACE("pdr", tout << mk_pp(result, m) << "\n";);
             return result;
         }

src/muz/rel/check_relation.cpp

@@ -6,7 +6,6 @@ Copyright (c) 2015 Microsoft Corporation
 
 #include "check_relation.h"
 #include "dl_relation_manager.h"
-#include "qe_util.h"
 #include "ast_util.h"
 #include "smt_kernel.h"
 #include <typeinfo>

src/muz/rel/udoc_relation.cpp

@@ -23,7 +23,6 @@ Notes:
 --*/
 #include "udoc_relation.h"
 #include "dl_relation_manager.h"
-#include "qe_util.h"
 #include "ast_util.h"
 #include "smt_kernel.h"
 

src/nlsat/nlsat_assignment.h

@@ -39,6 +39,17 @@ namespace nlsat {
             m_values.swap(other.m_values);
             m_assigned.swap(other.m_assigned);
         }
+        void copy(assignment const& other) {
+            m_assigned.reset();
+            m_assigned.append(other.m_assigned);
+            m_values.reserve(m_assigned.size(), anum());
+            for (unsigned i = 0; i < m_assigned.size(); ++i) {
+                if (is_assigned(i)) {
+                    am().set(m_values[i], other.value(i));
+                }
+            }
+        }
+
         void set_core(var x, anum & v) {
             m_values.reserve(x+1, anum());
             m_assigned.reserve(x+1, false); 
@@ -52,11 +63,26 @@ namespace nlsat {
             am().set(m_values[x], v); 
         }
         void reset(var x) { if (x < m_assigned.size()) m_assigned[x] = false; }
+        void reset() { m_assigned.reset(); }
         bool is_assigned(var x) const { return m_assigned.get(x, false); }
         anum const & value(var x) const { return m_values[x]; }
         virtual anum_manager & m() const { return am(); }
         virtual bool contains(var x) const { return is_assigned(x); }
         virtual anum const & operator()(var x) const { SASSERT(is_assigned(x)); return value(x); }
+        void swap(var x, var y) {
+            SASSERT(x < m_values.size() && y < m_values.size());
+            std::swap(m_assigned[x], m_assigned[y]);
+            std::swap(m_values[x], m_values[y]);
+        }
+        void display(std::ostream& out) const {
+            for (unsigned i = 0; i < m_assigned.size(); ++i) {
+                if (m_assigned[i]) {
+                    out << "x" << i << " := ";
+                    m_values.m().display(out, m_values[i]);
+                    out << "\n";
+                }
+            }
+        }
     };
     
     /**

src/nlsat/nlsat_evaluator.cpp

@@ -18,10 +18,12 @@ Revision History:
 
 --*/
 #include"nlsat_evaluator.h"
+#include"nlsat_solver.h"
 
 namespace nlsat {
 
     struct evaluator::imp {
+        solver&                  m_solver;
         assignment const &       m_assignment;
         pmanager &               m_pm;
         small_object_allocator & m_allocator;
@@ -357,7 +359,8 @@ namespace nlsat {
 
         sign_table m_sign_table_tmp;
 
-        imp(assignment const & x2v, pmanager & pm, small_object_allocator & allocator):
+        imp(solver& s, assignment const & x2v, pmanager & pm, small_object_allocator & allocator):
+            m_solver(s),
             m_assignment(x2v),
             m_pm(pm),
             m_allocator(allocator),
@@ -420,10 +423,25 @@ namespace nlsat {
             scoped_anum_vector & roots = m_tmp_values;
             roots.reset();
             m_am.isolate_roots(polynomial_ref(a->p(), m_pm), undef_var_assignment(m_assignment, a->x()), roots);
+            TRACE("nlsat",
+                  m_solver.display(tout << (neg?"!":""), *a); tout << "\n";
+                  if (roots.empty()) {
+                      tout << "No roots\n";
+                  }
+                  else {
+                      tout << "Roots for ";
+                      for (unsigned i = 0; i < roots.size(); ++i) {
+                          m_am.display_interval(tout, roots[i]); tout << " "; 
+                      }
+                      tout << "\n";
+                  }
+                  m_assignment.display(tout);
+                  );
             SASSERT(a->i() > 0);
-            if (a->i() > roots.size())
-                return false; // p does have sufficient roots
-            int sign = m_am.compare(m_assignment.value(a->x()), roots[a->i() - 1]);
+            if (a->i() > roots.size()) {
+                return neg;
+            }
+            int sign = m_am.compare(m_assignment.value(a->x()), roots[a->i() - 1]);            
             return satisfied(sign, k, neg);
         }
         
@@ -649,8 +667,8 @@ namespace nlsat {
         }
     };
     
-    evaluator::evaluator(assignment const & x2v, pmanager & pm, small_object_allocator & allocator) {
-        m_imp = alloc(imp, x2v, pm, allocator);
+    evaluator::evaluator(solver& s, assignment const & x2v, pmanager & pm, small_object_allocator & allocator) {
+        m_imp = alloc(imp, s, x2v, pm, allocator);
     }
 
     evaluator::~evaluator() {

src/nlsat/nlsat_evaluator.h

@@ -26,11 +26,13 @@ Revision History:
 
 namespace nlsat {
 
+    class solver;
+
     class evaluator {
         struct imp;
         imp *  m_imp;
     public:
-        evaluator(assignment const & x2v, pmanager & pm, small_object_allocator & allocator);
+        evaluator(solver& s, assignment const & x2v, pmanager & pm, small_object_allocator & allocator);
         ~evaluator();
 
         interval_set_manager & ism() const;

src/nlsat/nlsat_explain.cpp

@@ -36,6 +36,7 @@ namespace nlsat {
         polynomial::cache &     m_cache;
         pmanager &              m_pm;
         polynomial_ref_vector   m_ps;
+        polynomial_ref_vector   m_ps2;
         polynomial_ref_vector   m_psc_tmp;
         polynomial_ref_vector   m_factors;
         scoped_anum_vector      m_roots_tmp;
@@ -43,6 +44,7 @@ namespace nlsat {
         bool                    m_full_dimensional;
         bool                    m_minimize_cores;
         bool                    m_factor;
+        bool                    m_signed_project;
 
         struct todo_set {
             polynomial::cache  &    m_cache;
@@ -137,6 +139,7 @@ namespace nlsat {
             m_cache(u), 
             m_pm(u.pm()),
             m_ps(m_pm),
+            m_ps2(m_pm),
             m_psc_tmp(m_pm),
             m_factors(m_pm),
             m_roots_tmp(m_am),
@@ -148,6 +151,7 @@ namespace nlsat {
             m_simplify_cores   = false;
             m_full_dimensional = false;
             m_minimize_cores   = false;
+            m_signed_project   = false;
         }
         
         ~imp() {
@@ -202,7 +206,7 @@ namespace nlsat {
         void reset_already_added() {
             SASSERT(m_result != 0);
             unsigned sz = m_result->size();
-            for (unsigned i = 0; i < sz; i++)
+            for (unsigned i = 0; i < sz; i++) 
                 m_already_added_literal[(*m_result)[i].index()] = false;
         }
 
@@ -212,7 +216,7 @@ namespace nlsat {
            max_var(p) must be assigned in the current interpretation.
         */
         int sign(polynomial_ref const & p) {
-            TRACE("nlsat_explain", tout << "p: " << p << "\n";);
+            TRACE("nlsat_explain", tout << "p: " << p << " var: " << max_var(p) << "\n";);
             SASSERT(max_var(p) == null_var || m_assignment.is_assigned(max_var(p)));
             return m_am.eval_sign_at(p, m_assignment);
         }
@@ -697,39 +701,163 @@ namespace nlsat {
             }
         }
 
+        void test_root_literal(atom::kind k, var y, unsigned i, poly * p, scoped_literal_vector& result) {
+            m_result = &result;
+            add_root_literal(k, y, i, p);
+            reset_already_added();
+            m_result = 0;
+        }
+
         void add_root_literal(atom::kind k, var y, unsigned i, poly * p) {
+            polynomial_ref pr(p, m_pm);
+            TRACE("nlsat_explain", 
+                  display(tout << "x" << y << " " << k << "[" << i << "](", pr); tout << ")\n";);
+
+            if (!mk_linear_root(k, y, i, p) &&
+                //!mk_plinear_root(k, y, i, p) &&
+                !mk_quadratic_root(k, y, i, p)&&
+                true) {                
+                bool_var b = m_solver.mk_root_atom(k, y, i, p);
+                literal l(b, true);
+                TRACE("nlsat_explain", tout << "adding literal\n"; display(tout, l); tout << "\n";);
+                add_literal(l);
+            }
+        }
+
+        /**
+         * literal can be expressed using a linear ineq_atom
+         */
+        bool mk_linear_root(atom::kind k, var y, unsigned i, poly * p) {
             scoped_mpz c(m_pm.m());
-            bool_var b;
-            bool     lsign = false;
             if (m_pm.degree(p, y) == 1 && m_pm.const_coeff(p, y, 1, c)) {
                 SASSERT(!m_pm.m().is_zero(c));
-                // literal can be expressed using a linear ineq_atom
-                polynomial_ref p_prime(m_pm);
-                p_prime = p;
-                if (m_pm.m().is_neg(c)) 
-                    p_prime = neg(p_prime);
-                p = p_prime.get();
-                switch (k) {
-                case atom::ROOT_EQ: k = atom::EQ; lsign = false; break;
-                case atom::ROOT_LT: k = atom::LT; lsign = false; break;
-                case atom::ROOT_GT: k = atom::GT; lsign = false; break;
-                case atom::ROOT_LE: k = atom::GT; lsign = true; break;
-                case atom::ROOT_GE: k = atom::LT; lsign = true; break;
-                default:
-                    UNREACHABLE();
-                    break;
-                }
-                bool is_even = false;
-                b = m_solver.mk_ineq_atom(k, 1, &p, &is_even);
+                mk_linear_root(k, y, i, p, m_pm.m().is_neg(c));
+                return true;
             }
-            else {
-                b   = m_solver.mk_root_atom(k, y, i, p);
-                lsign = false;
+            return false;
+        }
+
+
+        /**
+           Create pseudo-linear root depending on the sign of the coefficient to y.
+         */
+        bool mk_plinear_root(atom::kind k, var y, unsigned i, poly * p) {
+            if (m_pm.degree(p, y) != 1) {
+                return false;
             }
-            lsign = !lsign; // adding as an assumption
-            literal l(b, lsign);
-            TRACE("nlsat_explain", tout << "adding literal\n"; display(tout, l); tout << "\n";);
-            add_literal(l);
+            polynomial_ref c(m_pm);
+            c = m_pm.coeff(p, y, 1);
+            int s = sign(c);
+            if (s == 0) {
+                return false;
+            }
+            ensure_sign(c);
+            mk_linear_root(k, y, i, p, s < 0);                
+            return true;
+        }
+
+        /**
+           Encode root conditions for quadratic polynomials.
+           
+           Basically implements Thom's theorem. The roots are characterized by the sign of polynomials and their derivatives.
+
+           b^2 - 4ac = 0:
+              - there is only one root, which is -b/2a.
+              - relation to root is a function of the sign of 
+              - 2ax + b
+           b^2 - 4ac > 0:
+              - assert i == 1 or i == 2
+              - relation to root is a function of the signs of:
+                - 2ax + b
+                - ax^2 + bx + c
+         */
+
+        bool mk_quadratic_root(atom::kind k, var y, unsigned i, poly * p) {
+            if (m_pm.degree(p, y) != 2) {
+                return false;
+            }
+            if (i != 1 && i != 2) {
+                return false;
+            }
+
+            SASSERT(m_assignment.is_assigned(y));
+            polynomial_ref A(m_pm), B(m_pm), C(m_pm), q(m_pm), p_diff(m_pm), yy(m_pm);
+            A = m_pm.coeff(p, y, 2);
+            B = m_pm.coeff(p, y, 1);
+            C = m_pm.coeff(p, y, 0);
+            // TBD throttle based on degree of q?
+            q = (B*B) - (4*A*C);
+            yy = m_pm.mk_polynomial(y);
+            p_diff = 2*A*yy + B;
+            p_diff = m_pm.normalize(p_diff);
+            int sq = ensure_sign(q); 
+            if (sq < 0) {
+                return false;
+            }
+            int sa = ensure_sign(A);
+            if (sa == 0) {
+                q = B*yy + C;
+                return mk_plinear_root(k, y, i, q);
+            } 
+            ensure_sign(p_diff);
+            if (sq > 0) {
+                polynomial_ref pr(p, m_pm);
+                ensure_sign(pr);
+            }
+            return true;
+        }
+
+        int ensure_sign(polynomial_ref & p) {
+#if 0
+            polynomial_ref f(m_pm);
+            factor(p, m_factors);
+            m_is_even.reset();
+            unsigned num_factors = m_factors.size();
+            int s = 1;
+            for (unsigned i = 0; i < num_factors; i++) {
+                f = m_factors.get(i);
+                s *= sign(f);
+                m_is_even.push_back(false);
+            } 
+            if (num_factors > 0) {
+                atom::kind k = atom::EQ;
+                if (s == 0) k = atom::EQ;
+                if (s < 0)  k = atom::LT;
+                if (s > 0)  k = atom::GT;
+                bool_var b = m_solver.mk_ineq_atom(k, num_factors, m_factors.c_ptr(), m_is_even.c_ptr());
+                add_literal(literal(b, true));
+            }
+            return s;
+#else
+            int s = sign(p);
+            if (!is_const(p)) {
+                add_simple_assumption(s == 0 ? atom::EQ : (s < 0 ? atom::LT : atom::GT), p);
+            }
+            return s;
+#endif
+        }
+
+        /**
+           Auxiliary function to linear roots.
+         */
+        void mk_linear_root(atom::kind k, var y, unsigned i, poly * p, bool mk_neg) {
+            polynomial_ref p_prime(m_pm);
+            p_prime = p;
+            bool lsign = false;
+            if (mk_neg)
+                p_prime = neg(p_prime);
+            p = p_prime.get();
+            switch (k) {
+            case atom::ROOT_EQ: k = atom::EQ; lsign = false; break;
+            case atom::ROOT_LT: k = atom::LT; lsign = false; break;
+            case atom::ROOT_GT: k = atom::GT; lsign = false; break;
+            case atom::ROOT_LE: k = atom::GT; lsign = true; break;
+            case atom::ROOT_GE: k = atom::LT; lsign = true; break;
+            default:
+                UNREACHABLE();
+                break;
+            }
+            add_simple_assumption(k, p, lsign);
         }
 
         /**
@@ -1332,10 +1460,333 @@ namespace nlsat {
             TRACE("nlsat_explain", tout << "[explain] result\n"; display(tout, result););
             CASSERT("nlsat", check_already_added());
         }
+
+
+        void project(var x, unsigned num, literal const * ls, scoped_literal_vector & result) {
+            m_result = &result;
+            svector<literal> lits;
+            TRACE("nlsat", tout << "project x" << x << "\n"; m_solver.display(tout););
+                  
+            DEBUG_CODE(
+                for (unsigned i = 0; i < num; ++i) {
+                    SASSERT(m_solver.value(ls[i]) == l_true);
+                    atom* a = m_atoms[ls[i].var()];
+                    SASSERT(!a || m_evaluator.eval(a, ls[i].sign()));
+                });
+            split_literals(x, num, ls, lits);
+            collect_polys(lits.size(), lits.c_ptr(), m_ps);
+            var mx_var = max_var(m_ps);
+            if (!m_ps.empty()) {                
+                svector<var> renaming;
+                if (x != mx_var) {
+                    for (var i = 0; i < m_solver.num_vars(); ++i) {
+                        renaming.push_back(i);
+                    }
+                    std::swap(renaming[x], renaming[mx_var]);
+                    m_solver.reorder(renaming.size(), renaming.c_ptr());
+                    TRACE("qe", tout << "x: " << x << " max: " << mx_var << " num_vars: " << m_solver.num_vars() << "\n";
+                          m_solver.display(tout););
+                }
+                elim_vanishing(m_ps);
+                if (m_signed_project) {
+                    signed_project(m_ps, mx_var);
+                }
+                else {
+                    project(m_ps, mx_var);
+                }
+                reset_already_added();
+                m_result = 0;
+                if (x != mx_var) {
+                    m_solver.restore_order();
+                }
+            }
+            else {
+                reset_already_added();
+                m_result = 0;
+            }
+            for (unsigned i = 0; i < result.size(); ++i) {
+                result.set(i, ~result[i]);
+            }
+            DEBUG_CODE(
+                for (unsigned i = 0; i < result.size(); ++i) {
+                    SASSERT(l_true == m_solver.value(result[i]));
+                });
+
+        }
+
+        void split_literals(var x, unsigned n, literal const* ls, svector<literal>& lits) {
+            var_vector vs;
+            for (unsigned i = 0; i < n; ++i) {                  
+                vs.reset();
+                m_solver.vars(ls[i], vs);
+                if (vs.contains(x)) {
+                    lits.push_back(ls[i]);
+                }
+                else {
+                    add_literal(~ls[i]);
+                }
+            }
+        }
+
+        /**
+           Signed projection. 
+
+           Assumptions:
+           - any variable in ps is at most x.
+           - root expressions are satisfied (positive literals)
+           
+           Effect:
+           - if x not in p, then
+              - if sign(p) < 0:   p < 0
+              - if sign(p) = 0:   p = 0
+              - if sign(p) > 0:   p > 0
+           else:
+           - let roots_j be the roots of p_j or roots_j[i] 
+           - let L = { roots_j[i] | M(roots_j[i]) < M(x) }
+           - let U = { roots_j[i] | M(roots_j[i]) > M(x) }
+           - let E = { roots_j[i] | M(roots_j[i]) = M(x) }
+           - let glb in L, s.t. forall l in L . M(glb) >= M(l)
+           - let lub in U, s.t. forall u in U . M(lub) <= M(u)
+           - if root in E, then 
+              - add E x . x = root & x > lb  for lb in L
+              - add E x . x = root & x < ub  for ub in U
+              - add E x . x = root & x = root2  for root2 in E \ { root }
+           - else 
+             - assume |L| <= |U| (other case is symmetric)
+             - add E x . lb <= x & x <= glb for lb in L
+             - add E x . x = glb & x < ub  for ub in U
+         */
+
+
+        void signed_project(polynomial_ref_vector& ps, var x) {
+            
+            TRACE("nlsat_explain", tout << "Signed projection\n";);
+            polynomial_ref p(m_pm);
+            unsigned eq_index = 0;
+            bool eq_valid = false;
+            unsigned eq_degree = 0;
+            for (unsigned i = 0; i < ps.size(); ++i) {
+                p = ps.get(i);
+                int s = sign(p);
+                if (max_var(p) != x) {
+                    atom::kind k = (s == 0)?(atom::EQ):((s < 0)?(atom::LT):(atom::GT));
+                    add_simple_assumption(k, p, false);
+                    ps[i] = ps.back();
+                    ps.pop_back();
+                    --i;
+                }
+                else if (s == 0) {
+                    if (!eq_valid || degree(p, x) < eq_degree) {
+                        eq_index = i;
+                        eq_valid = true;
+                        eq_degree = degree(p, x);
+                    }
+                }
+            }
+
+            if (ps.empty()) {
+                return;
+            }
+
+            if (ps.size() == 1) {
+                project_single(x, ps.get(0));
+                return;
+            }
+
+            // ax + b = 0, p(x) > 0 -> 
+
+            if (eq_valid) {
+                p = ps.get(eq_index);
+                if (degree(p, x) == 1) {
+                    // ax + b = 0
+                    // let d be maximal degree of x in p.
+                    // p(x) -> a^d*p(-b/a), a
+                    // perform virtual substitution with equality.
+                    solve_eq(x, eq_index, ps);
+                }
+                else {
+                    project_pairs(x, eq_index, ps);
+                }
+                return;
+            }
+            
+            unsigned num_lub = 0, num_glb = 0;
+            unsigned glb_index = 0, lub_index = 0;
+            scoped_anum lub(m_am), glb(m_am), x_val(m_am);
+            x_val = m_assignment.value(x);
+            for (unsigned i = 0; i < ps.size(); ++i) {
+                p = ps.get(i);
+                scoped_anum_vector & roots = m_roots_tmp;
+                roots.reset();
+                m_am.isolate_roots(p, undef_var_assignment(m_assignment, x), roots);
+                bool glb_valid = false, lub_valid = false;
+                for (unsigned j = 0; j < roots.size(); ++j) {
+                    int s = m_am.compare(x_val, roots[j]);
+                    SASSERT(s != 0);
+                    lub_valid |= s < 0;
+                    glb_valid |= s > 0;
+
+                    if (s < 0 && m_am.lt(roots[j], lub)) {
+                        lub_index = i;
+                        m_am.set(lub, roots[j]);
+                    }
+
+                    if (s > 0 && m_am.lt(glb, roots[j])) {
+                        glb_index = i;
+                        m_am.set(glb, roots[j]);                        
+                    }
+                }
+                if (glb_valid) {
+                    ++num_glb;
+                }
+                if (lub_valid) {
+                    ++num_lub;
+                }
+            }
+
+            if (num_lub == 0) {
+                project_plus_infinity(x, ps);
+                return;
+            }
+                
+            if (num_glb == 0) {
+                project_minus_infinity(x, ps);
+                return;
+            }
+
+            if (num_lub <= num_glb) {
+                glb_index = lub_index;
+            }
+
+            project_pairs(x, glb_index, ps);
+        }
+
+        void project_plus_infinity(var x, polynomial_ref_vector const& ps) {
+            polynomial_ref p(m_pm), lc(m_pm);
+            for (unsigned i = 0; i < ps.size(); ++i) {
+                p = ps.get(i);
+                unsigned d = degree(p, x);
+                lc = m_pm.coeff(p, x, d);
+                if (!is_const(lc)) {                    
+                    unsigned s = sign(p);
+                    SASSERT(s != 0);
+                    atom::kind k = (s > 0)?(atom::GT):(atom::LT);
+                    add_simple_assumption(k, lc);
+                }
+            }
+        }
+
+        void project_minus_infinity(var x, polynomial_ref_vector const& ps) {
+            polynomial_ref p(m_pm), lc(m_pm);
+            for (unsigned i = 0; i < ps.size(); ++i) {
+                p = ps.get(i);
+                unsigned d = degree(p, x);
+                lc = m_pm.coeff(p, x, d);
+                if (!is_const(lc)) {
+                    unsigned s = sign(p);
+                    SASSERT(s != 0);
+                    atom::kind k;
+                    if (s > 0) {
+                        k = (d % 2 == 0)?(atom::GT):(atom::LT);
+                    }
+                    else {
+                        k = (d % 2 == 0)?(atom::LT):(atom::GT);
+                    }
+                    add_simple_assumption(k, lc);
+                }
+            }
+        }
+
+        void project_pairs(var x, unsigned idx, polynomial_ref_vector const& ps) {
+            polynomial_ref p(m_pm);
+            p = ps.get(idx);
+            for (unsigned i = 0; i < ps.size(); ++i) {
+                if (i != idx) {
+                    project_pair(x, ps.get(i), p);
+                }
+            }
+        }
+
+        void project_pair(var x, polynomial::polynomial* p1, polynomial::polynomial* p2) {
+            m_ps2.reset();
+            m_ps2.push_back(p1);
+            m_ps2.push_back(p2);
+            project(m_ps2, x);
+        }
+
+        void project_single(var x, polynomial::polynomial* p) {
+            m_ps2.reset();
+            m_ps2.push_back(p);
+            project(m_ps2, x);
+        }
+
+        void solve_eq(var x, unsigned idx, polynomial_ref_vector const& ps) {
+            polynomial_ref p(m_pm), A(m_pm), B(m_pm), C(m_pm), D(m_pm), E(m_pm), q(m_pm), r(m_pm);
+            polynomial_ref_vector qs(m_pm);
+            p = ps.get(idx);
+            SASSERT(degree(p, x) == 1);
+            A = m_pm.coeff(p, x, 1);
+            B = m_pm.coeff(p, x, 0);
+            B = neg(B);
+            TRACE("nlsat_explain", tout << "p: " << p << " A: " << A << " B: " << B << "\n";);
+            // x = B/A
+            for (unsigned i = 0; i < ps.size(); ++i) {
+                if (i != idx) {
+                    q = ps.get(i);
+                    unsigned d = degree(q, x);
+                    D = m_pm.mk_const(rational(1));
+                    E = D;
+                    r = m_pm.mk_zero();
+                    for (unsigned j = 0; j <= d; ++j) {                       
+                        qs.push_back(D);
+                        D = D*A;
+                    }
+                    for (unsigned j = 0; j <= d; ++j) {
+                        // A^d*p0 + A^{d-1}*B*p1 + ... + B^j*A^{d-j}*pj + ... + B^d*p_d
+                        C = m_pm.coeff(q, x, j);
+                        if (!is_zero(C)) {
+                            D = qs.get(d-j);
+                            r = r + D*E*C;
+                        }
+                        E = E*B;
+                    }
+                    TRACE("nlsat_explain", tout << "q: " << q << " r: " << r << "\n";);
+                    ensure_sign(r);
+                }
+                else {
+                    ensure_sign(A);
+                }
+            }
+
+        }
+
+        void maximize(var x, unsigned num, literal const * ls, scoped_anum& val, bool& unbounded) {
+            svector<literal> lits;
+            polynomial_ref p(m_pm);
+            split_literals(x, num, ls, lits);
+            collect_polys(lits.size(), lits.c_ptr(), m_ps);
+            unbounded = true;
+            scoped_anum x_val(m_am);
+            x_val = m_assignment.value(x);
+            for (unsigned i = 0; i < m_ps.size(); ++i) {
+                p = m_ps.get(i);
+                scoped_anum_vector & roots = m_roots_tmp;
+                roots.reset();
+                m_am.isolate_roots(p, undef_var_assignment(m_assignment, x), roots);
+                for (unsigned j = 0; j < roots.size(); ++j) {
+                    int s = m_am.compare(x_val, roots[j]);
+                    if (s <= 0 && (unbounded || m_am.compare(roots[j], val) <= 0)) {
+                        unbounded = false;
+                        val = roots[j];
+                    }
+                }
+            }
+        }
+
     };
 
-    explain::explain(solver & s, assignment const & x2v, polynomial::cache & u, atom_vector const & atoms, atom_vector const & x2eq,
-                     evaluator & ev) {
+    explain::explain(solver & s, assignment const & x2v, polynomial::cache & u, 
+                     atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev) {
         m_imp = alloc(imp, s, x2v, u, atoms, x2eq, ev);
     }
 
@@ -1364,10 +1815,26 @@ namespace nlsat {
         m_imp->m_factor = f;
     }
 
+    void explain::set_signed_project(bool f) {
+        m_imp->m_signed_project = f;
+    }
+
     void explain::operator()(unsigned n, literal const * ls, scoped_literal_vector & result) {
         (*m_imp)(n, ls, result);
     }
 
+    void explain::project(var x, unsigned n, literal const * ls, scoped_literal_vector & result) {
+        m_imp->project(x, n, ls, result);
+    }
+
+    void explain::maximize(var x, unsigned n, literal const * ls, scoped_anum& val, bool& unbounded) {
+        m_imp->maximize(x, n, ls, val, unbounded);
+    }
+
+    void explain::test_root_literal(atom::kind k, var y, unsigned i, poly* p, scoped_literal_vector & result) {
+        m_imp->test_root_literal(k, y, i, p, result);
+    }
+
 };
 
 #ifdef Z3DEBUG
@@ -1398,3 +1865,4 @@ void pp_lit(nlsat::explain::imp & ex, nlsat::literal l) {
     std::cout << std::endl;
 }
 #endif
+

src/nlsat/nlsat_explain.h

@@ -22,9 +22,11 @@ Revision History:
 #include"nlsat_solver.h"
 #include"nlsat_scoped_literal_vector.h"
 #include"polynomial_cache.h"
+#include"algebraic_numbers.h"
 
 namespace nlsat {
     class evaluator;
+
     
     class explain {
     public:
@@ -32,8 +34,8 @@ namespace nlsat {
     private:
         imp * m_imp;
     public:
-        explain(solver & s, assignment const & x2v, polynomial::cache & u, atom_vector const & atoms, atom_vector const & x2eq,
-                evaluator & ev);
+        explain(solver & s, assignment const & x2v, polynomial::cache & u, 
+                atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev);
         ~explain();
 
         void reset();
@@ -41,6 +43,7 @@ namespace nlsat {
         void set_full_dimensional(bool f);
         void set_minimize_cores(bool f);
         void set_factor(bool f);
+        void set_signed_project(bool f);
 
         /**
            \brief Given a set of literals ls[0], ... ls[n-1] s.t.
@@ -60,6 +63,48 @@ namespace nlsat {
                  - s_1, ..., s_m are false in the current interpretation
         */
         void operator()(unsigned n, literal const * ls, scoped_literal_vector & result);
+
+        
+        /**
+           \brief projection for a given variable.
+
+             Given:    M |= l1[x] /\ ... /\ ln[x]
+           
+             Find:     M |= s1, ..., sm
+
+             Such that:  |= ~s1 \/ ... \/ ~sm \/ E x. l1[x] /\ ... /\ ln[x]
+
+           Contrast this with with the core-based projection above:
+
+             Given:     M |= A x . l1[x] \/  ... \/ ln[x]
+           
+             Find:      M |= ~s1, ..., ~sm.
+
+             Such that:   |= s1 \/ ... \/ sm \/ A x . l1[x] \/  ... \/ ln[x]           
+
+           Claim: the two compute the same solutions if the projection operators are independent of the value of x.
+           Claim: A complete, convergent projection operator can be obtained from M in a way that is independent of x.
+
+           
+         */
+        void project(var x, unsigned n, literal const * ls, scoped_literal_vector & result);
+
+        /**
+           Maximize the value of x (locally) under the current assignment to other variables and
+           while maintaining the assignment to the literals ls.
+           Set unbounded to 'true' if the value of x is unbounded.
+
+           Precondition: the set of literals are true in the current model.
+
+           By local optimization we understand that x is increased to the largest value within
+           the signs delineated by the roots of the polynomials in ls.
+         */
+        void maximize(var x, unsigned n, literal const * ls, scoped_anum& val, bool& unbounded);
+
+        /**
+           Unit test routine.
+         */
+        void test_root_literal(atom::kind k, var y, unsigned i, poly* p, scoped_literal_vector & result);
     };
 
 };

src/nlsat/nlsat_scoped_literal_vector.h

@@ -64,6 +64,13 @@ namespace nlsat {
             for (unsigned i = 0; i < sz; i++)
                 push_back(ls[i]);
         }
+        void append(scoped_literal_vector const& ls) {
+            append(ls.size(), ls.c_ptr());
+        }
+        void swap(scoped_literal_vector& other) {
+            SASSERT(&m_solver == &other.m_solver);
+            m_lits.swap(other.m_lits);
+        }
     };
 
 

src/nlsat/nlsat_solver.cpp

@@ -66,7 +66,6 @@ namespace nlsat {
         typedef polynomial::cache cache;
         typedef ptr_vector<interval_set> interval_set_vector;
 
-        solver &               m_solver;
         reslimit&              m_rlimit;
         small_object_allocator m_allocator;
         unsynch_mpq_manager    m_qm;
@@ -159,8 +158,7 @@ namespace nlsat {
         unsigned               m_stages;
         unsigned               m_irrational_assignments; // number of irrational witnesses
 
-        imp(solver & s, reslimit& rlim, params_ref const & p):
-            m_solver(s),
+        imp(solver& s, reslimit& rlim, params_ref const & p):
             m_rlimit(rlim),
             m_allocator("nlsat"),
             m_pm(rlim, m_qm, &m_allocator),
@@ -168,7 +166,7 @@ namespace nlsat {
             m_am(rlim, m_qm, p, &m_allocator),
             m_asm(*this, m_allocator),
             m_assignment(m_am),
-            m_evaluator(m_assignment, m_pm, m_allocator), 
+            m_evaluator(s, m_assignment, m_pm, m_allocator), 
             m_ism(m_evaluator.ism()),
             m_num_bool_vars(0),
             m_display_var(m_perm),
@@ -183,12 +181,7 @@ namespace nlsat {
         }
         
         ~imp() {
-            m_explain.reset();
-            m_lemma.reset();
-            m_lazy_clause.reset();
-            undo_until_size(0);
-            del_clauses();
-            del_unref_atoms();
+            reset();
         }
 
         void mk_true_bvar() {
@@ -216,6 +209,18 @@ namespace nlsat {
             m_am.updt_params(p.p);
         }
 
+        void reset() {
+            m_explain.reset();
+            m_lemma.reset();
+            m_lazy_clause.reset();
+            undo_until_size(0);
+            del_clauses();
+            del_unref_atoms();
+            m_cache.reset();
+            m_assignment.reset();
+        }
+
+
         void checkpoint() {
             if (!m_rlimit.inc()) throw solver_exception(m_rlimit.get_cancel_msg());
             if (memory::get_allocation_size() > m_max_memory) throw solver_exception(Z3_MAX_MEMORY_MSG);
@@ -252,6 +257,7 @@ namespace nlsat {
         }
 
         void inc_ref(bool_var b) {
+            TRACE("ref", tout << "inc: " << b << "\n";);
             if (b == null_bool_var)
                 return;
             if (m_atoms[b] == 0)
@@ -264,6 +270,7 @@ namespace nlsat {
         }
 
         void dec_ref(bool_var b) {
+            TRACE("ref", tout << "dec: " << b << "\n";);
             if (b == null_bool_var)
                 return;
             atom * a = m_atoms[b];
@@ -412,6 +419,34 @@ namespace nlsat {
             return x;
         }
 
+        svector<bool> m_found_vars;
+        void vars(literal l, var_vector& vs) {                
+            vs.reset();
+            atom * a = m_atoms[l.var()];
+            if (a == 0) {
+                
+            }
+            else if (a->is_ineq_atom()) {
+                unsigned sz = to_ineq_atom(a)->size();
+                var_vector new_vs;
+                for (unsigned j = 0; j < sz; j++) {
+                    m_found_vars.reset();
+                    m_pm.vars(to_ineq_atom(a)->p(j), new_vs);
+                    for (unsigned i = 0; i < new_vs.size(); ++i) {
+                        if (!m_found_vars.get(new_vs[i], false)) {
+                            m_found_vars.setx(new_vs[i], true, false);
+                            vs.push_back(new_vs[i]);
+                        }
+                    }
+                }
+            }
+            else {
+                m_pm.vars(to_root_atom(a)->p(), vs);
+                //vs.erase(max_var(to_root_atom(a)->p()));
+                vs.push_back(to_root_atom(a)->x());
+            }
+        }
+
         void deallocate(ineq_atom * a) {
             unsigned obj_sz = ineq_atom::get_obj_size(a->size());
             a->~ineq_atom();
@@ -491,6 +526,7 @@ namespace nlsat {
             TRACE("nlsat_table_bug", ineq_atom::hash_proc h; 
                   tout << "mk_ineq_atom hash: " << h(new_atom) << "\n"; display(tout, *new_atom, m_display_var); tout << "\n";);
             ineq_atom * old_atom = m_ineq_atoms.insert_if_not_there(new_atom);
+            CTRACE("nlsat_table_bug", old_atom->max_var() != max, display(tout, *old_atom, m_display_var); tout << "\n";);
             SASSERT(old_atom->max_var() == max);
             if (old_atom != new_atom) {
                 deallocate(new_atom);
@@ -726,7 +762,7 @@ namespace nlsat {
 
         template<typename Predicate>
         void undo_until(Predicate const & pred) {
-            while (pred()) {
+            while (pred() && !m_trail.empty()) {
                 trail & t = m_trail.back();
                 switch (t.m_kind) {
                 case trail::BVAR_ASSIGNMENT:
@@ -803,6 +839,14 @@ namespace nlsat {
             SASSERT(m_bvalues[b] == l_undef);
         }
 
+        struct true_pred {
+            bool operator()() const { return true; }
+        };
+
+        void undo_until_empty() {
+            undo_until(true_pred());
+        }
+
         /**
            \brief Create a new scope level
         */
@@ -868,10 +912,11 @@ namespace nlsat {
             var max = a->max_var();
             if (!m_assignment.is_assigned(max))
                 return l_undef;
-            TRACE("value_bug", tout << "value of: "; display(tout, l); tout << "\n"; tout << "xk: " << m_xk << ", a->max_var(): " << a->max_var() << "\n";
-                  display_assignment(tout);
-                  display_bool_assignment(tout););
-            return to_lbool(m_evaluator.eval(a, l.sign()));
+            val = to_lbool(m_evaluator.eval(a, l.sign()));
+            TRACE("value_bug", tout << "value of: "; display(tout, l); tout << " := " << val << "\n"; 
+                  tout << "xk: " << m_xk << ", a->max_var(): " << a->max_var() << "\n";
+                  display_assignment(tout););
+            return val;
         }
 
         /**
@@ -880,8 +925,10 @@ namespace nlsat {
         bool is_satisfied(clause const & cls) const {
             unsigned sz = cls.size();
             for (unsigned i = 0; i < sz; i++) {
-                if (const_cast<imp*>(this)->value(cls[i]) == l_true)
+                if (const_cast<imp*>(this)->value(cls[i]) == l_true) {
+                    TRACE("value_bug:", tout << cls[i] << " := true\n";);
                     return true;
+                }
             }
             return false;
         }
@@ -984,8 +1031,10 @@ namespace nlsat {
            If satisfy_learned is true, then learned clauses are satisfied even if m_lazy > 0
         */
         bool process_arith_clause(clause const & cls, bool satisfy_learned) {
-            if (!satisfy_learned && m_lazy >= 2 && cls.is_learned())
+            if (!satisfy_learned && m_lazy >= 2 && cls.is_learned()) {
+                TRACE("nlsat", tout << "skip learned\n";);
                 return true; // ignore lemmas in super lazy mode
+            }
             SASSERT(m_xk == max_var(cls));
             unsigned num_undef   = 0;                // number of undefined literals
             unsigned first_undef = UINT_MAX;         // position of the first undefined literal
@@ -1064,7 +1113,7 @@ namespace nlsat {
            If satisfy_learned is true, then (arithmetic) learned clauses are satisfied even if m_lazy > 0
         */
         bool process_clause(clause const & cls, bool satisfy_learned) {
-            TRACE("nlsat", tout << "processing clause:\n"; display(tout, cls); tout << "\n";);
+            TRACE("nlsat", tout << "processing clause: "; display(tout, cls); tout << "\n";);
             if (is_satisfied(cls))
                 return true;
             if (m_xk == null_var)
@@ -1151,7 +1200,7 @@ namespace nlsat {
                 }
                 TRACE("nlsat_bug", tout << "xk: x" << m_xk << " bk: b" << m_bk << "\n";);
                 if (m_bk == null_bool_var && m_xk >= num_vars()) {
-                    TRACE("nlsat", tout << "found model\n"; display_assignment(tout); display_bool_assignment(tout););
+                    TRACE("nlsat", tout << "found model\n"; display_assignment(tout););
                     return l_true; // all variables were assigned, and all clauses were satisfied.
                 }
                 TRACE("nlsat", tout << "processing variable "; 
@@ -1186,23 +1235,102 @@ namespace nlsat {
         lbool check() {
             TRACE("nlsat_smt2", display_smt2(tout););
             TRACE("nlsat_fd", tout << "is_full_dimensional: " << is_full_dimensional() << "\n";);
-            m_xk = null_var;
+            init_search();
             m_explain.set_full_dimensional(is_full_dimensional());
-            if (m_random_order) {
+            bool reordered = false;
+            if (!can_reorder()) {
+
+            }
+            else if (m_random_order) {
                 shuffle_vars();
+                reordered = true;
             }
             else if (m_reorder) {
                 heuristic_reorder();
+                reordered = true;
             }
             sort_watched_clauses();
             lbool r = search();
-            CTRACE("nlsat_model", r == l_true, tout << "model before restore order\n"; display_assignment(tout); display_bool_assignment(tout););
-            if (m_reorder)
+            CTRACE("nlsat_model", r == l_true, tout << "model before restore order\n"; display_assignment(tout););
+            if (reordered)
                 restore_order();
-            CTRACE("nlsat_model", r == l_true, tout << "model\n"; display_assignment(tout); display_bool_assignment(tout););
+            CTRACE("nlsat_model", r == l_true, tout << "model\n"; display_assignment(tout););
+            CTRACE("nlsat", r == l_false, display(tout););
             return r;
         }
 
+        void init_search() {
+            undo_until_empty();
+            while (m_scope_lvl > 0) {
+                undo_new_level();
+            }
+            m_xk = null_var;
+            for (unsigned i = 0; i < m_bvalues.size(); ++i) {
+                m_bvalues[i] = l_undef;
+            }
+            m_assignment.reset();
+        }
+
+        lbool check(literal_vector& assumptions) {
+            literal_vector result;
+            unsigned sz = assumptions.size();
+            literal const* ptr = assumptions.c_ptr();
+            for (unsigned i = 0; i < sz; ++i) {
+                mk_clause(1, ptr+i, (assumption)(ptr+i));
+            }
+            lbool r = check();
+
+            if (r == l_false) {
+                // collect used literals from m_lemma_assumptions
+                vector<assumption, false> deps;
+                m_asm.linearize(m_lemma_assumptions.get(), deps);
+                for (unsigned i = 0; i < deps.size(); ++i) {
+                    literal const* lp = (literal const*)(deps[i]);
+                    if (ptr <= lp && lp < ptr + sz) {
+                        result.push_back(*lp);
+                    } 
+                }
+            }
+            collect(assumptions, m_clauses);
+            collect(assumptions, m_learned);
+            
+            assumptions.reset();
+            assumptions.append(result);
+            return r;
+        }
+
+        void collect(literal_vector const& assumptions, clause_vector& clauses) {
+            unsigned n = clauses.size();
+            unsigned j  = 0;
+            for (unsigned i = 0; i < n; i++) {
+                clause * c = clauses[i];
+                if (collect(assumptions, *c)) {
+                    del_clause(c);
+                }
+                else {
+                    clauses[j] = c;
+                    j++;
+                }
+            }
+            clauses.shrink(j);
+        }
+
+        bool collect(literal_vector const& assumptions, clause const& c) {
+            unsigned sz = assumptions.size();
+            literal const* ptr = assumptions.c_ptr();            
+            _assumption_set asms = static_cast<_assumption_set>(c.assumptions());
+            if (asms == 0) {
+                return false;
+            }
+            vector<assumption, false> deps;
+            m_asm.linearize(asms, deps);
+            bool found = false;
+            for (unsigned i = 0; !found && i < deps.size(); ++i) {
+                found = ptr <= deps[i] && deps[i] < ptr + sz;
+            }
+            return found;
+        }
+
         // -----------------------
         //
         // Conflict Resolution
@@ -1447,7 +1575,7 @@ namespace nlsat {
             TRACE("nlsat", tout << "resolve, conflicting clause:\n"; display(tout, *conflict_clause); tout << "\n";
                   tout << "xk: "; if (m_xk != null_var) m_display_var(tout, m_xk); else tout << "<null>"; tout << "\n";
                   tout << "scope_lvl: " << scope_lvl() << "\n";
-                  tout << "current assignment\n"; display_assignment(tout); display_bool_assignment(tout););
+                  tout << "current assignment\n"; display_assignment(tout););
 
             // static unsigned counter = 0;
             // counter++;
@@ -1588,7 +1716,7 @@ namespace nlsat {
                 conflict_clause = new_cls;
                 goto start;
             }
-            TRACE("nlsat_resolve_done", display_assignment(tout); display_bool_assignment(tout););
+            TRACE("nlsat_resolve_done", display_assignment(tout););
             return true;
         }
 
@@ -1801,6 +1929,15 @@ namespace nlsat {
             reorder(p.size(), p.c_ptr());
         }
 
+        bool can_reorder() const {
+            for (unsigned i = 0; i < m_atoms.size(); ++i) {
+                if (m_atoms[i]) {
+                    if (m_atoms[i]->is_root_atom()) return false;
+                }
+            }
+            return true;
+        }
+
         /**
            \brief Reorder variables using the giving permutation.
            p maps internal variables to their new positions
@@ -1921,6 +2058,9 @@ namespace nlsat {
         void reinit_cache() {
             reinit_cache(m_clauses);
             reinit_cache(m_learned);
+            for (unsigned i = 0; i < m_atoms.size(); ++i) {
+                reinit_cache(m_atoms[i]);
+            }
         }
         void reinit_cache(clause_vector const & cs) {
             unsigned sz = cs.size();
@@ -1934,10 +2074,13 @@ namespace nlsat {
         }
         void reinit_cache(literal l) {
             bool_var b = l.var();
-            atom * a = m_atoms[b];
-            if (a == 0)
-                return;
-            if (a->is_ineq_atom()) {
+            reinit_cache(m_atoms[b]);
+        }
+        void reinit_cache(atom* a) {
+            if (a == 0) {
+
+            }
+            else if (a->is_ineq_atom()) {
                 var max = 0;
                 unsigned sz = to_ineq_atom(a)->size();
                 for (unsigned i = 0; i < sz; i++) {
@@ -2073,7 +2216,7 @@ namespace nlsat {
         //
         // -----------------------
         
-        void display_assignment(std::ostream & out, display_var_proc const & proc) const {
+        void display_num_assignment(std::ostream & out, display_var_proc const & proc) const {
             for (var x = 0; x < num_vars(); x++) {
                 if (m_assignment.is_assigned(x)) {
                     proc(out, x);
@@ -2084,7 +2227,7 @@ namespace nlsat {
             }
         }
 
-        void display_bool_assignment(std::ostream & out, display_var_proc const & proc) const {
+        void display_bool_assignment(std::ostream & out) const {
             unsigned sz = m_atoms.size();
             for (bool_var b = 0; b < sz; b++) {
                 if (m_atoms[b] == 0 && m_bvalues[b] != l_undef) {
@@ -2112,12 +2255,13 @@ namespace nlsat {
             return !first;
         }
 
-        void display_assignment(std::ostream & out) const { 
-            display_assignment(out, m_display_var);
+        void display_num_assignment(std::ostream & out) const { 
+            display_num_assignment(out, m_display_var);
         }
 
-        void display_bool_assignment(std::ostream & out) const { 
-            display_bool_assignment(out, m_display_var);
+        void display_assignment(std::ostream& out) const {
+            display_bool_assignment(out);
+            display_num_assignment(out);
         }
        
         void display(std::ostream & out, ineq_atom const & a, display_var_proc const & proc, bool use_star = false) const {
@@ -2511,6 +2655,7 @@ namespace nlsat {
 
         void display(std::ostream & out) const {
             display(out, m_display_var);
+            display_assignment(out);
         }
 
         void display_vars(std::ostream & out) const {
@@ -2562,6 +2707,20 @@ namespace nlsat {
         return m_imp->check();
     }
 
+    lbool solver::check(literal_vector& assumptions) {
+        return m_imp->check(assumptions);
+    }
+
+    void solver::reset() {
+        m_imp->reset();
+    }
+
+
+    void solver::updt_params(params_ref const & p) {
+        m_imp->updt_params(p);
+    }
+
+
     void solver::collect_param_descrs(param_descrs & d) {
         algebraic_numbers::manager::collect_param_descrs(d);
         nlsat_params::collect_param_descrs(d);
@@ -2583,6 +2742,10 @@ namespace nlsat {
         m_imp->m_display_var.m_proc = &proc;
     }
 
+    unsigned solver::num_vars() const {
+        return m_imp->num_vars();
+    }
+
     bool solver::is_int(var x) const {
         return m_imp->is_int(x);
     }
@@ -2590,10 +2753,61 @@ namespace nlsat {
     bool_var solver::mk_bool_var() {
         return m_imp->mk_bool_var();
     }
+    
+    literal solver::mk_true() {
+        return literal(0, false);
+    }
 
     atom * solver::bool_var2atom(bool_var b) {
         return m_imp->m_atoms[b];
     }
+
+    void solver::vars(literal l, var_vector& vs) {
+        m_imp->vars(l, vs);
+    }
+
+    atom_vector const& solver::get_atoms() {
+        return m_imp->m_atoms;
+    }
+
+    atom_vector const& solver::get_var2eq() {
+        return m_imp->m_var2eq;
+    }
+
+    evaluator& solver::get_evaluator() {
+        return m_imp->m_evaluator;
+    }
+
+    explain& solver::get_explain() {
+        return m_imp->m_explain;
+    }
+
+    void solver::reorder(unsigned sz, var const* p) {
+        m_imp->reorder(sz, p);
+    }
+
+    void solver::restore_order() {
+        m_imp->restore_order();
+    }
+
+    void solver::set_rvalues(assignment const& as) {
+        m_imp->m_assignment.copy(as);
+    }
+
+    void solver::get_rvalues(assignment& as) {
+        as.copy(m_imp->m_assignment);
+    }
+
+    void solver::get_bvalues(svector<lbool>& vs) {
+        vs.reset();
+        vs.append(m_imp->m_bvalues);
+    }
+
+    void solver::set_bvalues(svector<lbool> const& vs) {
+        m_imp->m_bvalues.reset();
+        m_imp->m_bvalues.append(vs);
+        m_imp->m_bvalues.resize(m_imp->m_atoms.size(), l_undef);        
+    }
     
     var solver::mk_var(bool is_int) {
         return m_imp->mk_var(is_int);
@@ -2631,10 +2845,21 @@ namespace nlsat {
         m_imp->display(out, l);
     }
 
+    void solver::display(std::ostream & out, unsigned n, literal const* ls) const {
+        for (unsigned i = 0; i < n; ++i) {
+            display(out, ls[i]);
+            out << ";  ";
+        }
+    }
+
     void solver::display(std::ostream & out, var x) const {
         m_imp->m_display_var(out, x);
     }
 
+    void solver::display(std::ostream & out, atom const& a) const {
+        m_imp->display(out, a, m_imp->m_display_var);
+    }
+
     display_var_proc const & solver::display_proc() const {
         return m_imp->m_display_var;
     }

src/nlsat/nlsat_solver.h

@@ -28,6 +28,9 @@ Revision History:
 
 namespace nlsat {
 
+    class evaluator;
+    class explain;
+
     class solver {
         struct imp;
         imp * m_imp;
@@ -63,7 +66,9 @@ namespace nlsat {
                   nonlinear arithmetic atom.
         */
         bool_var mk_bool_var();
-    
+   
+        literal  mk_true();
+
         /**
            \brief Create a real/integer variable.
         */
@@ -121,6 +126,48 @@ namespace nlsat {
         */
         atom * bool_var2atom(bool_var b);
 
+        /**
+           \brief extract free variables from literal.
+         */
+        void vars(literal l, var_vector& vs);
+
+        /**
+           \brief provide access to atoms. Used by explain.
+        */
+        atom_vector const& get_atoms();
+
+        /**
+           \brief Access var -> asserted equality.
+        */
+
+        atom_vector const& get_var2eq();        
+
+        /**
+           \brief expose evaluator.
+        */
+        
+        evaluator& get_evaluator();
+
+        /**
+           \brief Access explanation module.
+         */
+        explain& get_explain();
+
+        /**
+           \brief Access assignments to variables.
+         */
+        void get_rvalues(assignment& as);
+        void set_rvalues(assignment const& as);
+
+        void get_bvalues(svector<lbool>& vs);
+        void set_bvalues(svector<lbool> const& vs);
+
+        /**
+           \brief reorder variables. 
+         */
+        void reorder(unsigned sz, var const* permutation);
+        void restore_order();
+
         /**
            \brief Return number of integer/real variables
         */
@@ -135,6 +182,8 @@ namespace nlsat {
         // -----------------------
         lbool check();
 
+        lbool check(literal_vector& assumptions);
+
         // -----------------------
         //
         // Model
@@ -154,6 +203,7 @@ namespace nlsat {
         void updt_params(params_ref const & p);
         static void collect_param_descrs(param_descrs & d);
 
+        void reset();
         void collect_statistics(statistics & st);
         void reset_statistics();
         void display_status(std::ostream & out) const;
@@ -174,6 +224,10 @@ namespace nlsat {
         */
         void display(std::ostream & out, literal l) const;
 
+        void display(std::ostream & out, unsigned n, literal const* ls) const;
+
+        void display(std::ostream & out, atom const& a) const;
+
         /**
            \brief Display variable
         */

src/nlsat/nlsat_types.h

@@ -111,6 +111,21 @@ namespace nlsat {
         struct eq_proc { bool operator()(ineq_atom const * a1, ineq_atom const * a2) const; };
     };
 
+    inline std::ostream& operator<<(std::ostream& out, atom::kind k) {
+        switch (k) {
+        case atom::EQ: return out << "=";
+        case atom::LT: return out << "<";
+        case atom::GT: return out << ">";
+        case atom::ROOT_EQ: return out << "= root";
+        case atom::ROOT_LT: return out << "< root";
+        case atom::ROOT_LE: return out << "<= root";
+        case atom::ROOT_GT: return out << "> root";
+        case atom::ROOT_GE: return out << ">= root";
+        default: return out << (int)k;
+        }
+        return out;
+    }
+
     class root_atom : public atom {
         friend class solver;
         var      m_x;

src/nlsat/tactic/goal2nlsat.cpp

@@ -29,7 +29,9 @@ Notes:
 #include"expr2var.h"
 #include"arith_decl_plugin.h"
 #include"tactic.h"
-#include"ast_smt2_pp.h"
+#include"ast_pp.h"
+#include"polynomial.h"
+#include"algebraic_numbers.h"
 
 struct goal2nlsat::imp {
     struct nlsat_expr2polynomial : public expr2polynomial {
@@ -124,7 +126,7 @@ struct goal2nlsat::imp {
         m_qm.neg(d2);
         polynomial_ref p(m_pm);
         p = m_pm.addmul(d1, m_pm.mk_unit(), p1, d2, m_pm.mk_unit(), p2);
-        TRACE("goal2nlsat_bug", tout << "p: " << p << "\nk: " << k << "\n";);
+        TRACE("goal2nlsat_bug", tout << mk_pp(f, m) << " p: " << p << "\nk: " << k << "\n";);
         if (is_const(p)) {
             int sign;
             if (is_zero(p))
@@ -192,7 +194,7 @@ struct goal2nlsat::imp {
                 switch (to_app(f)->get_decl_kind()) {
                 case OP_TRUE:
                 case OP_FALSE:
-                    TRACE("goal2nlsat", tout << "f: " << mk_ismt2_pp(f, m) << "\n";);
+                    TRACE("goal2nlsat", tout << "f: " << mk_pp(f, m) << "\n";);
                     throw tactic_exception("apply simplify before applying nlsat");
                 case OP_AND:
                 case OP_OR:
@@ -257,6 +259,7 @@ struct goal2nlsat::imp {
             process(g.form(i), g.dep(i));
         }
     }
+
 };
 
 struct goal2nlsat::scoped_set_imp {
@@ -289,4 +292,154 @@ void goal2nlsat::operator()(goal const & g, params_ref const & p, nlsat::solver
     scoped_set_imp setter(*this, local_imp);
     local_imp(g);
 }
+
     
+
+struct nlsat2goal::imp {
+    ast_manager& m;
+    arith_util   a;
+    u_map<expr*> const* m_x2t;
+public:
+    imp(ast_manager& m):m(m),a(m) {}
+
+    expr_ref operator()(nlsat::solver& s, u_map<expr*> const& b2a, u_map<expr*> const& x2t, nlsat::literal l) {
+        m_x2t = &x2t;
+        expr_ref result(m);
+        expr* t;
+        if (b2a.find(l.var(), t)) {
+            result = t;
+        }
+        else {
+            nlsat::atom const* at = s.bool_var2atom(l.var());
+            SASSERT(at != 0);
+            if (at->is_ineq_atom()) {
+                nlsat::ineq_atom const* ia = to_ineq_atom(at);
+                unsigned sz = ia->size();
+                expr_ref_vector ps(m);
+                bool is_int = true;
+                for (unsigned i = 0; is_int && i < sz; ++i) {
+                    is_int = poly_is_int(ia->p(i));
+                }
+                for (unsigned i = 0; i < sz; ++i) {
+                    polynomial::polynomial* p = ia->p(i);
+                    expr_ref t = poly2expr(s, p, is_int);
+                    if (ia->is_even(i)) {
+                        t = a.mk_power(t, a.mk_numeral(rational(2), a.is_int(t)));
+                    }
+                    ps.push_back(t);
+                }
+                result = a.mk_mul_simplify(ps);
+                expr_ref zero(m);
+                zero = a.mk_numeral(rational(0), a.is_int(result));
+                switch (ia->get_kind()) {
+                case nlsat::atom::EQ:
+                    result = m.mk_eq(result, zero);
+                    break;
+                case nlsat::atom::LT:
+                    if (l.sign()) {
+                        l.neg();
+                        result = a.mk_ge(result, zero);
+                    }
+                    else {
+                        result = a.mk_lt(result, zero);
+                    }
+                    break;
+                case nlsat::atom::GT:
+                    if (l.sign()) {
+                        l.neg();
+                        result = a.mk_le(result, zero);
+                    }
+                    else {
+                        result = a.mk_gt(result, zero);
+                    }
+                    break;
+                default:
+                    UNREACHABLE();
+                }
+            }
+            else {
+                //nlsat::root_atom const* ra = nlsat::to_root_atom(at);
+                //ra->i();
+                //expr_ref p = poly2expr(s, ra->p());
+                //expr*    x = m_x2t->find(ra->x());
+                std::ostringstream strm;
+                s.display(strm, l.sign()?~l:l);
+                result = m.mk_const(symbol(strm.str().c_str()), m.mk_bool_sort());
+            }
+        }
+
+        if (l.sign()) {
+            result = m.mk_not(result);
+        }
+        return result;
+    }
+
+    expr_ref poly2expr(nlsat::solver& s, polynomial::polynomial* p, bool is_int) {
+        expr_ref result(m);
+        unsigned sz = polynomial::manager::size(p);
+        expr_ref_vector args(m);
+        for (unsigned i = 0; i < sz; ++i) {
+            args.push_back(mono2expr(s, 
+                                     polynomial::manager::coeff(p, i), 
+                                     polynomial::manager::get_monomial(p, i), is_int));
+        }
+        result = a.mk_add_simplify(args);
+        return result;
+    }
+
+    expr_ref mono2expr(nlsat::solver& s, polynomial::numeral const& c, polynomial::monomial* mon, bool is_int) {
+        expr_ref result(m);
+        expr_ref_vector args(m);
+        unsigned sz = polynomial::manager::size(mon);
+        for (unsigned i = 0; i < sz; ++i) {
+            unsigned d = polynomial::manager::degree(mon, i);
+            expr* t = m_x2t->find(polynomial::manager::get_var(mon, i));
+            SASSERT(d >= 1);
+            if (d == 1) {
+                args.push_back(t);
+            }
+            else {
+                args.push_back(a.mk_power(t, a.mk_numeral(rational(d), a.is_int(t))));
+            }
+        }
+        if (!s.pm().m().is_one(c)) {
+            args.push_back(a.mk_numeral(c, is_int));
+        }
+        result = a.mk_mul_simplify(args);
+        return result;
+    }
+
+    bool poly_is_int(polynomial::polynomial* p) {
+        bool is_int = true;
+        unsigned sz = polynomial::manager::size(p);
+        for (unsigned i = 0; is_int && i < sz; ++i) {
+            is_int = mono_is_int(polynomial::manager::get_monomial(p, i));
+        }
+        return is_int;
+    }
+
+    bool mono_is_int(polynomial::monomial* mon) {
+        bool is_int = true;
+        unsigned sz = polynomial::manager::size(mon);
+        for (unsigned i = 0; is_int && i < sz; ++i) {
+            is_int = a.is_int(m_x2t->find(polynomial::manager::get_var(mon, i)));
+        }
+        return is_int;
+    }
+};
+
+
+nlsat2goal::nlsat2goal(ast_manager& m) {
+    m_imp = alloc(imp, m);
+}
+
+
+nlsat2goal::~nlsat2goal() {
+    dealloc(m_imp);
+}
+
+expr_ref nlsat2goal::operator()(nlsat::solver& s, u_map<expr*> const& b2a, u_map<expr*> const& x2t, nlsat::literal l) {
+    return (*m_imp)(s, b2a, x2t, l);
+}
+
+

src/nlsat/tactic/goal2nlsat.h

@@ -57,17 +57,16 @@ class nlsat2goal {
     struct imp;
     imp *  m_imp;
 public:
-    nlsat2goal();
+    nlsat2goal(ast_manager& m);
     ~nlsat2goal();
 
     static void collect_param_descrs(param_descrs & r);
 
     /**
-       \brief Translate the state of the nlsat engine back into a goal.
-    */
-    void operator()(nlsat::solver const & s, expr2var const & a2b, expr2var const & t2x,
-                    params_ref const & p, goal & g, model_converter_ref & mc);
-    
+       \brief Translate a literal into a formula.
+    */   
+    expr_ref operator()(nlsat::solver& s, u_map<expr*> const& b2a, u_map<expr*> const& x2t, nlsat::literal l);
+
 };
 
 #endif

src/opt/opt_context.cpp

@@ -514,12 +514,10 @@ namespace opt {
 
     void context::init_solver() {
         setup_arith_solver();
-        #pragma omp critical (opt_context)
-        {
-            m_opt_solver = alloc(opt_solver, m, m_params, m_fm);
-            m_opt_solver->set_logic(m_logic);
-            m_solver = m_opt_solver.get();
-        }
+        m_opt_solver = alloc(opt_solver, m, m_params, m_fm);
+        m_opt_solver->set_logic(m_logic);
+        m_solver = m_opt_solver.get();
+    
         if (opt_params(m_params).priority() == symbol("pareto") ||
             (opt_params(m_params).priority() == symbol("lex") && m_objectives.size() > 1)) {
             m_opt_solver->ensure_pb();
@@ -556,10 +554,7 @@ namespace opt {
         for (unsigned i = 0; i < sz; ++i) {
             m_sat_solver->assert_expr(get_solver().get_assertion(i));
         }   
-        #pragma omp critical (opt_context)
-        {
-            m_solver = m_sat_solver.get();
-        }
+        m_solver = m_sat_solver.get();        
     }
 
     void context::enable_sls(bool force) {
@@ -649,10 +644,7 @@ namespace opt {
     void context::add_maxsmt(symbol const& id, unsigned index) {
         maxsmt* ms = alloc(maxsmt, *this, index);
         ms->updt_params(m_params);
-        #pragma omp critical (opt_context)
-        {
-            m_maxsmts.insert(id, ms);
-        }
+        m_maxsmts.insert(id, ms);        
     }
 
     bool context::is_numeral(expr* e, rational & n) const {
@@ -1277,10 +1269,7 @@ namespace opt {
     }
        
     void context::set_simplify(tactic* tac) {
-        #pragma omp critical (opt_context)
-        {
-            m_simplify = tac;
-        }
+        m_simplify = tac;        
     }
 
     void context::clear_state() {
@@ -1290,10 +1279,7 @@ namespace opt {
     }
 
     void context::set_pareto(pareto_base* p) {
-        #pragma omp critical (opt_context)
-        {
-            m_pareto = p;
-        }
+        m_pareto = p;        
     }
 
     void context::collect_statistics(statistics& stats) const {

src/qe/nlqsat.cpp

@@ -0,0 +1,928 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    nlqsat.cpp
+
+Abstract:
+
+    Quantifier Satisfiability Solver for nlsat
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-10-17
+
+Revision History:
+
+
+--*/
+
+#include "nlqsat.h"
+#include "nlsat_solver.h"
+#include "nlsat_explain.h"
+#include "nlsat_assignment.h"
+#include "qsat.h"
+#include "quant_hoist.h"
+#include "goal2nlsat.h"
+#include "expr2var.h"
+#include "uint_set.h"
+#include "ast_util.h"
+#include "tseitin_cnf_tactic.h"
+#include "expr_safe_replace.h"
+#include "ast_pp.h"
+
+namespace qe {
+
+    enum qsat_mode_t {
+        qsat_t,
+        elim_t,
+        interp_t
+    };
+
+    class nlqsat : public tactic {
+
+        typedef unsigned_vector assumption_vector;
+        typedef nlsat::scoped_literal_vector clause;
+
+        struct stats {
+            unsigned m_num_rounds;        
+            stats() { reset(); }
+            void reset() { memset(this, 0, sizeof(*this)); }            
+        };
+        
+        ast_manager&           m;
+        qsat_mode_t            m_mode;
+        params_ref             m_params;
+        nlsat::solver          m_solver;
+        tactic_ref             m_nftactic;
+        nlsat::literal_vector  m_asms;
+        nlsat::literal_vector  m_cached_asms;
+        unsigned_vector        m_cached_asms_lim;
+        nlsat::literal         m_is_true;
+        nlsat::assignment      m_rmodel;        
+        svector<lbool>         m_bmodel;
+        nlsat::assignment      m_rmodel0;        
+        svector<lbool>         m_bmodel0;
+        bool                   m_valid_model;
+        vector<nlsat::var_vector>            m_bound_rvars;
+        vector<svector<nlsat::bool_var> >    m_bound_bvars;
+        vector<nlsat::scoped_literal_vector> m_preds;
+        svector<max_level>                   m_rvar2level;
+        u_map<max_level>                     m_bvar2level;
+        expr2var                             m_a2b, m_t2x;
+        u_map<expr*>                         m_b2a, m_x2t;
+        volatile bool                        m_cancel;
+        stats                                m_stats;
+        statistics                           m_st;
+        obj_hashtable<expr>                  m_free_vars;
+        expr_ref_vector                      m_answer;
+        expr_safe_replace                    m_answer_simplify;
+        nlsat::literal_vector                m_assumptions;
+        u_map<expr*>                         m_asm2fml;
+        expr_ref_vector                      m_trail;
+        
+        lbool check_sat() {
+            while (true) {
+                ++m_stats.m_num_rounds;
+                check_cancel();
+                init_assumptions();   
+                lbool res = m_solver.check(m_asms);
+                switch (res) {
+                case l_true:
+                    TRACE("qe", display(tout); );
+                    save_model();
+                    push();
+                    break;
+                case l_false:
+                    if (0 == level()) return l_false;
+                    if (1 == level() && m_mode == qsat_t) return l_true;
+                    project();
+                    break;
+                case l_undef:
+                    return res;
+                }
+            }
+            return l_undef;
+        }
+        
+        void init_assumptions() {
+            unsigned lvl = level();
+            m_asms.reset();
+            m_asms.push_back(is_exists()?m_is_true:~m_is_true);
+            m_asms.append(m_assumptions);
+            TRACE("qe", tout << "model valid: " << m_valid_model << " level: " << lvl << " "; 
+                  display_assumptions(tout);
+                  m_solver.display(tout););
+
+            if (!m_valid_model) {
+                m_asms.append(m_cached_asms);
+                return;
+            }            
+            unsave_model();
+            if (lvl == 0) {
+                SASSERT(m_cached_asms.empty());
+                return;
+            }
+            if (lvl <= m_preds.size()) {
+                for (unsigned j = 0; j < m_preds[lvl - 1].size(); ++j) {
+                    add_literal(m_cached_asms, m_preds[lvl - 1][j]);
+                }
+            }
+            m_asms.append(m_cached_asms);
+            
+            for (unsigned i = lvl + 1; i < m_preds.size(); i += 2) {
+                for (unsigned j = 0; j < m_preds[i].size(); ++j) {
+                    nlsat::literal l = m_preds[i][j];
+                    max_level lv = m_bvar2level.find(l.var());
+                    bool use = 
+                        (lv.m_fa == i && (lv.m_ex == UINT_MAX || lv.m_ex < lvl)) ||
+                        (lv.m_ex == i && (lv.m_fa == UINT_MAX || lv.m_fa < lvl));
+                    if (use) {
+                        add_literal(m_asms, l);
+                    }
+                }
+            }
+            TRACE("qe", display(tout);
+                  for (unsigned i = 0; i < m_asms.size(); ++i) {
+                      m_solver.display(tout, m_asms[i]); tout << "\n";
+                  });
+            save_model();
+        }
+
+        void add_literal(nlsat::literal_vector& lits, nlsat::literal l) {
+            lbool r = m_solver.value(l);
+            switch (r) {
+            case l_true:
+                lits.push_back(l);
+                break;
+            case l_false:
+                lits.push_back(~l);
+                break;
+            default:
+                UNREACHABLE();
+                break; 
+            }
+        }
+
+        template<class S, class T>
+        void insert_set(S& set, T const& vec) {
+            for (unsigned i = 0; i < vec.size(); ++i) {
+                set.insert(vec[i]);
+            }
+        }
+        
+
+        void mbp(unsigned level, nlsat::scoped_literal_vector& result) {
+            nlsat::var_vector vars;
+            uint_set fvars;
+            extract_vars(level, vars, fvars);
+            mbp(vars, fvars, result);
+        }
+
+        void extract_vars(unsigned level, nlsat::var_vector& vars, uint_set& fvars) {
+            for (unsigned i = 0; i < m_bound_rvars.size(); ++i) {
+                if (i < level) {
+                    insert_set(fvars, m_bound_bvars[i]);
+                }
+                else {
+                    vars.append(m_bound_rvars[i]);
+                }
+            }
+        }
+
+        void mbp(nlsat::var_vector const& vars, uint_set const& fvars, clause& result) {
+            // 
+            // Also project auxiliary variables from clausification.
+            // 
+            unsave_model();
+            nlsat::explain& ex = m_solver.get_explain();
+            nlsat::scoped_literal_vector new_result(m_solver);
+            result.reset();
+            // project quantified Boolean variables.
+            for (unsigned i = 0; i < m_asms.size(); ++i) {
+                nlsat::literal lit = m_asms[i];
+                if (!m_b2a.contains(lit.var()) || fvars.contains(lit.var())) {
+                    result.push_back(lit);
+                }
+            }
+            TRACE("qe", m_solver.display(tout, result.size(), result.c_ptr()); tout << "\n";);
+            // project quantified real variables.
+            // They are sorted by size, so we project the largest variables first to avoid 
+            // renaming variables. 
+            for (unsigned i = vars.size(); i > 0;) {
+                --i;
+                new_result.reset();
+                ex.project(vars[i], result.size(), result.c_ptr(), new_result);
+                result.swap(new_result);
+                TRACE("qe", m_solver.display(tout, result.size(), result.c_ptr()); tout << "\n";);
+            }
+            negate_clause(result);
+        }
+
+        void negate_clause(clause& result) {
+            for (unsigned i = 0; i < result.size(); ++i) {
+                result.set(i, ~result[i]);
+            }
+        }
+
+        void save_model() {
+            m_solver.get_rvalues(m_rmodel);
+            m_solver.get_bvalues(m_bmodel);
+            m_valid_model = true;
+            if (is_exists(level())) {
+                m_rmodel0.copy(m_rmodel);
+                m_bmodel0.reset();
+                m_bmodel0.append(m_bmodel);
+            }
+        }
+
+        void unsave_model() {
+            SASSERT(m_valid_model);
+            m_solver.set_rvalues(m_rmodel);
+            m_solver.set_bvalues(m_bmodel);
+        }
+         
+        void clear_model() {
+            m_valid_model = false;
+            m_rmodel.reset();
+            m_bmodel.reset();
+            m_solver.set_rvalues(m_rmodel);
+        }
+
+        unsigned level() const { 
+            return m_cached_asms_lim.size();
+        }
+
+        void enforce_parity(clause& cl) {
+            cl.push_back(is_exists()?~m_is_true:m_is_true);
+        }
+
+        void add_clause(clause& cl) {
+            if (cl.empty()) {
+                cl.push_back(~m_solver.mk_true());
+            }
+            SASSERT(!cl.empty());
+            nlsat::literal_vector lits(cl.size(), cl.c_ptr());
+            m_solver.mk_clause(lits.size(), lits.c_ptr());
+        }
+
+        max_level get_level(clause const& cl) {
+            return get_level(cl.size(), cl.c_ptr());
+        }
+
+        max_level get_level(unsigned n, nlsat::literal const* ls) {
+            max_level level;
+            for (unsigned i = 0; i < n; ++i) {
+                level.merge(get_level(ls[i]));
+            }
+            return level;
+        }
+
+        max_level get_level(nlsat::literal l) {
+            max_level level;
+            if (m_bvar2level.find(l.var(), level)) {
+                return level;
+            }
+            nlsat::var_vector vs;
+            m_solver.vars(l, vs);
+            TRACE("qe", m_solver.display(tout, l); tout << "\n";);
+            for (unsigned i = 0; i < vs.size(); ++i) {
+                level.merge(m_rvar2level[vs[i]]);
+            }
+            set_level(l.var(), level);
+            return level;
+        }
+
+        void set_level(nlsat::bool_var v, max_level const& level) {
+            unsigned k = level.max();
+            while (m_preds.size() <= k) {
+                m_preds.push_back(nlsat::scoped_literal_vector(m_solver));
+            }
+            nlsat::literal l(v, false);
+            m_preds[k].push_back(l);
+            m_bvar2level.insert(v, level);            
+            TRACE("qe", m_solver.display(tout, l); tout << ": " << level << "\n";);
+        }
+        
+        void project() {
+            TRACE("qe", display_assumptions(tout););
+            if (!m_valid_model) {
+                pop(1);
+                return;
+            }
+            if (m_mode == elim_t) {
+                project_qe();
+                return;
+            }
+            SASSERT(level() >= 2);
+            unsigned num_scopes;
+            clause cl(m_solver);
+            mbp(level()-1, cl);            
+            
+            max_level clevel = get_level(cl);
+            enforce_parity(cl);
+            add_clause(cl);
+
+            if (clevel.max() == UINT_MAX) {
+                num_scopes = 2*(level()/2);
+            }
+            else {
+                SASSERT(clevel.max() + 2 <= level());
+                num_scopes = level() - clevel.max();
+                if ((num_scopes % 2) != 0) {
+                    --num_scopes;
+                }
+                SASSERT(num_scopes >= 2);
+            }
+            
+            TRACE("qe", tout << "backtrack: " << num_scopes << "\n";);
+            pop(num_scopes); 
+        }
+
+        void project_qe() {
+            SASSERT(level() >= 1 && m_mode == elim_t && m_valid_model);
+            clause cl(m_solver);
+            mbp(std::max(1u, level()-1), cl);            
+            
+            expr_ref fml = clause2fml(cl);
+            TRACE("qe", tout << level() << ": " << fml << "\n";);
+            max_level clevel = get_level(cl);
+            if (level() == 1 || clevel.max() == 0) {
+                add_assumption_literal(cl, fml);           
+            }
+            else {
+                enforce_parity(cl);
+            }
+            add_clause(cl);
+
+            if (level() == 1) { // is_forall() && clevel.max() == 0
+                add_to_answer(fml);
+            }
+
+            if (level() == 1) {
+                pop(1);
+            }
+            else {
+                pop(2);
+            }
+        }
+
+        void add_to_answer(expr_ref& fml) {
+            m_answer_simplify(fml);
+            expr* e;
+            if (m.is_not(fml, e)) {
+                m_answer_simplify.insert(e, m.mk_false());
+            }
+            else {
+                m_answer_simplify.insert(fml, m.mk_true());
+            }
+            m_answer.push_back(fml);
+        }
+
+        expr_ref clause2fml(nlsat::scoped_literal_vector const& clause) {
+            expr_ref_vector fmls(m);
+            expr_ref fml(m);
+            expr* t;
+            nlsat2goal n2g(m);
+            for (unsigned i = 0; i < clause.size(); ++i) {
+                nlsat::literal l = clause[i];
+                if (m_asm2fml.find(l.var(), t)) {
+                    fml = t;
+                    if (l.sign()) {
+                        fml = push_not(fml);
+                    }
+                    SASSERT(l.sign());
+                    fmls.push_back(fml);
+                }
+                else {
+                    fmls.push_back(n2g(m_solver, m_b2a, m_x2t, l));
+                }
+            }
+            fml = mk_or(fmls);
+            return fml;
+        }
+
+        void add_assumption_literal(clause& clause, expr* fml) {
+            nlsat::bool_var b = m_solver.mk_bool_var();
+            clause.push_back(nlsat::literal(b, true));
+            m_assumptions.push_back(nlsat::literal(b, false)); 
+            m_asm2fml.insert(b, fml);
+            m_trail.push_back(fml);            
+            m_bvar2level.insert(b, max_level());
+        }
+
+        bool is_exists() const { return is_exists(level()); }
+        bool is_forall() const { return is_forall(level()); }
+        bool is_exists(unsigned level) const { return (level % 2) == 0; }        
+        bool is_forall(unsigned level) const { return is_exists(level+1); }
+
+        void check_cancel() {
+            if (m_cancel) {
+                throw tactic_exception(TACTIC_CANCELED_MSG);
+            }
+        }
+
+        void reset() {
+            //m_solver.reset();
+            m_asms.reset();
+            m_cached_asms.reset();
+            m_cached_asms_lim.reset();
+            m_is_true = nlsat::null_literal;
+            m_rmodel.reset();
+            m_valid_model = false;
+            m_bound_rvars.reset();
+            m_bound_bvars.reset();
+            m_preds.reset();
+            m_rvar2level.reset();
+            m_bvar2level.reset();
+            m_t2x.reset();
+            m_a2b.reset();
+            m_b2a.reset();
+            m_x2t.reset();
+            m_cancel = false;
+            m_st.reset();        
+            m_solver.collect_statistics(m_st);
+            m_free_vars.reset();
+            m_answer.reset();
+            m_answer_simplify.reset();
+            m_assumptions.reset();
+            m_asm2fml.reset();
+            m_trail.reset();
+        }
+
+        void push() {
+            m_cached_asms_lim.push_back(m_cached_asms.size());
+        }
+
+        void pop(unsigned num_scopes) {
+            clear_model();
+            unsigned new_level = level() - num_scopes;
+            m_cached_asms.shrink(m_cached_asms_lim[new_level]);
+            m_cached_asms_lim.shrink(new_level);
+        }
+
+        void display(std::ostream& out) {
+            display_preds(out);
+            display_assumptions(out);
+            m_solver.display(out << "solver:\n");
+        }
+
+        void display_assumptions(std::ostream& out) {
+            m_solver.display(out << "assumptions: ", m_asms.size(), m_asms.c_ptr());
+            out << "\n";
+        }
+
+        void display_preds(std::ostream& out) {
+            for (unsigned i = 0; i < m_preds.size(); ++i) {                
+                m_solver.display(out << i << ": ", m_preds[i].size(), m_preds[i].c_ptr());
+                out << "\n";
+            }
+        }
+
+        // expr -> nlsat::solver
+
+        void hoist(expr_ref& fml) {
+            quantifier_hoister hoist(m);
+            vector<app_ref_vector> qvars;
+            app_ref_vector vars(m);
+            bool is_forall = false;   
+            pred_abs abs(m);
+            abs.get_free_vars(fml, vars);
+            insert_set(m_free_vars, vars);
+            qvars.push_back(vars); 
+            vars.reset();    
+            if (m_mode == elim_t) {
+                is_forall = true;
+                hoist.pull_quantifier(is_forall, fml, vars);
+                qvars.push_back(vars);
+            }
+            else {
+                hoist.pull_quantifier(is_forall, fml, vars);
+                qvars.back().append(vars);            
+            }
+            do {
+                is_forall = !is_forall;
+                vars.reset();
+                hoist.pull_quantifier(is_forall, fml, vars);
+                qvars.push_back(vars);
+            }
+            while (!vars.empty());
+            SASSERT(qvars.back().empty()); 
+            init_expr2var(qvars);
+
+            goal2nlsat g2s;
+
+            expr_ref is_true(m), fml1(m), fml2(m);
+            is_true = m.mk_fresh_const("is_true", m.mk_bool_sort());
+            fml = m.mk_iff(is_true, fml);
+            goal_ref g = alloc(goal, m);
+            g->assert_expr(fml);
+            proof_converter_ref pc;
+            expr_dependency_ref core(m);
+            model_converter_ref mc;
+            goal_ref_buffer result;
+            (*m_nftactic)(g, result, mc, pc, core);
+            SASSERT(result.size() == 1);
+            TRACE("qe", result[0]->display(tout););
+            g2s(*result[0], m_params, m_solver, m_a2b, m_t2x);
+
+            // insert variables and their levels.
+            for (unsigned i = 0; i < qvars.size(); ++i) {
+                m_bound_bvars.push_back(svector<nlsat::bool_var>());
+                m_bound_rvars.push_back(nlsat::var_vector());
+                max_level lvl;
+                if (is_exists(i)) lvl.m_ex = i; else lvl.m_fa = i;
+                for (unsigned j = 0; j < qvars[i].size(); ++j) {
+                    app* v = qvars[i][j].get();
+
+                    if (m_a2b.is_var(v)) {
+                        SASSERT(m.is_bool(v));
+                        nlsat::bool_var b = m_a2b.to_var(v);
+                        m_bound_bvars.back().push_back(b);
+                        set_level(b, lvl);
+                    }
+                    else if (m_t2x.is_var(v)) {
+                        nlsat::var w = m_t2x.to_var(v);
+                        TRACE("qe", tout << mk_pp(v, m) << " |-> " << w << "\n";);
+                        m_bound_rvars.back().push_back(w);
+                        m_rvar2level.setx(w, lvl, max_level());
+                    }
+                    else {
+                        TRACE("qe", tout << mk_pp(v, m) << " not found\n";);
+                    }
+                }
+            }
+            init_var2expr();
+            m_is_true = nlsat::literal(m_a2b.to_var(is_true), false);
+            // insert literals from arithmetical sub-formulas
+            nlsat::atom_vector const& atoms = m_solver.get_atoms();
+            TRACE("qe", m_solver.display(tout); );
+            for (unsigned i = 0; i < atoms.size(); ++i) {
+                if (atoms[i]) {
+                    get_level(nlsat::literal(i, false));
+                }
+            }
+            TRACE("qe", tout << fml << "\n";);
+        }
+
+        void init_expr2var(vector<app_ref_vector> const& qvars) {
+            for (unsigned i = 0; i < qvars.size(); ++i) {
+                init_expr2var(qvars[i]);
+            }
+        }
+
+        void init_expr2var(app_ref_vector const& qvars) {
+            for (unsigned i = 0; i < qvars.size(); ++i) {
+                app* v = qvars[i];
+                if (m.is_bool(v)) {
+                    m_a2b.insert(v, m_solver.mk_bool_var());
+                }
+                else {
+                    // TODO: assert it is of type Real.
+                    m_t2x.insert(v, m_solver.mk_var(false));
+                }
+            }
+        }
+
+        void init_var2expr() {
+            expr2var::iterator it = m_t2x.begin(), end = m_t2x.end();
+            for (; it != end; ++it) {
+                m_x2t.insert(it->m_value, it->m_key);
+            }
+            it = m_a2b.begin(), end = m_a2b.end();
+            for (; it != end; ++it) {
+                m_b2a.insert(it->m_value, it->m_key);
+            }
+        }
+
+        
+        // Return false if nlsat assigned noninteger value to an integer variable.
+        // [copied from nlsat_tactic.cpp]
+        bool mk_model(model_converter_ref & mc) {
+            bool ok = true;
+            model_ref md = alloc(model, m);
+            arith_util util(m);
+            expr2var::iterator it = m_t2x.begin(), end = m_t2x.end();
+            for (; it != end; ++it) {
+                nlsat::var x = it->m_value;
+                expr * t = it->m_key;
+                if (!is_uninterp_const(t) || !m_free_vars.contains(t))
+                    continue;
+                expr * v;
+                try {
+                    v = util.mk_numeral(m_rmodel0.value(x), util.is_int(t));
+                }
+                catch (z3_error & ex) {
+                    throw ex;
+                }
+                catch (z3_exception &) {
+                    v = util.mk_to_int(util.mk_numeral(m_rmodel0.value(x), false));
+                    ok = false;
+                }
+                md->register_decl(to_app(t)->get_decl(), v);
+            }
+            it = m_a2b.begin(), end = m_a2b.end();
+            for (; it != end; ++it) {
+                expr * a = it->m_key;
+                nlsat::bool_var b = it->m_value;
+                if (a == 0 || !is_uninterp_const(a) || b == m_is_true.var() || !m_free_vars.contains(a))
+                    continue;
+                lbool val = m_bmodel0.get(b, l_undef);
+                if (val == l_undef)
+                    continue; // don't care
+                md->register_decl(to_app(a)->get_decl(), val == l_true ? m.mk_true() : m.mk_false());
+            }
+            mc = model2model_converter(md.get());
+            return ok;
+        }
+
+    public:
+        nlqsat(ast_manager& m, qsat_mode_t mode, params_ref const& p):
+            m(m),
+            m_mode(mode),
+            m_params(p),
+            m_solver(m.limit(), p),
+            m_nftactic(0),
+            m_rmodel(m_solver.am()),
+            m_rmodel0(m_solver.am()),
+            m_valid_model(false),
+            m_a2b(m),
+            m_t2x(m),
+            m_cancel(false),
+            m_answer(m),
+            m_answer_simplify(m),
+            m_trail(m)
+        {
+            m_solver.get_explain().set_signed_project(true);
+            m_nftactic = mk_tseitin_cnf_tactic(m);
+        }
+
+        virtual ~nlqsat() {
+        }
+
+        void updt_params(params_ref const & p) {
+            params_ref p2(p);
+            p2.set_bool("factor", false);
+            m_solver.updt_params(p2);
+        }
+        
+        void collect_param_descrs(param_descrs & r) {
+        }
+
+        
+        void operator()(/* in */  goal_ref const & in, 
+                        /* out */ goal_ref_buffer & result, 
+                        /* out */ model_converter_ref & mc, 
+                        /* out */ proof_converter_ref & pc,
+                        /* out */ expr_dependency_ref & core) {
+
+            tactic_report report("nlqsat-tactic", *in);
+
+            ptr_vector<expr> fmls;
+            expr_ref fml(m);
+            mc = 0; pc = 0; core = 0;
+            in->get_formulas(fmls);
+            fml = mk_and(m, fmls.size(), fmls.c_ptr());
+            if (m_mode == elim_t) {
+                fml = m.mk_not(fml);
+            }                         
+            reset();
+            TRACE("qe", tout << fml << "\n";);
+            hoist(fml);
+            TRACE("qe", tout << "ex: " << fml << "\n";);
+            lbool is_sat = check_sat();
+            
+            switch (is_sat) {
+            case l_false:
+                in->reset();
+                in->inc_depth();
+                if (m_mode == elim_t) {
+                    fml = mk_and(m_answer);
+                }
+                else {
+                    fml = m.mk_false();
+                }
+                in->assert_expr(fml);
+                result.push_back(in.get());
+                break;
+            case l_true:
+                SASSERT(m_mode == qsat_t);
+                in->reset();
+                in->inc_depth();
+                result.push_back(in.get());
+                if (in->models_enabled()) {
+                    VERIFY(mk_model(mc));
+                }
+                break;
+            case l_undef:
+                result.push_back(in.get());
+                std::string s = "search failed";
+                throw tactic_exception(s.c_str()); 
+            }        
+        }
+
+
+        void collect_statistics(statistics & st) const {
+            st.copy(m_st);
+            st.update("qsat num rounds", m_stats.m_num_rounds); 
+        }
+
+        void reset_statistics() {
+            m_stats.reset();
+            m_solver.reset_statistics();
+        }
+
+        void cleanup() {
+            reset();
+        }
+        
+        void set_logic(symbol const & l) {
+        }
+        
+        void set_progress_callback(progress_callback * callback) {
+        }
+        
+        tactic * translate(ast_manager & m) {
+            return alloc(nlqsat, m, m_mode, m_params);
+        }
+
+#if 0        
+
+        /**
+         
+           Algorithm:
+           I := true
+           while there is M, such that M |= ~B & I:
+              find P, such that M => P => exists y . ~B & I
+              ; forall y B => ~P
+              C := core of P with respect to A
+              ; A => ~ C => ~ P 
+              I := I & ~C
+
+
+           Alternative Algorithm: 
+           R := false
+           while there is M, such that M |= A & ~R:
+              find I, such that M => I => forall y . B
+              R := R | I              
+              
+         */
+
+        lbool interpolate(expr* a, expr* b, expr_ref& result) {
+            SASSERT(m_mode == interp_t);
+            
+            reset();
+            app_ref enableA(m), enableB(m);
+            expr_ref A(m), B(m), fml(m);
+            expr_ref_vector fmls(m), answer(m);
+
+            // varsB are private to B.
+            nlsat::var_vector vars;
+            uint_set fvars;
+            private_vars(a, b, vars, fvars);
+            
+            enableA = m.mk_const(symbol("#A"), m.mk_bool_sort());
+            enableB = m.mk_not(enableA);
+            A = m.mk_implies(enableA, a);
+            B = m.mk_implies(enableB, m.mk_not(b));
+            fml = m.mk_and(A, B);
+            hoist(fml);
+
+            
+
+            nlsat::literal _enableB = nlsat::literal(m_a2b.to_var(enableB), false);
+            nlsat::literal _enableA = ~_enableB;
+
+            while (true) {
+                m_mode = qsat_t;
+                // enable B
+                m_assumptions.reset();
+                m_assumptions.push_back(_enableB);
+                lbool is_sat = check_sat();
+
+                switch (is_sat) {
+                case l_undef:
+                    return l_undef;
+                case l_true:                    
+                    break;
+                case l_false:
+                    result = mk_and(answer);
+                    return l_true;
+                }
+
+                // disable B, enable A
+                m_assumptions.reset();
+                m_assumptions.push_back(_enableA);
+                // add blocking clause to solver.
+
+                nlsat::scoped_literal_vector core(m_solver);
+                
+                m_mode = elim_t;
+
+                mbp(vars, fvars, core);
+
+                // minimize core.
+                nlsat::literal_vector _core(core.size(), core.c_ptr());
+                _core.push_back(_enableA);
+                is_sat = m_solver.check(_core); // TBD: only for quantifier-free A. Generalize output of elim_t to be a core.
+                switch (is_sat) {
+                case l_undef: 
+                    return l_undef;
+                case l_true:
+                    UNREACHABLE();
+                case l_false:
+                    core.reset();
+                    core.append(_core.size(), _core.c_ptr());
+                    break;
+                }
+                negate_clause(core);
+                // keep polarity of enableA, such that clause is only 
+                // used when checking satisfiability of B.
+                for (unsigned i = 0; i < core.size(); ++i) {
+                    if (core[i].var() == _enableA.var()) core.set(i, ~core[i]);
+                }
+                add_clause(core);                   // Invariant is added as assumption for B.
+                answer.push_back(clause2fml(core)); // TBD: remove answer literal.
+            }
+        }
+
+        /**
+           \brief extract variables that are private to a (not used in b).
+           vars cover the real variables, and fvars cover the Boolean variables.
+
+           TBD: We want fvars to be the complement such that returned core contains
+                Shared boolean variables, but not the ones private to B.
+         */
+        void private_vars(expr* a, expr* b, nlsat::var_vector& vars, uint_set& fvars) {
+            app_ref_vector varsA(m), varsB(m);
+            obj_hashtable<expr> varsAS;
+            pred_abs abs(m);
+            abs.get_free_vars(a, varsA);
+            abs.get_free_vars(b, varsB);
+            insert_set(varsAS, varsA);
+            for (unsigned i = 0; i < varsB.size(); ++i) {
+                if (varsAS.contains(varsB[i].get())) {
+                    varsB[i] = varsB.back();
+                    varsB.pop_back();
+                    --i;
+                }
+            }
+            for (unsigned j = 0; j < varsB.size(); ++j) {
+                app* v = varsB[j].get();
+                if (m_a2b.is_var(v)) {
+                    fvars.insert(m_a2b.to_var(v));
+                }
+                else if (m_t2x.is_var(v)) {
+                    vars.push_back(m_t2x.to_var(v));                    
+                }
+            }
+        }
+
+        lbool maximize(app* _x, expr* _fml, scoped_anum& result, bool& unbounded) {
+            expr_ref fml(_fml, m);
+            reset();
+            hoist(fml);
+            nlsat::literal_vector lits;
+            lbool is_sat = l_true;
+            nlsat::var x = m_t2x.to_var(_x);  
+            m_mode = qsat_t;
+            while (is_sat == l_true) {
+                is_sat = check_sat();
+                if (is_sat == l_true) {
+                    // m_asms is minimized set of literals that satisfy formula.
+                    nlsat::explain& ex = m_solver.get_explain();
+                    polynomial::manager& pm = m_solver.pm();
+                    anum_manager& am = m_solver.am();
+                    ex.maximize(x, m_asms.size(), m_asms.c_ptr(), result, unbounded);
+                    if (unbounded) {
+                        break;
+                    }
+                    // TBD: assert the new bound on x using the result.
+                    bool is_even = false;
+                    polynomial::polynomial_ref pr(pm);
+                    pr = pm.mk_polynomial(x);
+                    rational r;
+                    am.get_upper(result, r);
+                    // result is algebraic numeral, but polynomials are not defined over extension field.
+                    polynomial::polynomial* p = pr;
+                    nlsat::bool_var b = m_solver.mk_ineq_atom(nlsat::atom::GT, 1, &p, &is_even);
+                    nlsat::literal bound(b, false);
+                    m_solver.mk_clause(1, &bound);
+                }
+            }
+            return is_sat;
+        }
+#endif
+    };
+};
+
+tactic * mk_nlqsat_tactic(ast_manager & m, params_ref const& p) {
+    return alloc(qe::nlqsat, m, qe::qsat_t, p);
+}
+
+tactic * mk_nlqe_tactic(ast_manager & m, params_ref const& p) {
+    return alloc(qe::nlqsat, m, qe::elim_t, p);
+}
+
+

src/qe/nlqsat.h

@@ -0,0 +1,38 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    nlqsat.h
+
+Abstract:
+
+    Quantifier Satisfiability Solver for nlsat
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-10-17
+
+Revision History:
+
+
+--*/
+
+#ifndef QE_NLQSAT_H__
+#define QE_NLQSAT_H__
+
+#include "tactic.h"
+
+
+tactic * mk_nlqsat_tactic(ast_manager & m, params_ref const& p = params_ref());
+tactic * mk_nlqe_tactic(ast_manager & m, params_ref const& p = params_ref());
+
+
+/*
+  ADD_TACTIC("nlqsat", "apply a NL-QSAT solver.", "mk_nlqsat_tactic(m, p)") 
+
+*/
+
+// TBD_TACTIC("nlqe", "apply a NL-QE solver.", "mk_nlqe_tactic(m, p)") 
+
+#endif 

src/qe/qe.cpp

@@ -36,7 +36,6 @@ Revision History:
 #include "expr_functors.h"
 #include "quant_hoist.h"
 #include "bool_rewriter.h"
-#include "qe_util.h"
 #include "th_rewriter.h"
 #include "smt_kernel.h"
 #include "model_evaluator.h"
@@ -2281,7 +2280,7 @@ namespace qe {
         }    
     }
 
-    static void extract_vars(quantifier* q, expr_ref& new_body, app_ref_vector& vars) {
+    void extract_vars(quantifier* q, expr_ref& new_body, app_ref_vector& vars) {
         ast_manager& m = new_body.get_manager();
         expr_ref tmp(m);
         unsigned nd = q->get_num_decls();

src/qe/qe.h

@@ -223,6 +223,8 @@ namespace qe {
 
     qe_solver_plugin* mk_arith_plugin(i_solver_context& ctx, bool produce_models, smt_params& p);
 
+    void extract_vars(quantifier* q, expr_ref& new_body, app_ref_vector& vars);
+
     class def_vector {
         func_decl_ref_vector m_vars;
         expr_ref_vector      m_defs;

src/qe/qe_arith.h

@@ -9,16 +9,33 @@ Copyright (c) 2015 Microsoft Corporation
 #define QE_ARITH_H_
 
 #include "model.h"
+#include "arith_decl_plugin.h"
+#include "qe_mbp.h"
 
 namespace qe {
+
     /**
        Loos-Weispfenning model-based projection for a basic conjunction.
        Lits is a vector of literals.
        return vector of variables that could not be projected.
      */
-    expr_ref arith_project(model& model, app_ref_vector& vars, expr_ref_vector const& lits);
 
-    expr_ref arith_project(model& model, app_ref_vector& vars, expr* fml);
+    class arith_project_plugin : public project_plugin {
+        struct imp;
+        imp* m_imp;
+    public:
+        arith_project_plugin(ast_manager& m);
+        virtual ~arith_project_plugin();
+        virtual bool operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits);
+        virtual bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits);
+        virtual family_id get_family_id();
+    };
+
+    bool arith_project(model& model, app* var, expr_ref_vector& lits);
+
+    // match e := t mod k = 0.
+    bool is_divides(arith_util& a, expr* e, rational& k, expr_ref& t);
+
 };
 
 #endif

src/qe/qe_arith_plugin.cpp

@@ -32,6 +32,7 @@ Revision History:
 #include "nlarith_util.h"
 #include "model_evaluator.h"
 #include "smt_kernel.h"
+#include "qe_arith.h"
 
 namespace qe {
 
@@ -266,23 +267,8 @@ namespace qe {
         // 
         // match 0 == p mod k, p mod k == 0
         //
-        bool is_divides(app* e, numeral& k, expr_ref& p) {
-            expr* e1, *e2;
-            if (!m.is_eq(e, e1, e2)) {
-                return false;
-            }
-            return is_divides(e1, e2, k, p) || is_divides(e2, e1, k, p);
-        }
-    
-        bool is_divides(expr* e1, expr* e2, numeral& k, expr_ref& p) {  
-            if (m_arith.is_mod(e2) && 
-                m_arith.is_numeral(e1, k) && 
-                k.is_zero() &&
-                m_arith.is_numeral(to_app(e2)->get_arg(1), k)) {
-                p = to_app(e2)->get_arg(0);
-                return true;
-            }
-            return false;
+        bool is_divides(expr* e, numeral& k, expr_ref& p) {
+            return qe::is_divides(m_arith, e, k, p);
         }
 
         bool is_not_divides(app* e, app_ref& n, numeral& k, expr_ref& p) {

src/qe/qe_arrays.cpp

@@ -0,0 +1,427 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    qe_arrays.cpp
+
+Abstract:
+
+    Model based projection for arrays
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-06-13
+
+Revision History:
+
+--*/
+
+
+#include "qe_arrays.h"
+#include "rewriter_def.h"
+#include "expr_functors.h"
+#include "expr_safe_replace.h"
+#include "lbool.h"
+#include "ast_util.h"
+#include "ast_pp.h"
+
+namespace qe {
+
+    struct array_project_plugin::imp {
+
+        // rewriter or direct procedure.
+        struct rw_cfg : public default_rewriter_cfg {
+            ast_manager&    m;
+            array_util&     a;
+            expr_ref_vector m_lits;
+            model*          m_model; 
+            imp*            m_imp;
+            
+            rw_cfg(ast_manager& m, array_util& a):
+                m(m), a(a), m_lits(m), m_model(0) {}
+            
+            br_status reduce_app(func_decl* f, unsigned n, expr* const* args, expr_ref& result, proof_ref & pr) {
+                if (a.is_select(f) && a.is_store(args[0])) {                    
+                    expr_ref val1(m), val2(m); 
+                    app* b = to_app(args[0]);
+                    SASSERT(b->get_num_args() == n + 1);
+                    for (unsigned i = 1; i < n; ++i) {
+                        expr* arg1 = args[i];
+                        expr* arg2 = b->get_arg(i);
+                        if (arg1 == arg2) {
+                            val1 = val2 = arg1;
+                        }
+                        else {
+                            VERIFY(m_model->eval(arg1, val1));
+                            VERIFY(m_model->eval(arg2, val2));
+                        }
+                        switch(compare(val1, val2)) {
+                        case l_true:
+                            if (arg1 != arg2) {
+                                m_lits.push_back(m.mk_eq(arg1, arg2));
+                            }
+                            break;
+                        case l_false: {
+                            ptr_vector<expr> new_args;
+                            if (i > 0) {
+                                m_lits.resize(m_lits.size() - i);
+                            }
+                            m_lits.push_back(m.mk_not(m.mk_eq(arg1, arg2)));
+                            new_args.push_back(b->get_arg(0));
+                            new_args.append(n-1, args+1);
+                            result = m.mk_app(f, n, new_args.c_ptr());
+                            return BR_REWRITE1;
+                        }
+                        case l_undef:
+                            return BR_FAILED;
+                        }
+                    }
+                    result = b->get_arg(n);
+                    return BR_DONE;
+                }
+                return BR_FAILED;
+            }
+
+            lbool compare(expr* x, expr* y) {
+                NOT_IMPLEMENTED_YET();
+                return l_undef;
+            }
+        };
+
+        struct indices {
+            expr_ref_vector m_values;
+            expr* const*    m_vars;
+
+            indices(ast_manager& m, model& model, unsigned n, expr* const* vars): 
+                m_values(m), m_vars(vars) {
+                expr_ref val(m);
+                for (unsigned i = 0; i < n; ++i) {
+                    VERIFY(model.eval(vars[i], val));
+                    m_values.push_back(val);
+                }
+            }
+        };
+        
+        ast_manager& m;
+        array_util   a;
+        scoped_ptr<contains_app> m_var;
+        
+        imp(ast_manager& m): m(m), a(m) {}
+        ~imp() {}
+
+        virtual bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+            return false;
+        }
+
+        bool operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits) {
+
+            TRACE("qe", tout << mk_pp(var, m) << "\n" << lits;);
+            m_var = alloc(contains_app, m, var);
+
+            // reduce select-store redeces based on model.
+            // rw_cfg rw(m);
+            // rw(lits);
+
+            // try first to solve for var.
+            if (solve_eq(model, vars, lits)) {
+                return true;
+            } 
+
+            app_ref_vector selects(m);
+
+            // check that only non-select occurrences are in disequalities.
+            if (!check_diseqs(lits, selects)) {
+                TRACE("qe", tout << "Could not project " << mk_pp(var, m) << " for:\n" << lits << "\n";);
+                return false;
+            }
+
+            // remove disequalities.
+            elim_diseqs(lits);
+
+            // Ackerman reduction on remaining select occurrences
+            // either replace occurrences by model value or other node
+            // that is congruent to model value.
+
+            ackermanize_select(model, selects, vars, lits);
+           
+            TRACE("qe", tout << selects << "\n" << lits << "\n";);
+            return true;
+        }
+
+        void ackermanize_select(model& model, app_ref_vector const& selects, app_ref_vector& vars, expr_ref_vector& lits) {
+            expr_ref_vector vals(m), reps(m);
+            expr_ref val(m);
+            expr_safe_replace sub(m);
+
+            if (selects.empty()) {
+                return;
+            }
+
+            app_ref sel(m);
+            for (unsigned i = 0; i < selects.size(); ++i) {                
+                sel = m.mk_fresh_const("sel", m.get_sort(selects[i]));
+                VERIFY (model.eval(selects[i], val));
+                model.register_decl(sel->get_decl(), val);
+                vals.push_back(to_app(val));
+                reps.push_back(val);               // TODO: direct pass could handle nested selects.
+                vars.push_back(sel);
+                sub.insert(selects[i], val);
+            }
+
+            sub(lits);
+            remove_true(lits);
+            project_plugin::partition_args(model, selects, lits);
+            project_plugin::partition_values(model, reps, lits);
+        }
+
+        void remove_true(expr_ref_vector& lits) {
+            for (unsigned i = 0; i < lits.size(); ++i) {
+                if (m.is_true(lits[i].get())) {
+                    project_plugin::erase(lits, i);
+                }
+            }            
+        }
+
+        bool contains_x(expr* e) {
+            return (*m_var)(e);
+        }
+
+        void mk_eq(indices& x, indices y, expr_ref_vector& lits) {
+            unsigned n = x.m_values.size();
+            for (unsigned j = 0; j < n; ++j) {
+                lits.push_back(m.mk_eq(x.m_vars[j], y.m_vars[j]));
+            }
+        }
+        
+        // check that x occurs only under selects or in disequalities.
+        bool check_diseqs(expr_ref_vector const& lits, app_ref_vector& selects) {
+            expr_mark mark;
+            ptr_vector<app> todo;
+            app* e;
+            for (unsigned i = 0; i < lits.size(); ++i) {
+                e = to_app(lits[i]);
+                if (is_diseq_x(e)) {
+                    continue;
+                }
+                if (contains_x(e)) {
+                    todo.push_back(e);
+                }
+            }
+            while (!todo.empty()) {
+                e = todo.back();
+                todo.pop_back();                    
+                if (mark.is_marked(e)) {
+                    continue;
+                }
+                mark.mark(e);
+                if (m_var->x() == e) {
+                    return false;
+                }
+                unsigned start = 0;
+                if (a.is_select(e)) {
+                    if (e->get_arg(0) == m_var->x()) {
+                        start = 1;
+                        selects.push_back(e);
+                    } 
+                }
+                for (unsigned i = start; i < e->get_num_args(); ++i) {
+                    todo.push_back(to_app(e->get_arg(i)));
+                }
+            }
+            return true;
+        }
+
+        void elim_diseqs(expr_ref_vector& lits) {
+            for (unsigned i = 0; i < lits.size(); ++i) {
+                if (is_diseq_x(lits[i].get())) {
+                    project_plugin::erase(lits, i);
+                }
+            }
+        }
+
+        bool is_update_x(app* e) {
+            do {
+                if (m_var->x() == e) {
+                    return true;
+                }
+                if (a.is_store(e) && contains_x(e->get_arg(0))) {
+                    for (unsigned i = 1; i < e->get_num_args(); ++i) {
+                        if (contains_x(e->get_arg(i))) {
+                            return false;
+                        }
+                    }
+                    e = to_app(e->get_arg(0));
+                    continue;
+                }
+            }
+            while (false);
+            return false;
+        }
+
+        bool is_diseq_x(expr* e) {
+            expr *f, * s, *t;
+            if (m.is_not(e, f) && m.is_eq(f, s, t)) {
+                if (contains_x(s) && !contains_x(t) && is_update_x(to_app(s))) return true;
+                if (contains_x(t) && !contains_x(s) && is_update_x(to_app(t))) return true;
+            }
+            return false;
+        }
+
+        bool solve_eq(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+            // find an equality to solve for.
+            expr* s, *t;
+            for (unsigned i = 0; i < lits.size(); ++i) {
+                if (m.is_eq(lits[i].get(), s, t)) {
+                    vector<indices> idxs;
+                    expr_ref save(m), back(m);
+                    save = lits[i].get();
+                    back = lits.back();
+                    lits[i] = back;
+                    lits.pop_back();
+                    unsigned sz = lits.size();
+                    if (contains_x(s) && !contains_x(t) && is_app(s)) {
+                        if (solve(model, to_app(s), t, idxs, vars, lits)) {
+                            return true;
+                        }
+                    }
+                    else if (contains_x(t) && !contains_x(s) && is_app(t)) {
+                        if (solve(model, to_app(t), s, idxs, vars, lits)) {
+                            return true;
+                        }
+                    }
+                    // put back the equality literal.
+                    lits.resize(sz);
+                    lits.push_back(back);
+                    lits[i] = save;
+                }
+                // TBD: not distinct?
+            }
+            return false;
+        }
+
+        bool solve(model& model, app* s, expr* t, vector<indices>& idxs, app_ref_vector& vars, expr_ref_vector& lits) {
+            SASSERT(contains_x(s));
+            SASSERT(!contains_x(t));
+
+            if (s == m_var->x()) {
+                expr_ref result(s, m);
+                expr_ref_vector args(m);
+                sort* range = get_array_range(m.get_sort(s));
+                for (unsigned i = 0; i < idxs.size(); ++i) {
+                    app_ref var(m);
+                    var = m.mk_fresh_const("value", range);
+                    vars.push_back(var);
+                    args.reset();
+                    args.push_back(result);
+                    args.append(idxs[i].m_values.size(), idxs[i].m_vars);
+                    args.push_back(var);
+                    result = a.mk_store(args.size(), args.c_ptr());
+                }
+                expr_safe_replace sub(m);
+                sub.insert(s, result);
+                for (unsigned i = 0; i < lits.size(); ++i) {
+                    sub(lits[i].get(), result);
+                    lits[i] = result;
+                }
+                return true;
+            }
+
+            if (a.is_store(s)) {
+                unsigned n = s->get_num_args()-2;
+                indices idx(m, model, n, s->get_args()+1);
+                for (unsigned i = 1; i < n; ++i) {
+                    if (contains_x(s->get_arg(i))) {
+                        return false;
+                    }
+                } 
+                unsigned i;
+                expr_ref_vector args(m);
+                switch (contains(idx, idxs, i)) {
+                case l_true:
+                    mk_eq(idx, idxs[i], lits);
+                    return solve(model, to_app(s->get_arg(0)), t, idxs, vars, lits);
+                case l_false:
+                    for (unsigned i = 0; i < idxs.size(); ++i) {
+                        expr_ref_vector eqs(m);
+                        mk_eq(idx, idxs[i], eqs);
+                        lits.push_back(m.mk_not(mk_and(eqs))); // TBD: extract single index of difference based on model.
+                    }
+                    args.push_back(t);
+                    args.append(n, s->get_args()+1);
+                    lits.push_back(m.mk_eq(a.mk_select(args.size(), args.c_ptr()), s->get_arg(n+1)));
+                    idxs.push_back(idx);
+                    return solve(model, to_app(s->get_arg(0)), t, idxs, vars, lits);
+                case l_undef:
+                    return false;
+                }                
+            }
+            return false;
+        }
+
+        lbool contains(indices const& idx, vector<indices> const& idxs, unsigned& j) {
+            for (unsigned i = 0; i < idxs.size(); ++i) {
+                switch (compare(idx, idxs[i])) {
+                case l_true: 
+                    j = i;
+                    return l_true;
+                case l_false:
+                    break;
+                case l_undef:
+                    return l_undef;                
+                }
+            }
+            return l_false;
+        }
+
+        lbool compare(indices const& idx1, indices const& idx2) {
+            unsigned n = idx1.m_values.size();
+            for (unsigned i = 0; i < n; ++i) {
+                switch (compare(idx1.m_values[i], idx2.m_values[i])) {
+                case l_true:
+                    break;
+                case l_false:
+                    return l_false;
+                case l_undef:
+                    return l_undef;
+                }
+            }
+            return l_true;
+        }
+
+        lbool compare(expr* val1, expr* val2) {
+            if (val1 == val2) {
+                return l_true;
+            }
+            if (is_uninterp(val1) ||
+                is_uninterp(val2)) {
+                // TBD chase definition of nested array.
+                return l_undef;
+            }
+            return l_true;
+        }            
+    };
+    
+    
+    array_project_plugin::array_project_plugin(ast_manager& m) {
+        m_imp = alloc(imp, m);
+    }
+    
+    array_project_plugin::~array_project_plugin() {
+        dealloc(m_imp);
+    }
+    
+    bool array_project_plugin::operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits) {
+        return (*m_imp)(model, var, vars, lits);
+    }
+
+    bool array_project_plugin::solve(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+        return m_imp->solve(model, vars, lits);
+    }
+    
+    family_id array_project_plugin::get_family_id() {
+        return m_imp->a.get_family_id();
+    }
+
+};
+

src/qe/qe_arrays.h

@@ -0,0 +1,42 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    qe_arrays.h
+
+Abstract:
+
+    Model based projection for arrays
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-06-13
+
+Revision History:
+
+--*/
+
+
+#ifndef __QE_ARRAYS_H_
+#define __QE_ARRAYS_H_
+
+#include "array_decl_plugin.h"
+#include "qe_mbp.h"
+
+namespace qe {
+
+    class array_project_plugin : public project_plugin {
+        struct imp;
+        imp* m_imp;
+    public:
+        array_project_plugin(ast_manager& m);
+        virtual ~array_project_plugin();
+        virtual bool operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits);
+        virtual bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits);
+        virtual family_id get_family_id();
+    };
+
+};
+
+#endif

src/qe/qe_datatypes.cpp

@@ -0,0 +1,312 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    qe_datatypes.cpp
+
+Abstract:
+
+    Simple projection function for algebraic datatypes.
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-06-13
+
+Revision History:
+
+--*/
+
+#include "qe_arith.h"
+#include "ast_pp.h"
+#include "th_rewriter.h"
+#include "expr_functors.h"
+#include "model_v2_pp.h"
+#include "expr_safe_replace.h"
+#include "obj_pair_hashtable.h"
+#include "qe_datatypes.h"
+
+namespace qe {
+    
+    struct datatype_project_plugin::imp  {
+        ast_manager&              m;
+        datatype_util             dt;
+        app_ref                   m_val;
+        scoped_ptr<contains_app>  m_var;
+        
+        imp(ast_manager& m):
+            m(m), dt(m), m_val(m) {}
+        
+        virtual bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+            return lift_foreign(vars, lits);
+        }
+
+        bool operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits) {
+            expr_ref val(m);
+            VERIFY(model.eval(var, val));
+            SASSERT(is_app(val));
+            TRACE("qe", tout << mk_pp(var, m) << " := " << val << "\n";);
+            m_val = to_app(val);
+            if (!dt.is_constructor(m_val)) {
+                // assert: var does not occur in lits.
+                return true;
+            }
+            m_var = alloc(contains_app, m, var);
+
+
+            try {
+                if (dt.is_recursive(m.get_sort(var))) {
+                    project_rec(model, vars, lits);
+                }
+                else {
+                    project_nonrec(model, vars, lits);
+                }
+            }
+            catch (cant_project) {
+                TRACE("qe", tout << "can't project:" << mk_pp(var, m) << "\n";);
+                return false;
+            }
+            return true;
+        }        
+    
+        void project_nonrec(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+            expr_ref tmp(m), val(m);
+            expr_ref_vector args(m);
+            app_ref arg(m);
+            SASSERT(dt.is_constructor(m_val));
+            func_decl* f = m_val->get_decl();
+            ptr_vector<func_decl> const& acc = *dt.get_constructor_accessors(f);
+            for (unsigned i = 0; i < acc.size(); ++i) {
+                arg = m.mk_fresh_const(acc[i]->get_name().str().c_str(), acc[i]->get_range());
+                model.register_decl(arg->get_decl(), m_val->get_arg(i));
+                args.push_back(arg);
+            }
+            val = m.mk_app(f, args.size(), args.c_ptr());
+            TRACE("qe", tout << mk_pp(m_var->x(), m) << " |-> " << val << "\n";);
+            reduce(val, lits);
+        }
+
+        void project_rec(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+            func_decl* f = m_val->get_decl();
+            expr_ref rhs(m);
+            expr_ref_vector eqs(m);
+            for (unsigned i = 0; i < lits.size(); ++i) {
+                if (solve(model, vars, lits[i].get(), rhs, eqs)) {
+                    project_plugin::erase(lits, i);
+                    reduce(rhs, lits);
+                    lits.append(eqs);
+                    return;
+                }
+            }
+
+            // otherwise, unfold the constructor associated with m_var
+            // once according to the model. In this way, selector-constructor
+            // redexes are reduced and disequalities are eventually solved
+            // by virtue of the constructors being different.
+            project_nonrec(model, vars, lits);
+        }
+
+        void reduce(expr* val, expr_ref_vector& lits) {
+            expr_safe_replace sub(m);
+            th_rewriter rw(m);
+            expr_ref tmp(m);
+            sub.insert(m_var->x(), val);
+            TRACE("qe", tout << mk_pp(m_var->x(), m) << " = " << mk_pp(val, m) << "\n";
+                  tout << lits << "\n";);
+            for (unsigned i = 0; i < lits.size(); ++i) {                
+                sub(lits[i].get(), tmp);
+                rw(tmp);
+                lits[i] = tmp;
+            }
+        }
+
+        bool contains_x(expr* e) {
+            return (*m_var)(e);
+        }
+
+        bool solve(model& model, app_ref_vector& vars, expr* fml, expr_ref& t, expr_ref_vector& eqs) {
+            expr* t1, *t2;
+            if (m.is_eq(fml, t1, t2)) {
+                if (contains_x(t1) && !contains_x(t2) && is_app(t1)) {
+                    return solve(model, vars, to_app(t1), t2, t, eqs);
+                }
+                if (contains_x(t2) && !contains_x(t1) && is_app(t2)) {
+                    return solve(model, vars, to_app(t2), t1, t, eqs);
+                }
+            }
+            if (m.is_not(fml, t1) && m.is_distinct(t1)) {
+                expr_ref eq = project_plugin::pick_equality(m, model, t1);
+                return solve(model, vars, eq, t, eqs);
+            }
+            return false;
+        }
+
+        bool solve(model& model, app_ref_vector& vars, app* a, expr* b, expr_ref& t, expr_ref_vector& eqs) {
+            SASSERT(contains_x(a));
+            SASSERT(!contains_x(b));
+            if (m_var->x() == a) {
+                t = b;
+                return true;
+            }
+            if (!dt.is_constructor(a)) {
+                return false;
+            }
+            func_decl* c = a->get_decl();
+            func_decl* rec = dt.get_constructor_recognizer(c);
+            ptr_vector<func_decl> const & acc = *dt.get_constructor_accessors(c);
+            SASSERT(acc.size() == a->get_num_args());
+            //
+            // It suffices to solve just the first available equality.
+            // The others are determined by the first.
+            //
+            for (unsigned i = 0; i < a->get_num_args(); ++i) {
+                expr* l = a->get_arg(i);
+                if (is_app(l) && contains_x(l)) {
+                    expr_ref r(m);
+                    r = access(c, i, acc, b);
+                    if (solve(model, vars, to_app(l), r, t, eqs)) {
+                        for (unsigned j = 0; j < c->get_arity(); ++j) {
+                            if (i != j) {
+                                eqs.push_back(m.mk_eq(access(c, j, acc, b), a->get_arg(j)));
+                            }
+                        }
+                        if (!is_app_of(b, c)) {
+                            eqs.push_back(m.mk_app(rec, b));
+                        }
+
+                        return true;
+                    }
+                }
+            }
+            return false;
+        }
+
+
+        expr* access(func_decl* c, unsigned i, ptr_vector<func_decl> const& acc, expr* e) {
+            if (is_app_of(e,c)) {
+                return to_app(e)->get_arg(i);
+            }
+            else {
+                return m.mk_app(acc[i], e);
+            }
+        }
+
+        bool lift_foreign(app_ref_vector const& vars, expr_ref_vector& lits) {
+
+            bool reduced = false;
+            expr_mark visited;
+            expr_mark has_var;
+            bool inserted = false;
+            for (unsigned i = 0; i < vars.size(); ++i) { 
+                if (m.is_bool(vars[i])) continue;
+                if (dt.is_datatype(m.get_sort(vars[i]))) continue;
+                inserted = true;
+                has_var.mark(vars[i]);
+                visited.mark(vars[i]);
+            }
+            if (inserted) {
+                for (unsigned i = 0; i < lits.size(); ++i) {
+                    expr* e = lits[i].get(), *l, *r;
+                    if (m.is_eq(e, l, r) && reduce_eq(visited, has_var, l, r, lits)) {
+                        project_plugin::erase(lits, i);
+                        reduced = true;
+                    }
+                }
+                CTRACE("qe", reduced, tout << vars << "\n" << lits << "\n";);
+            }
+            return reduced;
+        }
+
+        bool reduce_eq(expr_mark& has_var, expr_mark& visited, expr* l, expr* r, expr_ref_vector& lits) {
+            if (!is_app(l) || !is_app(r)) {
+                return false;
+            }
+            bool reduce = false;
+            if (dt.is_constructor(to_app(r)) && contains_foreign(has_var, visited, r)) {
+                std::swap(l, r);
+                reduce = true;
+            }
+            reduce |= dt.is_constructor(to_app(l)) && contains_foreign(has_var, visited, l);
+            if (!reduce) {
+                return false;
+            }
+            func_decl* c = to_app(l)->get_decl();
+            ptr_vector<func_decl> const& acc = *dt.get_constructor_accessors(c);
+            if (!is_app_of(r, c)) {
+                lits.push_back(m.mk_app(dt.get_constructor_recognizer(c), r));
+            }
+            for (unsigned i = 0; i < acc.size(); ++i) {
+                lits.push_back(m.mk_eq(to_app(l)->get_arg(i), access(c, i, acc, r)));
+            }
+            return true;
+        }
+
+
+        ptr_vector<expr> todo;
+
+        bool contains_foreign(expr_mark& has_var, expr_mark& visited, expr* e) {
+            todo.push_back(e);
+            while (!todo.empty()) {
+                expr* _f = todo.back();
+                if (visited.is_marked(_f)) {
+                    todo.pop_back();
+                    continue;
+                }
+                if (!is_app(_f)) {
+                    visited.mark(_f);                   
+                    todo.pop_back();
+                    continue;
+                }
+                app* f = to_app(_f);
+                bool has_new = false, has_v = false;
+                for (unsigned i = 0; i < f->get_num_args(); ++i) {
+                    expr* arg = f->get_arg(i);
+                    if (!visited.is_marked(arg)) {
+                        todo.push_back(arg);
+                        has_new = true;
+                    }
+                    else {
+                        has_v |= has_var.is_marked(arg);
+                    }
+                }
+                if (has_new) {
+                    continue;
+                }
+                todo.pop_back();
+                if (has_v) {
+                    has_var.mark(f);
+                }
+                TRACE("qe", tout << "contains: " << mk_pp(f, m) << " " << has_var.is_marked(f) << "\n";);
+                visited.mark(f);
+            }
+            TRACE("qe", tout << "contains: " << mk_pp(e, m) << " " << has_var.is_marked(e) << "\n";);
+            return has_var.is_marked(e);
+        }
+        
+    };
+    
+    datatype_project_plugin::datatype_project_plugin(ast_manager& m) {
+        m_imp = alloc(imp, m);
+    }
+    
+    datatype_project_plugin::~datatype_project_plugin() {
+        dealloc(m_imp);
+    }
+    
+    bool datatype_project_plugin::operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits) {
+        return (*m_imp)(model, var, vars, lits);
+    }
+
+    bool datatype_project_plugin::solve(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+        return m_imp->solve(model, vars, lits);
+    }
+
+    
+    family_id datatype_project_plugin::get_family_id() {
+        return m_imp->dt.get_family_id();
+    }
+    
+}
+
+
+

src/qe/qe_datatypes.h

@@ -0,0 +1,42 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    qe_datatypes.h
+
+Abstract:
+
+    Model based projection for algebraic datatypes
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-06-13
+
+Revision History:
+
+--*/
+
+
+#ifndef __QE_DATATYPES_H_
+#define __QE_DATATYPES_H_
+
+#include "datatype_decl_plugin.h"
+#include "qe_mbp.h"
+
+namespace qe {
+
+    class datatype_project_plugin : public project_plugin {
+        struct imp;
+        imp* m_imp;
+    public:
+        datatype_project_plugin(ast_manager& m);
+        virtual ~datatype_project_plugin();
+        virtual bool operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits);
+        virtual bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits);
+        virtual family_id get_family_id();
+    };
+
+};
+
+#endif

src/qe/qe_lite.cpp

@@ -31,7 +31,6 @@ Revision History:
 #include "var_subst.h"
 #include "uint_set.h"
 #include "ast_util.h"
-#include "qe_util.h"
 #include "th_rewriter.h"
 #include "for_each_expr.h"
 #include "expr_safe_replace.h"

src/qe/qe_mbp.cpp

@@ -0,0 +1,369 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    qe_mbp.cpp
+
+Abstract:
+
+    Model-based projection utilities
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-5-29
+
+Revision History:
+
+
+--*/
+
+#include "qe_mbp.h"
+#include "qe_arith.h"
+#include "qe_arrays.h"
+#include "qe_datatypes.h"
+#include "expr_safe_replace.h"
+#include "ast_pp.h"
+#include "ast_util.h"
+#include "th_rewriter.h"
+#include "model_v2_pp.h"
+#include "expr_functors.h"
+
+
+using namespace qe;
+
+
+/**
+   \brief return two terms that are equal in the model.
+   The distinct term t is false in model, so there 
+   are at least two arguments of t that are equal in the model.
+*/
+expr_ref project_plugin::pick_equality(ast_manager& m, model& model, expr* t) {
+    SASSERT(m.is_distinct(t));
+    expr_ref val(m);
+    expr_ref_vector vals(m);
+    obj_map<expr, expr*> val2expr;
+    app* alit = to_app(t);
+    for (unsigned i = 0; i < alit->get_num_args(); ++i) {
+        expr* e1 = alit->get_arg(i), *e2;
+        VERIFY(model.eval(e1, val));
+        if (val2expr.find(val, e2)) {
+            return expr_ref(m.mk_eq(e1, e2), m);
+        }
+        val2expr.insert(val, e1);
+        vals.push_back(val);
+    }
+    UNREACHABLE();
+    return expr_ref(0, m);
+}
+
+void project_plugin::partition_values(model& model, expr_ref_vector const& vals, expr_ref_vector& lits) {
+    ast_manager& m = vals.get_manager();
+    expr_ref val(m);
+    expr_ref_vector trail(m), reps(m);
+    obj_map<expr, expr*> roots;
+    for (unsigned i = 0; i < vals.size(); ++i) {
+        expr* v = vals[i], *root;
+        VERIFY (model.eval(v, val));
+        if (roots.find(val, root)) {
+            lits.push_back(m.mk_eq(v, root));
+        }
+        else {
+            roots.insert(val, v);
+            trail.push_back(val);
+            reps.push_back(v);
+        }
+    }
+    if (reps.size() > 1) {                
+        lits.push_back(mk_distinct(reps));
+    }
+}
+
+void project_plugin::partition_args(model& model, app_ref_vector const& selects, expr_ref_vector& lits) {
+    ast_manager& m = selects.get_manager();
+    if (selects.empty()) return;
+    unsigned num_args = selects[0]->get_decl()->get_arity();
+    for (unsigned j = 1; j < num_args; ++j) {
+        expr_ref_vector args(m);            
+        for (unsigned i = 0; i < selects.size(); ++i) {
+            args.push_back(selects[i]->get_arg(j));
+        }
+        project_plugin::partition_values(model, args, lits);
+    }
+}
+
+void project_plugin::erase(expr_ref_vector& lits, unsigned& i) {
+    lits[i] = lits.back();
+    lits.pop_back();
+    --i;
+}
+
+void project_plugin::push_back(expr_ref_vector& lits, expr* e) {
+    if (lits.get_manager().is_true(e)) return;
+    lits.push_back(e);
+}
+
+
+class mbp::impl {
+    ast_manager& m;
+    ptr_vector<project_plugin> m_plugins;
+
+    void add_plugin(project_plugin* p) {
+        family_id fid = p->get_family_id();
+        SASSERT(!m_plugins.get(fid, 0));
+        m_plugins.setx(fid, p, 0);
+    }
+
+    project_plugin* get_plugin(app* var) {
+        family_id fid = m.get_sort(var)->get_family_id();
+        return m_plugins.get(fid, 0);
+    }
+
+    bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits) {
+        expr_mark is_var, is_rem;
+        if (vars.empty()) {
+            return false;
+        }
+        bool reduced = false;
+        for (unsigned i = 0; i < vars.size(); ++i) { 
+            is_var.mark(vars[i].get());
+        }
+        expr_ref tmp(m), t(m), v(m);            
+        th_rewriter rw(m);
+        for (unsigned i = 0; i < lits.size(); ++i) {
+            expr* e = lits[i].get(), *l, *r;
+            if (m.is_eq(e, l, r) && reduce_eq(is_var, l, r, v, t)) {
+                reduced = true;
+                lits[i] = lits.back();
+                lits.pop_back();
+                --i;
+                expr_safe_replace sub(m);
+                sub.insert(v, t);
+                is_rem.mark(v);
+                for (unsigned j = 0; j < lits.size(); ++j) {
+                    sub(lits[j].get(), tmp);
+                    rw(tmp);
+                    lits[j] = tmp;
+                }
+            }
+        }
+        if (reduced) {
+            for (unsigned i = 0; i < vars.size(); ++i) {
+                if (is_rem.is_marked(vars[i].get())) {
+                    vars[i] = vars.back();
+                    vars.pop_back();
+                }
+            }
+        }
+        return reduced;
+    }
+
+    bool reduce_eq(expr_mark& is_var, expr* l, expr* r, expr_ref& v, expr_ref& t) {
+        if (is_var.is_marked(r)) {
+            std::swap(l, r);
+        }
+        if (is_var.is_marked(l)) {
+            contains_app cont(m, to_app(l));
+            if (!cont(r)) {
+                v = to_app(l);
+                t = r;
+                return true;
+            }
+        }
+        return false;
+    }
+
+public:
+
+    void extract_literals(model& model, expr_ref_vector& fmls) {
+        expr_ref val(m);
+        for (unsigned i = 0; i < fmls.size(); ++i) {
+            expr* fml = fmls[i].get(), *nfml, *f1, *f2, *f3;
+            if (m.is_not(fml, nfml) && m.is_distinct(nfml)) {
+                fmls[i] = project_plugin::pick_equality(m, model, nfml);
+                --i;
+            }
+            else if (m.is_or(fml)) {
+                for (unsigned j = 0; j < to_app(fml)->get_num_args(); ++j) {
+                    VERIFY (model.eval(to_app(fml)->get_arg(j), val));
+                    if (m.is_true(val)) {
+                        fmls[i] = to_app(fml)->get_arg(j);
+                        --i;
+                        break;
+                    }
+                }
+            }
+            else if (m.is_and(fml)) {
+                fmls.append(to_app(fml)->get_num_args(), to_app(fml)->get_args());
+                project_plugin::erase(fmls, i);
+            }
+            else if (m.is_iff(fml, f1, f2) || (m.is_not(fml, nfml) && m.is_xor(nfml, f1, f2))) {
+                VERIFY (model.eval(f1, val));
+                if (m.is_false(val)) {
+                    f1 = mk_not(m, f1);
+                    f2 = mk_not(m, f2);
+                }
+                project_plugin::push_back(fmls, f1);
+                project_plugin::push_back(fmls, f2);
+                project_plugin::erase(fmls, i);
+            }
+            else if (m.is_implies(fml, f1, f2)) {
+                VERIFY (model.eval(f2, val));
+                if (m.is_true(val)) {
+                    project_plugin::push_back(fmls, f2);
+                }
+                else {
+                    project_plugin::push_back(fmls, mk_not(m, f1));
+                }
+                project_plugin::erase(fmls, i);
+            }
+            else if (m.is_ite(fml, f1, f2, f3)) {
+                VERIFY (model.eval(f1, val));                
+                if (m.is_true(val)) {
+                    project_plugin::push_back(fmls, f2);
+                }
+                else {
+                    project_plugin::push_back(fmls, f3);
+                }
+                project_plugin::erase(fmls, i);
+            }
+            else if (m.is_not(fml, nfml) && m.is_not(nfml, nfml)) {
+                project_plugin::push_back(fmls, nfml);
+                project_plugin::erase(fmls, i);
+            }
+            else if (m.is_not(fml, nfml) && m.is_and(nfml)) {
+                for (unsigned j = 0; j < to_app(nfml)->get_num_args(); ++j) {
+                    VERIFY (model.eval(to_app(nfml)->get_arg(j), val));
+                    if (m.is_false(val)) {
+                        fmls[i] = mk_not(m, to_app(nfml)->get_arg(j));
+                        --i;
+                        break;
+                    }
+                }
+            }
+            else if (m.is_not(fml, nfml) && m.is_or(nfml)) {
+                for (unsigned j = 0; j < to_app(nfml)->get_num_args(); ++j) {
+                    project_plugin::push_back(fmls, mk_not(m, to_app(nfml)->get_arg(j)));
+                }
+                project_plugin::erase(fmls, i);                
+            }
+            else if ((m.is_not(fml, nfml) && m.is_iff(nfml, f1, f2)) || m.is_xor(fml, f1, f2)) {
+                VERIFY (model.eval(f1, val));
+                if (m.is_true(val)) {
+                    f2 = mk_not(m, f2);
+                }
+                else {
+                    f1 = mk_not(m, f1);
+                }
+                project_plugin::push_back(fmls, f1);
+                project_plugin::push_back(fmls, f2);
+                project_plugin::erase(fmls, i);
+            }
+            else if (m.is_not(fml, nfml) && m.is_implies(nfml, f1, f2)) {
+                project_plugin::push_back(fmls, f1);
+                project_plugin::push_back(fmls, mk_not(m, f2));
+                project_plugin::erase(fmls, i);
+            }
+            else if (m.is_not(fml, nfml) && m.is_ite(nfml, f1, f2, f3)) {
+                VERIFY (model.eval(f1, val));                
+                if (m.is_true(val)) {
+                    project_plugin::push_back(fmls, mk_not(m, f2));
+                }
+                else {
+                    project_plugin::push_back(fmls, mk_not(m, f3));
+                }
+                project_plugin::erase(fmls, i);
+            }
+            else {
+                // TBD other Boolean operations.
+            }
+        }
+    }
+
+    impl(ast_manager& m):m(m) {
+        add_plugin(alloc(arith_project_plugin, m));
+        add_plugin(alloc(datatype_project_plugin, m));
+        add_plugin(alloc(array_project_plugin, m));
+    }
+
+    ~impl() {
+        std::for_each(m_plugins.begin(), m_plugins.end(), delete_proc<project_plugin>());
+    }
+
+    void preprocess_solve(model& model, app_ref_vector& vars, expr_ref_vector& fmls) {
+        extract_literals(model, fmls);
+        bool change = true;
+        while (change && !vars.empty()) {
+            change = solve(model, vars, fmls);
+            for (unsigned i = 0; i < m_plugins.size(); ++i) {
+                if (m_plugins[i] && m_plugins[i]->solve(model, vars, fmls)) {
+                    change = true;
+                }
+            }
+        }        
+    }
+
+    void operator()(bool force_elim, app_ref_vector& vars, model& model, expr_ref_vector& fmls) {
+        expr_ref val(m), tmp(m);
+        app_ref var(m);
+        th_rewriter rw(m);
+        bool progress = true;
+        while (progress && !vars.empty()) {
+            preprocess_solve(model, vars, fmls);
+            app_ref_vector new_vars(m);
+            progress = false;
+            while (!vars.empty()) {
+                var = vars.back();
+                vars.pop_back();
+                project_plugin* p = get_plugin(var);
+                if (p && (*p)(model, var, vars, fmls)) {
+                    progress = true;
+                }
+                else {
+                    new_vars.push_back(var);
+                }
+            }
+            if (!progress && !new_vars.empty() && force_elim) {
+                var = new_vars.back();
+                new_vars.pop_back();
+                expr_safe_replace sub(m);
+                VERIFY(model.eval(var, val));
+                sub.insert(var, val);
+                for (unsigned i = 0; i < fmls.size(); ++i) {
+                    sub(fmls[i].get(), tmp);
+                    rw(tmp);
+                    if (m.is_true(tmp)) {
+                        fmls[i] = fmls.back();
+                        fmls.pop_back();
+                        --i;
+                    }
+                    else {
+                        fmls[i] = tmp;
+                    }
+                }            
+                progress = true;
+            }
+            vars.append(new_vars);
+        }
+    }
+};
+    
+mbp::mbp(ast_manager& m) {
+    m_impl = alloc(impl, m);
+}
+        
+mbp::~mbp() {
+    dealloc(m_impl);
+}
+        
+void mbp::operator()(bool force_elim, app_ref_vector& vars, model& mdl, expr_ref_vector& fmls) {
+    (*m_impl)(force_elim, vars, mdl, fmls);
+}
+
+void mbp::solve(model& model, app_ref_vector& vars, expr_ref_vector& fmls) {
+    m_impl->preprocess_solve(model, vars, fmls);
+}
+        
+void mbp::extract_literals(model& model, expr_ref_vector& lits) {
+    m_impl->extract_literals(model, lits);
+}

src/qe/qe_mbp.h

@@ -0,0 +1,76 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    qe_mbp.h
+
+Abstract:
+
+    Model-based projection utilities
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-5-28
+
+Revision History:
+
+
+--*/
+
+#ifndef __QE_MBP_H__
+#define __QE_MBP_H__
+
+#include "ast.h"
+#include "params.h"
+#include "model.h"
+
+
+namespace qe {
+
+    struct cant_project {};
+
+    class project_plugin {
+    public:
+        virtual ~project_plugin() {}
+        virtual bool operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits) = 0;
+        virtual bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits) = 0;
+        virtual family_id get_family_id() = 0;
+
+        static expr_ref pick_equality(ast_manager& m, model& model, expr* t);
+        static void partition_values(model& model, expr_ref_vector const& vals, expr_ref_vector& lits);
+        static void partition_args(model& model, app_ref_vector const& sels, expr_ref_vector& lits);
+        static void erase(expr_ref_vector& lits, unsigned& i);
+        static void push_back(expr_ref_vector& lits, expr* lit);
+    };
+
+    class mbp {
+        class impl;
+        impl * m_impl;
+    public:
+        mbp(ast_manager& m);
+        
+        ~mbp();
+        
+        /**
+           \brief
+           Apply model-based qe on constants provided as vector of variables. 
+           Return the updated formula and updated set of variables that were not eliminated.           
+        */
+        void operator()(bool force_elim, app_ref_vector& vars, model& mdl, expr_ref_vector& fmls);
+
+        /**
+           \brief
+           Solve as many variables as possible using "cheap" quantifier elimination"
+        */
+        void solve(model& model, app_ref_vector& vars, expr_ref_vector& lits);
+
+        /**
+           \brief 
+           Extract literals from formulas based on model.
+         */
+        void extract_literals(model& model, expr_ref_vector& lits);
+    };
+}
+
+#endif 

src/qe/qe_tactic.cpp

@@ -22,6 +22,7 @@ Revision History:
 #include"qe.h"
 
 class qe_tactic : public tactic {
+    statistics               m_st;
     struct     imp {
         ast_manager &            m;
         smt_params               m_fparams;
@@ -78,10 +79,19 @@ class qe_tactic : public tactic {
                 g->update(i, new_f, new_pr, g->dep(i));                
             }
             g->inc_depth();
+            g->elim_true();
             result.push_back(g.get());
             TRACE("qe", g->display(tout););
             SASSERT(g->is_well_sorted());
         }
+
+        void collect_statistics(statistics & st) const {
+            m_qe.collect_statistics(st);
+        }
+
+        void reset_statistics() {            
+        }
+
     };
     
     imp *      m_imp;
@@ -117,7 +127,19 @@ public:
                             proof_converter_ref & pc,
                             expr_dependency_ref & core) {
         (*m_imp)(in, result, mc, pc, core);
+        m_st.reset();
+        m_imp->collect_statistics(m_st);
+        
     }
+
+    virtual void collect_statistics(statistics & st) const {
+        st.copy(m_st);
+    }
+
+    virtual void reset_statistics() {
+        m_st.reset();
+    }
+
     
     virtual void cleanup() {
         ast_manager & m = m_imp->m;

src/qe/qe_util.cpp

@@ -1,26 +0,0 @@
-
-/*++
-Copyright (c) 2015 Microsoft Corporation
-
---*/
-
-#include "qe_util.h"
-#include "bool_rewriter.h"
-
-namespace qe {
-
-    expr_ref mk_and(expr_ref_vector const& fmls) {
-        ast_manager& m = fmls.get_manager();
-        expr_ref result(m);
-        bool_rewriter(m).mk_and(fmls.size(), fmls.c_ptr(), result);
-        return result;
-    }
-
-    expr_ref mk_or(expr_ref_vector const& fmls) {
-        ast_manager& m = fmls.get_manager();
-        expr_ref result(m);
-        bool_rewriter(m).mk_or(fmls.size(), fmls.c_ptr(), result);
-        return result;
-    }
-
-}

src/qe/qe_util.h

@@ -1,31 +0,0 @@
-/*++
-Copyright (c) 2013 Microsoft Corporation
-
-Module Name:
-
-    qe_util.h
-
-Abstract:
-
-    Utilities for quantifiers.
-
-Author:
-
-    Nikolaj Bjorner (nbjorner) 2013-08-28
-
-Revision History:
-
---*/
-#ifndef QE_UTIL_H_
-#define QE_UTIL_H_
-
-#include "ast.h"
-
-namespace qe {
-
-    expr_ref mk_and(expr_ref_vector const& fmls);
-
-    expr_ref mk_or(expr_ref_vector const& fmls);
-
-}
-#endif

src/qe/qsat.h

@@ -0,0 +1,135 @@
+/*++
+Copyright (c) 2015 Microsoft Corporation
+
+Module Name:
+
+    qsat.h
+
+Abstract:
+
+    Quantifier Satisfiability Solver.
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2015-5-28
+
+Revision History:
+
+
+--*/
+
+#ifndef QE_QSAT_H__
+#define QE_QSAT_H__
+
+#include "tactic.h"
+#include "filter_model_converter.h"
+
+namespace qe {
+
+    struct max_level {
+        unsigned m_ex, m_fa;
+        max_level(): m_ex(UINT_MAX), m_fa(UINT_MAX) {}
+        void merge(max_level const& other) {
+            merge(m_ex, other.m_ex);
+            merge(m_fa, other.m_fa);
+        }
+        static unsigned max(unsigned a, unsigned b) {
+            if (a == UINT_MAX) return b;
+            if (b == UINT_MAX) return a;
+            return std::max(a, b);
+        }
+        unsigned max() const {
+            return max(m_ex, m_fa);
+        }
+        void merge(unsigned& lvl, unsigned other) {
+            lvl = max(lvl, other);
+        }
+        std::ostream& display(std::ostream& out) const {
+            if (m_ex != UINT_MAX) out << "e" << m_ex << " ";
+            if (m_fa != UINT_MAX) out << "a" << m_fa << " ";
+            return out;
+        }
+        
+        bool operator==(max_level const& other) const {
+            return 
+                m_ex == other.m_ex &&
+                m_fa == other.m_fa;
+        }
+    };
+
+    inline std::ostream& operator<<(std::ostream& out, max_level const& lvl) {
+        return lvl.display(out);
+    }
+
+    class pred_abs {
+        ast_manager&            m;
+        vector<app_ref_vector>  m_preds;
+        expr_ref_vector         m_asms;
+        unsigned_vector         m_asms_lim;
+        obj_map<expr, expr*>    m_pred2lit;    // maintain definitions of predicates.
+        obj_map<expr, app*>     m_lit2pred;    // maintain reverse mapping to predicates
+        obj_map<expr, app*>     m_asm2pred;    // maintain map from assumptions to predicates
+        obj_map<expr, expr*>    m_pred2asm;    // predicates |-> assumptions
+        expr_ref_vector         m_trail;
+        filter_model_converter_ref m_fmc;
+        ptr_vector<expr>        todo;
+        obj_map<expr, max_level>      m_elevel;
+        obj_map<func_decl, max_level> m_flevel;
+
+        template <typename T>
+        void dec_keys(obj_map<expr, T*>& map) {
+            typename obj_map<expr, T*>::iterator it = map.begin(), end = map.end();
+            for (; it != end; ++it) {
+                m.dec_ref(it->m_key);
+            }
+        }
+        void add_lit(app* p, app* lit);
+        void add_asm(app* p, expr* lit);        
+        bool is_predicate(app* a, unsigned l);
+        void mk_concrete(expr_ref_vector& fmls, obj_map<expr, expr*> const& map);
+    public:
+        
+        pred_abs(ast_manager& m);
+        filter_model_converter* fmc();
+        void reset();
+        max_level compute_level(app* e);
+        void push();
+        void pop(unsigned num_scopes);
+        void insert(app* a, max_level const& lvl);
+        void get_assumptions(model* mdl, expr_ref_vector& asms);
+        void set_expr_level(app* v, max_level const& lvl);
+        void set_decl_level(func_decl* v, max_level const& lvl);
+        void abstract_atoms(expr* fml, max_level& level, expr_ref_vector& defs);
+        void abstract_atoms(expr* fml, expr_ref_vector& defs);
+        expr_ref mk_abstract(expr* fml);
+        void pred2lit(expr_ref_vector& fmls);
+        expr_ref pred2asm(expr* fml);
+        void get_free_vars(expr* fml, app_ref_vector& vars);
+        expr_ref mk_assumption_literal(expr* a, model* mdl, max_level const& lvl, expr_ref_vector& defs);
+        void add_pred(app* p, app* lit);
+        app_ref fresh_bool(char const* name);
+        void display(std::ostream& out) const;
+        void display(std::ostream& out, expr_ref_vector const& asms) const;
+        void collect_statistics(statistics& st) const;
+    };
+
+
+}
+
+tactic * mk_qsat_tactic(ast_manager & m, params_ref const& p = params_ref());
+
+tactic * mk_qe2_tactic(ast_manager & m, params_ref const& p = params_ref());
+
+tactic * mk_qe_rec_tactic(ast_manager & m, params_ref const& p = params_ref());
+
+
+/*
+  ADD_TACTIC("qsat", "apply a QSAT solver.", "mk_qsat_tactic(m, p)") 
+
+  ADD_TACTIC("qe2", "apply a QSAT based quantifier elimination.", "mk_qe2_tactic(m, p)") 
+
+  ADD_TACTIC("qe_rec", "apply a QSAT based quantifier elimination recursively.", "mk_qe_rec_tactic(m, p)") 
+
+*/
+
+#endif 

src/sat/sat_solver/inc_sat_solver.cpp

@@ -257,8 +257,10 @@ public:
         if (m_preprocess) {
             m_preprocess->reset();
         }
+        if (!m_bb_rewriter) {
+            m_bb_rewriter = alloc(bit_blaster_rewriter, m, m_params);
+        }
         params_ref simp2_p = m_params;
-        m_bb_rewriter = alloc(bit_blaster_rewriter, m, m_params);
         simp2_p.set_bool("som", true);
         simp2_p.set_bool("pull_cheap_ite", true);
         simp2_p.set_bool("push_ite_bv", false);

src/sat/tactic/goal2sat.cpp

@@ -509,7 +509,7 @@ struct sat2goal::imp {
         // This information may be stored as a vector of pairs.
         // The mapping is only created during the model conversion.
         expr_ref_vector             m_var2expr;
-        ref<filter_model_converter> m_fmc; // filter for eliminating fresh variables introduced in the assertion-set --> sat conversion
+        filter_model_converter_ref  m_fmc; // filter for eliminating fresh variables introduced in the assertion-set --> sat conversion
         
         sat_model_converter(ast_manager & m):
             m_var2expr(m) {

src/shell/main.cpp

@@ -66,7 +66,7 @@ void display_usage() {
 #ifdef Z3GITHASH
     std::cout << " - build hashcode " << STRINGIZE_VALUE_OF(Z3GITHASH);
 #endif
-    std::cout << "]. (C) Copyright 2006-2014 Microsoft Corp.\n";
+    std::cout << "]. (C) Copyright 2006-2016 Microsoft Corp.\n";
     std::cout << "Usage: z3 [options] [-file:]file\n";
     std::cout << "\nInput format:\n";
     std::cout << "  -smt        use parser for SMT input format.\n";

src/smt/asserted_formulas.cpp

@@ -797,13 +797,7 @@ MK_SIMPLIFIER(apply_bit2int, bit2int& functor = m_bit2int, "bit2int", "propagate
 
 MK_SIMPLIFIER(cheap_quant_fourier_motzkin, elim_bounds_star functor(m_manager), "elim_bounds", "cheap-fourier-motzkin", true);
 
-// MK_SIMPLIFIER(quant_elim, qe::expr_quant_elim_star1 &functor = m_quant_elim, 
-//              "quantifiers", "quantifier elimination procedures", true);
 
-bool asserted_formulas::quant_elim() {
-    throw default_exception("QUANT_ELIM option is deprecated, please consider using the 'qe' tactic.");
-    return false;
-}
 
 MK_SIMPLIFIER(elim_bvs_from_quantifiers, bv_elim_star functor(m_manager), "bv_elim", "eliminate-bit-vectors-from-quantifiers", true);
 

src/smt/asserted_formulas.h

@@ -55,7 +55,6 @@ class asserted_formulas {
     maximise_bv_sharing         m_bv_sharing;
 
     bool                        m_inconsistent;
-    // qe::expr_quant_elim_star1   m_quant_elim;
 
     struct scope {
         unsigned                m_asserted_formulas_lim;
@@ -84,7 +83,6 @@ class asserted_formulas {
     void eliminate_and();
     void refine_inj_axiom();
     bool cheap_quant_fourier_motzkin();
-    bool quant_elim();
     void apply_distribute_forall();
     bool apply_bit2int();
     void lift_ite();

src/smt/proto_model/proto_model.cpp

@@ -25,19 +25,17 @@ Revision History:
 #include"well_sorted.h"
 #include"used_symbols.h"
 #include"model_v2_pp.h"
-#include"basic_simplifier_plugin.h"
 
-proto_model::proto_model(ast_manager & m, simplifier & s, params_ref const & p):
+proto_model::proto_model(ast_manager & m, params_ref const & p):
     model_core(m),
-    m_simplifier(s),
     m_afid(m.mk_family_id(symbol("array"))),
-    m_eval(*this) {
+    m_eval(*this),
+    m_rewrite(m) {
     register_factory(alloc(basic_factory, m));
     m_user_sort_factory = alloc(user_sort_factory, m);
     register_factory(m_user_sort_factory);
     
     m_model_partial = model_params(p).partial();
-    m_use_new_eval  = model_params(p).new_eval();
 }
 
 
@@ -85,61 +83,6 @@ expr * proto_model::mk_some_interp_for(func_decl * d) {
     return r;
 }
 
-// Auxiliary function for computing fi(args[0], ..., args[fi.get_arity() - 1]).
-// The result is stored in result.
-// Return true if succeeded, and false otherwise.
-// It uses the simplifier s during the computation.
-bool eval(func_interp & fi, simplifier & s, expr * const * args, expr_ref & result) {
-    bool actuals_are_values = true;
-    
-    if (fi.num_entries() != 0) {
-        for (unsigned i = 0; actuals_are_values && i < fi.get_arity(); i++) {
-            actuals_are_values = fi.m().is_value(args[i]);
-        }
-    }
-
-    func_entry * entry = fi.get_entry(args);
-    if (entry != 0) {
-        result = entry->get_result();
-        return true;
-    }
-    
-    TRACE("func_interp", tout << "failed to find entry for: "; 
-          for(unsigned i = 0; i < fi.get_arity(); i++) 
-             tout << mk_pp(args[i], fi.m()) << " "; 
-          tout << "\nis partial: " << fi.is_partial() << "\n";);
-    
-    if (!fi.eval_else(args, result)) {
-        return false;
-    }
-    
-    if (actuals_are_values && fi.args_are_values()) {
-        // cheap case... we are done
-        return true;
-    }
-
-    // build symbolic result... the actuals may be equal to the args of one of the entries.
-    basic_simplifier_plugin * bs = static_cast<basic_simplifier_plugin*>(s.get_plugin(fi.m().get_basic_family_id()));
-    for (unsigned k = 0; k < fi.num_entries(); k++) {
-        func_entry const * curr = fi.get_entry(k);
-        SASSERT(!curr->eq_args(fi.m(), fi.get_arity(), args));
-        if (!actuals_are_values || !curr->args_are_values()) {
-            expr_ref_buffer eqs(fi.m());
-            unsigned i = fi.get_arity();
-            while (i > 0) {
-                --i;
-                expr_ref new_eq(fi.m());
-                bs->mk_eq(curr->get_arg(i), args[i], new_eq);
-                eqs.push_back(new_eq);
-            }
-            SASSERT(eqs.size() == fi.get_arity());
-            expr_ref new_cond(fi.m());
-            bs->mk_and(eqs.size(), eqs.c_ptr(), new_cond);
-            bs->mk_ite(new_cond, curr->get_result(), result, result);
-        }
-    }
-    return true;
-}
 
 bool proto_model::is_select_of_model_value(expr* e) const {
     return 
@@ -159,192 +102,16 @@ bool proto_model::is_select_of_model_value(expr* e) const {
    So, if model_completion == true, the evaluator never fails if it doesn't contain quantifiers.
 */
 bool proto_model::eval(expr * e, expr_ref & result, bool model_completion) {
-    if (m_use_new_eval) {
-        m_eval.set_model_completion(model_completion);
-        try {
-            m_eval(e, result);
-            return true;
-        }
-        catch (model_evaluator_exception & ex) {
-            (void)ex;
-            TRACE("model_evaluator", tout << ex.msg() << "\n";);
-            return false;
-        }
+    m_eval.set_model_completion(model_completion);
+    try {
+        m_eval(e, result);
+        return true;
     }
-
-    bool is_ok = true;
-    SASSERT(is_well_sorted(m_manager, e));
-    TRACE("model_eval", tout << mk_pp(e, m_manager) << "\n";
-          tout << "sort: " << mk_pp(m_manager.get_sort(e), m_manager) << "\n";);
-    
-    obj_map<expr, expr*> eval_cache;
-    expr_ref_vector trail(m_manager);
-    sbuffer<std::pair<expr*, expr*>, 128> todo;
-    ptr_buffer<expr> args;
-    expr * null = static_cast<expr*>(0);
-    todo.push_back(std::make_pair(e, null));
-    
-
-    expr * a;
-    expr * expanded_a;
-    while (!todo.empty()) {
-        std::pair<expr *, expr *> & p = todo.back();
-        a          = p.first;
-        expanded_a = p.second;
-        if (expanded_a != 0) {
-            expr * r = 0;
-            eval_cache.find(expanded_a, r);
-            SASSERT(r != 0);
-            todo.pop_back();
-            eval_cache.insert(a, r);
-            TRACE("model_eval", 
-                  tout << "orig:\n" << mk_pp(a, m_manager) << "\n";
-                  tout << "after beta reduction:\n" << mk_pp(expanded_a, m_manager) << "\n";
-                  tout << "new:\n" << mk_pp(r, m_manager) << "\n";);
-        }
-        else {
-            switch(a->get_kind()) {
-            case AST_APP: {
-                app * t = to_app(a);
-                bool visited = true;
-                args.reset();
-                unsigned num_args = t->get_num_args();
-                for (unsigned i = 0; i < num_args; ++i) {
-                    expr * arg = 0;
-                    if (!eval_cache.find(t->get_arg(i), arg)) {
-                        visited = false;
-                        todo.push_back(std::make_pair(t->get_arg(i), null));
-                    }
-                    else {
-                        args.push_back(arg);
-                    }
-                }
-                if (!visited) {
-                    continue;
-                }
-                SASSERT(args.size() == t->get_num_args());
-                expr_ref new_t(m_manager);
-                func_decl * f   = t->get_decl();
-                
-                if (!has_interpretation(f)) {
-                    // the model does not assign an interpretation to f.
-                    SASSERT(new_t.get() == 0);
-                    if (f->get_family_id() == null_family_id) {
-                        if (model_completion) {
-                            // create an interpretation for f.
-                            new_t = mk_some_interp_for(f);
-                        }
-                        else {
-                            TRACE("model_eval", tout << f->get_name() << " is uninterpreted\n";);
-                            is_ok = false;
-                        }
-                    }
-                    if (new_t.get() == 0) {
-                        // t is interpreted or model completion is disabled.
-                        m_simplifier.mk_app(f, num_args, args.c_ptr(), new_t);
-                        TRACE("model_eval", tout << mk_pp(t, m_manager) << " -> " << new_t << "\n";);
-                        trail.push_back(new_t);
-                        if (!is_app(new_t) || to_app(new_t)->get_decl() != f || is_select_of_model_value(new_t)) {
-                            // if the result is not of the form (f ...), then assume we must simplify it.
-                            expr * new_new_t = 0;
-                            if (!eval_cache.find(new_t.get(), new_new_t)) {
-                                todo.back().second = new_t;
-                                todo.push_back(std::make_pair(new_t, null));
-                                continue;
-                            }
-                            else {
-                                new_t = new_new_t;
-                            }
-                        }
-                    }
-                }
-                else {
-                    // the model has an interpretaion for f.
-                    if (num_args == 0) {
-                        // t is a constant
-                        new_t = get_const_interp(f);
-                    }
-                    else {
-                        // t is a function application
-                        SASSERT(new_t.get() == 0);
-                        // try to use function graph first
-                        func_interp * fi = get_func_interp(f);
-                        SASSERT(fi->get_arity() == num_args);
-                        expr_ref r1(m_manager);
-                        // fi may be partial...
-                        if (!::eval(*fi, m_simplifier, args.c_ptr(), r1)) {
-                            SASSERT(fi->is_partial()); // fi->eval only fails when fi is partial.
-                            if (model_completion) {
-                                expr * r = get_some_value(f->get_range()); 
-                                fi->set_else(r);
-                                SASSERT(!fi->is_partial());
-                                new_t = r;
-                            }
-                            else {
-                                // f is an uninterpreted function, there is no need to use m_simplifier.mk_app
-                                new_t = m_manager.mk_app(f, num_args, args.c_ptr());
-                                trail.push_back(new_t);
-                                TRACE("model_eval", tout << f->get_name() << " is uninterpreted\n";);
-                                is_ok = false;
-                            }
-                        }
-                        else {
-                            SASSERT(r1);
-                            trail.push_back(r1);
-                            TRACE("model_eval", tout << mk_pp(a, m_manager) << "\nevaluates to: " << r1 << "\n";);
-                            expr * r2 = 0;
-                            if (!eval_cache.find(r1.get(), r2)) {
-                                todo.back().second = r1;
-                                todo.push_back(std::make_pair(r1, null));
-                                continue;
-                            }
-                            else {
-                                new_t = r2;
-                            }
-                        }
-                    }
-                }
-                TRACE("model_eval", 
-                      tout << "orig:\n" << mk_pp(t, m_manager) << "\n";
-                      tout << "new:\n" << mk_pp(new_t, m_manager) << "\n";);
-                todo.pop_back();
-                SASSERT(new_t.get() != 0);
-                eval_cache.insert(t, new_t);
-                break;
-            }
-            case AST_VAR:  
-                SASSERT(a != 0);
-                eval_cache.insert(a, a);
-                todo.pop_back();
-                break;
-            case AST_QUANTIFIER: 
-                TRACE("model_eval", tout << "found quantifier\n" << mk_pp(a, m_manager) << "\n";);
-                is_ok = false; // evaluator does not handle quantifiers.
-                SASSERT(a != 0);
-                eval_cache.insert(a, a);
-                todo.pop_back();
-                break;
-            default:
-                UNREACHABLE();
-                break;
-            }
-        }
+    catch (model_evaluator_exception & ex) {
+        (void)ex;
+        TRACE("model_evaluator", tout << ex.msg() << "\n";);
+        return false;
     }
-
-    if (!eval_cache.find(e, a)) {
-        TRACE("model_eval", tout << "FAILED e: " << mk_bounded_pp(e, m_manager) << "\n";);
-        UNREACHABLE();
-    }
-
-    result = a;
-    TRACE("model_eval", 
-          ast_ll_pp(tout << "original:  ", m_manager, e);
-          ast_ll_pp(tout << "evaluated: ", m_manager, a);
-          ast_ll_pp(tout << "reduced:   ", m_manager, result.get());
-          tout << "sort: " << mk_pp(m_manager.get_sort(e), m_manager) << "\n";
-          ); 
-    SASSERT(is_well_sorted(m_manager, result.get()));
-    return is_ok;
 }
 
 /**
@@ -400,7 +167,7 @@ void proto_model::cleanup_func_interp(func_interp * fi, func_decl_set & found_au
                 if (m_aux_decls.contains(f))
                     found_aux_fs.insert(f);
                 expr_ref new_t(m_manager);
-                m_simplifier.mk_app(f, num_args, args.c_ptr(), new_t);
+                new_t = m_rewrite.mk_app(f, num_args, args.c_ptr());
                 if (t != new_t.get())
                     trail.push_back(new_t);
                 todo.pop_back();

src/smt/proto_model/proto_model.h

@@ -32,23 +32,22 @@ Revision History:
 #include"model_evaluator.h"
 #include"value_factory.h"
 #include"plugin_manager.h"
-#include"simplifier.h"
 #include"arith_decl_plugin.h"
 #include"func_decl_dependencies.h"
 #include"model.h"
 #include"params.h"
+#include"th_rewriter.h"
 
 class proto_model : public model_core {
     plugin_manager<value_factory> m_factories;
     user_sort_factory *           m_user_sort_factory;
-    simplifier &                  m_simplifier;
     family_id                     m_afid;        //!< array family id: hack for displaying models in V1.x style
     func_decl_set                 m_aux_decls;
     ptr_vector<expr>              m_tmp;
     model_evaluator               m_eval;
+    th_rewriter                   m_rewrite;
 
     bool                          m_model_partial;
-    bool                          m_use_new_eval;
 
     expr * mk_some_interp_for(func_decl * d);
 
@@ -62,7 +61,7 @@ class proto_model : public model_core {
     bool is_select_of_model_value(expr* e) const;
 
 public:
-    proto_model(ast_manager & m, simplifier & s, params_ref const & p = params_ref());
+    proto_model(ast_manager & m, params_ref const & p = params_ref());
     virtual ~proto_model() {}
 
     void register_factory(value_factory * f) { m_factories.register_plugin(f); }

src/smt/smt_kernel.h

@@ -122,6 +122,10 @@ namespace smt {
         */
         lbool check(unsigned num_assumptions = 0, expr * const * assumptions = 0);
 
+        lbool check(expr_ref_vector const& asms) { return check(asms.size(), asms.c_ptr()); }
+
+        lbool check(app_ref_vector const& asms) { return check(asms.size(), (expr* const*)asms.c_ptr()); }
+
         /**
            \brief Return the model associated with the last check command.
         */

src/smt/smt_model_generator.cpp

@@ -49,7 +49,7 @@ namespace smt {
     void model_generator::init_model() {
         SASSERT(!m_model);
         // PARAM-TODO smt_params ---> params_ref
-        m_model = alloc(proto_model, m_manager, m_context->get_simplifier()); // , m_context->get_fparams());
+        m_model = alloc(proto_model, m_manager); // , m_context->get_fparams());
         ptr_vector<theory>::const_iterator it  = m_context->begin_theories();
         ptr_vector<theory>::const_iterator end = m_context->end_theories();
         for (; it != end; ++it) {

src/smt/smt_theory.h

@@ -315,10 +315,7 @@ namespace smt {
             return m_var2enode_lim[m_var2enode_lim.size() - num_scopes];
         }
         
-        virtual void display(std::ostream & out) const {
-            out << "Theory " << static_cast<int>(get_id()) << typeid(*this).name() << " does not have a display method\n";
-            display_var2enode(out);
-        }
+        virtual void display(std::ostream & out) const = 0;
 
         virtual void display_var2enode(std::ostream & out) const;
         

src/smt/theory_dummy.h

@@ -43,6 +43,7 @@ namespace smt {
         virtual bool build_models() const { 
             return false;
         }
+        virtual void display(std::ostream& out) const {}
 
     public:
         theory_dummy(family_id fid, char const * name);

src/smt/theory_seq_empty.h

@@ -122,6 +122,7 @@ namespace smt {
         virtual void new_diseq_eh(theory_var, theory_var) {}
         virtual theory* mk_fresh(context* new_ctx) { return alloc(theory_seq_empty, new_ctx->get_manager()); }
         virtual char const * get_name() const { return "seq-empty"; }
+        virtual void display(std::ostream& out) const {}
     public:
         theory_seq_empty(ast_manager& m):theory(m.mk_family_id("seq")), m_used(false) {}
         virtual void init_model(model_generator & mg) {

src/smt/theory_wmaxsat.h

@@ -94,6 +94,7 @@ namespace smt {
         virtual bool internalize_term(app * term) { return false; }
         virtual void new_eq_eh(theory_var v1, theory_var v2) { }
         virtual void new_diseq_eh(theory_var v1, theory_var v2) { }
+        virtual void display(std::ostream& out) const {}
 
         virtual void collect_statistics(::statistics & st) const {
             st.update("wmaxsat num blocks", m_stats.m_num_blocks);

src/solver/combined_solver.cpp

@@ -194,7 +194,7 @@ public:
         m_use_solver1_results = false;
 
         if (get_num_assumptions() != 0 ||            
-            num_assumptions > 0 || // assumptions were provided
+            num_assumptions > 0 ||  // assumptions were provided
             m_ignore_solver1)  {
             // must use incremental solver
             switch_inc_mode();

src/solver/solver_na2as.cpp

@@ -23,12 +23,11 @@ Notes:
 #include"ast_smt2_pp.h"
 
 solver_na2as::solver_na2as(ast_manager & m):
-    m_manager(m) {
+    m(m), 
+    m_assumptions(m) {
 }
 
-solver_na2as::~solver_na2as() {
-    restore_assumptions(0);
-}
+solver_na2as::~solver_na2as() {}
 
 void solver_na2as::assert_expr(expr * t, expr * a) {
     if (a == 0) {
@@ -36,20 +35,19 @@ void solver_na2as::assert_expr(expr * t, expr * a) {
     }
     else {
         SASSERT(is_uninterp_const(a));
-        SASSERT(m_manager.is_bool(a));
-        TRACE("solver_na2as", tout << "asserting\n" << mk_ismt2_pp(t, m_manager) << "\n" << mk_ismt2_pp(a, m_manager) << "\n";);
-        m_manager.inc_ref(a);
+        SASSERT(m.is_bool(a));
+        TRACE("solver_na2as", tout << "asserting\n" << mk_ismt2_pp(t, m) << "\n" << mk_ismt2_pp(a, m) << "\n";);
         m_assumptions.push_back(a);
-        expr_ref new_t(m_manager);
-        new_t = m_manager.mk_implies(a, t);
+        expr_ref new_t(m);
+        new_t = m.mk_implies(a, t);
         assert_expr(new_t);
     }
 }
 
 struct append_assumptions {
-    ptr_vector<expr> & m_assumptions;
+    expr_ref_vector & m_assumptions;
     unsigned           m_old_sz;
-    append_assumptions(ptr_vector<expr> & _m_assumptions, 
+    append_assumptions(expr_ref_vector & _m_assumptions, 
                        unsigned num_assumptions, 
                        expr * const * assumptions):
         m_assumptions(_m_assumptions) {
@@ -82,10 +80,6 @@ void solver_na2as::pop(unsigned n) {
 }
 
 void solver_na2as::restore_assumptions(unsigned old_sz) {
-  //    SASSERT(old_sz == 0);
-    for (unsigned i = old_sz; i < m_assumptions.size(); i++) {
-        m_manager.dec_ref(m_assumptions[i]);
-    }
     m_assumptions.shrink(old_sz);
 }
 

src/solver/solver_na2as.h

@@ -25,8 +25,8 @@ Notes:
 #include"solver.h"
 
 class solver_na2as : public solver {
-    ast_manager &      m_manager;
-    ptr_vector<expr>   m_assumptions;
+    ast_manager &      m;
+    expr_ref_vector    m_assumptions;
     unsigned_vector    m_scopes;
     void restore_assumptions(unsigned old_sz);
 public:

src/tactic/arith/nla2bv_tactic.cpp

@@ -60,7 +60,7 @@ class nla2bv_tactic : public tactic {
         expr_ref_vector             m_trail;
         unsigned                    m_num_bits;
         unsigned                    m_default_bv_size;
-        ref<filter_model_converter> m_fmc;
+        filter_model_converter_ref  m_fmc;
         
     public:
         imp(ast_manager & m, params_ref const& p):

src/tactic/bv/bv_size_reduction_tactic.cpp

@@ -60,7 +60,7 @@ struct bv_size_reduction_tactic::imp {
     obj_map<app, numeral>     m_unsigned_lowers;
     obj_map<app, numeral>     m_unsigned_uppers;
     ref<bv_size_reduction_mc> m_mc;
-    ref<filter_model_converter> m_fmc;
+    filter_model_converter_ref m_fmc;
     scoped_ptr<expr_replacer> m_replacer;
     bool                      m_produce_models;
 

src/tactic/core/propagate_values_tactic.cpp

@@ -26,7 +26,7 @@ Revision History:
 
 class propagate_values_tactic : public tactic {
     struct     imp {
-        ast_manager &                 m_manager;
+        ast_manager &                 m;
         th_rewriter                   m_r;
         scoped_ptr<expr_substitution> m_subst;
         goal *                        m_goal;
@@ -36,13 +36,15 @@ class propagate_values_tactic : public tactic {
         bool                          m_modified;
         
         imp(ast_manager & m, params_ref const & p):
-            m_manager(m),
+            m(m),
             m_r(m, p),
             m_goal(0),
             m_occs(m, true /* track atoms */) {
             updt_params_core(p);
         }
 
+        ~imp() { }
+
         void updt_params_core(params_ref const & p) {
             m_max_rounds = p.get_uint("max_rounds", 4);
         }
@@ -51,32 +53,28 @@ class propagate_values_tactic : public tactic {
             m_r.updt_params(p);
             updt_params_core(p);
         }
-
-        ast_manager & m() const { return m_manager; }
         
         
         bool is_shared(expr * t) {
             return m_occs.is_shared(t);
         }
         
-        bool is_shared_neg(expr * t, expr * & atom) {
-            if (!m().is_not(t))
+        bool is_shared_neg(expr * t, expr * & atom) {            
+            if (!m.is_not(t, atom))
                 return false;
-            atom = to_app(t)->get_arg(0);
             return is_shared(atom);
         }
 
         bool is_shared_eq(expr * t, expr * & lhs, expr * & value) {
-            if (!m().is_eq(t))
+            expr* arg1, *arg2;
+            if (!m.is_eq(t, arg1, arg2))
                 return false;
-            expr * arg1 = to_app(t)->get_arg(0);
-            expr * arg2 = to_app(t)->get_arg(1);
-            if (m().is_value(arg1) && is_shared(arg2)) {
+            if (m.is_value(arg1) && is_shared(arg2)) {
                 lhs   = arg2;
                 value = arg1;
                 return true;
             }
-            if (m().is_value(arg2) && is_shared(arg1)) {
+            if (m.is_value(arg2) && is_shared(arg1)) {
                 lhs   = arg1;
                 value = arg2;
                 return true;
@@ -87,15 +85,15 @@ class propagate_values_tactic : public tactic {
         void push_result(expr * new_curr, proof * new_pr) {
             if (m_goal->proofs_enabled()) {
                 proof * pr = m_goal->pr(m_idx);
-                new_pr     = m().mk_modus_ponens(pr, new_pr);
+                new_pr     = m.mk_modus_ponens(pr, new_pr);
             }
             
-            expr_dependency_ref new_d(m());
+            expr_dependency_ref new_d(m);
             if (m_goal->unsat_core_enabled()) {
                 new_d = m_goal->dep(m_idx);
                 expr_dependency * used_d = m_r.get_used_dependencies();
                 if (used_d != 0) {
-                    new_d = m().mk_join(new_d, used_d);
+                    new_d = m.mk_join(new_d, used_d);
                     m_r.reset_used_dependencies();
                 }
             }
@@ -103,34 +101,34 @@ class propagate_values_tactic : public tactic {
             m_goal->update(m_idx, new_curr, new_pr, new_d);
         
             if (is_shared(new_curr)) {
-                m_subst->insert(new_curr, m().mk_true(), m().mk_iff_true(new_pr), new_d);
+                m_subst->insert(new_curr, m.mk_true(), m.mk_iff_true(new_pr), new_d);
             }
             expr * atom;
             if (is_shared_neg(new_curr, atom)) {
-                m_subst->insert(atom, m().mk_false(), m().mk_iff_false(new_pr), new_d);
+                m_subst->insert(atom, m.mk_false(), m.mk_iff_false(new_pr), new_d);
             }
             expr * lhs, * value;
             if (is_shared_eq(new_curr, lhs, value)) {
-                TRACE("shallow_context_simplifier_bug", tout << "found eq:\n" << mk_ismt2_pp(new_curr, m()) << "\n";);
+                TRACE("shallow_context_simplifier_bug", tout << "found eq:\n" << mk_ismt2_pp(new_curr, m) << "\n";);
                 m_subst->insert(lhs, value, new_pr, new_d);
             }
         }
         
         void process_current() {
             expr * curr = m_goal->form(m_idx);
-            expr_ref   new_curr(m());
-            proof_ref  new_pr(m());
+            expr_ref   new_curr(m);
+            proof_ref  new_pr(m);
             
             if (!m_subst->empty()) {
                 m_r(curr, new_curr, new_pr);
             }
             else {
                 new_curr = curr;
-                if (m().proofs_enabled())
-                    new_pr   = m().mk_reflexivity(curr);
+                if (m.proofs_enabled())
+                    new_pr   = m.mk_reflexivity(curr);
             }
 
-            TRACE("shallow_context_simplifier_bug", tout << mk_ismt2_pp(curr, m()) << "\n---->\n" << mk_ismt2_pp(new_curr, m()) << "\n";);
+            TRACE("shallow_context_simplifier_bug", tout << mk_ismt2_pp(curr, m) << "\n---->\n" << mk_ismt2_pp(new_curr, m) << "\n";);
             push_result(new_curr, new_pr);
             
             if (new_curr != curr)
@@ -148,25 +146,26 @@ class propagate_values_tactic : public tactic {
             m_goal = g.get();
 
             bool forward   = true;
-            expr_ref   new_curr(m());
-            proof_ref  new_pr(m());
+            expr_ref   new_curr(m);
+            proof_ref  new_pr(m);
             unsigned size  = m_goal->size();
             m_idx          = 0;
             m_modified     = false;
             unsigned round = 0;
 
+
             if (m_goal->inconsistent())
                 goto end;
 
             if (m_max_rounds == 0)
                 goto end;
 
-            m_subst = alloc(expr_substitution, m(), g->unsat_core_enabled(), g->proofs_enabled());
+            m_subst = alloc(expr_substitution, m, g->unsat_core_enabled(), g->proofs_enabled());
             m_r.set_substitution(m_subst.get());
             m_occs(*m_goal);
 
             while (true) {
-                TRACE("propagate_values", tout << "while(true) loop\n"; m_goal->display(tout););
+                TRACE("propagate_values", tout << "while(true) loop\n"; m_goal->display_with_dependencies(tout););
                 if (forward) {
                     for (; m_idx < size; m_idx++) {
                         process_current();
@@ -255,15 +254,14 @@ public:
     }
     
     virtual void cleanup() {
-        ast_manager & m = m_imp->m();
-        imp * d = alloc(imp, m, m_params);
-        std::swap(d, m_imp);        
-        dealloc(d);
+        ast_manager & m = m_imp->m;
+        dealloc(m_imp);
+        m_imp = alloc(imp, m, m_params);
     }
     
 };
 
 tactic * mk_propagate_values_tactic(ast_manager & m, params_ref const & p) {
-    return clean(alloc(propagate_values_tactic, m, p));
+    return alloc(propagate_values_tactic, m, p);
 }
 

src/tactic/smtlogics/nra_tactic.cpp

@@ -22,7 +22,9 @@ Notes:
 #include"smt_tactic.h"
 #include"nnf_tactic.h"
 #include"qe_tactic.h"
+#include"nlqsat.h"
 #include"qfnra_nlsat_tactic.h"
+#include"qe_lite.h"
 #include"probe_arith.h"
 
 tactic * mk_nra_tactic(ast_manager & m, params_ref const& p) {
@@ -36,12 +38,19 @@ tactic * mk_nra_tactic(ast_manager & m, params_ref const& p) {
     return and_then(mk_simplify_tactic(m, p),
                     mk_nnf_tactic(m, p),
                     mk_propagate_values_tactic(m, p),
+                    //mk_qe_lite_tactic(m), 
                     mk_qe_tactic(m, p),
                     cond(mk_is_qfnra_probe(),
                          or_else(try_for(mk_qfnra_nlsat_tactic(m, p), 5000),
                                  try_for(mk_qfnra_nlsat_tactic(m, p1), 10000),
                                  mk_qfnra_nlsat_tactic(m, p2)),
-                         mk_smt_tactic(p)));
+#if 0
+                         or_else(mk_nlqsat_tactic(m, p),
+                                 mk_smt_tactic(p))
+#else
+                         mk_smt_tactic(p)
+#endif
+                         ));
 }
 
 

src/tactic/smtlogics/quant_tactics.cpp

@@ -23,6 +23,9 @@ Revision History:
 #include"elim_uncnstr_tactic.h"
 #include"qe_tactic.h"
 #include"qe_sat_tactic.h"
+#include"qe_lite.h"
+#include"qsat.h"
+#include"nlqsat.h"
 #include"ctx_simplify_tactic.h"
 #include"smt_tactic.h"
 
@@ -37,10 +40,12 @@ static tactic * mk_quant_preprocessor(ast_manager & m, bool disable_gaussian = f
     ctx_simp_p.set_uint("max_steps", 5000000);
 
     tactic * solve_eqs;
-    if (disable_gaussian)
+    if (disable_gaussian) {
         solve_eqs = mk_skip_tactic();
-    else
+    }
+    else {
         solve_eqs = when(mk_not(mk_has_pattern_probe()), mk_solve_eqs_tactic(m));
+    }
  
     // remark: investigate if gaussian elimination is useful when patterns are not provided.
     return and_then(mk_simplify_tactic(m), 
@@ -49,6 +54,7 @@ static tactic * mk_quant_preprocessor(ast_manager & m, bool disable_gaussian = f
                     using_params(mk_simplify_tactic(m), pull_ite_p),
                     solve_eqs,
                     mk_elim_uncnstr_tactic(m),
+                    mk_qe_lite_tactic(m),
                     mk_simplify_tactic(m));    
 }
 
@@ -98,13 +104,18 @@ tactic * mk_aufnira_tactic(ast_manager & m, params_ref const & p) {
 }
 
 tactic * mk_lra_tactic(ast_manager & m, params_ref const & p) {
+#if 0
     tactic * st = and_then(mk_quant_preprocessor(m),
                            or_else(try_for(mk_smt_tactic(), 100), 
                                    try_for(qe::mk_sat_tactic(m), 1000), 
                                    try_for(mk_smt_tactic(), 1000),
                                    and_then(mk_qe_tactic(m), mk_smt_tactic())
                                    ));
-
+#else
+    tactic * st = and_then(mk_quant_preprocessor(m),
+                           or_else(mk_qsat_tactic(m, p),
+                                   and_then(mk_qe_tactic(m), mk_smt_tactic())));
+#endif
     st->updt_params(p);
     return st;
 }
@@ -116,3 +127,4 @@ tactic * mk_lia_tactic(ast_manager & m, params_ref const & p) {
 tactic * mk_lira_tactic(ast_manager & m, params_ref const & p) {
     return mk_lra_tactic(m, p);
 }
+

src/tactic/tactical.cpp

@@ -131,19 +131,19 @@ public:
         SASSERT(r1_size > 0);                                                                               
         if (r1_size == 1) {                                                                                 
             if (r1[0]->is_decided()) {
-                result.push_back(r1[0]);                                                                    
-                if (models_enabled) mc = mc1;                                                                                 
+                result.push_back(r1[0]);    
+                if (models_enabled) mc = mc1; 
                 SASSERT(!pc); SASSERT(!core);
                 return;                                                                                     
             }                                                                                               
-            goal_ref r1_0 = r1[0];                                                                          
-            m_t2->operator()(r1_0, result, mc, pc, core);                                              
-            if (models_enabled) mc = concat(mc1.get(), mc.get());                                                               
-            if (proofs_enabled) pc = concat(pc1.get(), pc.get());                                                               
-            if (cores_enabled) core = m.mk_join(core1.get(), core);                                                            
-        }                                                                                     
-        else {                                                                                              
-            if (cores_enabled) core = core1;                                                                                   
+            goal_ref r1_0 = r1[0];      
+            m_t2->operator()(r1_0, result, mc, pc, core);
+            if (models_enabled) mc = concat(mc1.get(), mc.get());
+            if (proofs_enabled) pc = concat(pc1.get(), pc.get()); 
+            if (cores_enabled) core = m.mk_join(core1.get(), core); 
+        }
+        else {
+            if (cores_enabled) core = core1;
             proof_converter_ref_buffer pc_buffer;                                                           
             model_converter_ref_buffer mc_buffer;                                                           
             sbuffer<unsigned>          sz_buffer;                                                           
@@ -179,16 +179,16 @@ public:
                         SASSERT(!core2);
                         if (models_enabled) mc_buffer.push_back(0);
                         if (proofs_enabled) pc_buffer.push_back(proof2proof_converter(m, r2[0]->pr(0)));
-                        if (models_enabled || proofs_enabled) sz_buffer.push_back(0);                                                             
+                        if (models_enabled || proofs_enabled) sz_buffer.push_back(0);
                         if (cores_enabled) core = m.mk_join(core.get(), r2[0]->dep(0));
                     }                                                                         
                 }                                                                                       
                 else {                                                                                      
-                    result.append(r2.size(), r2.c_ptr());                                                   
-                    if (models_enabled) mc_buffer.push_back(mc2.get());                                                         
-                    if (proofs_enabled) pc_buffer.push_back(pc2.get());                                                         
-                    if (models_enabled || proofs_enabled) sz_buffer.push_back(r2.size());                                                         
-                    if (cores_enabled) core = m.mk_join(core.get(), core2.get());                                              
+                    result.append(r2.size(), r2.c_ptr());
+                    if (models_enabled) mc_buffer.push_back(mc2.get());
+                    if (proofs_enabled) pc_buffer.push_back(pc2.get());
+                    if (models_enabled || proofs_enabled) sz_buffer.push_back(r2.size()); 
+                    if (cores_enabled) core = m.mk_join(core.get(), core2.get());
                 }                                                                                           
             }
             
@@ -651,12 +651,12 @@ public:
             }                                                                                               
             goal_ref r1_0 = r1[0];                                                                          
             m_t2->operator()(r1_0, result, mc, pc, core);                                              
-            if (models_enabled) mc = concat(mc1.get(), mc.get());                                                               
-            if (proofs_enabled) pc = concat(pc1.get(), pc.get());                                                               
-            if (cores_enabled) core = m.mk_join(core1.get(), core);                                                            
+            if (models_enabled) mc = concat(mc1.get(), mc.get());
+            if (proofs_enabled) pc = concat(pc1.get(), pc.get());
+            if (cores_enabled) core = m.mk_join(core1.get(), core); 
         }                                                                                     
         else {                                                                                              
-            if (cores_enabled) core = core1;                                                                                   
+            if (cores_enabled) core = core1;  
 
             scoped_ptr_vector<ast_manager> managers;
             tactic_ref_vector              ts2;
@@ -670,8 +670,8 @@ public:
                 ts2.push_back(m_t2->translate(*new_m));
             }
 
-            proof_converter_ref_buffer             pc_buffer;                                                           
-            model_converter_ref_buffer             mc_buffer;                                                           
+            proof_converter_ref_buffer             pc_buffer; 
+            model_converter_ref_buffer             mc_buffer; 
             scoped_ptr_vector<expr_dependency_ref> core_buffer;
             scoped_ptr_vector<goal_ref_buffer>     goals_vect;
 
@@ -687,7 +687,7 @@ public:
             std::string  ex_msg;
 
             #pragma omp parallel for
-            for (int i = 0; i < static_cast<int>(r1_size); i++) {                                                        
+            for (int i = 0; i < static_cast<int>(r1_size); i++) { 
                 ast_manager & new_m = *(managers[i]);
                 goal_ref new_g = g_copies[i];
 
@@ -772,7 +772,7 @@ public:
                                     md = alloc(model, m);
                                     apply(mc2, md, 0);
                                     apply(mc1, md, i);
-                                    mc   = model2model_converter(md.get());                                             
+                                    mc   = model2model_converter(md.get());
                                 }
                                 SASSERT(!pc); SASSERT(!core);
                             }       
@@ -969,9 +969,9 @@ class repeat_tactical : public unary_tactical {
             m_t->operator()(in, r1, mc1, pc1, core1);                                                            
             if (is_equal(orig_in, *(in.get()))) {
                 result.push_back(r1[0]);                                                                    
-                if (models_enabled) mc = mc1;                                                                                 
-                if (proofs_enabled) pc = pc1;                                                                                 
-                if (cores_enabled)  core = core1;                                                                               
+                if (models_enabled) mc = mc1;
+                if (proofs_enabled) pc = pc1;
+                if (cores_enabled)  core = core1; 
                 return;                                                                                     
             }
         }
@@ -980,18 +980,18 @@ class repeat_tactical : public unary_tactical {
         if (r1_size == 1) {                                                                                 
             if (r1[0]->is_decided()) {
                 result.push_back(r1[0]);                                                                    
-                if (models_enabled) mc = mc1;                                                                                 
+                if (models_enabled) mc = mc1;
                 SASSERT(!pc); SASSERT(!core);
                 return;                                                                                     
             }                                                                                               
             goal_ref r1_0 = r1[0];                                                                          
-            operator()(depth+1, r1_0, result, mc, pc, core);                                              
-            if (models_enabled) mc = concat(mc.get(), mc1.get());                                                               
-            if (proofs_enabled) pc = concat(pc.get(), pc1.get());                                                               
-            if (cores_enabled)  core = m.mk_join(core1.get(), core);                                                            
+            operator()(depth+1, r1_0, result, mc, pc, core); 
+            if (models_enabled) mc = concat(mc.get(), mc1.get());
+            if (proofs_enabled) pc = concat(pc.get(), pc1.get()); 
+            if (cores_enabled)  core = m.mk_join(core1.get(), core); 
         }                                                                                                   
-        else {                                                                                              
-            if (cores_enabled) core = core1;                                                                                   
+        else {
+            if (cores_enabled) core = core1;
             proof_converter_ref_buffer pc_buffer;                                                           
             model_converter_ref_buffer mc_buffer;                                                           
             sbuffer<unsigned>          sz_buffer;                                                           

src/test/nlsat.cpp

@@ -21,6 +21,8 @@ Notes:
 #include"nlsat_evaluator.h"
 #include"nlsat_solver.h"
 #include"util.h"
+#include"nlsat_explain.h"
+#include"polynomial_cache.h"
 #include"rlimit.h"
 
 nlsat::interval_set_ref tst_interval(nlsat::interval_set_ref const & s1,
@@ -29,7 +31,6 @@ nlsat::interval_set_ref tst_interval(nlsat::interval_set_ref const & s1,
                                      bool check_num_intervals = true) {
     nlsat::interval_set_manager & ism = s1.m();
     nlsat::interval_set_ref r(ism);
-    std::cout << "------------------\n";
     std::cout << "s1:            " << s1 << "\n";
     std::cout << "s2:            " << s2 << "\n";
     r = ism.mk_union(s1, s2);
@@ -277,10 +278,12 @@ static void tst5() {
     nlsat::assignment           as(am);
     small_object_allocator      allocator;
     nlsat::interval_set_manager ism(am, allocator);
-    nlsat::evaluator            ev(as, pm, allocator);
+    nlsat::evaluator            ev(s, as, pm, allocator);
     nlsat::var                  x0, x1;
     x0 = pm.mk_var();
     x1 = pm.mk_var();
+    nlsat::interval_set_ref i(ism);
+
     polynomial_ref p(pm);
     polynomial_ref _x0(pm), _x1(pm);
     _x0 = pm.mk_polynomial(x0);
@@ -291,7 +294,6 @@ static void tst5() {
     nlsat::bool_var b = s.mk_ineq_atom(nlsat::atom::GT, 1, _p, is_even);
     nlsat::atom * a = s.bool_var2atom(b);
     SASSERT(a != 0);
-    nlsat::interval_set_ref  i(ism);
     scoped_anum zero(am);
     am.set(zero, 0);
     as.set(0, zero);
@@ -302,8 +304,414 @@ static void tst5() {
     std::cout << "2) " << i << "\n";
 }
 
+
+
+static void project(nlsat::solver& s, nlsat::explain& ex, nlsat::var x, unsigned num, nlsat::literal const* lits) {
+    std::cout << "Project ";
+    s.display(std::cout, num, lits);
+    nlsat::scoped_literal_vector result(s);
+    ex.project(x, num, lits, result);
+    s.display(std::cout << "\n==>\n", result.size(), result.c_ptr());
+    std::cout << "\n";
+}
+
+static nlsat::literal mk_gt(nlsat::solver& s, nlsat::poly* p) {
+    nlsat::poly * _p[1] = { p };
+    bool is_even[1] = { false };
+    return s.mk_ineq_literal(nlsat::atom::GT, 1, _p, is_even);
+}
+
+static nlsat::literal mk_eq(nlsat::solver& s, nlsat::poly* p) {
+    nlsat::poly * _p[1] = { p };
+    bool is_even[1] = { false };
+    return s.mk_ineq_literal(nlsat::atom::EQ, 1, _p, is_even);
+}
+
+static void tst6() {
+    params_ref      ps;
+    reslimit        rlim;
+    nlsat::solver s(rlim, ps);
+    anum_manager & am     = s.am();
+    nlsat::pmanager & pm  = s.pm();
+    nlsat::assignment as(am);
+    nlsat::explain& ex    = s.get_explain();
+    nlsat::var x0, x1, x2, a, b, c, d;
+    a  = s.mk_var(false);
+    b  = s.mk_var(false);
+    c  = s.mk_var(false);
+    d  = s.mk_var(false);
+    x0 = s.mk_var(false);
+    x1 = s.mk_var(false);
+    x2 = s.mk_var(false);
+
+    polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
+    polynomial_ref _x0(pm), _x1(pm), _x2(pm);
+    polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
+    _x0 = pm.mk_polynomial(x0);
+    _x1 = pm.mk_polynomial(x1);
+    _x2 = pm.mk_polynomial(x2);
+    _a  = pm.mk_polynomial(a);
+    _b  = pm.mk_polynomial(b);
+    _c  = pm.mk_polynomial(c);
+    _d  = pm.mk_polynomial(d);
+
+    p1 = (_a*(_x0^2)) + _x2 + 2;
+    p2 = (_b*_x1) - (2*_x2) - _x0 + 8;
+    nlsat::scoped_literal_vector lits(s);
+    lits.push_back(mk_gt(s, p1));
+    lits.push_back(mk_gt(s, p2));
+    lits.push_back(mk_gt(s, (_c*_x0) + _x2 + 1));
+    lits.push_back(mk_gt(s, (_d*_x0) - _x1 + 5*_x2));
+
+    scoped_anum zero(am), one(am), two(am);
+    am.set(zero, 0);
+    am.set(one,  1);
+    am.set(two,  2);
+    as.set(0, one);
+    as.set(1, one);
+    as.set(2, two);
+    as.set(3, two);
+    as.set(4, two);
+    as.set(5, one);
+    as.set(6, one); 
+    s.set_rvalues(as);
+
+
+    project(s, ex, x0, 2, lits.c_ptr());
+    project(s, ex, x1, 3, lits.c_ptr());
+    project(s, ex, x2, 3, lits.c_ptr());
+    project(s, ex, x2, 2, lits.c_ptr());
+    project(s, ex, x2, 4, lits.c_ptr());
+    project(s, ex, x2, 3, lits.c_ptr()+1);
+    
+    
+}
+
+static void tst7() {
+    params_ref      ps;
+    reslimit        rlim;
+    nlsat::solver s(rlim, ps);
+    anum_manager & am     = s.am();
+    nlsat::pmanager & pm  = s.pm();
+    nlsat::var x0, x1, x2, a, b, c, d;
+    a  = s.mk_var(false);
+    b  = s.mk_var(false);
+    c  = s.mk_var(false);
+    d  = s.mk_var(false);
+    x0 = s.mk_var(false);
+    x1 = s.mk_var(false);
+    x2 = s.mk_var(false);
+    polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
+    polynomial_ref _x0(pm), _x1(pm), _x2(pm);
+    polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
+    _x0 = pm.mk_polynomial(x0);
+    _x1 = pm.mk_polynomial(x1);
+    _x2 = pm.mk_polynomial(x2);
+    _a  = pm.mk_polynomial(a);
+    _b  = pm.mk_polynomial(b);
+    _c  = pm.mk_polynomial(c);
+    _d  = pm.mk_polynomial(d);
+
+    p1 = _x0 + _x1;
+    p2 = _x2 - _x0;
+    p3 = (-1*_x0) - _x1;
+    
+    nlsat::scoped_literal_vector lits(s);
+    lits.push_back(mk_gt(s, p1));
+    lits.push_back(mk_gt(s, p2));
+    lits.push_back(mk_gt(s, p3));
+
+    nlsat::literal_vector litsv(lits.size(), lits.c_ptr());
+    lbool res = s.check(litsv);
+    SASSERT(res == l_false);
+    for (unsigned i = 0; i < litsv.size(); ++i) {
+        s.display(std::cout, litsv[i]);
+        std::cout << " ";
+    }
+    std::cout << "\n";
+
+    litsv.reset();
+    litsv.append(2, lits.c_ptr());
+    res = s.check(litsv);
+    SASSERT(res == l_true);
+    s.display(std::cout);
+    s.am().display(std::cout, s.value(x0)); std::cout << "\n";
+    s.am().display(std::cout, s.value(x1)); std::cout << "\n";
+    s.am().display(std::cout, s.value(x2)); std::cout << "\n";
+
+}
+
+static void tst8() {
+    params_ref      ps;
+    reslimit        rlim;
+    nlsat::solver s(rlim, ps);
+    anum_manager & am     = s.am();
+    nlsat::pmanager & pm  = s.pm();
+    nlsat::assignment as(am);
+    nlsat::explain& ex    = s.get_explain();
+    nlsat::var x0, x1, x2, a, b, c, d;
+    a  = s.mk_var(false);
+    b  = s.mk_var(false);
+    c  = s.mk_var(false);
+    d  = s.mk_var(false);
+    x0 = s.mk_var(false);
+    x1 = s.mk_var(false);
+    x2 = s.mk_var(false);
+
+    polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
+    polynomial_ref _x0(pm), _x1(pm), _x2(pm);
+    polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
+    _x0 = pm.mk_polynomial(x0);
+    _x1 = pm.mk_polynomial(x1);
+    _x2 = pm.mk_polynomial(x2);
+    _a  = pm.mk_polynomial(a);
+    _b  = pm.mk_polynomial(b);
+    _c  = pm.mk_polynomial(c);
+    _d  = pm.mk_polynomial(d);
+    
+    scoped_anum zero(am), one(am), two(am), six(am);
+    am.set(zero, 0);
+    am.set(one,  1);
+    am.set(two,  2);
+    am.set(six,  6);
+    as.set(0, two); // a
+    as.set(1, one); // b
+    as.set(2, six); // c
+    as.set(3, zero); // d
+    as.set(4, zero); // x0
+    as.set(5, zero); // x1
+    as.set(6, two); // x2
+    s.set_rvalues(as);
+
+    nlsat::scoped_literal_vector lits(s);
+    lits.push_back(mk_eq(s, (_a*_x2*_x2) - (_b*_x2) - _c));
+    project(s, ex, x2, 1, lits.c_ptr());
+}
+
+
+
+static void tst9() {
+    params_ref      ps;
+    reslimit        rlim;
+    nlsat::solver s(rlim, ps);
+    anum_manager & am     = s.am();
+    nlsat::pmanager & pm  = s.pm();
+    nlsat::assignment as(am);
+    nlsat::explain& ex    = s.get_explain();
+    int num_lo = 4;
+    int num_hi = 5;
+    svector<nlsat::var> los, his;
+    for (int i = 0; i < num_lo; ++i) {
+        los.push_back(s.mk_var(false));
+        scoped_anum num(am);
+        am.set(num, - i - 1);
+        as.set(i, num);
+    }
+    for (int i = 0; i < num_hi; ++i) {
+        his.push_back(s.mk_var(false));
+        scoped_anum num(am);
+        am.set(num, i + 1);
+        as.set(num_lo + i, num);
+    }
+    nlsat::var _z = s.mk_var(false);
+    nlsat::var _x = s.mk_var(false);
+    polynomial_ref x(pm), z(pm);
+    x = pm.mk_polynomial(_x);
+    scoped_anum val(am);
+    am.set(val, 0);
+    as.set(num_lo + num_hi, val);
+    as.set(num_lo + num_hi + 1, val);
+    s.set_rvalues(as);
+    nlsat::scoped_literal_vector lits(s);
+
+    for (int i = 0; i < num_lo; ++i) {
+        polynomial_ref y(pm);
+        y = pm.mk_polynomial(los[i]);
+        lits.push_back(mk_gt(s, x - y));
+    }
+    for (int i = 0; i < num_hi; ++i) {
+        polynomial_ref y(pm);
+        y = pm.mk_polynomial(his[i]);
+        lits.push_back(mk_gt(s, y - x));
+    }
+    z = pm.mk_polynomial(_z);
+    lits.push_back(mk_eq(s, x - z));
+
+#define TEST_ON_OFF()                                   \
+    std::cout << "Off ";                                \
+    ex.set_signed_project(false);                       \
+    project(s, ex, _x, lits.size()-1, lits.c_ptr());    \
+    std::cout << "On ";                                 \
+    ex.set_signed_project(true);                        \
+    project(s, ex, _x, lits.size()-1, lits.c_ptr());    \
+    std::cout << "Off ";                                \
+    ex.set_signed_project(false);                       \
+    project(s, ex, _x, lits.size(), lits.c_ptr());      \
+    std::cout << "On ";                                 \
+    ex.set_signed_project(true);                        \
+    project(s, ex, _x, lits.size(), lits.c_ptr())       \
+
+    TEST_ON_OFF();
+
+    lits.reset();
+    polynomial_ref u(pm);
+    u = pm.mk_polynomial(his[1]);
+    for (int i = 0; i < num_lo; ++i) {
+        polynomial_ref y(pm);
+        y = pm.mk_polynomial(los[i]);
+        lits.push_back(mk_gt(s, u*x - y));
+    }
+    for (int i = 0; i < num_hi; ++i) {
+        polynomial_ref y(pm);
+        y = pm.mk_polynomial(his[i]);
+        lits.push_back(mk_gt(s, y - u*x));
+    }
+    z = pm.mk_polynomial(_z);
+    lits.push_back(mk_eq(s, u*x - z));
+
+    TEST_ON_OFF();
+
+    lits.reset();
+    u = pm.mk_polynomial(los[1]);
+    for (int i = 0; i < num_lo; ++i) {
+        polynomial_ref y(pm);
+        y = pm.mk_polynomial(los[i]);
+        lits.push_back(mk_gt(s, u*x - y));
+    }
+    for (int i = 0; i < num_hi; ++i) {
+        polynomial_ref y(pm);
+        y = pm.mk_polynomial(his[i]);
+        lits.push_back(mk_gt(s, y - u*x));
+    }
+    z = pm.mk_polynomial(_z);
+    lits.push_back(mk_eq(s, x - z));
+
+    TEST_ON_OFF();
+}
+
+
+#if 0
+
+
+#endif
+
+static void test_root_literal(nlsat::solver& s, nlsat::explain& ex, nlsat::var x, nlsat::atom::kind k, unsigned i, nlsat::poly* p) {
+    nlsat::scoped_literal_vector result(s);
+    ex.test_root_literal(k, x, 1, p, result);
+    nlsat::bool_var b = s.mk_root_atom(k, x, i, p);
+    s.display(std::cout, nlsat::literal(b, false));
+    s.display(std::cout << " ==> ", result.size(), result.c_ptr());
+    std::cout << "\n";
+}
+
+static bool satisfies_root(nlsat::solver& s, nlsat::atom::kind k, nlsat::poly* p) {
+    nlsat::pmanager & pm  = s.pm();
+    anum_manager & am     = s.am();
+    nlsat::assignment as(am);
+    s.get_rvalues(as);
+    polynomial_ref pr(p, pm);
+    switch (k) {
+    case nlsat::atom::ROOT_EQ: return am.eval_sign_at(pr, as) == 0; 
+    case nlsat::atom::ROOT_LE: return am.eval_sign_at(pr, as) <= 0;
+    case nlsat::atom::ROOT_LT: return am.eval_sign_at(pr, as) <  0;
+    case nlsat::atom::ROOT_GE: return am.eval_sign_at(pr, as) >= 0;
+    case nlsat::atom::ROOT_GT: return am.eval_sign_at(pr, as) >  0;
+    default:
+        UNREACHABLE();
+        return false;
+    }
+}
+
+static void tst10() {
+    params_ref      ps;
+    reslimit        rlim;
+    nlsat::solver s(rlim, ps);
+    anum_manager & am     = s.am();
+    nlsat::pmanager & pm  = s.pm();
+    nlsat::assignment as(am);
+    nlsat::explain& ex    = s.get_explain();
+    nlsat::var _a = s.mk_var(false);
+    nlsat::var _b = s.mk_var(false);
+    nlsat::var _c = s.mk_var(false);
+    nlsat::var _x = s.mk_var(false);
+
+    polynomial_ref x(pm), a(pm), b(pm), c(pm), p(pm);
+    x = pm.mk_polynomial(_x);
+    a = pm.mk_polynomial(_a);
+    b = pm.mk_polynomial(_b);
+    c = pm.mk_polynomial(_c);
+    p = a*x*x + b*x + c;
+    scoped_anum one(am), two(am), three(am), mone(am), mtwo(am), mthree(am), zero(am), one_a_half(am);
+    am.set(zero, 0);
+    am.set(one, 1);
+    am.set(two, 2);
+    am.set(three, 3);
+    am.set(mone, -1);
+    am.set(mtwo, -2);
+    am.set(mthree, -3);
+    rational oah(1,2);
+    am.set(one_a_half, oah.to_mpq());
+    
+ 
+    scoped_anum_vector nums(am);
+    nums.push_back(one);
+    nums.push_back(two);
+    nums.push_back(one_a_half);
+    nums.push_back(mone);
+    nums.push_back(three);
+
+    // a = 1, b = -3, c = 2: 
+    // has roots x = 2, x = 1:
+    //  2^2 - 3*2 + 2 = 0
+    //  1 - 3 + 2 = 0
+    as.set(_a, one);
+    as.set(_b, mthree);
+    as.set(_c, two);
+
+    for (unsigned i = 0; i < nums.size(); ++i) {
+        as.set(_x, nums[i]);
+        s.set_rvalues(as);
+        std::cout << p << "\n";
+        as.display(std::cout);
+        for (unsigned k = nlsat::atom::ROOT_EQ; k <= nlsat::atom::ROOT_GE; ++k) {
+            if (satisfies_root(s, (nlsat::atom::kind) k, p)) {
+                test_root_literal(s, ex, _x, (nlsat::atom::kind) k, 1, p);
+            }
+        }
+    }
+    as.set(_a, mone);
+    as.set(_b, three);
+    as.set(_c, mtwo);
+    for (unsigned i = 0; i < nums.size(); ++i) {
+        as.set(_x, nums[i]);
+        s.set_rvalues(as);
+        std::cout << p << "\n";
+        as.display(std::cout);
+        for (unsigned k = nlsat::atom::ROOT_EQ; k <= nlsat::atom::ROOT_GE; ++k) {
+            if (satisfies_root(s, (nlsat::atom::kind) k, p)) {
+                test_root_literal(s, ex, _x, (nlsat::atom::kind) k, 1, p);
+            }
+        }
+    }
+    std::cout << "\n";
+}
+
 void tst_nlsat() {
+    tst10();
+    std::cout << "------------------\n";
+    exit(0);
+    tst9();
+    std::cout << "------------------\n";
+    exit(0);
+    tst8();
+    std::cout << "------------------\n";
+    tst7();
+    std::cout << "------------------\n";
+    tst6();
+    std::cout << "------------------\n";
     tst5();
+    std::cout << "------------------\n";
     tst4();
+    std::cout << "------------------\n";
     tst3();
 }

src/test/qe_arith.cpp

@@ -12,9 +12,9 @@ Copyright (c) 2015 Microsoft Corporation
 #include "reg_decl_plugins.h"
 #include "arith_rewriter.h"
 #include "ast_pp.h"
-#include "qe_util.h"
 #include "smt_context.h"
 #include "expr_abstract.h"
+#include "expr_safe_replace.h"
 
 static expr_ref parse_fml(ast_manager& m, char const* str) {
     expr_ref result(m);
@@ -29,6 +29,11 @@ static expr_ref parse_fml(ast_manager& m, char const* str) {
            << "(declare-const t Real)\n"
            << "(declare-const a Real)\n"
            << "(declare-const b Real)\n"
+           << "(declare-const i Int)\n"
+           << "(declare-const j Int)\n"
+           << "(declare-const k Int)\n"
+           << "(declare-const l Int)\n"
+           << "(declare-const m Int)\n"
            << "(assert " << str << ")\n";
     std::istringstream is(buffer.str());
     VERIFY(parse_smt2_commands(ctx, is));
@@ -42,6 +47,8 @@ static char const* example2 = "(and (<= z x) (<= x 3.0) (<= (* 3.0 x) y) (<= z y
 static char const* example3 = "(and (<= z x) (<= x 3.0) (< (* 3.0 x) y) (<= z y))";
 static char const* example4 = "(and (<= z x) (<= x 3.0) (not (>= (* 3.0 x) y)) (<= z y))";
 static char const* example5 = "(and (<= y x) (<= z x) (<= x u) (<= x v) (<= x t))";
+static char const* example7 = "(and (<= x y) (<= x z) (<= u x) (< v x))";
+static char const* example8 = "(and  (<= (* 2 i) k) (<= j (* 3 i)))";
 
 static char const* example6 = "(and (<= 0 (+ x z))\
      (>= y x) \
@@ -51,30 +58,175 @@ static char const* example6 = "(and (<= 0 (+ x z))\
      (>= x 0.0)\
      (<= x 1.0))";
 
+// phi[M] => result => E x . phi[x] 
 
-static void test(char const *ex) {
+static void test(app* var, expr_ref& fml) {
+
+    ast_manager& m = fml.get_manager();
     smt_params params;
     params.m_model = true;
+
+    symbol x_name(var->get_decl()->get_name());   
+    sort* x_sort = m.get_sort(var);
+
+    expr_ref pr(m);
+    expr_ref_vector lits(m);
+    flatten_and(fml, lits);
+
+    model_ref md;
+    {
+        smt::context ctx(m, params);
+        ctx.assert_expr(fml);
+        lbool result = ctx.check();
+        if (result != l_true) return;
+        ctx.get_model(md);
+    }    
+    VERIFY(qe::arith_project(*md, var, lits));
+    pr = mk_and(lits);
+   
+    std::cout << "original:  " << mk_pp(fml, m) << "\n";
+    std::cout << "projected: " << mk_pp(pr,  m) << "\n";
+
+    // projection is consistent with model.
+    expr_ref tmp(m);
+    VERIFY(md->eval(pr, tmp) && m.is_true(tmp));       
+
+    // projection implies E x. fml
+    {
+        qe::expr_quant_elim qelim(m, params);
+        expr_ref result(m), efml(m);
+        expr* x = var;
+        expr_abstract(m, 0, 1, &x, fml, efml);
+        efml = m.mk_exists(1, &x_sort, &x_name, efml);
+        qelim(m.mk_true(), efml, result);
+
+        smt::context ctx(m, params);
+        ctx.assert_expr(pr);
+        ctx.assert_expr(m.mk_not(result));
+        std::cout << "exists: " << pr << " =>\n" << result << "\n";
+        VERIFY(l_false == ctx.check());
+    }    
+
+    std::cout << "\n";
+}
+
+
+
+static void testR(char const *ex) {
     ast_manager m;
     reg_decl_plugins(m);
     arith_util a(m);
     expr_ref fml = parse_fml(m, ex);
-    app_ref_vector vars(m);
-    expr_ref_vector lits(m);
-    vars.push_back(m.mk_const(symbol("x"), a.mk_real()));
-    flatten_and(fml, lits);
+    symbol x_name("x");
+    sort_ref x_sort(a.mk_real(), m);
+    app_ref var(m.mk_const(x_name, x_sort), m);
+    test(var, fml);
+}
 
-    smt::context ctx(m, params);
-    ctx.assert_expr(fml);
-    lbool result = ctx.check();
-    SASSERT(result == l_true);
-    ref<model> md;
-    ctx.get_model(md);    
-    expr_ref pr = qe::arith_project(*md, vars, lits);
-    
-    std::cout << mk_pp(fml, m) << "\n";
-    std::cout << mk_pp(pr, m) << "\n";
+static void testI(char const *ex) {
+    ast_manager m;
+    reg_decl_plugins(m);
+    arith_util a(m);
+    expr_ref fml = parse_fml(m, ex);
+    symbol x_name("i");
+    sort_ref x_sort(a.mk_int(), m);
+    app_ref var(m.mk_const(x_name, x_sort), m);
+    test(var, fml);
+}
+
+static expr_ref_vector mk_ineqs(app* x, app* y, app_ref_vector const& nums) {
+    ast_manager& m = nums.get_manager();
+    arith_util a(m);
+    expr_ref_vector result(m);
+    for (unsigned i = 0; i < nums.size(); ++i) {
+        expr_ref ax(a.mk_mul(nums[i], x), m);
+        result.push_back(a.mk_le(ax, y));
+        result.push_back(m.mk_not(a.mk_ge(ax, y)));
+        result.push_back(m.mk_not(a.mk_gt(y, ax)));
+        result.push_back(a.mk_lt(y, ax));
+    }
+    return result;
+}
+
+static app_ref generate_ineqs(ast_manager& m, sort* s, vector<expr_ref_vector>& cs, bool mods_too) {
+    arith_util a(m);
+    app_ref_vector vars(m), nums(m);
+    vars.push_back(m.mk_const(symbol("x"), s));
+    vars.push_back(m.mk_const(symbol("y"), s));
+    vars.push_back(m.mk_const(symbol("z"), s));
+    vars.push_back(m.mk_const(symbol("u"), s));
+    vars.push_back(m.mk_const(symbol("v"), s));
+    vars.push_back(m.mk_const(symbol("w"), s));
+    nums.push_back(a.mk_numeral(rational(1),  s));
+    nums.push_back(a.mk_numeral(rational(2),  s));
+    nums.push_back(a.mk_numeral(rational(3),  s));
     
+    app* x = vars[0].get();
+    app* y = vars[1].get();
+    app* z = vars[2].get();
+    // 
+    // ax <= by, ax < by, not (ax >= by), not (ax > by)
+    // 
+    cs.push_back(mk_ineqs(x, vars[1].get(), nums));
+    cs.push_back(mk_ineqs(x, vars[2].get(), nums));
+    cs.push_back(mk_ineqs(x, vars[3].get(), nums));
+    cs.push_back(mk_ineqs(x, vars[4].get(), nums));
+    cs.push_back(mk_ineqs(x, vars[5].get(), nums));
+
+    if (mods_too) {
+        expr_ref_vector mods(m);
+        expr_ref zero(a.mk_numeral(rational(0), s), m);
+        mods.push_back(m.mk_true());
+        for (unsigned j = 0; j < nums.size(); ++j) {
+            mods.push_back(m.mk_eq(a.mk_mod(a.mk_add(a.mk_mul(nums[j].get(),x), y), nums[1].get()), zero));
+        }
+        cs.push_back(mods);
+        mods.resize(1);
+        for (unsigned j = 0; j < nums.size(); ++j) {
+            mods.push_back(m.mk_eq(a.mk_mod(a.mk_add(a.mk_mul(nums[j].get(),x), y), nums[2].get()), zero));
+        }
+        cs.push_back(mods);
+    }
+    return app_ref(x, m);
+}
+
+
+static void test_c(app* x, expr_ref_vector const& c) {
+    ast_manager& m = c.get_manager();
+    expr_ref fml(m);
+    fml = m.mk_and(c.size(), c.c_ptr());
+    test(x, fml);
+}
+
+static void test_cs(app* x, expr_ref_vector& c, vector<expr_ref_vector> const& cs) {
+    if (c.size() == cs.size()) {
+        test_c(x, c);
+        return;
+    }
+    expr_ref_vector const& c1 = cs[c.size()];
+    for (unsigned i = 0; i < c1.size(); ++i) {
+        c.push_back(c1[i]);
+        test_cs(x, c, cs);
+        c.pop_back();
+    }
+}
+
+
+static void test_ineqs(ast_manager& m, sort* s, bool mods_too) {
+    vector<expr_ref_vector> ineqs;
+    app_ref x = generate_ineqs(m, s, ineqs, mods_too);
+    expr_ref_vector cs(m);
+    test_cs(x, cs, ineqs);
+}
+
+static void test_ineqs() {
+    ast_manager m;
+    reg_decl_plugins(m);
+    arith_util a(m);
+    sort* s_int = a.mk_int();
+    sort* s_real = a.mk_real();
+    test_ineqs(m, s_int, true);
+    test_ineqs(m, s_real, false);
 }
 
 static void test2(char const *ex) {
@@ -102,7 +254,7 @@ static void test2(char const *ex) {
     
     std::cout << mk_pp(fml, m) << "\n";
 
-    expr_ref pr2(m), fml2(m);
+    expr_ref pr1(m), pr2(m), fml2(m);
     expr_ref_vector bound(m);
     ptr_vector<sort> sorts;
     svector<symbol> names;
@@ -114,7 +266,10 @@ static void test2(char const *ex) {
     expr_abstract(m, 0, bound.size(), bound.c_ptr(), fml, fml2);
     fml2 = m.mk_exists(bound.size(), sorts.c_ptr(), names.c_ptr(), fml2);
     qe::expr_quant_elim qe(m, params);
-    expr_ref pr1 = qe::arith_project(*md, vars, lits);
+    for (unsigned i = 0; i < vars.size(); ++i) {
+        VERIFY(qe::arith_project(*md, vars[i].get(), lits));
+    }
+    pr1 = mk_and(lits);
     qe(m.mk_true(), fml2, pr2);
     std::cout << mk_pp(pr1, m) << "\n";
     std::cout << mk_pp(pr2, m) << "\n";
@@ -131,11 +286,17 @@ static void test2(char const *ex) {
 }
 
 void tst_qe_arith() {
+//    enable_trace("qe");
+    testI(example8);    
+    testR(example7);
+    test_ineqs();
+    return;
+    testR(example1);
+    testR(example2);
+    testR(example3);
+    testR(example4);
+    testR(example5);
+    return;
     test2(example6);
     return;
-    test(example1);
-    test(example2);
-    test(example3);
-    test(example4);
-    test(example5);
 }

src/util/obj_pair_set.h

@@ -45,6 +45,7 @@ public:
     bool contains(T1 * t1, T2 * t2) const { return m_set.contains(obj_pair(t1, t2)); }
     bool contains(obj_pair const & p) const { return m_set.contains(p); }
     void reset() { m_set.reset(); }
+    bool empty() const { return m_set.empty(); }
 };
 
 #endif

src/util/small_object_allocator.cpp

@@ -69,6 +69,7 @@ void small_object_allocator::reset() {
 #define MASK ((1 << PTR_ALIGNMENT) - 1)
 
 void small_object_allocator::deallocate(size_t size, void * p) {
+    if (size == 0) return;
 #if defined(Z3DEBUG) && !defined(_WINDOWS)
     // Valgrind friendly
     memory::deallocate(p);
@@ -91,6 +92,7 @@ void small_object_allocator::deallocate(size_t size, void * p) {
 }
 
 void * small_object_allocator::allocate(size_t size) {
+    if (size == 0) return 0;
 #if defined(Z3DEBUG) && !defined(_WINDOWS)
     // Valgrind friendly
     return memory::allocate(size);