add recfun to API

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

examples/c++/example.cpp

@@ -1190,6 +1190,20 @@ void mk_model_example() {
     std::cout << m.eval(a + b < 2)<< std::endl;
 }
 
+void recfun_example() {
+    std::cout << "recfun example\n";
+    context c;    
+    expr x = c.int_const("x");
+    expr y = c.int_const("y");
+    expr b = c.bool_const("b");
+    sort I = c.int_sort();
+    sort B = c.bool_sort();    
+    func_decl f = recfun("f", I, B, I);
+    expr_vector args(c);
+    args.push_back(x); args.push_back(b);
+    c.recdef(f, args, ite(b, x, f(x + 1, !b)));
+    prove(f(x,c.bool_val(false)) > x);
+}
 
 int main() {
 
@@ -1239,6 +1253,7 @@ int main() {
         consequence_example(); std::cout << "\n";
         parse_example(); std::cout << "\n";
         mk_model_example(); std::cout << "\n";
+        recfun_example(); std::cout << "\n";
         std::cout << "done\n";
     }
     catch (exception & ex) {

src/api/api_ast.cpp

@@ -38,6 +38,8 @@ Revision History:
 #include "util/cancel_eh.h"
 #include "util/scoped_timer.h"
 #include "ast/pp_params.hpp"
+#include "ast/expr_abstract.h"
+
 
 extern bool is_numeral_sort(Z3_context c, Z3_sort ty);
 
@@ -110,6 +112,54 @@ extern "C" {
         Z3_CATCH_RETURN(nullptr);
     }
 
+    Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const* domain,
+                                            Z3_sort range) {
+        Z3_TRY;
+        LOG_Z3_mk_rec_func_decl(c, s, domain_size, domain, range);
+        RESET_ERROR_CODE();
+        // 
+        recfun::promise_def def = 
+            mk_c(c)->recfun().get_plugin().mk_def(to_symbol(s),                                      
+                                          domain_size,
+                                          to_sorts(domain),
+                                          to_sort(range));
+        func_decl* d = def.get_def()->get_decl();
+        mk_c(c)->save_ast_trail(d);
+        RETURN_Z3(of_func_decl(d));
+        Z3_CATCH_RETURN(nullptr);
+    }
+
+    void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body) {
+        Z3_TRY;
+        LOG_Z3_add_rec_def(c, f, n, args, body);
+        func_decl* d = to_func_decl(f);
+        ast_manager& m = mk_c(c)->m();
+        recfun::decl::plugin& p = mk_c(c)->recfun().get_plugin();
+        expr_ref abs_body(m);
+        expr_ref_vector _args(m);
+        var_ref_vector _vars(m);
+        for (unsigned i = 0; i < n; ++i) {
+            _args.push_back(to_expr(args[i]));
+            _vars.push_back(m.mk_var(n - i - 1, m.get_sort(_args.back())));
+            if (m.get_sort(_args.back()) != d->get_domain(i)) {
+                SET_ERROR_CODE(Z3_INVALID_ARG, nullptr);            
+                return;            
+            }
+        }
+        expr_abstract(m, 0, n, _args.c_ptr(), to_expr(body), abs_body);
+        recfun::promise_def pd = p.get_promise_def(d);
+        if (!pd.get_def()) {
+            SET_ERROR_CODE(Z3_INVALID_ARG, nullptr);
+            return;
+        }
+        if (m.get_sort(abs_body) != d->get_range()) {
+            SET_ERROR_CODE(Z3_INVALID_ARG, nullptr);            
+            return;
+        }
+        p.set_definition(pd, n, _vars.c_ptr(), abs_body);
+        Z3_CATCH;
+    }
+
     Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const * args) {
         Z3_TRY;
         LOG_Z3_mk_app(c, d, num_args, args);

src/api/api_context.cpp

@@ -79,6 +79,7 @@ namespace api {
         m_datalog_util(m()),
         m_fpa_util(m()),
         m_sutil(m()),
+        m_recfun(m()),
         m_last_result(m()),
         m_ast_trail(m()),
         m_pmanager(m_limit) {

src/api/api_context.h

@@ -29,6 +29,7 @@ Revision History:
 #include "ast/datatype_decl_plugin.h"
 #include "ast/dl_decl_plugin.h"
 #include "ast/fpa_decl_plugin.h"
+#include "ast/recfun_decl_plugin.h"
 #include "smt/smt_kernel.h"
 #include "smt/params/smt_params.h"
 #include "util/event_handler.h"
@@ -62,6 +63,7 @@ namespace api {
         datalog::dl_decl_util      m_datalog_util;
         fpa_util                   m_fpa_util;
         seq_util                   m_sutil;
+        recfun_util                m_recfun;
 
         // Support for old solver API
         smt_params                 m_fparams;
@@ -128,6 +130,7 @@ namespace api {
         fpa_util & fpautil() { return m_fpa_util; }
         datatype_util& dtutil() { return m_dt_plugin->u(); }
         seq_util& sutil() { return m_sutil; }
+        recfun_util& recfun() { return m_recfun; }
         family_id get_basic_fid() const { return m_basic_fid; }
         family_id get_array_fid() const { return m_array_fid; }
         family_id get_arith_fid() const { return m_arith_fid; }

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

@@ -311,6 +311,13 @@ namespace z3 {
         func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & range);
         func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & d5, sort const & range);
 
+        func_decl recfun(symbol const & name, unsigned arity, sort const * domain, sort const & range);
+        func_decl recfun(char const * name, unsigned arity, sort const * domain, sort const & range);
+        func_decl recfun(char const * name, sort const & domain, sort const & range);
+        func_decl recfun(char const * name, sort const & d1, sort const & d2, sort const & range);
+
+        void      recdef(func_decl, expr_vector const& args, expr const& body);
+
         expr constant(symbol const & name, sort const & s);
         expr constant(char const * name, sort const & s);
         expr bool_const(char const * name);
@@ -2815,6 +2822,37 @@ namespace z3 {
         return func_decl(*this, f);
     }
 
+    inline func_decl context::recfun(symbol const & name, unsigned arity, sort const * domain, sort const & range) {
+        array<Z3_sort> args(arity);
+        for (unsigned i = 0; i < arity; i++) {
+            check_context(domain[i], range);
+            args[i] = domain[i];
+        }
+        Z3_func_decl f = Z3_mk_rec_func_decl(m_ctx, name, arity, args.ptr(), range);
+        check_error();
+        return func_decl(*this, f);
+
+    }
+
+    inline func_decl context::recfun(char const * name, unsigned arity, sort const * domain, sort const & range) {
+        return recfun(str_symbol(name), arity, domain, range);
+    }
+
+    inline func_decl context::recfun(char const * name, sort const& d1, sort const & range) {
+        return recfun(str_symbol(name), 1, &d1, range);
+    }
+
+    inline func_decl context::recfun(char const * name, sort const& d1, sort const& d2, sort const & range) {
+        sort dom[2] = { d1, d2 };
+        return recfun(str_symbol(name), 2, dom, range);
+    }
+
+    void context::recdef(func_decl f, expr_vector const& args, expr const& body) {
+        check_context(f, args); check_context(f, body);
+        array<Z3_ast> vars(args);
+        Z3_add_rec_def(f.ctx(), f, vars.size(), vars.ptr(), body);
+    }
+
     inline expr context::constant(symbol const & name, sort const & s) {
         Z3_ast r = Z3_mk_const(m_ctx, name, s);
         check_error();
@@ -2976,6 +3014,19 @@ namespace z3 {
         return range.ctx().function(name.c_str(), domain, range);
     }
 
+    inline func_decl recfun(symbol const & name, unsigned arity, sort const * domain, sort const & range) {
+        return range.ctx().recfun(name, arity, domain, range);
+    }
+    inline func_decl recfun(char const * name, unsigned arity, sort const * domain, sort const & range) {
+        return range.ctx().recfun(name, arity, domain, range);
+    }
+    inline func_decl recfun(char const * name, sort const& d1, sort const & range) {
+        return range.ctx().recfun(name, d1, range);
+    }
+    inline func_decl recfun(char const * name, sort const& d1, sort const& d2, sort const & range) {
+        return range.ctx().recfun(name, d1, d2, range);
+    }
+
     inline expr select(expr const & a, expr const & i) {
         check_context(a, i);
         Z3_ast r = Z3_mk_select(a.ctx(), a, i);

src/api/z3_api.h

@@ -2081,6 +2081,7 @@ extern "C" {
                                         Z3_sort range);
 
 
+
     /**
        \brief Create a constant or function application.
 
@@ -2140,6 +2141,48 @@ extern "C" {
        def_API('Z3_mk_fresh_const', AST, (_in(CONTEXT), _in(STRING), _in(SORT)))
     */
     Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty);
+
+
+    /**
+       \brief Declare a recursive function
+
+       \param c logical context.
+       \param s name of the function.
+       \param domain_size number of arguments. It should be greater than 0.
+       \param domain array containing the sort of each argument. The array must contain domain_size elements. 
+       \param range sort of the constant or the return sort of the function.
+
+       After declaring recursive function, it should be associated with a recursive definition #Z3_mk_rec_def.
+       The function #Z3_mk_app can be used to create a constant or function
+       application.
+
+       \sa Z3_mk_app
+       \sa Z3_mk_rec_def
+
+       def_API('Z3_mk_rec_func_decl', FUNC_DECL, (_in(CONTEXT), _in(SYMBOL), _in(UINT), _in_array(2, SORT), _in(SORT)))
+    */
+    Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s,
+                                        unsigned domain_size, Z3_sort const domain[],
+                                        Z3_sort range);
+
+    /**
+       \brief Define the body of a recursive function.
+       
+       \param c logical context.
+       \param f function declaration.
+       \param n number of arguments to the function
+       \param args constants that are used as arguments to the recursive function in the definition.
+       \param body body of the recursive function
+
+       After declaring a recursive function or a collection of  mutually recursive functions, use 
+       this function to provide the definition for the recursive function.
+
+       \sa Z3_mk_rec_func_decl
+
+       def_API('Z3_add_rec_def', VOID, (_in(CONTEXT), _in(FUNC_DECL), _in(UINT), _in_array(2, AST), _in(AST)))
+     */
+    void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body);
+
     /*@}*/
 
     /** @name Propositional Logic and Equality */

src/ast/recfun_decl_plugin.cpp

@@ -312,8 +312,8 @@ namespace recfun {
      * Main manager for defined functions
      */
 
-    util::util(ast_manager & m, family_id id)
+    util::util(ast_manager & m)
-        : m_manager(m), m_fid(id), m_th_rw(m),
+        : m_manager(m), m_fid(m.get_family_id("recfun")), m_th_rw(m),
           m_plugin(dynamic_cast<decl::plugin*>(m.get_plugin(m_fid))) {
     }
 
@@ -385,15 +385,15 @@ namespace recfun {
             SASSERT(m_manager);
             SASSERT(m_family_id != null_family_id);
             if (!m_util.get()) {
-                m_util = alloc(util, *m_manager, m_family_id);
+                m_util = alloc(util, *m_manager);
             }
             return *(m_util.get());
         }
 
         promise_def plugin::mk_def(symbol const& name, unsigned n, sort *const * params, sort * range) {
-            SASSERT(! m_defs.contains(name));
             def* d = u().decl_fun(name, n, params, range);
-            m_defs.insert(name, d);
+            SASSERT(! m_defs.contains(d->get_decl()));
+            m_defs.insert(d->get_decl(), d);
             return promise_def(&u(), d);
         }
         
@@ -410,8 +410,8 @@ namespace recfun {
 
         def* plugin::mk_def(symbol const& name, unsigned n, sort ** params, sort * range,
                             unsigned n_vars, var ** vars, expr * rhs) {
-            SASSERT(! m_defs.contains(name));
             promise_def d = mk_def(name, n, params, range);
+            SASSERT(! m_defs.contains(d.get_def()->get_decl()));
             set_definition(d, n_vars, vars, rhs);
             return d.get_def();
         }

src/ast/recfun_decl_plugin.h

@@ -140,7 +140,7 @@ namespace recfun {
     namespace decl {
 
         class plugin : public decl_plugin {
-            typedef map<symbol, def*, symbol_hash_proc, symbol_eq_proc> def_map;
+            typedef obj_map<func_decl, def*> def_map;
             typedef obj_map<func_decl, case_def*> case_def_map;
 
             mutable scoped_ptr<util> m_util;
@@ -173,14 +173,14 @@ namespace recfun {
             
             def* mk_def(symbol const& name, unsigned n, sort ** params, sort * range, unsigned n_vars, var ** vars, expr * rhs);
 
-            bool has_def(const symbol& s) const { return m_defs.contains(s); }
+            bool has_def(func_decl* f) const { return m_defs.contains(f); }
             bool has_defs() const;
-            def const& get_def(const symbol& s) const { return *(m_defs[s]); }
+            def const& get_def(func_decl* f) const { return *(m_defs[f]); }
-            promise_def get_promise_def(const symbol &s) const { return promise_def(&u(), m_defs[s]); }
+            promise_def get_promise_def(func_decl* f) const { return promise_def(&u(), m_defs[f]); }
-            def& get_def(symbol const& s) { return *(m_defs[s]); }
+            def& get_def(func_decl* f) { return *(m_defs[f]); }
             bool has_case_def(func_decl* f) const { return m_case_defs.contains(f); }
             case_def& get_case_def(func_decl* f) { SASSERT(has_case_def(f)); return *(m_case_defs[f]); }
-            bool is_declared(symbol const& s) const { return m_defs.contains(s); }
+            //bool is_declared(symbol const& s) const { return m_defs.contains(s); }
         };
     }
 
@@ -197,7 +197,7 @@ namespace recfun {
         void set_definition(promise_def & d, unsigned n_vars, var * const * vars, expr * rhs);
 
     public:
-        util(ast_manager &m, family_id);
+        util(ast_manager &m);
         ~util();
 
         ast_manager & m() { return m_manager; }
@@ -213,9 +213,10 @@ namespace recfun {
         //<! add a function declaration
         def * decl_fun(symbol const & s, unsigned n_args, sort *const * args, sort * range);
 
-        def& get_def(symbol const & s) {
+
-            SASSERT(m_plugin->has_def(s));
+        def& get_def(func_decl* f) {
-            return m_plugin->get_def(s);
+            SASSERT(m_plugin->has_def(f));
+            return m_plugin->get_def(f);
         }
 
         case_def& get_case_def(expr* e) {
@@ -232,6 +233,8 @@ namespace recfun {
         }
 
         app_ref mk_depth_limit_pred(unsigned d);
+
+        decl::plugin& get_plugin() { return *m_plugin; }
     };
 }
 

src/cmd_context/cmd_context.cpp

@@ -475,7 +475,6 @@ cmd_context::cmd_context(bool main_ctx, ast_manager * m, symbol const & l):
     m_manager(m),
     m_own_manager(m == nullptr),
     m_manager_initialized(false),
-    m_rec_fun_declared(false),
     m_pmanager(nullptr),
     m_sexpr_manager(nullptr),
     m_regular("stdout", std::cout),
@@ -900,20 +899,15 @@ void cmd_context::model_del(func_decl* f) {
 }
 
 
-recfun_decl_plugin * cmd_context::get_recfun_plugin() {
+recfun_decl_plugin& cmd_context::get_recfun_plugin() {
-    ast_manager & m = get_ast_manager();
+    recfun::util u(get_ast_manager());
-    family_id id = m.get_family_id("recfun");
+    return u.get_plugin();
-    recfun_decl_plugin* p = reinterpret_cast<recfun_decl_plugin*>(m.get_plugin(id));
-    SASSERT(p);
-    return p;
 }
 
 
 recfun::promise_def cmd_context::decl_rec_fun(const symbol &name, unsigned int arity, sort *const *domain, sort *range) {        
     SASSERT(logic_has_recfun());
-    recfun_decl_plugin* p = get_recfun_plugin();
+    return get_recfun_plugin().mk_def(name, arity, domain, range);
-    recfun::promise_def def = p->mk_def(name, arity, domain, range);
-    return def;
 }
 
 // insert a recursive function as a regular quantified axiom
@@ -936,15 +930,6 @@ void cmd_context::insert_rec_fun_as_axiom(func_decl *f, expr_ref_vector const& b
         eq  = m().mk_forall(ids.size(), f->get_domain(), ids.c_ptr(), eq, 0, m().rec_fun_qid(), symbol::null, 2, pats);
     }
 
-    //
-    // disable warning given the current way they are used
-    // (Z3 will here silently assume and not check the definitions to be well founded,
-    // and please use HSF for everything else).
-    //
-    if (false && !ids.empty() && !m_rec_fun_declared) {
-        warning_msg("recursive function definitions are assumed well-founded");
-        m_rec_fun_declared = true;
-    }
     assert_expr(eq);
 }
 
@@ -959,7 +944,7 @@ void cmd_context::insert_rec_fun(func_decl* f, expr_ref_vector const& binding, s
 
     TRACE("recfun", tout<< "define recfun " << f->get_name()  << " = " << mk_pp(rhs, m()) << "\n";);
 
-    recfun_decl_plugin* p = get_recfun_plugin();
+    recfun_decl_plugin& p = get_recfun_plugin();
 
     var_ref_vector vars(m());
     for (expr* b : binding) {
@@ -967,8 +952,8 @@ void cmd_context::insert_rec_fun(func_decl* f, expr_ref_vector const& binding, s
         vars.push_back(to_var(b));
     }
     
-    recfun::promise_def d = p->get_promise_def(f->get_name());
+    recfun::promise_def d = p.get_promise_def(f);
-    p->set_definition(d, vars.size(), vars.c_ptr(), rhs);
+    p.set_definition(d, vars.size(), vars.c_ptr(), rhs);
 }
 
 func_decl * cmd_context::find_func_decl(symbol const & s) const {

src/cmd_context/cmd_context.h

@@ -200,7 +200,6 @@ protected:
     ast_manager *                m_manager;
     bool                         m_own_manager;
     bool                         m_manager_initialized;
-    bool                         m_rec_fun_declared;
     pdecl_manager *              m_pmanager;
     sexpr_manager *              m_sexpr_manager;
     check_logic                  m_check_logic;
@@ -308,7 +307,7 @@ protected:
     void erase_macro(symbol const& s);
     bool macros_find(symbol const& s, unsigned n, expr*const* args, expr*& t) const;
 
-    recfun_decl_plugin * get_recfun_plugin();
+    recfun_decl_plugin& get_recfun_plugin();
 
 public:
     cmd_context(bool main_ctx = true, ast_manager * m = nullptr, symbol const & l = symbol::null);

src/smt/theory_recfun.h

@@ -42,8 +42,7 @@ namespace smt {
             m_lhs(n), m_def(nullptr), m_args()  {
                 SASSERT(u.is_defined(n));
                 func_decl * d = n->get_decl();
-                const symbol& name = d->get_name();
+                m_def = &u.get_def(d);
-                m_def = &u.get_def(name);
                 m_args.append(n->get_num_args(), n->get_args());
             }
             case_expansion(case_expansion const & from)