diff --git a/src/ast/array_decl_plugin.cpp b/src/ast/array_decl_plugin.cpp
index af451f9c5..fa17b591d 100644
--- a/src/ast/array_decl_plugin.cpp
+++ b/src/ast/array_decl_plugin.cpp
@@ -253,7 +253,10 @@ func_decl* array_decl_plugin::mk_select(unsigned arity, sort * const * domain) {
         if (!parameters[i].is_ast() || 
             !is_sort(parameters[i].get_ast()) || 
             !m_manager->compatible_sorts(domain[i+1], to_sort(parameters[i].get_ast()))) {
-            m_manager->raise_exception("domain sort and parameter do not match");
+            std::stringstream strm;
+            strm << "domain sort " << sort_ref(domain[i+1], *m_manager) << " and parameter ";
+            strm << parameter_pp(parameters[i], *m_manager) << " do not match";
+            m_manager->raise_exception(strm.str().c_str());
             UNREACHABLE();
             return nullptr;
         }
@@ -292,8 +295,12 @@ func_decl * array_decl_plugin::mk_store(unsigned arity, sort * const * domain) {
             m_manager->raise_exception("expecting sort parameter");
             return nullptr;
         }
-        if (!m_manager->compatible_sorts(to_sort(parameters[i].get_ast()), domain[i+1])) {
-            m_manager->raise_exception("domain sort and parameter do not match");
+        sort* srt1 = to_sort(parameters[i].get_ast());
+        sort* srt2 = domain[i+1];
+        if (!m_manager->compatible_sorts(srt1, srt2)) {
+            std::stringstream strm;
+            strm << "domain sort " << sort_ref(srt2, *m_manager) << " and parameter sort " << sort_ref(srt2, *m_manager) << " do not match";
+            m_manager->raise_exception(strm.str());
             UNREACHABLE();
             return nullptr;
         }
@@ -326,13 +333,13 @@ bool array_decl_plugin::check_set_arguments(unsigned arity, sort * const * domai
         if (domain[i] != domain[0]) {
             std::ostringstream buffer;
             buffer << "arguments " << 1 << " and " << (i+1) << " have different sorts";
-            m_manager->raise_exception(buffer.str().c_str());
+            m_manager->raise_exception(buffer.str());
             return false;
         }
         if (domain[i]->get_family_id() != m_family_id) {
             std::ostringstream buffer;
             buffer << "argument " << (i+1) << " is not of array sort";
-            m_manager->raise_exception(buffer.str().c_str());
+            m_manager->raise_exception(buffer.str());
             return false;
         }
     }
@@ -517,6 +524,7 @@ func_decl * array_decl_plugin::mk_func_decl(decl_kind k, unsigned num_parameters
 
 void array_decl_plugin::get_sort_names(svector<builtin_name>& sort_names, symbol const & logic) {
     sort_names.push_back(builtin_name(ARRAY_SORT_STR, ARRAY_SORT));
+    sort_names.push_back(builtin_name("=>", ARRAY_SORT));
     // TBD: this could easily break users even though it is already used in CVC4: 
     // sort_names.push_back(builtin_name("Set", _SET_SORT));
 }
diff --git a/src/ast/ast.cpp b/src/ast/ast.cpp
index 8750425a8..99e861b16 100644
--- a/src/ast/ast.cpp
+++ b/src/ast/ast.cpp
@@ -1542,6 +1542,16 @@ void ast_manager::raise_exception(char const * msg) {
 }
 
 
+std::ostream& ast_manager::display(std::ostream& out, parameter const& p) {
+    switch (p.get_kind()) {
+    case parameter::PARAM_AST:
+        return out << mk_pp(p.get_ast(), *this);
+    default:
+        return p.display(out);
+    }
+    return out;
+}
+
 void ast_manager::copy_families_plugins(ast_manager const & from) {
     TRACE("copy_families_plugins",
           tout << "target:\n";
diff --git a/src/ast/ast.h b/src/ast/ast.h
index c1193dfbd..ee39f4032 100644
--- a/src/ast/ast.h
+++ b/src/ast/ast.h
@@ -1558,6 +1558,9 @@ public:
 
     // Equivalent to throw ast_exception(msg)
     Z3_NORETURN void raise_exception(char const * msg);
+    Z3_NORETURN void raise_exception(std::string const& msg) { raise_exception(msg.c_str()); }
+
+    std::ostream& display(std::ostream& out, parameter const& p);
 
     bool is_format_manager() const { return m_format_manager == nullptr; }
 
@@ -2569,6 +2572,16 @@ public:
     void operator()(AST * n) { m_manager.inc_ref(n); }
 };
 
+struct parameter_pp {
+    parameter const& p;
+    ast_manager& m;
+    parameter_pp(parameter const& p, ast_manager& m): p(p), m(m) {}
+};
+
+inline std::ostream& operator<<(std::ostream& out, parameter_pp const& pp) {
+    return pp.m.display(out, pp.p);
+}
+
 
 #endif /* AST_H_ */
 
diff --git a/src/ast/rewriter/seq_rewriter.cpp b/src/ast/rewriter/seq_rewriter.cpp
index 84c05d53e..e4ad3bb9d 100644
--- a/src/ast/rewriter/seq_rewriter.cpp
+++ b/src/ast/rewriter/seq_rewriter.cpp
@@ -859,10 +859,6 @@ br_status seq_rewriter::mk_seq_replace(expr* a, expr* b, expr* c, expr_ref& resu
         result = m_util.str.mk_concat(c, a);
         return BR_REWRITE1;
     }
-    if (m_util.str.is_string(a, s1) && s1.length() == 0) {
-        result = a;
-        return BR_DONE;
-    }
     return BR_FAILED;
 }
 
diff --git a/src/sat/sat_config.cpp b/src/sat/sat_config.cpp
index e9e6c4ee6..29221c0e8 100644
--- a/src/sat/sat_config.cpp
+++ b/src/sat/sat_config.cpp
@@ -86,6 +86,7 @@ namespace sat {
             m_local_search_mode = local_search_mode::gsat;
         else
             m_local_search_mode = local_search_mode::wsat;
+        m_local_search_dbg_flips = p.local_search_dbg_flips();
         m_unit_walk       = p.unit_walk();
         m_unit_walk_threads = p.unit_walk_threads();
         m_lookahead_simplify = p.lookahead_simplify();
diff --git a/src/sat/sat_config.h b/src/sat/sat_config.h
index 63e979394..ba5c9aaf3 100644
--- a/src/sat/sat_config.h
+++ b/src/sat/sat_config.h
@@ -105,6 +105,7 @@ namespace sat {
         unsigned           m_local_search_threads;
         bool               m_local_search;
         local_search_mode  m_local_search_mode;
+        bool               m_local_search_dbg_flips;
         unsigned           m_unit_walk_threads;
         bool               m_unit_walk;
         bool               m_lookahead_simplify;
diff --git a/src/sat/sat_local_search.cpp b/src/sat/sat_local_search.cpp
index 9b79e2964..b65abfd23 100644
--- a/src/sat/sat_local_search.cpp
+++ b/src/sat/sat_local_search.cpp
@@ -553,6 +553,7 @@ namespace sat {
         PROGRESS(tries, total_flips);
         
         for (tries = 1; !m_unsat_stack.empty() && m_limit.inc(); ++tries) {
+            ++m_stats.m_num_restarts;
             for (step = 0; step < m_max_steps && !m_unsat_stack.empty(); ++step) {
                 pick_flip_walksat();
                 if (m_unsat_stack.size() < m_best_unsat) {
@@ -622,7 +623,6 @@ namespace sat {
             break;
         }
 
-
         // remove unit clauses from assumptions.
         m_constraints.shrink(num_constraints() - sz);
 
@@ -779,8 +779,11 @@ namespace sat {
     }
 
     void local_search::flip_walksat(bool_var flipvar) {
+        ++m_stats.m_num_flips;
         VERIFY(!is_unit(flipvar));
         m_vars[flipvar].m_value = !cur_solution(flipvar);
+        m_vars[flipvar].m_flips++;
+        m_vars[flipvar].m_slow_break.update(abs(m_vars[flipvar].m_slack_score));
 
         bool flip_is_true = cur_solution(flipvar);
         coeff_vector const& truep = m_vars[flipvar].m_watch[flip_is_true];
@@ -1062,6 +1065,19 @@ namespace sat {
         return out << "v" << v << " := " << (vi.m_value?"true":"false") << " bias: " << vi.m_bias << "\n";
     }
 
+    void local_search::collect_statistics(statistics& st) const {
+        if (m_config.dbg_flips()) {
+            unsigned i = 0;
+            for (var_info const& vi : m_vars) {
+                IF_VERBOSE(0, verbose_stream() << "flips: " << i << " " << vi.m_flips << " " << vi.m_slow_break  << "\n");               
+                ++i;
+            }
+        }
+        st.update("local-search-flips", m_stats.m_num_flips);
+        st.update("local-search-restarts", m_stats.m_num_restarts);
+    }
+
+
     bool local_search::check_goodvar() {
         unsigned g = 0;
         for (unsigned v = 0; v < num_vars(); ++v) {
diff --git a/src/sat/sat_local_search.h b/src/sat/sat_local_search.h
index baf072419..849b4f26b 100644
--- a/src/sat/sat_local_search.h
+++ b/src/sat/sat_local_search.h
@@ -23,6 +23,8 @@
 #include "sat/sat_types.h"
 #include "sat/sat_config.h"
 #include "util/rlimit.h"
+#include "util/ema.h"
+#include "util/statistics.h"
 
 namespace sat {
 
@@ -33,18 +35,21 @@ namespace sat {
         int               m_best_known_value;
         local_search_mode m_mode;
         bool              m_phase_sticky;
+        bool              m_dbg_flips;
     public:
         local_search_config() {
             m_random_seed = 0;
             m_best_known_value = INT_MAX;
             m_mode = local_search_mode::wsat;
             m_phase_sticky = false;
+            m_dbg_flips = false;
         }
 
         unsigned random_seed() const { return m_random_seed; }
         unsigned best_known_value() const { return m_best_known_value;  }
         local_search_mode mode() const { return m_mode; }
         bool phase_sticky() const { return m_phase_sticky; }
+        bool dbg_flips() const { return m_dbg_flips; }
         
         void set_random_seed(unsigned s) { m_random_seed = s;  }
         void set_best_known_value(unsigned v) { m_best_known_value = v; }
@@ -53,6 +58,7 @@ namespace sat {
             m_mode         = cfg.m_local_search_mode;
             m_random_seed  = cfg.m_random_seed;
             m_phase_sticky = cfg.m_phase_sticky;
+            m_dbg_flips    = cfg.m_local_search_dbg_flips;
         }
     };
 
@@ -74,6 +80,13 @@ namespace sat {
             int coefficient;                     // non-zero integer
             ob_term(bool_var v, int c): var_id(v), coefficient(c) {}
         };
+
+        struct stats {
+            unsigned m_num_flips;
+            unsigned m_num_restarts;
+            void reset() { memset(this, 0, sizeof(*this)); }
+            stats() { reset(); }
+        };
         
         struct var_info {
             bool m_value;                        // current solution
@@ -89,6 +102,8 @@ namespace sat {
             bool_var_vector m_neighbors;         // neighborhood variables
             coeff_vector m_watch[2];
             literal_vector m_bin[2];
+            unsigned m_flips;
+            ema  m_slow_break;
             var_info():
                 m_value(true),
                 m_bias(50), 
@@ -97,7 +112,9 @@ namespace sat {
                 m_in_goodvar_stack(false),
                 m_score(0),
                 m_slack_score(0),
-                m_cscc(0)
+                m_cscc(0),
+                m_flips(0),
+                m_slow_break(1e-5)
             {}
         };
 
@@ -115,6 +132,8 @@ namespace sat {
             literal const* end() const { return m_literals.end(); }
         };
 
+        stats              m_stats;
+
         local_search_config m_config;
 
         // objective function: maximize
@@ -145,7 +164,6 @@ namespace sat {
         
         inline void set_best_unsat();
         /* TBD: other scores */
-        
 
         vector<constraint> m_constraints;
 
@@ -293,6 +311,8 @@ namespace sat {
 
         model& get_model() { return m_model; }
 
+        void collect_statistics(statistics& st) const;        
+
     };
 }
 
diff --git a/src/sat/sat_params.pyg b/src/sat/sat_params.pyg
index 3f0479707..2aef881ca 100644
--- a/src/sat/sat_params.pyg
+++ b/src/sat/sat_params.pyg
@@ -48,6 +48,7 @@ def_module_params('sat',
                           ('local_search', BOOL, False, 'use local search instead of CDCL'),
                           ('local_search_threads', UINT, 0, 'number of local search threads to find satisfiable solution'),
                           ('local_search_mode', SYMBOL, 'wsat', 'local search algorithm, either default wsat or qsat'),
+                          ('local_search_dbg_flips', BOOL, False, 'write debug information for number of flips'),
 	                  ('unit_walk', BOOL, False, 'use unit-walk search instead of CDCL'),
                           ('unit_walk_threads', UINT, 0, 'number of unit-walk search threads to find satisfiable solution'),
                           ('lookahead.cube.cutoff', SYMBOL, 'depth', 'cutoff type used to create lookahead cubes: depth, freevars, psat, adaptive_freevars, adaptive_psat'),
diff --git a/src/sat/sat_solver.cpp b/src/sat/sat_solver.cpp
index 2032445ed..fea45c07b 100644
--- a/src/sat/sat_solver.cpp
+++ b/src/sat/sat_solver.cpp
@@ -68,6 +68,7 @@ namespace sat {
         m_simplifications         = 0;
         m_ext                     = nullptr;
         m_cuber                   = nullptr;
+        m_local_search            = nullptr;
         m_mc.set_solver(this);
     }
 
@@ -764,9 +765,9 @@ namespace sat {
         m_not_l    = not_l;
     }
 
-    void solver::assign_core(literal l, justification j) {
+    void solver::assign_core(literal l, unsigned lvl, justification j) {
         SASSERT(value(l) == l_undef);
-        TRACE("sat_assign_core", tout << l << " " << j << " level: " << scope_lvl() << "\n";);
+        TRACE("sat_assign_core", tout << l << " " << j << " level: " << lvl << "\n";);
         if (at_base_lvl()) {
             if (m_config.m_drat) m_drat.add(l, !j.is_none());
             j = justification(); // erase justification for level 0
@@ -774,7 +775,7 @@ namespace sat {
         m_assignment[l.index()]    = l_true;
         m_assignment[(~l).index()] = l_false;
         bool_var v = l.var();
-        m_level[v]                 = scope_lvl();
+        m_level[v]                 = lvl;
         m_justification[v]         = j;
         m_phase[v]                 = static_cast<phase>(l.sign());
         m_assigned_since_gc[v]     = true;
@@ -882,7 +883,7 @@ namespace sat {
                         return false;
                     case l_undef:
                         m_stats.m_bin_propagate++;
-                        assign_core(l1, justification(not_l));
+                        assign_core(l1, scope_lvl(), justification(not_l));
                         break;
                     case l_true:
                         break; // skip
@@ -897,11 +898,11 @@ namespace sat {
                     val2 = value(l2);
                     if (val1 == l_false && val2 == l_undef) {
                         m_stats.m_ter_propagate++;
-                        assign_core(l2, justification(l1, not_l));
+                        assign_core(l2, scope_lvl(), justification(l1, not_l));
                     }
                     else if (val1 == l_undef && val2 == l_false) {
                         m_stats.m_ter_propagate++;
-                        assign_core(l1, justification(l2, not_l));
+                        assign_core(l1, scope_lvl(), justification(l2, not_l));
                     }
                     else if (val1 == l_false && val2 == l_false) {
                         CONFLICT_CLEANUP();
@@ -964,7 +965,7 @@ namespace sat {
                         it2++;
                         m_stats.m_propagate++;
                         c.mark_used();
-                        assign_core(c[0], justification(cls_off));
+                        assign_core(c[0], scope_lvl(), justification(cls_off));
 #ifdef UPDATE_GLUE
                         if (update && c.is_learned() && c.glue() > 2) {
                             unsigned glue;
@@ -1042,7 +1043,7 @@ namespace sat {
                 literal l(v, false);
                 if (mdl[v] != l_true) l.neg();
                 push();
-                assign_core(l, justification());
+                assign_core(l, scope_lvl(), justification());
             }
             mk_model();
             break;
@@ -1160,13 +1161,16 @@ namespace sat {
 
     lbool solver::do_local_search(unsigned num_lits, literal const* lits) {
         scoped_limits scoped_rl(rlimit());
-        local_search srch;
+        SASSERT(!m_local_search);
+        m_local_search = alloc(local_search);
+        local_search& srch = *m_local_search;
         srch.config().set_config(m_config);
         srch.import(*this, false);
         scoped_rl.push_child(&srch.rlimit());
         lbool r = srch.check(num_lits, lits, nullptr);
         m_model = srch.get_model();
-        // srch.collect_statistics(m_aux_stats);
+        m_local_search = nullptr;
+        dealloc(&srch);
         return r;
     }
 
@@ -3379,6 +3383,7 @@ namespace sat {
         m_asymm_branch.collect_statistics(st);
         m_probing.collect_statistics(st);
         if (m_ext) m_ext->collect_statistics(st);
+        if (m_local_search) m_local_search->collect_statistics(st);
         st.copy(m_aux_stats);
     }
 
diff --git a/src/sat/sat_solver.h b/src/sat/sat_solver.h
index a9a9fcee0..27c2e123c 100644
--- a/src/sat/sat_solver.h
+++ b/src/sat/sat_solver.h
@@ -163,6 +163,7 @@ namespace sat {
         bool                    m_par_syncing_clauses;
 
         class lookahead*        m_cuber;
+        class local_search*     m_local_search;
 
         statistics              m_aux_stats;
 
@@ -305,11 +306,11 @@ namespace sat {
             TRACE("sat_assign", tout << l << " previous value: " << value(l) << "\n";);
             switch (value(l)) {
             case l_false: set_conflict(j, ~l); break;
-            case l_undef: assign_core(l, j); break;
+            case l_undef: assign_core(l, scope_lvl(), j); break;
             case l_true:  return;
             }
         }
-        void assign_core(literal l, justification jst);
+        void assign_core(literal l, unsigned lvl, justification jst);
         void set_conflict(justification c, literal not_l);
         void set_conflict(justification c) { set_conflict(c, null_literal); }
         lbool status(clause const & c) const;        
diff --git a/src/shell/dimacs_frontend.cpp b/src/shell/dimacs_frontend.cpp
index 3a2af72cf..d0fce359f 100644
--- a/src/shell/dimacs_frontend.cpp
+++ b/src/shell/dimacs_frontend.cpp
@@ -178,21 +178,21 @@ unsigned read_dimacs(char const * file_name) {
             std::cerr << "(error \"failed to open file '" << file_name << "'\")" << std::endl;
             exit(ERR_OPEN_FILE);
         }
-        parse_dimacs(in, solver);
+        parse_dimacs(in, *g_solver);
     }
     else {
-        parse_dimacs(std::cin, solver);
+        parse_dimacs(std::cin, *g_solver);
     }
-    IF_VERBOSE(20, solver.display_status(verbose_stream()););
+    IF_VERBOSE(20, g_solver->display_status(verbose_stream()););
     
     lbool r;
     vector<sat::literal_vector> tracking_clauses;
-    sat::solver solver2(p, limit);
-    if (p.get_bool("dimacs.core", false)) {
-        g_solver = &solver2;        
+    sat::solver solver2( p, limit);
+    if (p.get_bool("dimacs.core", false)) {        
         sat::literal_vector assumptions;
         track_clauses(solver, solver2, assumptions, tracking_clauses);
-        r = g_solver->check(assumptions.size(), assumptions.c_ptr());
+        g_solver = &solver2;        
+        r = solver2.check(assumptions.size(), assumptions.c_ptr());
     }
     else {
         r = g_solver->check();