Complete theory_finite_set.h header and implement finite set theory solver (#7976)

* Initial plan

* Implement theory_finite_set header and implementation

Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

* Add theory registration to smt_setup

Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>

* Update theory_finite_set.cpp

* Refactor membership_atoms and add elements list

Renamed membership_atoms to membership_elements and added elements list.

* Change membership elements to use enode type

* Update theory_finite_set.cpp

* Fix typo in internalize_atom function

* Update theory_finite_set.cpp

* Refactor final_check_eh by removing comments

Removed redundant comments and cleaned up code.

* Add m_lemmas member to theory_finite_set class

* Improve clause management and instantiation logic

Refactor clause handling and instantiate logic in finite set theory.

* Add friend class declaration for testing

* Add placeholder methods for lemma instantiation

Added placeholder methods for lemma instantiation.

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/smt/CMakeLists.txt

@@ -57,6 +57,7 @@ z3_add_component(smt
     theory_char.cpp
     theory_datatype.cpp
     theory_dense_diff_logic.cpp
+    theory_finite_set.cpp
     theory_diff_logic.cpp
     theory_dl.cpp
     theory_dummy.cpp

src/smt/smt_setup.cpp

@@ -40,6 +40,7 @@ Revision History:
 #include "smt/theory_pb.h"
 #include "smt/theory_fpa.h"
 #include "smt/theory_polymorphism.h"
+#include "smt/theory_finite_set.h"
 
 namespace smt {
 
@@ -784,6 +785,10 @@ namespace smt {
         m_context.register_plugin(alloc(smt::theory_char, m_context));        
     }
 
+    void setup::setup_finite_set() {
+        m_context.register_plugin(alloc(smt::theory_finite_set, m_context));
+    }
+
     void setup::setup_special_relations() {
         m_context.register_plugin(alloc(smt::theory_special_relations, m_context, m_manager));
     }
@@ -807,6 +812,7 @@ namespace smt {
         setup_dl();
         setup_seq_str(st);
         setup_fpa();
+        setup_finite_set();
         setup_special_relations();
         setup_polymorphism();
         setup_relevancy(st);

src/smt/smt_setup.h

@@ -102,6 +102,7 @@ namespace smt {
         void setup_seq_str(static_features const & st);
         void setup_seq();
         void setup_char();
+        void setup_finite_set();
         void setup_card();
         void setup_sls();
         void setup_i_arith();

src/smt/theory_finite_set.cpp

@@ -0,0 +1,209 @@
+/*++
+Copyright (c) 2025 Microsoft Corporation
+
+Module Name:
+
+    theory_finite_set.cpp
+
+Abstract:
+
+    Theory solver for finite sets.
+    Implements axiom schemas for finite set operations.
+
+Author:
+
+    GitHub Copilot Agent 2025
+
+Revision History:
+
+--*/
+
+#include "smt/theory_finite_set.h"
+#include "smt/smt_context.h"
+#include "smt/smt_model_generator.h"
+#include "ast/ast_pp.h"
+
+namespace smt {
+
+    theory_finite_set::theory_finite_set(context& ctx):
+        theory(ctx, ctx.get_manager().mk_family_id("finite_set")),
+        u(m),
+        m_axioms(m)
+    {
+        // Setup the add_clause callback for axioms
+        std::function<void(expr_ref_vector const &)> add_clause_fn = 
+            [this](expr_ref_vector const& clause) {
+                this->m_lemmas.push_back(clause);
+            };
+        m_axioms.set_add_clause(add_clause_fn);
+    }
+
+    bool theory_finite_set::internalize_atom(app * atom, bool gate_ctx) {
+        TRACE("finite_set", tout << "internalize_atom: " << mk_pp(atom, m) << "\n";);
+
+        internalize_term(atom);
+        
+        // Track membership elements (set.in)
+        expr* elem = nullptr, *set = nullptr;
+        if (u.is_in(atom, elem, set)) {
+            auto n = ctx.get_enode(elem);
+            if (!m_elements.contains(n)) {
+                m_elements.insert(n);
+                ctx.push_trail(insert_obj_trail(n));
+            }
+        }
+        
+        return true;
+    }
+
+    bool theory_finite_set::internalize_term(app * term) {
+        TRACE("finite_set", tout << "internalize_term: " << mk_pp(term, m) << "\n";);
+        
+        // Internalize all arguments first
+        for (expr* arg : *term) 
+            ctx.internalize(arg, false);
+        
+        // Create boolean variable for Boolean terms
+        if (m.is_bool(term) && !ctx.b_internalized(term)) {
+            bool_var bv = ctx.mk_bool_var(term);
+            ctx.set_var_theory(bv, get_id());
+        }
+        
+        // Create enode for the term if needed
+        enode* e = nullptr;
+        if (ctx.e_internalized(term)) 
+            e = ctx.get_enode(term);         
+        else 
+            e = ctx.mk_enode(term, false, m.is_bool(term), true);        
+        
+        // Attach theory variable if this is a set
+        if (!is_attached_to_var(e))             
+            ctx.attach_th_var(e, this, mk_var(e));
+                
+        return true;
+    }
+
+    void theory_finite_set::new_eq_eh(theory_var v1, theory_var v2) {
+        TRACE("finite_set", tout << "new_eq_eh: v" << v1 << " = v" << v2 << "\n";);
+        // When two sets are equal, propagate membership constraints
+        // This is handled by congruence closure, so no additional work needed here
+    }
+
+    void theory_finite_set::new_diseq_eh(theory_var v1, theory_var v2) {
+        TRACE("finite_set", tout << "new_diseq_eh: v" << v1 << " != v" << v2 << "\n";);
+        // Disequalities could trigger extensionality axioms
+        // For now, we rely on the final_check to handle this
+    }
+
+    final_check_status theory_finite_set::final_check_eh() {
+        TRACE("finite_set", tout << "final_check_eh\n";);
+
+        // walk all parents of elem in congruence table.
+        // if a parent is of the form elem' in S u T, or similar.
+        // create clauses for elem in S u T.
+
+        expr* elem1 = nullptr, *set1 = nullptr;
+        m_lemmas.reset();
+        for (auto elem : m_elements) {
+            for (auto p : enode::parents(elem)) {
+                if (!u.is_in(p->get_expr(), elem1, set1)) 
+                    continue;
+                if (elem->get_root() != p->get_arg(0)->get_root())                    
+                    continue; // elem is then equal to set1 but not elem1. This is a different case.
+                for (auto sib : *p->get_arg(1))
+                    instantiate_axioms(elem->get_expr(), sib->get_expr());
+            }
+        }
+        if (instantiate_false_lemma())
+            return FC_CONTINUE;
+        if (instantiate_unit_propagation())
+            return FC_CONTINUE;
+        if (instantiate_free_lemma())
+            return FC_CONTINUE;
+        
+        return FC_DONE;
+    }
+
+    void theory_finite_set::instantiate_axioms(expr* elem, expr* set) {
+        TRACE("finite_set", tout << "instantiate_axioms: " << mk_pp(elem, m) << " in " << mk_pp(set, m) << "\n";);
+        
+        // Instantiate appropriate axiom based on set structure
+        if (u.is_empty(set)) {
+            m_axioms.in_empty_axiom(elem);
+        }
+        else if (u.is_singleton(set)) {
+            m_axioms.in_singleton_axiom(elem, set);
+        }
+        else if (u.is_union(set)) {
+            m_axioms.in_union_axiom(elem, set);
+        }
+        else if (u.is_intersect(set)) {
+            m_axioms.in_intersect_axiom(elem, set);
+        }
+        else if (u.is_difference(set)) {
+            m_axioms.in_difference_axiom(elem, set);
+        }
+        else if (u.is_range(set)) {
+            m_axioms.in_range_axiom(elem, set);
+        }
+        else if (u.is_map(set)) {
+            m_axioms.in_map_axiom(elem, set);
+            m_axioms.in_map_image_axiom(elem, set);
+        }
+        else if (u.is_select(set)) {
+            m_axioms.in_select_axiom(elem, set);
+        }
+        
+        // Instantiate size axioms for singleton sets
+        // TODO, such axioms don't belong here
+        if (u.is_singleton(set)) {
+            m_axioms.size_singleton_axiom(set);
+        }
+    }
+
+    void theory_finite_set::add_clause(expr_ref_vector const& clause) {
+        TRACE("finite_set", 
+            tout << "add_clause: " << clause << "\n");
+        
+        // Convert expressions to literals and assert the clause
+        literal_vector lits;
+        for (expr* e : clause) {
+            ctx.internalize(e, false);
+            literal lit = ctx.get_literal(lit_expr);
+            lits.push_back(lit);
+        }
+        
+        if (!lits.empty()) {
+            scoped_trace_stream _sts(*this, lits);
+            ctx.mk_th_axiom(get_id(), lits);
+        }
+    }
+
+    theory * theory_finite_set::mk_fresh(context * new_ctx) {
+        return alloc(theory_finite_set, *new_ctx);
+    }
+
+    void theory_finite_set::display(std::ostream & out) const {
+        out << "theory_finite_set:\n";
+    }
+
+    void theory_finite_set::init_model(model_generator & mg) {
+        TRACE("finite_set", tout << "init_model\n";);
+        // Model generation will use default interpretation for sets
+        // The model will be constructed based on the membership literals that are true
+    }
+
+    model_value_proc * theory_finite_set::mk_value(enode * n, model_generator & mg) {
+        TRACE("finite_set", tout << "mk_value: " << mk_pp(n->get_expr(), m) << "\n";);
+        
+        // For now, return nullptr to use default model construction
+        // A complete implementation would construct explicit set values
+        // based on true membership literals
+        return nullptr;
+    }
+
+    void theory_finite_set::instantiate_false_lemma() {}
+    void theory_finite_set::instantiate_unit_propagation() {}
+    void theory_finite_set::instantiate_free_lemma() {}
+
+}  // namespace smt

src/smt/theory_finite_set.h

@@ -86,13 +86,42 @@ theory_finite_set.cpp.
 
 #include "ast/ast.h"
 #include "ast/ast_pp.h"
+#include "ast/finite_set_decl_plugin.h"
+#include "ast/rewriter/finite_set_axioms.h"
 #include "smt/smt_theory.h"
 
 namespace smt {
     class theory_finite_set : public theory {
+        friend class theory_finite_set_test;
+        finite_set_util           u;
+        finite_set_axioms         m_axioms;
+        obj_hashtable<enode>      m_elements;             // set of all 'x' where there is an 'x in S' atom
+        vector<expr_ref_vector>   m_lemmas;
+        
+    protected:
+        // Override relevant methods from smt::theory
+        bool internalize_atom(app * atom, bool gate_ctx) override;
+        bool internalize_term(app * term) override;
+        void new_eq_eh(theory_var v1, theory_var v2) override;
+        void new_diseq_eh(theory_var v1, theory_var v2) override;
+        final_check_status final_check_eh() override;
+        
+        theory * mk_fresh(context * new_ctx) override;
+        char const * get_name() const override { return "finite_set"; }
+        void display(std::ostream & out) const override;
+        void init_model(model_generator & mg) override;
+        model_value_proc * mk_value(enode * n, model_generator & mg) override;
+
+        // Helper methods for axiom instantiation
+        void instantiate_axioms(expr* elem, expr* set);
+        void add_clause(expr_ref_vector const& clause);
+        void instantiate_false_lemma();
+        void instantiate_unit_propagation();
+        void instantiate_free_lemma();
+        
     public:
-        theory_finite_set(ast_manager & m);
+        theory_finite_set(context& ctx);
         ~theory_finite_set() override {}
     };
 
-}  // namespace smt 
+}  // namespace smt