add facility to solve for a linear term over API

src/api/api_solver.cpp

@@ -967,6 +967,20 @@ extern "C" {
         Z3_CATCH_RETURN(nullptr);
     }
 
+    Z3_ast Z3_API Z3_solver_solve_for(Z3_context c, Z3_solver s, Z3_ast a) {
+        Z3_TRY;
+        LOG_Z3_solver_solve_for(c, s, a);
+        RESET_ERROR_CODE();
+        init_solver(c, s);
+        ast_manager& m = mk_c(c)->m();        
+        expr_ref term(m);
+        if (!to_solver_ref(s)->solve_for(to_expr(a), term)) 
+            term = to_expr(a);
+        mk_c(c)->save_ast_trail(term.get());
+        RETURN_Z3(of_expr(term.get()));
+        Z3_CATCH_RETURN(nullptr);
+    }
+
     class api_context_obj : public user_propagator::context_obj {
         api::context* c;
     public:

src/api/python/z3/z3.py

@@ -7351,6 +7351,12 @@ class Solver(Z3PPObject):
         """
         return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
 
+    def solve_for(self, t):
+        t = _py2expr(t, self.ctx)
+        """Retrieve a solution for t relative to linear equations maintained in the current state.
+        The function primarily works for SimpleSolver and when there is a solution using linear arithmetic."""
+        return _to_expr_ref(Z3_solver_solve_for(self.ctx.ref(), self.solver, t.ast), self.ctx)
+
     def proof(self):
         """Return a proof for the last `check()`. Proof construction must be enabled."""
         return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)

src/api/z3_api.h

@@ -7077,6 +7077,14 @@ extern "C" {
     Z3_ast Z3_API Z3_solver_congruence_next(Z3_context c, Z3_solver s, Z3_ast a);
 
 
+    /**
+       \brief retrieve a 'solution' for \c t as defined by equalities in maintained by solvers.
+       At this point, only linear solution are supported.
+
+       def_API('Z3_solver_solve_for', AST, (_in(CONTEXT), _in(SOLVER), _in(AST)))
+    */
+    Z3_ast Z3_API Z3_solver_solve_for(Z3_context c, Z3_solver s, Z3_ast t);
+    
     /**
        \brief register a callback to that retrieves assumed, inferred and deleted clauses during search.
        

src/math/lp/lar_solver.cpp

@@ -617,6 +617,34 @@ namespace lp {
             m_touched_rows.insert(rid);
     }
 
+    bool lar_solver::solve_for(unsigned j, lar_term& t, mpq& coeff) {
+        t.clear();        
+        if (column_is_fixed(j)) {
+            coeff = get_value(j);
+            return true;
+        }
+        if (!is_base(j)) {
+            for (const auto & c : A_r().m_columns[j]) {
+                lpvar basic_in_row = r_basis()[c.var()];
+                pivot(j, basic_in_row);
+                break;
+            }
+        }
+        if (!is_base(j))
+            return false;
+        auto const& r = basic2row(j);
+        for (auto const& c : r) {
+            if (c.var() == j)
+                continue;
+            if (column_is_fixed(c.var()))
+                coeff -= get_value(c.var());
+            else
+                t.add_monomial(-c.coeff(), c.var());
+        }
+        return true;
+    }
+
+
     void lar_solver::remove_fixed_vars_from_base() {
         // this will allow to disable and restore the tracking of the touched rows
         flet<indexed_uint_set*> f(m_mpq_lar_core_solver.m_r_solver.m_touched_rows, nullptr);

src/math/lp/lar_solver.h

@@ -346,6 +346,12 @@ public:
     void set_value_for_nbasic_column(unsigned j, const impq& new_val);
 
     void remove_fixed_vars_from_base();
+    /**
+     * \brief set j to basic (if not already basic)
+     * return the rest of the row as t comprising of non-fixed variables and coeff as sum of fixed variables.
+     * return false if j has no rows.
+     */
+    bool solve_for(unsigned j, lar_term& t, mpq& coeff);
 
     inline unsigned get_base_column_in_row(unsigned row_index) const {
         return m_mpq_lar_core_solver.m_r_solver.get_base_column_in_row(row_index);

src/smt/smt_context.cpp

@@ -4654,6 +4654,15 @@ namespace smt {
             return false;
         return th->get_value(n, value);
     }
+    
+    bool context::solve_for(enode * n, expr_ref & term) {
+        sort * s      = n->get_sort();
+        family_id fid = s->get_family_id();
+        theory * th   = get_theory(fid);
+        if (th == nullptr)
+            return false;
+        return th->solve_for(n, term);
+    }    
 
     bool context::update_model(bool refinalize) {
         final_check_status fcs = FC_DONE;

src/smt/smt_context.h

@@ -1375,11 +1375,6 @@ namespace smt {
         bool can_propagate() const;
 
 
-        // Retrieve arithmetic values. 
-        bool get_arith_lo(expr* e, rational& lo, bool& strict);
-        bool get_arith_up(expr* e, rational& up, bool& strict);
-        bool get_arith_value(expr* e, rational& value);
-
         // -----------------------------------
         //
         // Model checking... (must be improved)
@@ -1388,6 +1383,8 @@ namespace smt {
     public:
         bool get_value(enode * n, expr_ref & value);
 
+        bool solve_for(enode* n, expr_ref& term);
+
         // -----------------------------------
         //
         // Pretty Printing

src/smt/smt_kernel.cpp

@@ -213,8 +213,15 @@ namespace smt {
         return out;
     }
 
+    bool kernel::solve_for(expr* e, expr_ref& term) {
+        smt::enode* n = m_imp->m_kernel.find_enode(e);        
+        if (!n)
+            return false;
+        return m_imp->m_kernel.solve_for(n, term);        
+    }
+
     expr* kernel::congruence_root(expr * e) {
-        smt::enode* n = m_imp->m_kernel.find_enode(e);
+        smt::enode* n = m_imp->m_kernel.find_enode(e);        
         if (!n)
             return e;
         return n->get_root()->get_expr();

src/smt/smt_kernel.h

@@ -246,6 +246,7 @@ namespace smt {
 
         expr* congruence_root(expr* e);
 
+        bool solve_for(expr* e, expr_ref& term);
 
         /**
            \brief retrieve depth of variables from decision stack.

src/smt/smt_solver.cpp

@@ -337,6 +337,7 @@ namespace {
 
         expr* congruence_next(expr* e) override { return m_context.congruence_next(e); }
         expr* congruence_root(expr* e) override { return m_context.congruence_root(e); }
+        bool  solve_for(expr* e, expr_ref& term) override { return m_context.solve_for(e, term); }
 
 
         expr_ref_vector cube(expr_ref_vector& vars, unsigned cutoff) override {

src/smt/smt_theory.h

@@ -605,6 +605,8 @@ namespace smt {
 
         virtual char const * get_name() const { return "unknown"; }
 
+        virtual bool solve_for(enode* n, expr_ref& r) { return false; }
+
         // -----------------------------------
         //
         // Return a fresh new instance of the given theory.

src/smt/theory_lra.cpp

@@ -3627,7 +3627,21 @@ public:
         lpvar vi = get_lpvar(v);
         u_dependency* dep = nullptr;
         return lp().has_upper_bound(vi, dep, val, is_strict);
+    }
 
+    bool solve_for(enode* n, expr_ref& term) {
+        theory_var v = n->get_th_var(get_id());
+        if (!is_registered_var(v))
+            return false;
+        lpvar vi = get_lpvar(v);
+        lp::lar_term t;
+        rational coeff;
+        if (!lp().solve_for(vi, t, coeff))
+            return false;
+        term = mk_term(t, is_int(v));
+        if (coeff != 0)
+            term = a.mk_add(a.mk_numeral(coeff, is_int(v)), term);
+        return true;
     }
 
     bool get_upper(enode* n, expr_ref& r) {
@@ -4140,6 +4154,10 @@ bool theory_lra::get_lower(enode* n, rational& r, bool& is_strict) {
 bool theory_lra::get_upper(enode* n, rational& r, bool& is_strict) {
     return m_imp->get_upper(n, r, is_strict);
 }
+bool theory_lra::solve_for(enode* n, expr_ref& r) {
+    return m_imp->solve_for(n, r);
+}
+
 void theory_lra::display(std::ostream & out) const {
     m_imp->display(out);
 }

src/smt/theory_lra.h

@@ -93,6 +93,7 @@ namespace smt {
         bool get_upper(enode* n, expr_ref& r);
         bool get_lower(enode* n, rational& r, bool& is_strict);
         bool get_upper(enode* n, rational& r, bool& is_strict);
+        bool solve_for(enode* n, expr_ref& r) override;
                 
         void display(std::ostream & out) const override;
         

src/solver/solver.h

@@ -248,6 +248,11 @@ public:
     */
     virtual expr* congruence_next(expr* e) = 0;
 
+    /**
+       \brief try to solve for term e (when e is arithmetical).
+    */
+    virtual bool solve_for(expr* e, expr_ref& term) { return false; }
+
     /**
        \brief Display the content of this solver.
     */