fill in missing pieces of proof hint checker for Farkas and RUP

The proof validator based on SMT format proof logs uses RUP to check propositional inferences and has plugins for theory axioms/lemmas.

src/cmd_context/extra_cmds/proof_cmds.cpp

@@ -15,28 +15,51 @@ Author:
 
 Notes:
 
-- add theory hint bypass using proof checker plugins of SMT
-  - arith_proof_checker.h is currently
-- could use m_drat for drup premises.
+Proof checker for clauses created during search.
+1. Clauses annotated by RUP (reverse unit propagation)
+   are checked to be inferrable using reverse unit propagation
+   based on previous clauses.
+2. Clauses annotated by supported proof rules (proof hints)
+   are checked by custom proof checkers. There is a proof checker
+   for each proof rule. Main proof checkers just have a single step
+   but the framework allows to compose proof rules, each inference
+   is checked for correctness by a plugin. 
+3. When there are no supported plugin to justify the derived
+   clause, or a custom check fails, the fallback is to check that the
+   derived clause is a consequence of the input clauses using SMT.
+   The last approach is a bail-out and offers a weaker notion of
+   self-validation. It is often (but not always) sufficient for using proof
+   checking for debugging, as the root-cause for an unsound inference in z3
+   does not necessarily manifest when checking the conclusion of the
+   inference. An external proof checker that uses such fallbacks could
+   use several solvers, or bootstrap from a solver that can generate certificates
+   when z3 does not.
+   
+
+
 
 --*/
 
 #include "util/small_object_allocator.h"
 #include "ast/ast_util.h"
-#include "cmd_context/cmd_context.h"
 #include "smt/smt_solver.h"
 #include "sat/sat_solver.h"
 #include "sat/sat_drat.h"
 #include "sat/smt/euf_proof_checker.h"
+#include "cmd_context/cmd_context.h"
 #include <iostream>
 
 class smt_checker {
     ast_manager& m;
     params_ref   m_params;
+
+    // for checking proof rules (hints)
     euf::proof_checker m_checker;
 
+    // for fallback SMT checker
     scoped_ptr<solver> m_solver;
 
+    // for RUP
     symbol       m_rup;
     sat::solver  m_sat_solver;
     sat::drat    m_drat;
@@ -63,11 +86,10 @@ public:
         m_rup = symbol("rup");
     }
 
-    bool is_rup(expr* proof_hint) {
+    bool is_rup(app* proof_hint) {
         return
             proof_hint &&
-            is_app(proof_hint) &&
-            to_app(proof_hint)->get_name() == m_rup;        
+            proof_hint->get_name() == m_rup;        
     }
 
     void mk_clause(expr_ref_vector const& clause) {
@@ -79,6 +101,14 @@ public:
             m_clause.push_back(sat::literal(e->get_id(), sign));
         }
     }
+
+    void mk_clause(expr* e) {
+        m_clause.reset();
+        bool sign = false;
+        while (m.is_not(e, e))
+            sign = !sign;
+        m_clause.push_back(sat::literal(e->get_id(), sign));
+    }
     
     bool check_rup(expr_ref_vector const& clause) {
         add_units();
@@ -86,25 +116,38 @@ public:
         return m_drat.is_drup(m_clause.size(), m_clause.data(), m_units);
     }
 
+    bool check_rup(expr* u) {
+        add_units();
+        mk_clause(u);
+        return m_drat.is_drup(m_clause.size(), m_clause.data(), m_units);
+    }
+
     void add_clause(expr_ref_vector const& clause) {
         mk_clause(clause);
         m_drat.add(m_clause, sat::status::input());
     }
 
-    void check(expr_ref_vector const& clause, expr* proof_hint) {
-
-
+    void check(expr_ref_vector& clause, app* proof_hint) {
+        
         if (is_rup(proof_hint) && check_rup(clause)) {
             std::cout << "(verified-rup)\n";
             return;
         }
 
-        if (m_checker.check(clause, proof_hint)) {
-            if (is_app(proof_hint))
-                std::cout << "(verified-" << to_app(proof_hint)->get_name() << ")\n";
-            else
-                std::cout << "(verified-checker)\n";
-            return;
+        expr_ref_vector units(m);
+        if (m_checker.check(clause, proof_hint, units)) {
+            bool units_are_rup = true;
+            for (expr* u : units) {
+                if (!check_rup(u)) {
+                    std::cout << "unit " << mk_pp(u, m) << " is not rup\n";
+                    units_are_rup = false;
+                }
+            }
+            if (units_are_rup) {
+                std::cout << "(verified-" << proof_hint->get_name() << ")\n";
+                add_clause(clause);
+                return;
+            }
         }
 
         m_solver->push();
@@ -123,7 +166,7 @@ public:
         }
         m_solver->pop(1);
         std::cout << "(verified-smt)\n";
-        // assume(clause);
+        add_clause(clause);
     }
 
     void assume(expr_ref_vector const& clause) {
@@ -135,14 +178,14 @@ public:
 class proof_cmds_imp : public proof_cmds {
     ast_manager&    m;
     expr_ref_vector m_lits;
-    expr_ref        m_proof_hint;
+    app_ref         m_proof_hint;
     smt_checker     m_checker;
 public:
     proof_cmds_imp(ast_manager& m): m(m), m_lits(m), m_proof_hint(m), m_checker(m) {}
 
     void add_literal(expr* e) override {
         if (m.is_proof(e))
-            m_proof_hint = e;
+            m_proof_hint = to_app(e);
         else
             m_lits.push_back(e);
     }

src/sat/sat_drat.cpp

@@ -416,6 +416,8 @@ namespace sat {
     void drat::verify(unsigned n, literal const* c) {
         if (!m_check_unsat) 
             return;
+        if (m_inconsistent)
+            return;
         for (unsigned i = 0; i < n; ++i) 
             declare(c[i]);
         if (is_drup(n, c)) {
@@ -690,7 +692,7 @@ namespace sat {
             ++m_stats.m_num_add;
         if (m_check) {
             switch (sz) {
-            case 0: add(); break;
+            case 0: if (st.is_input()) m_inconsistent = true; else add(); break;
             case 1: append(lits[0], st); break;
             default: append(mk_clause(sz, lits, st.is_redundant()), st); break;
             }

src/sat/smt/arith_proof_checker.h

@@ -140,11 +140,13 @@ namespace arith {
             SASSERT(m_todo.empty());
             m_todo.push_back({ mul, e });
             rational coeff1;
-            expr* e1, *e2;
+            expr* e1, *e2, *e3;
             for (unsigned i = 0; i < m_todo.size(); ++i) {
                 auto [coeff, e] = m_todo[i];
                 if (a.is_mul(e, e1, e2) && a.is_numeral(e1, coeff1))
                     m_todo.push_back({coeff*coeff1, e2});
+                else if (a.is_mul(e, e1, e2) && a.is_uminus(e1, e3) && a.is_numeral(e3, coeff1))
+                    m_todo.push_back({-coeff*coeff1, e2});
                 else if (a.is_mul(e, e1, e2) && a.is_numeral(e2, coeff1))
                     m_todo.push_back({coeff*coeff1, e1});
                 else if (a.is_add(e))
@@ -158,6 +160,8 @@ namespace arith {
                 }
                 else if (a.is_numeral(e, coeff1)) 
                     r.m_coeff += coeff*coeff1;
+                else if (a.is_uminus(e, e1) && a.is_numeral(e1, coeff1))
+                    r.m_coeff -= coeff*coeff1;
                 else
                     add(r, e, coeff);
             }
@@ -361,8 +365,14 @@ namespace arith {
             return out;
         }
 
-        bool check(expr_ref_vector const& clause, app* jst) override {
+        bool check(expr_ref_vector const& clause, app* jst, expr_ref_vector& units) override {
             reset();
+            expr_mark pos, neg;
+            for (expr* e : clause)
+                if (m.is_not(e, e))
+                    neg.mark(e, true);
+                else
+                    pos.mark(e, true);
 
             if (jst->get_name() == symbol("farkas")) {
                 bool even = true;
@@ -387,13 +397,24 @@ namespace arith {
                         }
                         else
                             return false;
+
+                        if (sign && !pos.is_marked(arg)) {
+                            units.push_back(m.mk_not(arg));
+                            pos.mark(arg, false);
+                        }
+                        else if (!sign && !neg.is_marked(arg)) {
+                            units.push_back(arg);
+                            neg.mark(arg, false);
+                        }
+                            
                     }                        
                     even = !even;
                 }
-                if (check_farkas())
+                if (check_farkas()) {
                     return true;
+                }
                 
-                IF_VERBOSE(0, verbose_stream() << "did not check farkas\n" << mk_pp(jst, m) << "\n");
+                IF_VERBOSE(0, verbose_stream() << "did not check farkas\n" << mk_pp(jst, m) << "\n"; display(verbose_stream()); );
                 return false;
             }
 

src/sat/smt/euf_proof_checker.cpp

@@ -35,13 +35,14 @@ namespace euf {
         m_map.insert(rule, p);
     }
 
-    bool proof_checker::check(expr_ref_vector const& clause, expr* e) {
+    bool proof_checker::check(expr_ref_vector const& clause, expr* e, expr_ref_vector& units) {
         if (!e || !is_app(e))
             return false;
+        units.reset();
         app* a = to_app(e);
         proof_checker_plugin* p = nullptr;
         if (m_map.find(a->get_decl()->get_name(), p)) 
-            return p->check(clause, a);
+            return p->check(clause, a, units);
         return false;
     }
 

src/sat/smt/euf_proof_checker.h

@@ -27,7 +27,7 @@ namespace euf {
     class proof_checker_plugin {
     public:
         virtual ~proof_checker_plugin() {}
-        virtual bool check(expr_ref_vector const& clause, app* jst) = 0;        
+        virtual bool check(expr_ref_vector const& clause, app* jst, expr_ref_vector& units) = 0;        
         virtual void register_plugins(proof_checker& pc) = 0;
     };
 
@@ -39,7 +39,7 @@ namespace euf {
         proof_checker(ast_manager& m);
         ~proof_checker();
         void register_plugin(symbol const& rule, proof_checker_plugin*);
-        bool check(expr_ref_vector const& clause, expr* e);
+        bool check(expr_ref_vector const& clause, expr* e, expr_ref_vector& units);
     };
 
 }

src/smt/smt_model_checker.cpp

@@ -255,9 +255,8 @@ namespace smt {
                     return false;                    
                 ptr_vector<sort> sorts(f->get_arity(), f->get_domain());
                 svector<symbol> names;
-                for (unsigned i = 0; i < f->get_arity(); ++i) {
+                for (unsigned i = 0; i < f->get_arity(); ++i) 
                     names.push_back(symbol(i));
-                }
                 defined_names dn(m);
                 body = replace_value_from_ctx(body);
                 body = m.mk_lambda(sorts.size(), sorts.data(), names.data(), body);
@@ -575,16 +574,16 @@ namespace smt {
                     for (unsigned i = 0; i < n; ++i) {
                         proof* pr = nullptr;
                         expr* arg = args[i];
-                        if (m.proofs_enabled()) {
+                        if (m.proofs_enabled()) 
                             pr = m.mk_def_intro(arg);
-                        }
                         m_context->internalize_assertion(arg, pr, gen);
                     }
                 }
 
                 TRACE("model_checker_bug_detail", tout << "instantiating... q:\n" << mk_pp(q, m) << "\n";
                       tout << "inconsistent: " << m_context->inconsistent() << "\n";
-                      tout << "bindings:\n" << expr_ref_vector(m, num_decls, m_pinned_exprs.data() + offset) << "\n";);
+                      tout << "bindings:\n" << expr_ref_vector(m, num_decls, m_pinned_exprs.data() + offset) << "\n";
+                      tout << "def " << mk_pp(inst.m_def, m) << "\n";);
                 m_context->add_instance(q, nullptr, num_decls, bindings.data(), inst.m_def, gen, gen, gen, dummy);
                 TRACE("model_checker_bug_detail", tout << "after instantiating, inconsistent: " << m_context->inconsistent() << "\n";);
             }