Computing missing coeff for assign-bounds lemma

src/muz/spacer/spacer_proof_utils.cpp

@@ -73,6 +73,129 @@ namespace spacer {
 
 
 
+    class linear_combinator {
+        struct scaled_lit {
+            bool is_pos;
+            app *lit;
+            rational coeff;
+            scaled_lit(bool is_pos, app *lit, const rational &coeff) :
+                is_pos(is_pos), lit(lit), coeff(coeff) {}
+        };
+        ast_manager &m;
+        th_rewriter m_rw;
+        arith_util m_arith;
+        expr_ref m_sum;
+        bool m_is_strict;
+        rational m_lc;
+        vector<scaled_lit> m_lits;
+    public:
+        linear_combinator(ast_manager &m) : m(m), m_rw(m), m_arith(m),
+                                            m_sum(m), m_is_strict(false),
+                                            m_lc(1) {}
+
+        void add_lit(app* lit, rational const &coeff, bool is_pos = true) {
+            m_lits.push_back(scaled_lit(is_pos, lit, coeff));
+        }
+
+        void normalize_coeff() {
+            for (auto &lit : m_lits)
+                m_lc = lcm(m_lc, denominator(lit.coeff));
+            if (!m_lc.is_one()) {
+                for (auto &lit : m_lits)
+                    lit.coeff *= m_lc;
+            }
+        }
+
+        rational const &lc() const {return m_lc;}
+
+        bool process_lit(scaled_lit &lit0) {
+            arith_util a(m);
+            app* lit = lit0.lit;
+            rational &coeff = lit0.coeff;
+            bool is_pos = lit0.is_pos;
+
+
+            if (m.is_not(lit)) {
+                lit = to_app(lit->get_arg(0));
+                is_pos = !is_pos;
+            }
+            if (!m_arith.is_le(lit) && !m_arith.is_lt(lit) &&
+                !m_arith.is_ge(lit) && !m_arith.is_gt(lit) && !m.is_eq(lit)) {
+                return false;
+            }
+            SASSERT(lit->get_num_args() == 2);
+            sort* s = m.get_sort(lit->get_arg(0));
+            bool is_int = m_arith.is_int(s);
+            if (!is_int && m_arith.is_int_expr(lit->get_arg(0))) {
+                is_int = true;
+                s = m_arith.mk_int();
+            }
+
+            if (!is_int && is_pos && (m_arith.is_gt(lit) || m_arith.is_lt(lit))) {
+                m_is_strict = true;
+            }
+            if (!is_int && !is_pos && (m_arith.is_ge(lit) || m_arith.is_le(lit))) {
+                m_is_strict = true;
+            }
+
+
+            SASSERT(m_arith.is_int(s) || m_arith.is_real(s));
+            expr_ref sign1(m), sign2(m), term(m);
+            sign1 = m_arith.mk_numeral(m.is_eq(lit)?coeff:abs(coeff), s);
+            sign2 = m_arith.mk_numeral(m.is_eq(lit)?-coeff:-abs(coeff), s);
+            if (!m_sum.get()) {
+                m_sum = m_arith.mk_numeral(rational(0), s);
+            }
+
+            expr* a0 = lit->get_arg(0);
+            expr* a1 = lit->get_arg(1);
+
+            if (is_pos && (m_arith.is_ge(lit) || m_arith.is_gt(lit))) {
+                std::swap(a0, a1);
+            }
+            if (!is_pos && (m_arith.is_le(lit) || m_arith.is_lt(lit))) {
+                std::swap(a0, a1);
+            }
+
+            //
+            // Multiplying by coefficients over strict
+            // and non-strict inequalities:
+            //
+            // (a <= b) * 2
+            // (a - b <= 0) * 2
+            // (2a - 2b <= 0)
+
+            // (a < b) * 2       <=>
+            // (a +1 <= b) * 2   <=>
+            // 2a + 2 <= 2b      <=>
+            // 2a+2-2b <= 0
+
+            bool strict_ineq =
+                is_pos?(m_arith.is_gt(lit) || m_arith.is_lt(lit)):(m_arith.is_ge(lit) || m_arith.is_le(lit));
+
+            if (is_int && strict_ineq) {
+                m_sum = m_arith.mk_add(m_sum, sign1);
+            }
+
+            term = m_arith.mk_mul(sign1, a0);
+            m_sum = m_arith.mk_add(m_sum, term);
+            term = m_arith.mk_mul(sign2, a1);
+            m_sum = m_arith.mk_add(m_sum, term);
+
+            m_rw(m_sum);
+            return true;
+        }
+
+        expr_ref operator()(){
+            if (!m_sum) normalize_coeff();
+            m_sum.reset();
+            for (auto &lit : m_lits) {
+                if (!process_lit(lit)) return expr_ref(m);
+            }
+            return m_sum;
+        }
+    };
+
 /*
  * ====================================
  * methods for transforming proofs
@@ -101,6 +224,60 @@ namespace spacer {
         return pf;
     }
 
+    static bool match_mul(expr *e, expr_ref &var, expr_ref &val, arith_util &a) {
+        expr *e1 = nullptr, *e2 = nullptr;
+        if (!a.is_mul(e, e1, e2)) {
+            if (a.is_numeral(e)) return false;
+            if (!var || var == e) {
+                var = e;
+                val = a.mk_numeral(rational(1), get_sort(e));
+                return true;
+            }
+            return false;
+        }
+
+        if (!a.is_numeral(e1)) std::swap(e1, e2);
+        if (!a.is_numeral(e1)) return false;
+
+        // if variable is given, match it as well
+        if (!var || var == e2) {
+            var = e2;
+            val = e1;
+            return true;
+        }
+        return false;
+    }
+
+    static expr_ref get_coeff(expr *lit0, expr_ref &var) {
+        ast_manager &m = var.m();
+        arith_util a(m);
+
+        expr *lit = nullptr;
+        if (!m.is_not(lit0, lit)) lit = lit0;
+
+        expr *e1 = nullptr, *e2 = nullptr;
+        // assume e2 is numeral and ignore it
+        if ((a.is_le(lit, e1, e2) || a.is_lt(lit, e1, e2) ||
+               a.is_ge(lit, e1, e2) || a.is_gt(lit, e1, e2) ||
+               m.is_eq(lit, e1, e2))) {
+            if (a.is_numeral(e1)) std::swap(e1, e2);
+        }
+        else {
+            e1 = lit;
+        }
+
+        expr_ref val(m);
+        if (!a.is_add(e1))  {
+            if (match_mul(e1, var, val, a)) return val;
+        }
+        else {
+            for (auto *arg : *to_app(e1)) {
+                if (match_mul(arg, var, val, a)) return val;
+            }
+        }
+        return expr_ref(m);
+    }
+
     // convert assign-bounds lemma to a farkas lemma by adding missing coeff
     // assume that missing coeff is for premise at position 0
     static proof_ref mk_fk_from_ab(ast_manager &m,
@@ -108,9 +285,44 @@ namespace spacer {
                                    unsigned num_params,
                                    parameter const *params) {
         SASSERT(num_params == parents.size() + 1 /* one param is missing */);
+
+        // compute missing coefficient
+        linear_combinator lcb(m);
+        for (unsigned i = 1, sz = parents.size(); i < sz; ++i) {
+            app *p = to_app(m.get_fact(parents.get(i)));
+            rational const &r = params[i+1].get_rational();
+            lcb.add_lit(p, r);
+        }
+
+        TRACE("spacer.fkab",
+              tout << "lit0 is: " << mk_pp(m.get_fact(parents.get(0)), m) << "\n"
+              << "LCB is: " << lcb() << "\n";);
+
+        expr_ref var(m), val1(m), val2(m);
+        val1 = get_coeff(m.get_fact(parents.get(0)), var);
+        val2 = get_coeff(lcb(), var);
+        TRACE("spacer.fkab",
+              tout << "var: " << var
+              << " val1: " << val1 << " val2: "  << val2 << "\n";);
+
+        rational rat1, rat2, coeff0;
+        arith_util a(m);
+        if (a.is_numeral(val1, rat1) && a.is_numeral(val2, rat2)) {
+            coeff0 = abs(rat2/rat1);
+            coeff0 = coeff0 / lcb.lc();
+            TRACE("spacer.fkab", tout << "coeff0: " << coeff0 << "\n";);
+        }
+        else {
+            IF_VERBOSE(1, verbose_stream()
+                       << "\n\n\nFAILED TO FIND COEFFICIENT\n\n\n";);
+            // failed to find a coefficient
+            return proof_ref(m);
+        }
+
+
         buffer<parameter> v;
         v.push_back(parameter(symbol("farkas")));
-        v.push_back(parameter(rational(1)));
+        v.push_back(parameter(coeff0));
         for (unsigned i = 2; i < num_params; ++i)
             v.push_back(params[i]);
 
@@ -124,11 +336,11 @@ namespace spacer {
                            v.size(), v.c_ptr());
 
         SASSERT(is_arith_lemma(m, pf));
+
         DEBUG_CODE(
             proof_checker pc(m);
             expr_ref_vector side(m);
-            SASSERT(pc.check(pf, side));
+            ENSURE(pc.check(pf, side)););
-            );
         return pf;
 
     }
@@ -179,7 +391,9 @@ namespace spacer {
                                              d->get_num_parameters(),
                                              d->get_parameters());
                 }
-                else {
+
+                // fall back to th-lemma
+                if (!th_lemma) {
                     th_lemma = mk_th_lemma(m, hyps,
                                            d->get_num_parameters(),
                                            d->get_parameters());