files to make build easier

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/smt/smt_induction.cpp

@@ -0,0 +1,368 @@
+/*++
+  Copyright (c) 2020 Microsoft Corporation
+
+  Module Name:
+
+   smt_induction.cpp
+
+  Abstract:
+   
+   Add induction lemmas to context.
+
+  Author:
+
+    Nikolaj Bjorner 2020-04-25
+
+  Notes:
+
+  - work in absence of recursive functions but instead presence of quantifiers
+    - relax current requirement of model sweeping when terms don't have value simplifications
+  - k-induction
+    - also to deal with mutually recursive datatypes
+  - beyond literal induction lemmas
+  - refine initialization of values when term is equal to constructor application, 
+      
+--*/
+
+#include "ast/ast_pp.h"
+#include "ast/ast_util.h"
+#include "ast/recfun_decl_plugin.h"
+#include "ast/datatype_decl_plugin.h"
+#include "ast/arith_decl_plugin.h"
+#include "ast/rewriter/value_sweep.h"
+#include "ast/rewriter/expr_safe_replace.h"
+#include "smt/smt_context.h"
+#include "smt/smt_induction.h"
+
+using namespace smt;
+
+/**
+ * collect literals that are assigned to true, 
+ * but evaluate to false under all extensions of 
+ * the congruence closure.
+ */
+
+literal_vector collect_induction_literals::pre_select() {
+    literal_vector result;
+    for (unsigned i = m_literal_index; i < ctx.assigned_literals().size(); ++i) {
+        literal lit = ctx.assigned_literals()[i];
+        smt::bool_var v = lit.var();            
+        if (!ctx.has_enode(v)) {                
+            continue;
+        }
+        expr* e = ctx.bool_var2expr(v);
+        if (!lit.sign() && m.is_eq(e))
+            continue;
+        result.push_back(lit);
+    }
+    ctx.push_trail(value_trail<context, unsigned>(m_literal_index));
+    m_literal_index = ctx.assigned_literals().size();
+    return result;
+}
+
+void collect_induction_literals::model_sweep_filter(literal_vector& candidates) {
+    expr_ref_vector terms(m);
+    for (literal lit : candidates) {
+        terms.push_back(ctx.bool_var2expr(lit.var()));
+    }
+    vector<expr_ref_vector> values;
+    vs(terms, values);
+    unsigned j = 0;
+    IF_VERBOSE(1, 
+               verbose_stream() << "terms: " << terms << "\n";
+               for (auto const& vec : values) {
+                   verbose_stream() << "assignment: " << vec << "\n";
+               });
+    for (unsigned i = 0; i < terms.size(); ++i) {
+        literal lit = candidates[i];
+        bool is_viable_candidate = true;
+        for (auto const& vec : values) {
+            if (vec[i] && lit.sign() && m.is_true(vec[i]))
+                continue;
+            if (vec[i] && !lit.sign() && m.is_false(vec[i]))
+                continue;
+            is_viable_candidate = false;
+            break;
+        }
+        if (is_viable_candidate)
+            candidates[j++] = lit;
+    }
+    candidates.shrink(j);
+}
+
+
+collect_induction_literals::collect_induction_literals(context& ctx, ast_manager& m, value_sweep& vs):
+    ctx(ctx),
+    m(m),
+    vs(vs),
+    m_literal_index(0)
+{}
+    
+literal_vector collect_induction_literals::operator()() {    
+    literal_vector candidates = pre_select();
+    model_sweep_filter(candidates);
+    return candidates;
+}
+
+
+// --------------------------------------
+// create_induction_lemmas
+
+bool create_induction_lemmas::is_induction_candidate(enode* n) {
+    expr* e = n->get_owner();
+    if (m.is_value(e))
+        return false;
+    // TBD: filter if n is equivalent to a value.
+    sort* s = m.get_sort(e);
+    if (m_dt.is_datatype(s) && m_dt.is_recursive(s))
+        return true;
+
+    // potentially also induction on integers, sequences
+    // m_arith.is_int(s)
+    //  return true;
+    return false;
+}
+
+/**
+ * positions in n that can be used for induction
+ * the positions are distinct roots
+ * and none of the roots are equivalent to a value in the current
+ * congruence closure.
+ */
+enode_vector create_induction_lemmas::induction_positions(enode* n) {
+    enode_vector result;
+    enode_vector todo;
+    auto add_todo = [&](enode* n) { 
+        if (!n->is_marked()) { 
+            n->set_mark(); 
+            todo.push_back(n); 
+        } 
+    };
+    add_todo(n);
+    for (unsigned i = 0; i < todo.size(); ++i) {
+        n = todo[i];
+        for (enode* a : smt::enode::args(n)) 
+            add_todo(a);        
+        if (is_induction_candidate(n)) 
+            result.push_back(n);
+    }
+    for (enode* n : todo)
+        n->unset_mark();
+    return result;
+}
+
+
+/**
+ * abstraction candidates for replacing different occurrence of t in n by x
+ * it returns all possible non-empty subsets of t replaced by x.
+ * 
+ * TBD: add term sharing throttle.
+ * TDD: add depth throttle.
+ */
+void create_induction_lemmas::abstract(enode* n, enode* t, expr* x, abstractions& result) {
+    if (n->get_root() == t->get_root()) {
+        result.push_back(abstraction(m, x, n->get_owner(), t->get_owner()));
+    }
+    abstraction_args r1, r2;
+    r1.push_back(abstraction_arg(m));
+    for (enode* arg : enode::args(n)) {
+        unsigned n = result.size();
+        abstract(arg, t, x, result);
+        for (unsigned i = n; i < result.size(); ++i) {
+            abstraction& a = result[i];
+            for (auto const& v : r1) {
+                r2.push_back(v);
+                r2.back().push_back(a);
+            }
+        }
+        r1.swap(r2);
+        r2.reset();
+        result.shrink(n);
+    }
+    for (auto const& a : r1) {
+        result.push_back(abstraction(m, m.mk_app(n->get_decl(), a.m_terms), a.m_eqs));
+    }
+};
+    
+/**
+ * filter generalizations based on value_generator
+ * If all evaluations are counter-examples, include 
+ * candidate generalization.
+ */
+void create_induction_lemmas::filter_abstractions(bool sign, abstractions& abs) {
+    vector<expr_ref_vector> values;
+    expr_ref_vector fmls(m);
+    for (auto & a : abs) fmls.push_back(a.m_term);
+    vs(fmls, values);
+    unsigned j = 0;
+    for (unsigned i = 0; i < fmls.size(); ++i) {
+        bool all_cex = true;
+        for (auto const& vec : values) {
+            if (vec[i] && (m.is_true(vec[i]) == sign))
+                continue;
+            all_cex = false;
+            break;
+        }
+        if (all_cex) {
+            abs[j++] = abs.get(i);
+        }
+    }
+    abs.shrink(j);
+}
+
+/*
+ * Create simple induction lemmas of the form:
+ *
+ * lit & a.eqs() & is-c(t) => is-c(sk);
+ * lit & a.eqs() => alpha
+ * lit & a.eqs() & is-c(t) => ~beta
+ *
+ * where alpha = a.term()
+ *       beta  = alpha[sk/access_k(sk)]
+ * for each constructor c, that is recursive 
+ * and contains argument of datatype sort s
+ *
+ * TBD: consider k-inductive lemmas.
+ */
+void create_induction_lemmas::create_lemmas(expr* t, expr* sk, abstraction& a, literal lit) {
+    std::cout << "abstraction: " << a.m_term << "\n";
+    sort* s = m.get_sort(sk);
+    if (!m_dt.is_datatype(s))
+        return;
+    family_id fid = s->get_family_id();
+    expr_ref alpha = a.m_term;
+    auto const& eqs = a.m_eqs;
+    literal_vector common_literals; 
+    for (func_decl* c : *m_dt.get_datatype_constructors(s)) {
+        func_decl* is_c = m_dt.get_constructor_recognizer(c);
+        bool has_1recursive = false;
+        for (func_decl* acc : *m_dt.get_constructor_accessors(c)) {
+            if (acc->get_range() != s)
+                continue;
+            if (common_literals.empty()) {
+                common_literals.push_back(~lit);
+                for (auto const& p : eqs) {
+                    common_literals.push_back(~mk_literal(m.mk_eq(p.first, p.second)));
+                }
+            }
+            has_1recursive = true;
+            literal_vector lits(common_literals);
+            lits.push_back(~mk_literal(m.mk_app(is_c, t))); 
+            expr_ref beta(alpha);
+            expr_safe_replace rep(m);
+            rep.insert(sk, m.mk_app(acc, sk));
+            rep(beta);
+            literal b_lit = mk_literal(beta);
+            if (lit.sign()) b_lit.neg();
+            lits.push_back(~b_lit);
+            add_th_lemma(lits);               
+        }
+        if (has_1recursive) {
+            literal_vector lits(common_literals);
+            lits.push_back(~mk_literal(m.mk_app(is_c, t)));
+            lits.push_back(mk_literal(m.mk_app(is_c, sk)));
+            add_th_lemma(lits);
+        }
+    }
+    if (!common_literals.empty()) {
+        literal_vector lits(common_literals);
+        literal a_lit = mk_literal(alpha);
+        if (lit.sign()) a_lit.neg();
+        lits.push_back(a_lit);
+        add_th_lemma(lits);
+    }
+}
+
+void create_induction_lemmas::add_th_lemma(literal_vector const& lits) {
+    IF_VERBOSE(1, ctx.display_literals_verbose(verbose_stream() << "lemma:\n", lits) << "\n");
+    ctx.mk_clause(lits.size(), lits.c_ptr(), nullptr, smt::CLS_TH_LEMMA);
+    ++m_num_lemmas;
+}
+
+literal create_induction_lemmas::mk_literal(expr* e) {
+    if (!ctx.e_internalized(e)) {
+        ctx.internalize(e, false);
+    }
+    enode* n = ctx.get_enode(e);
+    ctx.mark_as_relevant(n);
+    return ctx.get_literal(e);
+}
+
+func_decl* create_induction_lemmas::mk_skolem(sort* s) {
+    func_decl* f = nullptr;
+    if (!m_sort2skolem.find(s, f)) {
+        sort* domain[2] = { s, m.mk_bool_sort() };
+        f = m.mk_fresh_func_decl("sk", 2, domain, s);
+        m_pinned.push_back(f);
+        m_pinned.push_back(s);
+        m_sort2skolem.insert(s, f);
+    }
+    return f;
+}
+
+
+bool create_induction_lemmas::operator()(literal lit) {
+    unsigned num = m_num_lemmas;
+    enode* r = ctx.bool_var2enode(lit.var());
+    for (enode* n : induction_positions(r)) {
+        expr* t = n->get_owner();
+        sort* s = m.get_sort(t);
+        expr_ref sk(m.mk_app(mk_skolem(s), t, r->get_owner()), m);
+        std::cout << "abstract " << mk_pp(t, m) << " " << sk << "\n";
+        abstractions abs;
+        abstract(r, n, sk, abs);            
+        abs.pop_back(); // last position has no generalizations
+        filter_abstractions(lit.sign(), abs);
+        for (abstraction& a : abs) {
+            create_lemmas(t, sk, a, lit);
+        }
+    }
+    return m_num_lemmas > num;
+}
+
+create_induction_lemmas::create_induction_lemmas(context& ctx, ast_manager& m, value_sweep& vs):
+    ctx(ctx),
+    m(m),
+    vs(vs),
+    m_dt(m),
+    m_pinned(m),
+    m_num_lemmas(0)
+{}
+
+induction::induction(context& ctx, ast_manager& m):
+    ctx(ctx),
+    m(m),
+    vs(m),
+    m_collect_literals(ctx, m, vs),
+    m_create_lemmas(ctx, m, vs)
+{}
+
+// TBD: use smt_arith_value to also include state from arithmetic solver
+void induction::init_values() {
+    for (enode* n : ctx.enodes()) 
+        if (m.is_value(n->get_owner())) 
+            for (enode* r : *n) 
+                vs.set_value(r->get_owner(), n->get_owner());
+}
+
+bool induction::operator()() {
+    bool added_lemma = false;
+    vs.reset_values();
+    literal_vector candidates = m_collect_literals();
+    for (literal lit : candidates) {
+        if (m_create_lemmas(lit))
+            added_lemma = true;
+    }
+    return added_lemma;
+}
+
+// state contains datatypes + recursive functions
+// more comprehensive: 
+// state contains integers / datatypes / sequences + recursive function / quantifiers
+
+bool induction::should_try(context& ctx) {
+    recfun::util u(ctx.get_manager());
+    datatype::util dt(ctx.get_manager());
+    theory* adt = ctx.get_theory(dt.get_family_id());
+    return adt && adt->get_num_vars() > 0 && !u.get_rec_funs().empty();
+}

src/smt/smt_induction.h

@@ -0,0 +1,123 @@
+/*++
+  Copyright (c) 2020 Microsoft Corporation
+
+  Module Name:
+
+   smt_induction.h
+
+  Abstract:
+   
+   Add induction lemmas to context.
+
+  Author:
+
+    Nikolaj Bjorner 2020-04-25
+  
+--*/
+
+#pragma once
+
+#include "smt/smt_types.h"
+#include "ast/rewriter/value_sweep.h"
+#include "ast/datatype_decl_plugin.h"
+
+namespace smt {
+
+    class context;
+
+    /**
+     * Collect literals that are potentially useful for induction lemmas.
+     */
+    class collect_induction_literals {
+        context&                  ctx;
+        ast_manager&              m;
+        value_sweep&              vs;        
+        unsigned                  m_literal_index;
+
+        literal_vector pre_select();
+
+        void model_sweep_filter(literal_vector& candidates);
+
+    public:
+        collect_induction_literals(context& ctx, ast_manager& m, value_sweep& vs);
+
+        literal_vector operator()();               
+    };
+
+    /**
+     * Synthesize induction lemmas from induction candidates
+     */
+    class create_induction_lemmas {
+        context&     ctx;
+        ast_manager& m;
+        value_sweep& vs;
+        datatype::util m_dt;
+        obj_map<sort, func_decl*> m_sort2skolem;
+        ast_ref_vector m_pinned;
+        unsigned m_num_lemmas;
+
+        typedef svector<std::pair<expr*,expr*>> expr_pair_vector;
+
+        func_decl* mk_skolem(sort* s);
+
+        struct abstraction {
+            expr_ref          m_term;
+            expr_pair_vector m_eqs;
+            abstraction(expr_ref& e): m_term(e) {}
+            abstraction(ast_manager& m, expr* e, expr* n1, expr* n2): m_term(e, m) {
+                if (n1 != n2) m_eqs.push_back(std::make_pair(n1, n2));
+            }
+            abstraction(ast_manager& m, expr* e, expr_pair_vector const& eqs): 
+                m_term(e, m), m_eqs(eqs) {
+            }
+            
+        };
+        typedef vector<abstraction> abstractions;
+        
+        struct abstraction_arg {
+            expr_ref_vector   m_terms;
+            expr_pair_vector m_eqs;
+            abstraction_arg(ast_manager& m): m_terms(m) {}
+            void push_back(abstraction& a) {
+                m_terms.push_back(a.m_term);
+                m_eqs.append(a.m_eqs);
+            }
+        };
+        typedef vector<abstraction_arg> abstraction_args;
+
+        bool is_induction_candidate(enode* n);
+        enode_vector induction_positions(enode* n);
+        void abstract(enode* n, enode* t, expr* x, abstractions& result);
+        void filter_abstractions(bool sign, abstractions& abs);
+        void create_lemmas(expr* t, expr* sk, abstraction& a, literal lit);
+        literal mk_literal(expr* e);
+        void add_th_lemma(literal_vector const& lits);
+
+    public:
+        create_induction_lemmas(context& ctx, ast_manager& m, value_sweep& vs);
+
+        bool operator()(literal lit);
+    };
+
+    /**
+     * Establish induction clauses.
+     */
+
+    class induction {
+        context&     ctx;
+        ast_manager& m;
+        value_sweep  vs;
+        collect_induction_literals m_collect_literals;
+        create_induction_lemmas m_create_lemmas;
+
+        void init_values();
+
+    public:
+        induction(context& ctx, ast_manager& m);
+
+        bool operator()();
+
+        static bool should_try(context& ctx);
+    };
+
+}