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https://github.com/Z3Prover/z3
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511 lines
21 KiB
C++
511 lines
21 KiB
C++
/*++
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Copyright (c) 2011 Microsoft Corporation
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Module Name:
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theory_seq.h
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Abstract:
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Native theory solver for sequences.
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Author:
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Nikolaj Bjorner (nbjorner) 2015-6-12
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Revision History:
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--*/
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#ifndef THEORY_SEQ_H_
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#define THEORY_SEQ_H_
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#include "smt_theory.h"
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#include "seq_decl_plugin.h"
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#include "theory_seq_empty.h"
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#include "th_rewriter.h"
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#include "ast_trail.h"
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#include "scoped_vector.h"
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#include "scoped_ptr_vector.h"
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#include "automaton.h"
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#include "seq_rewriter.h"
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namespace smt {
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class theory_seq : public theory {
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struct assumption {
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enode* n1, *n2;
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literal lit;
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assumption(enode* n1, enode* n2): n1(n1), n2(n2), lit(null_literal) {}
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assumption(literal lit): n1(0), n2(0), lit(lit) {}
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};
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typedef scoped_dependency_manager<assumption> dependency_manager;
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typedef dependency_manager::dependency dependency;
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typedef trail_stack<theory_seq> th_trail_stack;
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typedef std::pair<expr*, dependency*> expr_dep;
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typedef obj_map<expr, expr_dep> eqdep_map_t;
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// cache to track evaluations under equalities
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class eval_cache {
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eqdep_map_t m_map;
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expr_ref_vector m_trail;
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public:
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eval_cache(ast_manager& m): m_trail(m) {}
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bool find(expr* v, expr_dep& r) const { return m_map.find(v, r); }
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void insert(expr* v, expr_dep& r) { m_trail.push_back(v); m_trail.push_back(r.first); m_map.insert(v, r); }
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void reset() { m_map.reset(); m_trail.reset(); }
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};
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// map from variables to representatives
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// + a cache for normalization.
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class solution_map {
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enum map_update { INS, DEL };
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ast_manager& m;
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dependency_manager& m_dm;
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eqdep_map_t m_map;
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eval_cache m_cache;
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expr_ref_vector m_lhs, m_rhs;
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ptr_vector<dependency> m_deps;
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svector<map_update> m_updates;
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unsigned_vector m_limit;
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void add_trail(map_update op, expr* l, expr* r, dependency* d);
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public:
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solution_map(ast_manager& m, dependency_manager& dm):
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m(m), m_dm(dm), m_cache(m), m_lhs(m), m_rhs(m) {}
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bool empty() const { return m_map.empty(); }
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void update(expr* e, expr* r, dependency* d);
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void add_cache(expr* v, expr_dep& r) { m_cache.insert(v, r); }
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bool find_cache(expr* v, expr_dep& r) { return m_cache.find(v, r); }
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expr* find(expr* e, dependency*& d);
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expr* find(expr* e);
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bool is_root(expr* e) const;
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void cache(expr* e, expr* r, dependency* d);
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void reset_cache() { m_cache.reset(); }
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void push_scope() { m_limit.push_back(m_updates.size()); }
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void pop_scope(unsigned num_scopes);
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void display(std::ostream& out) const;
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};
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// Table of current disequalities
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class exclusion_table {
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typedef obj_pair_hashtable<expr, expr> table_t;
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ast_manager& m;
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table_t m_table;
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expr_ref_vector m_lhs, m_rhs;
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unsigned_vector m_limit;
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public:
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exclusion_table(ast_manager& m): m(m), m_lhs(m), m_rhs(m) {}
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~exclusion_table() { }
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bool empty() const { return m_table.empty(); }
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void update(expr* e, expr* r);
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bool contains(expr* e, expr* r) const;
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void push_scope() { m_limit.push_back(m_lhs.size()); }
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void pop_scope(unsigned num_scopes);
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void display(std::ostream& out) const;
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};
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// Asserted or derived equality with dependencies
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struct eq {
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expr_ref m_lhs;
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expr_ref m_rhs;
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dependency* m_dep;
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eq(expr_ref& l, expr_ref& r, dependency* d):
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m_lhs(l), m_rhs(r), m_dep(d) {}
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eq(eq const& other): m_lhs(other.m_lhs), m_rhs(other.m_rhs), m_dep(other.m_dep) {}
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eq& operator=(eq const& other) { m_lhs = other.m_lhs; m_rhs = other.m_rhs; m_dep = other.m_dep; return *this; }
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};
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// asserted or derived disqequality with dependencies
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struct ne {
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bool m_solved;
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expr_ref m_l, m_r;
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expr_ref_vector m_lhs;
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expr_ref_vector m_rhs;
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literal_vector m_lits;
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dependency* m_dep;
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ne(expr_ref& l, expr_ref& r):
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m_solved(false), m_l(l), m_r(r), m_lhs(l.get_manager()), m_rhs(r.get_manager()), m_dep(0) {
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m_lhs.push_back(l);
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m_rhs.push_back(r);
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}
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ne(ne const& other):
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m_solved(other.m_solved), m_l(other.m_l), m_r(other.m_r), m_lhs(other.m_lhs), m_rhs(other.m_rhs), m_lits(other.m_lits), m_dep(other.m_dep) {}
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ne& operator=(ne const& other) {
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m_solved = other.m_solved;
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m_l = other.m_l;
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m_r = other.m_r;
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m_lhs.reset(); m_lhs.append(other.m_lhs);
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m_rhs.reset(); m_rhs.append(other.m_rhs);
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m_lits.reset(); m_lits.append(other.m_lits);
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m_dep = other.m_dep;
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return *this;
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}
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bool is_solved() const { return m_solved; }
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};
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class pop_lit : public trail<theory_seq> {
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unsigned m_idx;
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literal m_lit;
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public:
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pop_lit(theory_seq& th, unsigned idx): m_idx(idx), m_lit(th.m_nqs[idx].m_lits.back()) {
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th.m_nqs.ref(m_idx).m_lits.pop_back();
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}
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virtual void undo(theory_seq & th) { th.m_nqs.ref(m_idx).m_lits.push_back(m_lit); }
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};
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class push_lit : public trail<theory_seq> {
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unsigned m_idx;
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public:
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push_lit(theory_seq& th, unsigned idx, literal lit): m_idx(idx) {
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th.m_nqs.ref(m_idx).m_lits.push_back(lit);
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}
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virtual void undo(theory_seq & th) { th.m_nqs.ref(m_idx).m_lits.pop_back(); }
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};
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class set_lit : public trail<theory_seq> {
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unsigned m_idx;
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unsigned m_i;
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literal m_lit;
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public:
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set_lit(theory_seq& th, unsigned idx, unsigned i, literal lit):
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m_idx(idx), m_i(i), m_lit(th.m_nqs[idx].m_lits[i]) {
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th.m_nqs.ref(m_idx).m_lits[i] = lit;
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}
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virtual void undo(theory_seq & th) { th.m_nqs.ref(m_idx).m_lits[m_i] = m_lit; }
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};
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class solved_ne : public trail<theory_seq> {
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unsigned m_idx;
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public:
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solved_ne(theory_seq& th, unsigned idx) : m_idx(idx) { th.m_nqs.ref(idx).m_solved = true; }
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virtual void undo(theory_seq& th) { th.m_nqs.ref(m_idx).m_solved = false; }
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};
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void mark_solved(unsigned idx);
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class push_ne : public trail<theory_seq> {
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unsigned m_idx;
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public:
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push_ne(theory_seq& th, unsigned idx, expr* l, expr* r) : m_idx(idx) {
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th.m_nqs.ref(m_idx).m_lhs.push_back(l);
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th.m_nqs.ref(m_idx).m_rhs.push_back(r);
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}
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virtual void undo(theory_seq& th) { th.m_nqs.ref(m_idx).m_lhs.pop_back(); th.m_nqs.ref(m_idx).m_rhs.pop_back(); }
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};
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class pop_ne : public trail<theory_seq> {
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expr_ref m_lhs;
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expr_ref m_rhs;
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unsigned m_idx;
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public:
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pop_ne(theory_seq& th, unsigned idx):
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m_lhs(th.m_nqs[idx].m_lhs.back(), th.m),
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m_rhs(th.m_nqs[idx].m_rhs.back(), th.m),
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m_idx(idx) {
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th.m_nqs.ref(idx).m_lhs.pop_back();
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th.m_nqs.ref(idx).m_rhs.pop_back();
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}
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virtual void undo(theory_seq& th) {
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th.m_nqs.ref(m_idx).m_lhs.push_back(m_lhs);
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th.m_nqs.ref(m_idx).m_rhs.push_back(m_rhs);
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m_lhs.reset();
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m_rhs.reset();
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}
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};
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class set_ne : public trail<theory_seq> {
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expr_ref m_lhs;
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expr_ref m_rhs;
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unsigned m_idx;
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unsigned m_i;
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public:
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set_ne(theory_seq& th, unsigned idx, unsigned i, expr* l, expr* r):
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m_lhs(th.m_nqs[idx].m_lhs[i], th.m),
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m_rhs(th.m_nqs[idx].m_rhs[i], th.m),
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m_idx(idx),
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m_i(i) {
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th.m_nqs.ref(idx).m_lhs[i] = l;
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th.m_nqs.ref(idx).m_rhs[i] = r;
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}
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virtual void undo(theory_seq& th) {
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th.m_nqs.ref(m_idx).m_lhs[m_i] = m_lhs;
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th.m_nqs.ref(m_idx).m_rhs[m_i] = m_rhs;
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m_lhs.reset();
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m_rhs.reset();
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}
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};
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class push_dep : public trail<theory_seq> {
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dependency* m_dep;
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unsigned m_idx;
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public:
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push_dep(theory_seq& th, unsigned idx, dependency* d): m_dep(th.m_nqs[idx].m_dep), m_idx(idx) {
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th.m_nqs.ref(idx).m_dep = d;
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}
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virtual void undo(theory_seq& th) {
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th.m_nqs.ref(m_idx).m_dep = m_dep;
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}
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};
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class apply {
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public:
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virtual ~apply() {}
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virtual void operator()(theory_seq& th) = 0;
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};
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class replay_length_coherence : public apply {
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expr_ref m_e;
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public:
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replay_length_coherence(ast_manager& m, expr* e) : m_e(e, m) {}
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virtual void operator()(theory_seq& th) {
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th.check_length_coherence(m_e);
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m_e.reset();
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}
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};
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class replay_axiom : public apply {
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expr_ref m_e;
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public:
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replay_axiom(ast_manager& m, expr* e) : m_e(e, m) {}
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virtual void operator()(theory_seq& th) {
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th.enque_axiom(m_e);
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m_e.reset();
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}
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};
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class push_replay : public trail<theory_seq> {
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apply* m_apply;
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public:
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push_replay(apply* app): m_apply(app) {}
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virtual void undo(theory_seq& th) {
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th.m_replay.push_back(m_apply);
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}
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};
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class pop_branch : public trail<theory_seq> {
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expr_ref m_l, m_r;
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public:
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pop_branch(ast_manager& m, expr* l, expr* r): m_l(l, m), m_r(r, m) {}
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virtual void undo(theory_seq& th) {
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th.m_branch_start.erase(m_l, m_r);
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m_l.reset();
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m_r.reset();
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}
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};
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void erase_index(unsigned idx, unsigned i);
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struct stats {
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stats() { reset(); }
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void reset() { memset(this, 0, sizeof(stats)); }
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unsigned m_num_splits;
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unsigned m_num_reductions;
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unsigned m_propagate_automata;
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unsigned m_check_length_coherence;
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unsigned m_branch_variable;
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unsigned m_solve_nqs;
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unsigned m_solve_eqs;
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unsigned m_add_axiom;
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};
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ast_manager& m;
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dependency_manager m_dm;
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solution_map m_rep; // unification representative.
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scoped_vector<eq> m_eqs; // set of current equations.
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scoped_vector<ne> m_nqs; // set of current disequalities.
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seq_factory* m_factory; // value factory
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exclusion_table m_exclude; // set of asserted disequalities.
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expr_ref_vector m_axioms; // list of axioms to add.
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obj_hashtable<expr> m_axiom_set;
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unsigned m_axioms_head; // index of first axiom to add.
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bool m_incomplete; // is the solver (clearly) incomplete for the fragment.
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obj_hashtable<expr> m_length; // is length applied
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scoped_ptr_vector<apply> m_replay; // set of actions to replay
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model_generator* m_mg;
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th_rewriter m_rewrite;
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seq_util m_util;
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arith_util m_autil;
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th_trail_stack m_trail_stack;
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stats m_stats;
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symbol m_prefix, m_suffix, m_contains_left, m_contains_right, m_accept, m_reject;
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symbol m_tail, m_nth, m_seq_first, m_seq_last, m_indexof_left, m_indexof_right, m_aut_step;
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symbol m_extract_prefix, m_at_left, m_at_right;
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ptr_vector<expr> m_todo;
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expr_ref_vector m_ls, m_rs, m_lhs, m_rhs;
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// maintain automata with regular expressions.
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scoped_ptr_vector<eautomaton> m_automata;
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obj_map<expr, eautomaton*> m_re2aut;
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// queue of asserted atoms
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ptr_vector<expr> m_atoms;
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unsigned_vector m_atoms_lim;
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unsigned m_atoms_qhead;
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bool m_new_solution; // new solution added
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bool m_new_propagation; // new propagation to core
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virtual final_check_status final_check_eh();
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virtual bool internalize_atom(app* atom, bool) { return internalize_term(atom); }
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virtual bool internalize_term(app*);
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virtual void internalize_eq_eh(app * atom, bool_var v) {}
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virtual void new_eq_eh(theory_var, theory_var);
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virtual void new_diseq_eh(theory_var, theory_var);
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virtual void assign_eh(bool_var v, bool is_true);
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virtual bool can_propagate();
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virtual void propagate();
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virtual void push_scope_eh();
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virtual void pop_scope_eh(unsigned num_scopes);
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virtual void restart_eh();
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virtual void relevant_eh(app* n);
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virtual theory* mk_fresh(context* new_ctx) { return alloc(theory_seq, new_ctx->get_manager()); }
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virtual char const * get_name() const { return "seq"; }
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virtual theory_var mk_var(enode* n);
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virtual void apply_sort_cnstr(enode* n, sort* s);
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virtual void display(std::ostream & out) const;
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virtual void collect_statistics(::statistics & st) const;
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virtual model_value_proc * mk_value(enode * n, model_generator & mg);
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virtual void init_model(model_generator & mg);
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// final check
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bool simplify_and_solve_eqs(); // solve unitary equalities
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bool branch_variable(); // branch on a variable
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bool split_variable(); // split a variable
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bool is_solved();
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bool check_length_coherence();
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bool check_length_coherence(expr* e);
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bool propagate_length_coherence(expr* e);
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bool solve_eqs(unsigned start);
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bool solve_eq(expr* l, expr* r, dependency* dep);
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bool simplify_eq(expr* l, expr* r, dependency* dep);
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bool solve_unit_eq(expr* l, expr* r, dependency* dep);
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bool is_binary_eq(expr* l, expr* r, expr*& x, ptr_vector<expr>& xunits, ptr_vector<expr>& yunits, expr*& y);
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bool solve_binary_eq(expr* l, expr* r, dependency* dep);
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bool propagate_max_length(expr* l, expr* r, dependency* dep);
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bool solve_nqs(unsigned i);
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void solve_ne(unsigned i);
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bool unchanged(expr* e, expr_ref_vector& es) const { return es.size() == 1 && es[0] == e; }
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bool unchanged(expr* e, expr_ref_vector& es, expr* f, expr_ref_vector& fs) const {
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return
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(unchanged(e, es) && unchanged(f, fs)) ||
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(unchanged(e, fs) && unchanged(e, fs));
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}
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// asserting consequences
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void linearize(dependency* dep, enode_pair_vector& eqs, literal_vector& lits) const;
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void propagate_lit(dependency* dep, literal lit) { propagate_lit(dep, 0, 0, lit); }
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void propagate_lit(dependency* dep, unsigned n, literal const* lits, literal lit);
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void propagate_eq(dependency* dep, enode* n1, enode* n2);
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void propagate_eq(literal lit, expr* e1, expr* e2, bool add_to_eqs = false);
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void set_conflict(dependency* dep, literal_vector const& lits = literal_vector());
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obj_pair_map<expr, expr, unsigned> m_branch_start;
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void insert_branch_start(expr* l, expr* r, unsigned s);
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unsigned find_branch_start(expr* l, expr* r);
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bool find_branch_candidate(unsigned& start, dependency* dep, expr_ref_vector const& ls, expr_ref_vector const& rs);
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bool can_be_equal(unsigned szl, expr* const* ls, unsigned szr, expr* const* rs) const;
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lbool assume_equality(expr* l, expr* r);
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// variable solving utilities
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bool occurs(expr* a, expr* b);
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bool is_var(expr* b);
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bool add_solution(expr* l, expr* r, dependency* dep);
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bool is_nth(expr* a) const;
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bool is_tail(expr* a, expr*& s, unsigned& idx) const;
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expr_ref mk_nth(expr* s, expr* idx);
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expr_ref mk_last(expr* e);
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expr_ref canonize(expr* e, dependency*& eqs);
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void canonize(expr* e, expr_ref_vector& es, dependency*& eqs);
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expr_ref expand(expr* e, dependency*& eqs);
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void add_dependency(dependency*& dep, enode* a, enode* b);
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void get_concat(expr* e, ptr_vector<expr>& concats);
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// terms whose meaning are encoded using axioms.
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void enque_axiom(expr* e);
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void deque_axiom(expr* e);
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void add_axiom(literal l1, literal l2 = null_literal, literal l3 = null_literal, literal l4 = null_literal);
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void add_indexof_axiom(expr* e);
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void add_replace_axiom(expr* e);
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void add_extract_axiom(expr* e);
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void add_length_axiom(expr* n);
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bool has_length(expr *e) const { return m_length.contains(e); }
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void add_length(expr* e);
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void enforce_length(enode* n);
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void enforce_length_coherence(enode* n1, enode* n2);
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void add_elim_string_axiom(expr* n);
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void add_at_axiom(expr* n);
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void add_in_re_axiom(expr* n);
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literal mk_literal(expr* n);
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literal mk_eq_empty(expr* n);
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literal mk_equals(expr* a, expr* b);
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void tightest_prefix(expr* s, expr* x, literal lit, literal lit2 = null_literal);
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expr_ref mk_sub(expr* a, expr* b);
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enode* ensure_enode(expr* a);
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// arithmetic integration
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bool lower_bound(expr* s, rational& lo);
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bool upper_bound(expr* s, rational& hi);
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bool get_length(expr* s, rational& val);
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void mk_decompose(expr* e, expr_ref& head, expr_ref& tail);
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expr_ref mk_skolem(symbol const& s, expr* e1, expr* e2 = 0, expr* e3 = 0, sort* range = 0);
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bool is_skolem(symbol const& s, expr* e) const;
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void set_incomplete(app* term);
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// automata utilities
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void propagate_in_re(expr* n, bool is_true);
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eautomaton* get_automaton(expr* e);
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literal mk_accept(expr* s, expr* idx, expr* re, expr* state);
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literal mk_accept(expr* s, expr* idx, expr* re, unsigned i) { return mk_accept(s, idx, re, m_autil.mk_int(i)); }
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bool is_accept(expr* acc) const { return is_skolem(m_accept, acc); }
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bool is_accept(expr* acc, expr*& s, expr*& idx, expr*& re, unsigned& i, eautomaton*& aut) {
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return is_acc_rej(m_accept, acc, s, idx, re, i, aut);
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}
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literal mk_reject(expr* s, expr* idx, expr* re, expr* state);
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literal mk_reject(expr* s, expr* idx, expr* re, unsigned i) { return mk_reject(s, idx, re, m_autil.mk_int(i)); }
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bool is_reject(expr* rej) const { return is_skolem(m_reject, rej); }
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|
bool is_reject(expr* rej, expr*& s, expr*& idx, expr*& re, unsigned& i, eautomaton*& aut) {
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|
return is_acc_rej(m_reject, rej, s, idx, re, i, aut);
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|
}
|
|
bool is_acc_rej(symbol const& ar, expr* e, expr*& s, expr*& idx, expr*& re, unsigned& i, eautomaton*& aut);
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|
expr_ref mk_step(expr* s, expr* tail, expr* re, unsigned i, unsigned j, expr* t);
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|
bool is_step(expr* e, expr*& s, expr*& tail, expr*& re, expr*& i, expr*& j, expr*& t) const;
|
|
bool is_step(expr* e) const;
|
|
void propagate_step(literal lit, expr* n);
|
|
bool add_reject2reject(expr* rej);
|
|
bool add_accept2step(expr* acc);
|
|
bool add_step2accept(expr* step);
|
|
bool add_prefix2prefix(expr* e);
|
|
bool add_suffix2suffix(expr* e);
|
|
bool add_contains2contains(expr* e);
|
|
void ensure_nth(literal lit, expr* s, expr* idx);
|
|
bool canonizes(bool sign, expr* e);
|
|
void propagate_non_empty(literal lit, expr* s);
|
|
void propagate_is_conc(expr* e, expr* conc);
|
|
void propagate_acc_rej_length(literal lit, expr* acc_rej);
|
|
bool propagate_automata();
|
|
void add_atom(expr* e);
|
|
void new_eq_eh(dependency* dep, enode* n1, enode* n2);
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|
|
|
// diagnostics
|
|
void display_equations(std::ostream& out) const;
|
|
void display_disequations(std::ostream& out) const;
|
|
void display_disequation(std::ostream& out, ne const& e) const;
|
|
void display_deps(std::ostream& out, dependency* deps) const;
|
|
public:
|
|
theory_seq(ast_manager& m);
|
|
virtual ~theory_seq();
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|
|
|
// model building
|
|
app* mk_value(app* a);
|
|
|
|
};
|
|
};
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#endif /* THEORY_SEQ_H_ */
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