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Z3 sources
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura
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281
lib/grobner.h
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281
lib/grobner.h
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/*++
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Copyright (c) 2006 Microsoft Corporation
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Module Name:
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grobner.h
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Abstract:
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<abstract>
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Author:
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Leonardo de Moura (leonardo) 2008-12-04.
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Revision History:
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--*/
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#ifndef _GROBNER_H_
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#define _GROBNER_H_
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#include"ast.h"
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#include"arith_decl_plugin.h"
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#include"heap.h"
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#include"obj_hashtable.h"
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#include"region.h"
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#include"dependency.h"
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struct grobner_stats {
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long m_simplify; long m_superpose; long m_compute_basis; long m_num_processed;
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void reset() { memset(this, 0, sizeof(grobner_stats)); }
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grobner_stats() { reset(); }
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};
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/**
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\brief Simple Grobner basis implementation with no indexing.
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*/
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class grobner {
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protected:
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struct monomial_lt;
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public:
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grobner_stats m_stats;
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class monomial {
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rational m_coeff;
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ptr_vector<expr> m_vars; //!< sorted variables
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friend class grobner;
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friend struct monomial_lt;
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monomial() {}
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public:
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rational const & get_coeff() const { return m_coeff; }
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unsigned get_degree() const { return m_vars.size(); }
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unsigned get_size() const { return get_degree(); }
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expr * get_var(unsigned idx) const { return m_vars[idx]; }
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};
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class equation {
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unsigned m_scope_lvl; //!< scope level when this equation was created.
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unsigned m_bidx:31; //!< position at m_equations_to_delete
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unsigned m_lc:1; //!< true if equation if a linear combination of the input equations.
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ptr_vector<monomial> m_monomials; //!< sorted monomials
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v_dependency * m_dep; //!< justification for the equality
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friend class grobner;
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equation() {}
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public:
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unsigned get_num_monomials() const { return m_monomials.size(); }
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monomial const * get_monomial(unsigned idx) const { return m_monomials[idx]; }
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monomial * const * get_monomials() const { return m_monomials.c_ptr(); }
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v_dependency * get_dependency() const { return m_dep; }
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unsigned hash() const { return m_bidx; }
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bool is_linear_combination() const { return m_lc; }
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};
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protected:
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static bool is_eq_monomial_body(monomial const * m1, monomial const * m2);
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struct var_lt {
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obj_map<expr, int> & m_var2weight;
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var_lt(obj_map<expr, int> & m):m_var2weight(m) {}
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bool operator()(expr * v1, expr * v2) const;
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};
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struct monomial_lt {
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var_lt & m_var_lt;
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monomial_lt(var_lt & lt):m_var_lt(lt) {}
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bool operator()(monomial * m1, monomial * m2) const;
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};
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typedef obj_hashtable<equation> equation_set;
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typedef ptr_vector<equation> equation_vector;
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ast_manager & m_manager;
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v_dependency_manager & m_dep_manager;
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arith_util m_util;
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obj_map<expr, int> m_var2weight;
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var_lt m_var_lt;
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monomial_lt m_monomial_lt;
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equation_set m_processed;
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equation_set m_to_process;
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equation_vector m_equations_to_unfreeze;
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equation_vector m_equations_to_delete;
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bool m_changed_leading_term; // set to true, if the leading term was simplified.
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equation * m_unsat;
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struct scope {
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unsigned m_equations_to_unfreeze_lim;
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unsigned m_equations_to_delete_lim;
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};
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svector<scope> m_scopes;
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ptr_vector<monomial> m_tmp_monomials;
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ptr_vector<expr> m_tmp_vars1;
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ptr_vector<expr> m_tmp_vars2;
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unsigned m_num_new_equations; // temporary variable
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bool is_monomial_lt(monomial const & m1, monomial const & m2) const;
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void display_vars(std::ostream & out, unsigned num_vars, expr * const * vars) const;
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void display_var(std::ostream & out, expr * var) const;
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void display_monomials(std::ostream & out, unsigned num_monomials, monomial * const * monomials) const;
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void display_equations(std::ostream & out, equation_set const & v, char const * header) const;
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void del_equations(unsigned old_size);
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void unfreeze_equations(unsigned old_size);
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void del_equation(equation * eq);
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void flush();
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bool update_order(equation * eq);
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void update_order(equation_set & s, bool processed);
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void add_var(monomial * m, expr * v);
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monomial * mk_monomial(rational const & coeff, expr * m);
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void init_equation(equation * eq, v_dependency * d);
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void extract_monomials(expr * lhs, ptr_buffer<expr> & monomials);
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void merge_monomials(ptr_vector<monomial> & monomials);
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bool is_inconsistent(equation * eq) const;
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bool is_trivial(equation * eq) const;
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void normalize_coeff(ptr_vector<monomial> & monomials);
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void simplify(ptr_vector<monomial> & monomials);
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void simplify(equation * eq);
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bool is_subset(monomial const * m1, monomial const * m2, ptr_vector<expr> & rest) const;
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void mul_append(unsigned start_idx, equation const * source, rational const & coeff, ptr_vector<expr> const & vars, ptr_vector<monomial> & result);
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monomial * copy_monomial(monomial const * m);
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equation * copy_equation(equation const * eq);
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equation * simplify(equation const * source, equation * target);
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equation * simplify_using_processed(equation * eq);
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bool is_better_choice(equation * eq1, equation * eq2);
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equation * pick_next();
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void simplify_processed(equation * eq);
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void simplify_to_process(equation * eq);
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bool unify(monomial const * m1, monomial const * m2, ptr_vector<expr> & rest1, ptr_vector<expr> & rest2);
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void superpose(equation * eq1, equation * eq2);
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void superpose(equation * eq);
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void copy_to(equation_set const & s, ptr_vector<equation> & result) const;
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public:
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grobner(ast_manager & m, v_dependency_manager & dep_m);
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~grobner();
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unsigned get_scope_level() const { return m_scopes.size(); }
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/**
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\brief Set the weight of a term that is viewed as a variable by this module.
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The weight is used to order monomials. If the weight is not set for a term t, then the
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weight of t is assumed to be 0.
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*/
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void set_weight(expr * n, int weight);
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int get_weight(expr * n) const { int w = 0; m_var2weight.find(n, w); return w; }
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/**
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\brief Update equations after set_weight was invoked once or more.
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*/
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void update_order();
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/**
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\brief Create a new monomial. The caller owns the monomial until it invokes assert_eq_0.
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A monomial cannot be use to create several equations.
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*/
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monomial * mk_monomial(rational const & coeff, unsigned num_vars, expr * const * vars);
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void del_monomial(monomial * m);
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/**
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\brief Assert the given equality.
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This method assumes eq is simplified.
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*/
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void assert_eq(expr * eq, v_dependency * ex = 0);
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/**
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\brief Assert the equality monomials[0] + ... + monomials[num_monomials - 1] = 0.
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This method assumes the monomials were simplified.
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*/
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void assert_eq_0(unsigned num_monomials, expr * const * monomials, v_dependency * ex = 0);
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/**
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\brief Assert the equality monomials[0] + ... + monomials[num_monomials - 1] = 0.
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This method assumes the monomials were simplified.
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*/
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void assert_eq_0(unsigned num_monomials, monomial * const * monomials, v_dependency * ex = 0);
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/**
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\brief Assert the equality coeffs[0] * monomials[0] + ... + coeffs[num_monomials-1] * monomials[num_monomials - 1] = 0.
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This method assumes the monomials were simplified.
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*/
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void assert_eq_0(unsigned num_monomials, rational const * coeffs, expr * const * monomials, v_dependency * ex = 0);
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/**
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\brief Assert the monomial tautology (quote (x_1 * ... * x_n)) - x_1 * ... * x_n = 0
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*/
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void assert_monomial_tautology(expr * m);
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/**
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\brief Compute Grobner basis.
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Return true if the threshold was not reached.
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*/
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bool compute_basis(unsigned threshold);
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/**
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\brief Return true if an inconsistency was detected.
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*/
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bool inconsistent() const { return m_unsat != 0; }
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/**
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\brief Simplify the given expression using the equalities asserted
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using assert_eq. Store the result in 'result'.
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*/
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void simplify(expr * n, expr_ref & result);
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/**
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\brief Reset state. Remove all equalities asserted with assert_eq.
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*/
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void reset();
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void get_equations(ptr_vector<equation> & result) const;
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void push_scope();
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void pop_scope(unsigned num_scopes);
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void display_equation(std::ostream & out, equation const & eq) const;
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void display_monomial(std::ostream & out, monomial const & m) const;
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void display(std::ostream & out) const;
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};
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#endif /* _GROBNER_H_ */
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