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/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
nlsat_solver.h
Abstract:
Nonlinear arithmetic satisfiability procedure. The procedure is
complete for nonlinear real arithmetic, but it also has limited
support for integers.
Author:
Leonardo de Moura (leonardo) 2012-01-02.
Revision History:
--*/
#pragma once
#include "nlsat/nlsat_types.h"
#include "nlsat/nlsat_transcendentals.h"
#include "util/params.h"
#include "util/statistics.h"
#include "util/rlimit.h"
#include "util/dependency.h"
namespace nlsat {
class evaluator;
class explain;
class display_assumption_proc {
public:
virtual ~display_assumption_proc() = default;
virtual std::ostream& operator()(std::ostream& out, assumption a) const = 0;
};
struct bound_constraint {
var x;
polynomial_ref A, B;
bool is_strict;
clause* c;
bound_constraint(var x, polynomial_ref& A, polynomial_ref& B, bool is_strict, clause* c) :
x(x), A(A), B(B), is_strict(is_strict), c(c) {}
};
class solver {
struct imp;
struct ctx;
imp * m_imp;
ctx * m_ctx;
solver(ctx& c);
public:
solver(reslimit& rlim, params_ref const & p, bool incremental);
~solver();
/**
\brief Return reference to rational manager.
*/
unsynch_mpq_manager & qm();
/**
\brief Return reference to algebraic number manager.
*/
anum_manager & am();
/**
\brief Return a reference to the polynomial manager used by the solver.
*/
pmanager & pm();
void set_display_var(display_var_proc const & proc);
void set_display_assumption(display_assumption_proc const& proc);
// -----------------------
//
// Variable, Atoms, Clauses & Assumption creation
//
// -----------------------
/**
\brief Create a fresh boolean variable that is not associated with any
nonlinear arithmetic atom.
*/
bool_var mk_bool_var();
literal mk_true();
/**
\brief Create a real/integer variable.
*/
var mk_var(bool is_int);
/**
\brief Create an atom of the form: p=0, p<0, p>0
Where p = ps[0]^e[0]*...*ps[sz-1]^e[sz-1]
e[i] = 1 if is_even[i] is false
e[i] = 2 if is_even[i] is true
\pre sz > 0
*/
bool_var mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even);
/**
\brief Create a literal for the p=0, p<0, p>0.
Where p = ps[0]^e[0]*...*ps[sz-1]^e[sz-1] for sz > 0
p = 1 for sz = 0
e[i] = 1 if is_even[i] is false
e[i] = 2 if is_even[i] is true
*/
literal mk_ineq_literal(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool simplify = false);
/**
\brief Create an atom of the form: x=root[i](p), x<root[i](p), x>root[i](p)
*/
bool_var mk_root_atom(atom::kind k, var x, unsigned i, poly * p);
/**
\brief Register a transcendental function application (sin/cos/exp/atan)
to be refined directly by nlsat's own search loop; see
nlsat_transcendentals.h. Refinement is enabled automatically the
moment at least one such application is registered - there is no
separate on/off parameter.
*/
void add_transcendental(transcendental_op_kind op, var arg, var val);
/**
\brief Register the nullary constant pi with the persistent
transcendentals engine (see nlsat_transcendentals.h::add_pi).
*/
void add_pi(var val);
/**
\brief Register a binary atan2(y, x) application to be refined
directly by nlsat's own search loop (see
nlsat_transcendentals.h::add_atan2).
*/
void add_atan2(var y, var x, var val);
/**
\brief True if at least one transcendental application has been
registered (see add_transcendental/add_pi/add_atan2), i.e. this
solver's own search loop refines them.
*/
bool transcendentals_enabled() const;
void inc_ref(bool_var b);
void inc_ref(literal l) { inc_ref(l.var()); }
void dec_ref(bool_var b);
void dec_ref(literal l) { dec_ref(l.var()); }
void inc_ref(assumption a);
void dec_ref(assumption a);
/**
\brief Create a new clause.
*/
void mk_clause(unsigned num_lits, literal * lits, assumption a = nullptr);
/**
\brief Borrow the learned clauses and inspect their external assumption tags.
Clause pointers remain valid only until the next solver mutation.
*/
ptr_vector<clause> const& get_lemmas() const;
void get_dependencies(clause const& c, vector<assumption, false>& deps) const;
/**
\brief Retract clauses depending on the non-null external scope_tag,
preserving independent learned clauses without rebuilding surviving atoms.
Keep at most max_lemmas learned clauses, preferring shorter clauses.
Requires an incremental solver. Invalidates the model and unsat core.
*/
void retract(assumption scope_tag, unsigned max_lemmas = UINT_MAX);
// -----------------------
//
// Basic
//
// -----------------------
/**
\brief Return the number of Boolean variables.
*/
unsigned num_bool_vars() const;
/**
\brief Get atom associated with Boolean variable. Return 0 if there is none.
*/
atom * bool_var2atom(bool_var b);
/**
\brief extract free variables from literal.
*/
void vars(literal l, var_vector& vs);
/**
\brief provide access to atoms. Used by explain.
*/
atom_vector const& get_atoms();
/**
\brief Access var -> asserted equality.
*/
atom_vector const& get_var2eq();
/**
\brief expose evaluator.
*/
evaluator& get_evaluator();
/**
\brief Access explanation module.
*/
explain& get_explain();
/**
\brief Access assignments to variables.
*/
void get_rvalues(assignment& as);
void set_rvalues(assignment const& as);
void get_bvalues(svector<bool_var> const& bvars, svector<lbool>& vs);
void set_bvalues(svector<lbool> const& vs);
/**
* \brief Access functions for simplify module.
*/
void del_clause(clause* c);
clause* mk_clause(unsigned n, literal const* lits, bool learned, internal_assumption a);
bool has_root_atom(clause const& c) const;
assumption join(assumption a, assumption b);
void inc_simplify();
void record_levelwise_result(bool success);
void add_bound(bound_constraint const& c);
/**
\brief reorder variables.
*/
/**
\brief Optimization support: when x is the designated maximization
variable, the solver assigns x the largest value compatible with the
current infeasible intervals (instead of an arbitrary witness) and
does not reorder variables, so that x keeps its position in the
variable order. Use null_var to disable.
*/
void set_max_var(var x);
/**
\brief Query right after check() returns l_true. If the feasible set
of the maximization variable is bounded above, set sup to its
supremum, set attained to true when the assigned value equals sup
(false when the supremum is open and the value lies below it), and
return true. Return false when the feasible set is unbounded above;
that is not a verdict on the problem, since clauses learned in later
rounds may still bound the variable. The answer is read from the
solver's infeasible-interval sets, so it goes stale after further
mk_clause or check calls.
*/
bool max_var_sup(anum & sup, bool & attained) const;
void reorder(unsigned sz, var const* permutation);
void restore_order();
/**
\brief Return number of integer/real variables
*/
unsigned num_vars() const;
bool is_int(var x) const;
// -----------------------
//
// Search
//
// -----------------------
lbool check();
lbool check(literal_vector& assumptions);
/**
\brief Decide whether feasible values of x approach bound from below,
or are unbounded above when bound is null.
Project satisfying regions onto x and cover them until a feasible
interval reaches the limit or no feasible values remain. A finite
limit need not be an upper bound of the original problem.
Requires an incremental solver with x == 0 and no active reordering.
Integer variables return l_undef. Resource exceptions propagate.
Temporary clauses are retracted on exit, including on cancellation;
the previous model and unsat core are invalidated.
*/
lbool check_limit(var x, anum const* bound = nullptr);
//
// check satisfiability of asserted formulas relative to state of the nlsat solver.
// produce either,
// l_true - a model is available (rvalues can be ignored) or,
// l_false - a clause (not core v not cell) excluding a cell around rvalues if core (consisting of atoms
// passed to nlsat) is asserted.
// l_undef - if the search was interrupted by a resource limit.
// clause is a list of literals. Their disjunction is valid.
// Different implementations of check are possible. One where cell comprises of linear polynomials could
// produce lemmas that are friendly to linear arithmetic solvers.
//
lbool check(assignment const& rvalues, literal_vector& clause);
// -----------------------
//
// Model
//
// -----------------------
anum const & value(var x) const;
lbool bvalue(bool_var b) const;
bool is_interpreted(bool_var b) const;
lbool value(literal l) const;
// -----------------------
//
// Core
//
// -----------------------
void get_core(vector<assumption, false>& deps);
// -----------------------
//
// Misc
//
// -----------------------
void updt_params(params_ref const & p);
static void collect_param_descrs(param_descrs & d);
const assignment& sample() const;
assignment& sample();
bool apply_levelwise() const;
unsigned lws_spt_threshold() const;
bool lws_witness_subs_lc() const;
bool lws_witness_subs_disc() const;
void reset();
void collect_statistics(statistics & st);
void reset_statistics();
void display_status(std::ostream & out) const;
// -----------------------
//
// Pretty printing
//
// -----------------------
/**
\brief Display solver's state.
*/
std::ostream& display(std::ostream & out) const;
/**
\brief Display literal
*/
std::ostream& display(std::ostream & out, literal l) const;
std::ostream& display(std::ostream & out, unsigned n, literal const* ls) const;
std::ostream& display(std::ostream& out, clause const& c) const;
std::ostream& display(std::ostream & out, literal_vector const& ls) const;
std::ostream& display(std::ostream & out, atom const& a) const;
std::ostream& display_smt2(std::ostream & out, literal l) const;
std::ostream& display_smt2(std::ostream & out, unsigned n, literal const* ls) const;
std::ostream& display_smt2(std::ostream & out, literal_vector const& ls) const;
std::ostream& display_smt2(std::ostream & out) const;
/**
\brief Display variable
*/
std::ostream& display(std::ostream & out, var x) const;
display_var_proc const & display_proc() const;
std::ostream& display_assignment(std::ostream& out) const;
std::ostream& display_var(std::ostream& out, unsigned j) const;
};
}