feat(library/blast): add congruence closure skeleton
This commit is contained in:
parent
60945e95b4
commit
39ec756331
3 changed files with 158 additions and 1 deletions
|
@ -2,4 +2,4 @@ add_library(blast OBJECT expr.cpp state.cpp blast.cpp blast_tactic.cpp
|
||||||
init_module.cpp simplifier.cpp simple_actions.cpp intros_action.cpp proof_expr.cpp
|
init_module.cpp simplifier.cpp simple_actions.cpp intros_action.cpp proof_expr.cpp
|
||||||
options.cpp choice_point.cpp simple_strategy.cpp backward_action.cpp util.cpp
|
options.cpp choice_point.cpp simple_strategy.cpp backward_action.cpp util.cpp
|
||||||
gexpr.cpp revert_action.cpp subst_action.cpp no_confusion_action.cpp
|
gexpr.cpp revert_action.cpp subst_action.cpp no_confusion_action.cpp
|
||||||
simplify_actions.cpp strategy.cpp recursor_action.cpp)
|
simplify_actions.cpp strategy.cpp recursor_action.cpp congruence_closure.cpp)
|
||||||
|
|
14
src/library/blast/congruence_closure.cpp
Normal file
14
src/library/blast/congruence_closure.cpp
Normal file
|
@ -0,0 +1,14 @@
|
||||||
|
/*
|
||||||
|
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
|
||||||
|
Released under Apache 2.0 license as described in the file LICENSE.
|
||||||
|
|
||||||
|
Author: Leonardo de Moura
|
||||||
|
*/
|
||||||
|
#include "library/blast/congruence_closure.h"
|
||||||
|
|
||||||
|
namespace lean {
|
||||||
|
namespace blast {
|
||||||
|
void congruence_closure::display() const {
|
||||||
|
// TODO(Leo):
|
||||||
|
}
|
||||||
|
}}
|
143
src/library/blast/congruence_closure.h
Normal file
143
src/library/blast/congruence_closure.h
Normal file
|
@ -0,0 +1,143 @@
|
||||||
|
/*
|
||||||
|
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
|
||||||
|
Released under Apache 2.0 license as described in the file LICENSE.
|
||||||
|
|
||||||
|
Author: Leonardo de Moura
|
||||||
|
*/
|
||||||
|
#pragma once
|
||||||
|
#include "kernel/expr.h"
|
||||||
|
#include "library/expr_lt.h"
|
||||||
|
#include "library/blast/hypothesis.h"
|
||||||
|
|
||||||
|
namespace lean {
|
||||||
|
namespace blast {
|
||||||
|
class congruence_closure {
|
||||||
|
/*
|
||||||
|
We maintain several equivalence relations.
|
||||||
|
Any relation tagged as [refl], [symm] and [trans] is handled by this module.
|
||||||
|
|
||||||
|
We use a union-find based data-structure for storing the equivalence relations.
|
||||||
|
Each equivalence class contains one or more expressions.
|
||||||
|
We store the additional information for each expression in the 'entry' structure.
|
||||||
|
We use a mapping from (R, e) to 'entry', where 'R' is the equivalence relation name, and
|
||||||
|
'e' is an expression.
|
||||||
|
|
||||||
|
To find the equivalence class for expression 'e' with respect to equivalence relation 'R',
|
||||||
|
we create a key (R, e) and get the associated entry. The entry has a 'm_next' field,
|
||||||
|
that is the next element in the equivalence class containing 'e'.
|
||||||
|
|
||||||
|
We used functional-datastructures because we must be able to create copies efficiently.
|
||||||
|
It will be part of the blast::state object.
|
||||||
|
|
||||||
|
Remark: only a subset of use-defined congruence rules are considered.
|
||||||
|
We ignore user-defined congruence rules that have hypotheses and/or are contextual.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* Equivalence class data associated with an expression 'e' */
|
||||||
|
struct entry {
|
||||||
|
expr m_next; // next element in the equivalence class.
|
||||||
|
expr m_root; // root (aka canonical) representative of the equivalence class.
|
||||||
|
expr m_cg_root; // root of the congruence class, it is meaningless if 'e' is not an application.
|
||||||
|
// When 'e' was added to this equivalence class because of an equality (H : e ~ target), then we
|
||||||
|
// store 'target' at 'm_target', and 'H' at 'm_proof'. Both fields are none if 'e' == m_root
|
||||||
|
optional<expr> m_target;
|
||||||
|
optional<expr> m_proof;
|
||||||
|
unsigned m_rank; // rank of the equivalence class, it is meaningless if 'e' != m_root
|
||||||
|
/* Each equivalence class may contain at most one "interpreted" element. The interpreted element will
|
||||||
|
always be the root. For example, we tag 'true' and 'false' as interpreted. */
|
||||||
|
bool m_interpreted;
|
||||||
|
};
|
||||||
|
|
||||||
|
/* Key (R, e) for the mapping (R, e) -> entry */
|
||||||
|
struct eqc_key {
|
||||||
|
name m_R;
|
||||||
|
expr m_expr;
|
||||||
|
eqc_key() {}
|
||||||
|
eqc_key(name const & n, expr const & e):m_R(n), m_expr(e) {}
|
||||||
|
};
|
||||||
|
|
||||||
|
struct eqc_key_cmp {
|
||||||
|
int operator()(eqc_key const & k1, eqc_key const & k2) {
|
||||||
|
int r = quick_cmp(k1.m_R, k2.m_R);
|
||||||
|
if (r != 0) return r;
|
||||||
|
else return is_lt(k1.m_expr, k2.m_expr, true);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
/* Key for the congruence set */
|
||||||
|
struct congr_key {
|
||||||
|
name m_R;
|
||||||
|
expr m_expr;
|
||||||
|
/* We track unequivalences using congruence table.
|
||||||
|
The idea is to store (not a = b) by putting (a = b) in the equivalence class of false.
|
||||||
|
So, we want (a = b) and (b = a) to be the "same" key in the congruence table.
|
||||||
|
eq and iff are ubiquitous. So, we have special treatment for them.
|
||||||
|
|
||||||
|
\remark: the trick can be used with commutative operators, but we currently don't do it. */
|
||||||
|
unsigned m_eq:1; // true if m_expr is an equality
|
||||||
|
unsigned m_iff:1; // true if m_expr is an iff
|
||||||
|
unsigned m_symm_rel; // true if m_expr is another symmetric relation.
|
||||||
|
};
|
||||||
|
|
||||||
|
struct congr_key_cmp {
|
||||||
|
int operator()(congr_key const & k1, congr_key const & k2);
|
||||||
|
};
|
||||||
|
|
||||||
|
typedef rb_tree<expr, expr_quick_cmp> expr_set;
|
||||||
|
typedef rb_map<eqc_key, entry, eqc_key_cmp> entries;
|
||||||
|
typedef rb_map<expr, expr_set, expr_quick_cmp> parents;
|
||||||
|
typedef rb_tree<congr_key, congr_key_cmp> congruences;
|
||||||
|
|
||||||
|
entries m_entries;
|
||||||
|
parents m_parents;
|
||||||
|
congruences m_congruences;
|
||||||
|
|
||||||
|
public:
|
||||||
|
/** \brief Register expression \c e in this data-structure.
|
||||||
|
It creates entries for each sub-expression in \c e.
|
||||||
|
It also updates the m_parents mapping.
|
||||||
|
|
||||||
|
We ignore the following subterms of \c e.
|
||||||
|
1- and, or and not-applications are not inserted into the data-structures, but
|
||||||
|
their arguments are visited.
|
||||||
|
2- (Pi (x : A), B), the subterms A and B are not visited if B depends on x.
|
||||||
|
3- (A -> B) is not inserted into the data-structures, but their arguments are visited
|
||||||
|
if they are propositions.
|
||||||
|
4- Terms containing meta-variables.
|
||||||
|
5- The subterms of lambda-expressions. */
|
||||||
|
void internalize(expr const & e);
|
||||||
|
|
||||||
|
/** \brief Given a hypothesis H, this method will do the following based on the type of H
|
||||||
|
1- (H : a ~ b): merge equivalence classes of 'a' and 'b', and propagate congruences.
|
||||||
|
|
||||||
|
2- (H : not a ~ b): add the equivalence ((a ~ b) <-> false)
|
||||||
|
|
||||||
|
3- (H : P), if P is a proposition, add the equivalence (P <-> true)
|
||||||
|
|
||||||
|
4- (H : not P), add the equivalence (P <-> false)
|
||||||
|
|
||||||
|
If H is none of the forms above, this method does nothing. */
|
||||||
|
void add(hypothesis_idx hidx);
|
||||||
|
|
||||||
|
/** \brief Return true if an inconsistency has been detected, i.e., true and false are in the same equivalence class */
|
||||||
|
bool is_inconsistent() const;
|
||||||
|
/** \brief Return the proof of inconsistency */
|
||||||
|
optional<expr> get_inconsistency_proof() const;
|
||||||
|
|
||||||
|
/** \brief Return true iff 'e1' and 'e2' are in the same equivalence class for relation \c rel_name. */
|
||||||
|
bool is_eqv(name const & rel_name, expr const & e1, expr const & e2) const;
|
||||||
|
optional<expr> get_eqv_proof(name const & rel_name, expr const & e1, expr const & e2) const;
|
||||||
|
|
||||||
|
/** \brief Return true iff `e1 ~ e2` is in the equivalence class of false for iff. */
|
||||||
|
bool is_uneqv(name const & rel_name, expr const & e1, expr const & e2) const;
|
||||||
|
optional<expr> get_uneqv_proof(name const & rel_name, expr const & e1, expr const & e2) const;
|
||||||
|
|
||||||
|
bool is_congr_root(expr const & e) const;
|
||||||
|
bool is_root(expr const & e) const;
|
||||||
|
expr get_root(expr const & e) const;
|
||||||
|
expr get_next(expr const & e) const;
|
||||||
|
|
||||||
|
/** \brief dump for debugging purposes. */
|
||||||
|
void display() const;
|
||||||
|
};
|
||||||
|
}}
|
Loading…
Reference in a new issue