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/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
inj_axiom.cpp
Abstract:
<abstract>
Author:
Leonardo de Moura (leonardo) 2008-06-23.
Revision History:
--*/
#include "ast/rewriter/inj_axiom.h"
#include "ast/ast_pp.h"
#include "ast/ast_ll_pp.h"
#include "ast/has_free_vars.h"
#include "ast/well_sorted.h"
/**
\brief Little HACK for simplifying injectivity axioms
\remark It is not covering all possible cases.
*/
bool simplify_inj_axiom(ast_manager & m, quantifier * q, expr_ref & result) {
expr * n = q->get_expr();
expr* arg1 = nullptr, * arg2 = nullptr, *narg = nullptr;
expr* app1 = nullptr, * app2 = nullptr;
expr* var1 = nullptr, * var2 = nullptr;
if (is_forall(q) && m.is_or(n, arg1, arg2)) {
if (m.is_not(arg2))
std::swap(arg1, arg2);
if (m.is_not(arg1, narg) &&
m.is_eq(narg, app1, app2) &&
m.is_eq(arg2, var1, var2)) {
if (is_app(app1) &&
is_app(app2) &&
to_app(app1)->get_decl() == to_app(app2)->get_decl() &&
to_app(app1)->get_num_args() == to_app(app2)->get_num_args() &&
to_app(app1)->get_family_id() == null_family_id &&
to_app(app1)->get_num_args() > 0 &&
is_var(var1) &&
is_var(var2) &&
var1 != var2) {
app * f1 = to_app(app1);
app * f2 = to_app(app2);
bool found_vars = false;
unsigned num = f1->get_num_args();
unsigned idx = UINT_MAX;
unsigned num_vars = 1;
for (unsigned i = 0; i < num; ++i) {
expr * c1 = f1->get_arg(i);
expr * c2 = f2->get_arg(i);
if (!is_var(c1) && !is_uninterp_const(c1))
return false;
if ((c1 == var1 && c2 == var2) || (c1 == var2 && c2 == var1)) {
if (found_vars)
return false;
found_vars = true;
idx = i;
}
else if (c1 == c2 && c1 != var1 && c1 != var2) {
if (is_var(c1)) {
// the reconstructed axiom introduces a fresh variable per
// position, so repeated passive variables cannot be handled.
for (unsigned j = 0; j < i; ++j)
if (f1->get_arg(j) == c1)
return false;
++num_vars;
}
}
else {
return false;
}
}
if (found_vars && !has_free_vars(q)) {
(void)num_vars;
TRACE(inj_axiom,
tout << "Cadidate for simplification:\n" << mk_ll_pp(q, m) << mk_pp(app1, m) << "\n" << mk_pp(app2, m) << "\n" <<
mk_pp(var1, m) << "\n" << mk_pp(var2, m) << "\nnum_vars: " << num_vars << "\n";);
// Building new (optimized) axiom
func_decl * decl = f1->get_decl();
unsigned var_idx = 0;
ptr_buffer<expr> f_args, inv_vars;
ptr_buffer<sort> decls;
buffer<symbol> names;
expr * var = nullptr;
for (unsigned i = 0; i < num; ++i) {
expr * c = f1->get_arg(i);
if (is_var(c)) {
names.push_back(symbol(i));
sort * s = decl->get_domain(i);
decls.push_back(s);
expr * new_c = m.mk_var(var_idx, s);
var_idx++;
f_args.push_back(new_c);
if (i == idx) {
var = new_c;
}
else {
inv_vars.push_back(new_c);
}
}
else {
SASSERT(is_uninterp_const(c));
f_args.push_back(c);
}
}
SASSERT(var != 0);
app * f = m.mk_app(decl, f_args.size(), f_args.data());
ptr_vector<sort> domain;
inv_vars.push_back(f);
for (unsigned i = 0; i < inv_vars.size(); ++i) {
domain.push_back(inv_vars[i]->get_sort());
}
sort * d = decl->get_domain(idx);
func_decl * inv_decl = m.mk_fresh_func_decl("inj", domain.size(), domain.data(), d);
expr * proj = m.mk_app(inv_decl, inv_vars.size(), inv_vars.data());
expr * eq = m.mk_eq(proj, var);
expr * p = m.mk_pattern(f);
// decls are in the wrong order...
// Remark: the sort of the var 0 must be in the last position.
std::reverse(decls.begin(), decls.end());
result = m.mk_forall(decls.size(), decls.data(), names.data(), eq,
0, symbol(), symbol(), 1, &p);
TRACE(inj_axiom, tout << "new axiom:\n" << mk_pp(result, m) << "\n";);
SASSERT(is_well_sorted(m, result));
return true;
}
}
}
}
return false;
}