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/********************* */
/*! \file fun_def_process.cpp
** \verbatim
** Top contributors (to current version):
** Andrew Reynolds, Tim King
** This file is part of the CVC4 project.
** Copyright (c) 2009-2016 by the authors listed in the file AUTHORS
** in the top-level source directory) and their institutional affiliations.
** All rights reserved. See the file COPYING in the top-level source
** directory for licensing information.\endverbatim
**
** \brief Sort inference module
**
** This class implements pre-process steps for well-defined functions
**/
#include <vector>
#include "theory/quantifiers/fun_def_process.h"
#include "theory/rewriter.h"
#include "theory/quantifiers/term_database.h"
#include "theory/quantifiers/quant_util.h"
#include "proof/proof_manager.h"
using namespace CVC4;
using namespace std;
using namespace CVC4::theory;
using namespace CVC4::theory::quantifiers;
using namespace CVC4::kind;
void FunDefFmf::simplify( std::vector< Node >& assertions, bool doRewrite ) {
std::vector< int > fd_assertions;
std::map< int, Node > subs_head;
//first pass : find defined functions, transform quantifiers
for( unsigned i=0; i<assertions.size(); i++ ){
Node n = TermDb::getFunDefHead( assertions[i] );
if( !n.isNull() ){
Assert( n.getKind()==APPLY_UF );
Node f = n.getOperator();
//check if already defined, if so, throw error
if( d_sorts.find( f )!=d_sorts.end() ){
Message() << "Cannot define function " << f << " more than once." << std::endl;
exit( 0 );
}
Node bd = TermDb::getFunDefBody( assertions[i] );
Trace("fmf-fun-def-debug") << "Process function " << n << ", body = " << bd << std::endl;
if( !bd.isNull() ){
d_funcs.push_back( f );
bd = NodeManager::currentNM()->mkNode( n.getType().isBoolean() ? IFF : EQUAL, n, bd );
//create a sort S that represents the inputs of the function
std::stringstream ss;
ss << "I_" << f;
TypeNode iType = NodeManager::currentNM()->mkSort( ss.str() );
AbsTypeFunDefAttribute atfda;
iType.setAttribute(atfda,true);
d_sorts[f] = iType;
//create functions f1...fn mapping from this sort to concrete elements
for( unsigned j=0; j<n.getNumChildren(); j++ ){
TypeNode typ = NodeManager::currentNM()->mkFunctionType( iType, n[j].getType() );
std::stringstream ss;
ss << f << "_arg_" << j;
d_input_arg_inj[f].push_back( NodeManager::currentNM()->mkSkolem( ss.str(), typ, "op created during fun def fmf" ) );
}
//construct new quantifier forall S. F[f1(S)/x1....fn(S)/xn]
std::vector< Node > children;
Node bv = NodeManager::currentNM()->mkBoundVar("?i", iType );
Node bvl = NodeManager::currentNM()->mkNode( kind::BOUND_VAR_LIST, bv );
std::vector< Node > subs;
std::vector< Node > vars;
for( unsigned j=0; j<n.getNumChildren(); j++ ){
vars.push_back( n[j] );
subs.push_back( NodeManager::currentNM()->mkNode( APPLY_UF, d_input_arg_inj[f][j], bv ) );
}
bd = bd.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
subs_head[i] = n.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
Trace("fmf-fun-def") << "FMF fun def: FUNCTION : rewrite " << assertions[i] << std::endl;
Trace("fmf-fun-def") << " to " << std::endl;
Node new_q = NodeManager::currentNM()->mkNode( FORALL, bvl, bd );
new_q = Rewriter::rewrite( new_q );
PROOF( ProofManager::currentPM()->addDependence(new_q, assertions[i]); );
assertions[i] = new_q;
Trace("fmf-fun-def") << " " << assertions[i] << std::endl;
fd_assertions.push_back( i );
}else{
//can be, e.g. in corner cases forall x. f(x)=f(x), forall x. f(x)=f(x)+1
}
}
}
//second pass : rewrite assertions
for( unsigned i=0; i<assertions.size(); i++ ){
int is_fd = std::find( fd_assertions.begin(), fd_assertions.end(), i )!=fd_assertions.end() ? 1 : 0;
//constant boolean function definitions do not add domain constraints
if( is_fd==0 || ( is_fd==1 && ( assertions[i][1].getKind()==EQUAL || assertions[i][1].getKind()==IFF ) ) ){
std::vector< Node > constraints;
Trace("fmf-fun-def-rewrite") << "Rewriting " << assertions[i] << ", is_fd = " << is_fd << std::endl;
Node n = simplifyFormula( assertions[i], true, true, constraints, is_fd==1 ? subs_head[i] : Node::null(), is_fd );
Assert( constraints.empty() );
if( n!=assertions[i] ){
n = Rewriter::rewrite( n );
Trace("fmf-fun-def-rewrite") << "FMF fun def : rewrite " << assertions[i] << std::endl;
Trace("fmf-fun-def-rewrite") << " to " << std::endl;
Trace("fmf-fun-def-rewrite") << " " << n << std::endl;
PROOF( ProofManager::currentPM()->addDependence(n, assertions[i]); );
assertions[i] = n;
}
}
}
}
//is_fun_def 1 : top of fun-def, 2 : top of fun-def body, 0 : not top
Node FunDefFmf::simplifyFormula( Node n, bool pol, bool hasPol, std::vector< Node >& constraints, Node hd, int is_fun_def ) {
Trace("fmf-fun-def-debug") << "Simplify " << n << " " << pol << " " << hasPol << " " << is_fun_def << std::endl;
if( n.getKind()==FORALL ){
Node c = simplifyFormula( n[1], pol, hasPol, constraints, hd, is_fun_def );
//append prenex to constraints
for( unsigned i=0; i<constraints.size(); i++ ){
constraints[i] = NodeManager::currentNM()->mkNode( FORALL, n[0], constraints[i] );
constraints[i] = Rewriter::rewrite( constraints[i] );
}
if( c!=n[1] ){
return NodeManager::currentNM()->mkNode( FORALL, n[0], c );
}else{
return n;
}
}else{
Node nn = n;
bool isBool = n.getType().isBoolean();
if( isBool && n.getKind()!=APPLY_UF && is_fun_def!=2 ){
std::vector< Node > children;
bool childChanged = false;
for( unsigned i=0; i<n.getNumChildren(); i++ ){
Node c = n[i];
//do not process LHS of definition
if( is_fun_def!=1 || c!=hd ){
bool newHasPol;
bool newPol;
QuantPhaseReq::getPolarity( n, i, hasPol, pol, newHasPol, newPol );
//get child constraints
std::vector< Node > cconstraints;
c = simplifyFormula( n[i], newPol, newHasPol, cconstraints, hd, is_fun_def==1 ? 2 : 0 );
constraints.insert( constraints.end(), cconstraints.begin(), cconstraints.end() );
}
children.push_back( c );
childChanged = c!=n[i] || childChanged;
}
if( childChanged ){
nn = NodeManager::currentNM()->mkNode( n.getKind(), children );
}
}else{
//simplify term
simplifyTerm( n, constraints );
}
if( !constraints.empty() && isBool && hasPol ){
std::vector< Node > c;
c.push_back( nn );
//conjoin with current
for( unsigned i=0; i<constraints.size(); i++ ){
if( pol ){
c.push_back( constraints[i] );
}else{
c.push_back( constraints[i].negate() );
}
}
constraints.clear();
return c.size()==1 ? c[0] : NodeManager::currentNM()->mkNode( pol ? AND : OR, c );
}else{
return nn;
}
}
}
void FunDefFmf::simplifyTerm( Node n, std::vector< Node >& constraints ) {
Trace("fmf-fun-def-debug") << "Simplify term " << n << std::endl;
if( n.getKind()==ITE ){
simplifyTerm( n[0], constraints );
std::vector< Node > ccons1;
std::vector< Node > ccons2;
simplifyTerm( n[1], ccons1 );
simplifyTerm( n[2], ccons2 );
if( !ccons1.empty() || !ccons2.empty() ){
Node n1 = ccons1.empty() ? NodeManager::currentNM()->mkConst( true ) : ( ccons1.size()==1 ? ccons1[0] : NodeManager::currentNM()->mkNode( AND, ccons1 ) );
Node n2 = ccons2.empty() ? NodeManager::currentNM()->mkConst( true ) : ( ccons2.size()==1 ? ccons2[0] : NodeManager::currentNM()->mkNode( AND, ccons2 ) );
constraints.push_back( NodeManager::currentNM()->mkNode( ITE, n[0], n1, n2 ) );
}
}else{
if( n.getKind()==APPLY_UF ){
//check if f is defined, if so, we must enforce domain constraints for this f-application
Node f = n.getOperator();
std::map< Node, TypeNode >::iterator it = d_sorts.find( f );
if( it!=d_sorts.end() ){
//create existential
Node z = NodeManager::currentNM()->mkBoundVar("?z", it->second );
Node bvl = NodeManager::currentNM()->mkNode( BOUND_VAR_LIST, z );
std::vector< Node > children;
for( unsigned j=0; j<n.getNumChildren(); j++ ){
Node uz = NodeManager::currentNM()->mkNode( APPLY_UF, d_input_arg_inj[f][j], z );
if( !n[j].getType().isBoolean() ){
children.push_back( uz.eqNode( n[j] ) );
}else{
children.push_back( uz.iffNode( n[j] ) );
}
}
Node bd = children.size()==1 ? children[0] : NodeManager::currentNM()->mkNode( AND, children );
bd = bd.negate();
Node ex = NodeManager::currentNM()->mkNode( FORALL, bvl, bd );
ex = ex.negate();
constraints.push_back( ex );
Trace("fmf-fun-def-debug") << "---> add constraint " << ex << std::endl;
}
}
for( unsigned i=0; i<n.getNumChildren(); i++ ){
simplifyTerm( n[i], constraints );
}
}
}
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