Theorem TheoryArith::canonSimp(const Expr& e)
{
DebugAssert(canonRec(e).getRHS() == e, "canonSimp expects input to be canonized");
int ar = e.arity();
if (isLeaf(e)) return find(e);
if (ar > 0) {
vector<Theorem> newChildrenThm;
vector<unsigned> changed;
Theorem thm;
for (int k = 0; k < ar; ++k) {
thm = canonSimp(e[k]);
if (thm.getLHS() != thm.getRHS()) {
newChildrenThm.push_back(thm);
changed.push_back(k);
}
}
if(changed.size() > 0) {
thm = canonThm(substitutivityRule(e, changed, newChildrenThm));
return transitivityRule(thm, find(thm.getRHS()));
}
else return find(e);
}
return find(e);
}
Theorem TheoryArith::canonRec(const Expr& e)
{
if (isLeaf(e)) return reflexivityRule(e);
int ar = e.arity();
if (ar > 0) {
vector<Theorem> newChildrenThm;
vector<unsigned> changed;
for(int k = 0; k < ar; ++k) {
// Recursively canonize the kids
Theorem thm = canonRec(e[k]);
if (thm.getLHS() != thm.getRHS()) {
newChildrenThm.push_back(thm);
changed.push_back(k);
}
}
if(changed.size() > 0) {
return canonThm(substitutivityRule(e, changed, newChildrenThm));
}
}
return canon(e);
}
Lit CNF_Manager::translateExprRec(const Expr& e, CNF_Formula& cnf, const Theorem& thmIn)
{
if (e.isFalse()) return Lit::getFalse();
if (e.isTrue()) return Lit::getTrue();
if (e.isNot()) return !translateExprRec(e[0], cnf, thmIn);
ExprHashMap<Var>::iterator iMap = d_cnfVars.find(e);
if (e.isTranslated()) {
DebugAssert(iMap != d_cnfVars.end(), "Translated expr should be in map");
return Lit((*iMap).second);
}
else e.setTranslated(d_bottomScope);
Var v(int(d_varInfo.size()));
bool translateOnly = false;
if (iMap != d_cnfVars.end()) {
v = (*iMap).second;
translateOnly = true;
d_varInfo[v].fanouts.clear();
}
else {
d_varInfo.resize(v+1);
d_varInfo.back().expr = e;
d_cnfVars[e] = v;
}
Expr::iterator i, iend;
bool isAnd = false;
switch (e.getKind()) {
case AND:
isAnd = true;
case OR: {
vector<Lit> lits;
unsigned idx;
for (i = e.begin(), iend = e.end(); i != iend; ++i) {
lits.push_back(translateExprRec(*i, cnf, thmIn));
}
// DebugAssert(concreteExpr(e,Lit(v)) == e,"why here");
for (idx = 0; idx < lits.size(); ++idx) {
cnf.newClause();
cnf.addLiteral(Lit(v),isAnd);
cnf.addLiteral(lits[idx], !isAnd);
// DebugAssert(concreteExpr(e[idx],lits[idx]) == e[idx], "why here");
std::string reasonStr = (isAnd ? "and_mid" : "or_mid");
Expr after = e[idx] ;
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, after, reasonStr, idx)); // by yeting
}
cnf.newClause();
cnf.addLiteral(Lit(v),!isAnd);
for (idx = 0; idx < lits.size(); ++idx) {
cnf.addLiteral(lits[idx], isAnd);
}
std::string reasonStr = (isAnd ? "and_final" : "or_final") ;
Expr after = e ;
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, after, reasonStr, 0)); // by yeting
break;
}
case IMPLIES: {
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
// DebugAssert(concreteExpr(e, Lit(v)) == e, "why here");
// DebugAssert(concreteExpr(e[0], arg0) == e[0], "why here");
// DebugAssert(concreteExpr(e[1], arg1) == e[1], "why here");
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.getCurrentClause().setClauseTheorem( d_rules->CNFtranslate(e, e, "imp", 0)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem( d_rules->CNFtranslate(e, e, "imp", 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem( d_rules->CNFtranslate(e, e, "imp", 2)); // by yeting
break;
}
case IFF: {
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
// DebugAssert(concreteExpr(e, Lit(v)) == e, "why here");
// DebugAssert(concreteExpr(e[0], arg0) == e[0], "why here");
// DebugAssert(concreteExpr(e[1], arg1) == e[1], "why here");
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 0)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 2)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 3)); // by yeting
break;
}
case XOR: {
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
// DebugAssert(concreteExpr(e, Lit(v)) == e, "why here");
// DebugAssert(concreteExpr(e[0], arg0) == e[0], "why here");
// DebugAssert(concreteExpr(e[1], arg1) == e[1], "why here");
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 0)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 2)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 3)); // by yeting
break;
}
case ITE:
{
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
Lit arg2 = translateExprRec(e[2], cnf, thmIn);
Expr aftere0 = concreteExpr(e[0], arg0);
Expr aftere1 = concreteExpr(e[1], arg1);
Expr aftere2 = concreteExpr(e[2], arg2);
vector<Expr> after ;
after.push_back(aftere0);
after.push_back(aftere1);
after.push_back(aftere2);
Theorem e0thm;
Theorem e1thm;
Theorem e2thm;
{ e0thm = d_iteMap[e[0]];
if (e0thm.isNull()) e0thm = d_commonRules->reflexivityRule(e[0]);
e1thm = d_iteMap[e[1]];
if (e1thm.isNull()) e1thm = d_commonRules->reflexivityRule(e[1]);
e2thm = d_iteMap[e[2]];
if (e2thm.isNull()) e2thm = d_commonRules->reflexivityRule(e[2]);
}
vector<Theorem> thms ;
thms.push_back(e0thm);
thms.push_back(e1thm);
thms.push_back(e2thm);
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0);
cnf.addLiteral(arg2);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.addLiteral(arg2,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 2)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 3)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 4)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg1,true);
cnf.addLiteral(arg2,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 5)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg1);
cnf.addLiteral(arg2);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 6)); // by yeting
break;
}
default:
{
DebugAssert(!e.isAbsAtomicFormula() || d_varInfo[v].expr == e,
"Corrupted Varinfo");
if (e.isAbsAtomicFormula()) {
registerAtom(e, thmIn);
return Lit(v);
}
Theorem thm = replaceITErec(e, v, translateOnly);
const Expr& e2 = thm.getRHS();
DebugAssert(e2.isAbsAtomicFormula(), "Expected AbsAtomicFormula");
if (e2.isTranslated()) {
// Ugly corner case: we happen to create an expression that has been
// created before. We remove the current variable and fix up the
// translation stack.
if (translateOnly) {
DebugAssert(v == d_cnfVars[e2], "Expected literal match");
}
else {
d_varInfo.resize(v);
while (!d_translateQueueVars.empty() &&
d_translateQueueVars.back() == v) {
d_translateQueueVars.pop_back();
}
DebugAssert(d_cnfVars.find(e2) != d_cnfVars.end(),
"Expected existing literal");
v = d_cnfVars[e2];
d_cnfVars[e] = v;
while (d_translateQueueVars.size() < d_translateQueueThms.size()) {
d_translateQueueVars.push_back(v);
}
}
}
else {
e2.setTranslated(d_bottomScope);
// Corner case: don't register reflexive equality
if (!e2.isEq() || e2[0] != e2[1]) registerAtom(e2, thmIn);
if (!translateOnly) {
if (d_cnfVars.find(e2) == d_cnfVars.end()) {
d_varInfo[v].expr = e2;
d_cnfVars[e2] = v;
}
else {
// Same corner case in an untranslated expr
d_varInfo.resize(v);
while (!d_translateQueueVars.empty() &&
d_translateQueueVars.back() == v) {
d_translateQueueVars.pop_back();
}
v = d_cnfVars[e2];
d_cnfVars[e] = v;
while (d_translateQueueVars.size() < d_translateQueueThms.size()) {
d_translateQueueVars.push_back(v);
}
}
}
}
return Lit(v);
}
}
// Record fanins / fanouts
Lit l;
for (i = e.begin(), iend = e.end(); i != iend; ++i) {
l = getCNFLit(*i);
DebugAssert(!l.isNull(), "Expected non-null literal");
if (!translateOnly) d_varInfo[v].fanins.push_back(l);
if (l.isVar()) d_varInfo[l.getVar()].fanouts.push_back(v);
}
return Lit(v);
}