/*
* Let the "tail formula" of the exit path be the path formula for all edges of the
* exit path except the first. We find the set of all terms in the tail formula in which
* all program variables appear with SSA index 1 (meaning this regards their state upon exit
* of the loop, and prior to any subsequent modification), and we form a fresh-parameter
* linear combination of these terms for the LHS of our template. The RHS is another
* fresh parameter, and the relation is the one passed as argument.
*
* The idea is to try this method after the exitHeadNegationMethod. If that one failed,
* then probably we didn't enter the error state simply because of the edge along which
* we exited the loop; instead, it might have been because something which is actually
* true of the program variables on loop exit was supposed not to be. For example, we might
* have reached the error state because of a failed 'assert' statement, which simply asserts
* something about the variables involved in the loop. Our hope is to build as invariant the
* very statement that is asserted.
*/
private Template exitTailIndexOneFreeCombMethod(InfixReln relation) {
// Get top-level terms.
Set<TemplateTerm> terms = exitFormulaTail.getTopLevelTerms();
// Keep just those that have max index 1.
Set<TemplateTerm> indexone = new HashSet<>();
int n;
for (TemplateTerm t : terms) {
n = t.getMaxIndex();
if (n == 1) {
indexone.add(t);
}
}
// Combine these for LHS.
TemplateSum LHS = TemplateSum.freshParamLinComb(type, indexone);
// Make RHS parameter.
TemplateTerm RHS = makeRHSParameter();
// Build template formula as constraint.
TemplateFormula formula = new TemplateConstraint(LHS, relation, RHS);
formula.unindex();
// Make nonzero parameter clause.
// Namely, we simply ask that not all of the top-level parameters on
// the LHS be zero.
Set<TemplateVariable> topLevelLHSparams = LHS.getTopLevelParameters();
TemplateFormula nzpc = makeBasicParamClause(topLevelLHSparams);
Template choice = new Template(formula, nzpc);
return choice;
}
private Template topLevelTermFormsMethod(InfixReln relation) {
Template choice = null;
// Get all forms.
Set<TermForm> forms = entryFormula.getTopLevelTermForms();
forms.addAll(loopFormula.getTopLevelTermForms());
forms.addAll(exitFormula.getTopLevelTermForms());
// Convert to terms, and sum up for LHS.
Vector<TemplateTerm> terms = new Vector<>();
for (TermForm f : forms) {
terms.add(f.getTemplate());
}
TemplateSum LHS = new TemplateSum(FormulaType.RationalType, terms);
// Make RHS parameter.
TemplateTerm RHS = makeRHSParameter();
// Build template formula as constraint.
TemplateFormula formula = new TemplateConstraint(LHS, relation, RHS);
// Make nonzero parameter clause.
// Namely, we simply ask that not all of the top-level parameters on
// the LHS be zero.
Set<TemplateVariable> topLevelLHSparams = LHS.getTopLevelParameters();
TemplateFormula nzpc = makeBasicParamClause(topLevelLHSparams);
choice = new Template(formula, nzpc);
return choice;
}
private Template loopVarsAndHeadFreeCombMethod(InfixReln relation) {
Template choice = null;
// Get all loop head and loop tail variables.
Set<TemplateTerm> headVars = getUnindexedVarsAsTerms(loopFormulaHead);
Set<TemplateTerm> tailVars = getUnindexedVarsAsTerms(loopFormulaTail);
// Declare a list of terms for each conjunct.
List<TemplateTerm> headTerms = new Vector<>();
List<TemplateTerm> tailTerms = new Vector<>();
// Add the loop vars.
headTerms.addAll(headVars);
tailTerms.addAll(tailVars);
// Create a fresh parameter linear combination of the terms for each conjunct.
TemplateSum headLHS = TemplateSum.freshParamLinComb(type, headTerms);
TemplateSum tailLHS = TemplateSum.freshParamLinComb(type, tailTerms);
// Make RHS parameters.
TemplateVariable param = TemplateTerm.getNextFreshParameter(type);
TemplateTerm headRHS = new TemplateTerm(type);
headRHS.setParameter(param);
param = TemplateTerm.getNextFreshParameter(type);
TemplateTerm tailRHS = new TemplateTerm(type);
tailRHS.setParameter(param);
// Build the conjuncts as constraints.
TemplateFormula headFormula = new TemplateConstraint(headLHS, InfixReln.LEQ, headRHS);
TemplateFormula tailFormula = new TemplateConstraint(tailLHS, InfixReln.EQUAL, tailRHS);
// Form the conjunction.
TemplateFormula formula =
TemplateConjunction.conjoin((TemplateBoolean) headFormula, (TemplateBoolean) tailFormula);
// Make nonzero parameter clause.
// Namely, we simply ask that not all of the top-level parameters on
// the LHS be zero.
Set<TemplateVariable> topLevelLHSparams = headLHS.getTopLevelParameters();
topLevelLHSparams.addAll(tailLHS.getTopLevelParameters());
TemplateFormula nzpc = makeBasicParamClause(topLevelLHSparams);
choice = new Template(formula, nzpc);
return choice;
}
private Template loopVarsFreeCombMethod(InfixReln relation) {
Template choice = null;
// Get all loop variables.
Set<TemplateTerm> loopVars = getUnindexedVarsAsTerms(loopFormula);
// Get all distinct UIF names occurring at the top level in the loop formula,
// and their arities.
Map<String, Integer> uifNA = getTopLevelUIFnamesAndArities(loopFormula);
// Declare the list of terms for the template.
List<TemplateTerm> templateTerms = new Vector<>();
// First add one term for each UIF name.
int arity;
TemplateUIF uif;
for (String name : uifNA.keySet()) {
arity = uifNA.get(name).intValue();
TemplateSum[] args = new TemplateSum[arity];
// each arg is a fresh parameter linear combination over loopVars
for (int i = 0; i < arity; i++) {
args[i] = TemplateSum.freshParamLinComb(type, loopVars);
}
// create the uif
uif = new TemplateUIF(name, type, new TemplateSumList(args));
// put it in a term
templateTerms.add(new TemplateTerm(uif));
}
// Now add the loop vars themselves.
templateTerms.addAll(loopVars);
// Finally create a fresh parameter linear combination of all the terms.
TemplateSum LHS = TemplateSum.freshParamLinComb(type, templateTerms);
// Make RHS parameter.
TemplateVariable param = TemplateTerm.getNextFreshParameter(type);
TemplateTerm RHS = new TemplateTerm(type);
RHS.setParameter(param);
// Build template formula as constraint.
TemplateFormula formula = new TemplateConstraint(LHS, relation, RHS);
// Make nonzero parameter clause.
// Namely, we simply ask that not all of the top-level parameters on
// the LHS be zero.
Set<TemplateVariable> topLevelLHSparams = LHS.getTopLevelParameters();
TemplateFormula nzpc = makeBasicParamClause(topLevelLHSparams);
choice = new Template(formula, nzpc);
return choice;
}