/// <summary>
/// Return lookup lemmas for each element in the old relation as well as the definition of the old relation, which
/// is defined via an association list
/// </summary>
private static StateRelationData OldRelation(
ISet <Variable> oldGlobalVars,
IVariableTranslation <Variable> variableTranslation,
out IList <OuterDecl> oldRelDecls)
{
//assume that passive version representing old variable of "g" is "g" itself
var oldRelTuples = new List <Term>();
var varList = new List <Variable>();
var varToLookupLemma = new Dictionary <Variable, LemmaDecl>();
var uniqueNamer = new IsaUniqueNamer();
foreach (var v in oldGlobalVars)
{
if (variableTranslation.TryTranslateVariableId(v, out var varTermId, out _))
{
oldRelTuples.Add(new TermTuple(varTermId, IsaCommonTerms.Inl(varTermId)));
var lemma = new LemmaDecl(
"lookup_old_rel" + uniqueNamer.GetName(v, v.Name),
TermBinary.Eq(new TermApp(oldRel, varTermId),
IsaCommonTerms.SomeOption(IsaCommonTerms.Inl(varTermId))),
new Proof(new List <string>
{
"unfolding " + oldRelListName + "_def " + oldRelName + "_def",
"by simp"
})
);
varToLookupLemma.Add(v, lemma);
varList.Add(v);
}
private List <OuterDecl> GenerateLemma()
{
var varIds = new List <Tuple <int, Variable> >();
foreach (var v in liveEntryVars)
{
if (varTranslation.TryTranslateVariableId(v, out var termId, out _))
{
varIds.Add(Tuple.Create((termId as NatConst).Val, v));
}
private void AddHint(IDictionary <TypeVariable, Type> unifier)
{
var typeIsaVisitor = new TypeIsaVisitor(tyVarTranslation);
IDictionary <int, Term> indexToType = new Dictionary <int, Term>();
foreach (var entry in unifier)
{
if (tyVarTranslation.TryTranslateVariableId(entry.Key, out var idTerm, out _) &&
idTerm is NatConst idNat)
{
indexToType.Add(idNat.Val, typeIsaVisitor.Translate(entry.Value));
}
public static Term LocalStateVariableAssumption(Variable v, Term varContext, Term normalState, Term vcVar,
IVariableTranslation <Variable> varTranslation)
{
if (varTranslation.TryTranslateVariableId(v, out var varId, out var isBoundVar) && !isBoundVar)
{
var left = IsaBoogieTerm.LookupVar(varContext, normalState, varId);
var right =
IsaCommonTerms.SomeOption(pureToBoogieValConverter.ConvertToBoogieVal(v.TypedIdent.Type, vcVar));
return(new TermBinary(left, right, TermBinary.BinaryOpCode.Eq));
}
throw new ProofGenUnexpectedStateException(typeof(LemmaHelper), "Can't retrieve variable id");
}
//must be called in a topological backwards order
public Tuple <LemmaDecl, LemmaDecl> GenerateBlockLemma(Block block, string localLemmaName,
Func <Block, string> cfgLemmaNameFunc)
{
var cmdsDefName = programAccessor.BlockInfo().CmdsQualifiedName(block);
Term cmds = IsaCommonTerms.TermIdentFromName(cmdsDefName);
var passiveBlock = origToPassiveBlock[block];
var passiveCmdsDefName = passiveProgramAccessor.BlockInfo().CmdsQualifiedName(passiveBlock);
Term passiveCmds = IsaCommonTerms.TermIdentFromName(passiveCmdsDefName);
#region compute variable relation update information
var successors = cfg.GetSuccessorBlocks(block);
var varRelUpdates = _relationGen.GenerateVariableRelUpdates(block, out _);
var constrainedPassiveVars = new List <Term>();
var modifiedVarRelTerm = new List <Term>();
var lookupTyUpdatesLemmas = new List <Tuple <string, string> >();
foreach (var tuple in varRelUpdates)
{
var origVar = tuple.Item1;
if (varTranslation.TryTranslateVariableId(origVar, out var origVarTerm, out _))
{
if (tuple.Item2 is IdentifierExpr ie)
{
var passiveVar = ie.Decl;
if (passiveVarTranslation.TryTranslateVariableId(passiveVar, out var passiveVarTerm, out _))
{
modifiedVarRelTerm.Add(new TermTuple(origVarTerm, IsaCommonTerms.Inl(passiveVarTerm)));
/* don't add variable to newly constrained variables if update is associated with constant propagation
* in which case the variable is not newly constrained */
if (!tuple.Item3)
{
constrainedPassiveVars.Add(passiveVarTerm);
}
lookupTyUpdatesLemmas.Add(
Tuple.Create(programAccessor.LookupVarTyLemma(origVar),
passiveProgramAccessor.LookupVarTyLemma(passiveVar))
);
}
else
{
throw new ProofGenUnexpectedStateException(GetType(), "Could not translate variables.");
}
}
