public Tuple <string, IEnumerable <LemmaDecl> > GenerateTactic(Expr e)
{
var varCollector = new VariableCollector();
varCollector.Visit(e);
var lookupTyThms = new List <string>();
var funMemThms = new List <string>();
foreach (var v in varCollector.usedVars)
{
try
{
lookupTyThms.Add(programAccessor.LookupVarTyLemma(v));
}
catch
{
//variable not found, possible if, for example, v is bound
}
}
var usedFuncs = functionCollector.UsedFunctions(e);
foreach (var f in usedFuncs)
{
funMemThms.Add(programAccessor.MembershipLemma(f));
}
var hintLemmas = equalityHintGenerator.GetHints(e);
var hintsML = MLUtil.IsaToMLThms(hintLemmas.Select(lemma => lemma.Name));
var lookupTyML = MLUtil.IsaToMLThms(lookupTyThms);
var funMemML = MLUtil.IsaToMLThms(funMemThms);
var args = new List <string>
{
MLUtil.ContextAntiquotation(),
hintsML,
lookupTyML,
funMemML
};
var tactic = ProofUtil.Apply(ProofUtil.MLTactic("typing_tac " + string.Join(" ", args), 1));
return(Tuple.Create(tactic, hintLemmas));
}
public LemmaDecl AxiomVcLemma(string lemmaName, Axiom axiom, VCExpr vcAxiom, out IList <OuterDecl> requiredDecls)
{
var vc = vcAxiomInst.GetVCObjInstantiation(vcAxiom, declToVCMapping);
var axiomTerm = basicCmdIsaVisitor.Translate(axiom.Expr);
requiredDecls = new List <OuterDecl>();
vcRewriteLemmaGen.RequiredVcRewrite(axiom.Expr, true, out var vcRewriteLemmas);
VCExprHint exprHint;
if (vcRewriteLemmas != null && vcRewriteLemmas.Any())
{
exprHint = new VCExprHint(vcRewriteLemmas);
requiredDecls.AddRange(vcRewriteLemmas);
}
else
{
exprHint = VCExprHint.EmptyExprHint();
}
var assumption =
IsaBoogieTerm.RedExpr(boogieContext, axiomTerm, normalInitState, IsaBoogieTerm.BoolVal(true));
var statement = vc;
return
(new LemmaDecl(lemmaName,
ContextElem.CreateWithAssumptions(assumption),
statement,
new Proof(new List <string>
{
"unfolding " + vcAxiomInst.GetVCObjNameRef(vcAxiom) + "_def",
ProofUtil.By(
ProofUtil.MLTactic(
"prove_axiom_vc_tac @{context} (" + exprHint.GetMLString() + ") " +
MLUtil.IsaToMLThm("assms(1)") + " " + MLUtil.IsaToMLThms(globalAssmsName) +
" (@{thm forall_poly_thm}, @{thm exists_poly_thm}) []", 1)
)
})
));
}
//assume that block identities in the two CFGs are the same (only edges may be different)
private static IDictionary <Block, IList <OuterDecl> > GenerateVCLemmas(
CFGRepr afterPassificationCfg,
CFGRepr finalCfg,
IDictionary <Block, Block> afterPassiveToFinalBlock,
IDictionary <Block, Block> afterPassiveToOrigBlock,
HashSet <Block> reachableBlocks,
VcPhaseLemmaManager vcPhaseLemmaManager,
VCHintManager vcHintManager,
IsaUniqueNamer lemmaNamer)
{
var blockToLemmaDecls = new Dictionary <Block, IList <OuterDecl> >();
foreach (var bAfterPassive in afterPassificationCfg.GetBlocksBackwards())
{
var result = new List <OuterDecl>();
if (afterPassiveToFinalBlock.TryGetValue(bAfterPassive, out var bFinal))
{
string vcHintsName = null;
if (vcHintManager.TryGetHints(afterPassiveToOrigBlock[bAfterPassive], out var hints,
out var requiredDecls))
{
//FIXME potential val name clash
vcHintsName = GetLemmaName(bAfterPassive, lemmaNamer) + "_hints";
var code = MLUtil.DefineVal(vcHintsName, MLUtil.MLList(hints));
//required declarations must be added first
result.AddRange(requiredDecls);
result.Add(new MLDecl(code));
}
result.Add(vcPhaseLemmaManager.GenerateBlockLemma(
bAfterPassive, bFinal, finalCfg.GetSuccessorBlocks(bFinal), GetLemmaName(bFinal, lemmaNamer),
vcHintsName));
//do not use identity of final CFG block to be consistent with other branches
blockToLemmaDecls.Add(bAfterPassive, result);
}
else if (reachableBlocks.Contains(bAfterPassive))
{
//block was removed after peephole but is reachable before peephole
if (bAfterPassive.Cmds.Count == 0)
{
//find the successors of b in the final cfg (i.e., the first non-empty reachable blocks)
var nonEmptyReachableSuccessors =
GetNonEmptyReachableSuccessors(bAfterPassive, afterPassificationCfg, finalCfg,
afterPassiveToFinalBlock);
//add lemma
var decls = new List <OuterDecl>
{
vcPhaseLemmaManager.GenerateEmptyBlockLemma(
bAfterPassive,
nonEmptyReachableSuccessors.Select(b => afterPassiveToFinalBlock[b]),
GetLemmaName(bAfterPassive, lemmaNamer))
};
blockToLemmaDecls.Add(bAfterPassive, decls);
}
else
{
throw new ProofGenUnexpectedStateException(
"Non-empty reachable block removed during peep-hole");
}
}
}
return(blockToLemmaDecls);
}
