private Expression makeMapWriteMap(FAE fae)
{
Debug.Assert(fae.function is MapWrite);
Debug.Assert(fae.arguments[0].type is MapType);
var mu = fae.function as MapWrite;
Expression result;
if (!versionMap.TryGetValue(fae.ToString(), out result))
{
var ot = fae.arguments[0].type as MapType;
Debug.Assert(ot != null);
var s = new TypeParameterInstantiation(ot.typeParameters, mu.typeArguments.Skip(1).ToArray());
// var ots = new MapType(new TypeVariable[0], (from m in ot.domain select m.substitute(s)).ToArray(), ot.range.substitute(s));
Expression m = fae.arguments[0];
Expression[] i = fae.arguments.Take(fae.arguments.count - 1).Skip(1).ToArray();
if (fae.freeVariables.Count > 0)
{
//m(fv)[i(fv):=x(fv)] ==> v(fv) (assume v(fv)[i]==x, assume forall fv : forall j : j!=i(fv) ==> v(fv)[j] == m(fv)[j]
var fvt = TypeTuple.make(from fv in fae.freeVariables select fv.type);
string fn = getFreshMUName("mu");
var ft = new BFunctionTemplate(fn, "", new TypeVariable[0], new BasicFunctionSignature(ot, fvt),
null);
Function f = ft.getInstance();
IEnumerable <BasicBoundVariableExpression> fve = from fv in fae.freeVariables
select new BasicBoundVariableExpression(fv);
result = new BasicFAE(f, new ExpressionList(fve));
}
else
{
//m[i:=x] ==> v (assume v[i]==x, assume forall j : j!=i ==> v[j] == m[j]
string nvn = getFreshMUName("mu");
var nv = new ProgramVariable(nvn, ot, false, false, false, false);
procedure.addVariable(nv);
result = new BasicProgramVariableExpression(nv);
}
Expression[] j =
(from e in i select new BasicBoundVariableExpression(makeBoundVariable(e.type))).ToArray();
//forall j : j!=i ==> v[j]==m[j]
addConditionalMapEqualityAxiom(i, result, m, mu.typeArguments);
//v[i]==x;
Expression x = fae.arguments.Last();
addEqualityAxiom(ml(result, i, mu.typeArguments.Skip(1).ToArray(), x.type), fae.arguments.Last());
}
return(result);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
private Function makeFreshPredicate(List <BoundVariable> list)
{
string name = "P$TQ_" + predicateIndex.ToString();
predicateIndex++;
var ft =
new BFunctionTemplate(
name,
"",
new TypeVariable[0],
new BasicFunctionSignature(
BooleanType.booleanType,
(from bv in list select bv.type).ToArray()
),
null
);
procedure.parentScope.addFunctionTemplate(
ft
);
return(ft.getInstance());
}