/// <summary>
/// Performs lambda lifting (see <see cref="LambdaHelper.ExpandLambdas"/>) by replacing the lambda's
/// free variables with bound ones.
/// </summary>
/// <param name="lambda">A lambda expression
/// <code>(lambda x1: T1 ... x_n: T_n :: t)</code>
/// where <c>t</c> contains the free variables <c>y1</c>, ..., <c>y_m</c>.
/// </param>
/// <returns>
/// <list type="bullet">
/// <item>
/// A function application <c>f(y1, ..., y_m)</c> where <c>f</c>'s body is defined to be the result of
/// replacing the free variables <c>y1</c>, ..., <c>y_m</c> in <c>t</c> with bound variables
/// <c>b1</c>, ..., <c>b_m</c>.
/// </item>
/// <item>
/// Adds a definition and axiom for <c>f</c> to <see cref="lambdaFunctions"/> and <see cref="lambdaAxioms"/>.
/// Memoizes <c>f</c> as the lifted lambda for <para>lambda</para>.
/// </item>
/// </list>
/// </returns>
private Expr LiftLambdaFreeVars(LambdaExpr lambda)
{
// We start by getting rid of any use of "old" inside the lambda. This is done as follows.
// For each variable "g" occurring inside lambda as "old(... g ...)", create a new name "og".
// Replace each old occurrence of "g" with "og", removing the enclosing "old" wrappers.
var oldFinder = new OldFinder();
oldFinder.Visit(lambda);
var oldSubst = new Dictionary<Variable, Expr>(); // g -> g0
var callOldMapping = new Dictionary<Variable, Expr>(); // g0 -> old(g)
foreach (var v in oldFinder.FreeOldVars)
{
var g = v as GlobalVariable;
if (g != null)
{
var g0 = new GlobalVariable(g.tok, new TypedIdent(g.tok, g.TypedIdent.Name + "@old", g.TypedIdent.Type));
oldSubst.Add(g, new IdentifierExpr(g0.tok, g0));
callOldMapping.Add(g0, new OldExpr(g0.tok, new IdentifierExpr(g.tok, g)));
}
}
var lambdaBody = Substituter.ApplyReplacingOldExprs(
Substituter.SubstitutionFromDictionary(new Dictionary<Variable, Expr>()),
Substituter.SubstitutionFromDictionary(oldSubst),
lambda.Body);
var lambdaAttrs = Substituter.ApplyReplacingOldExprs(
Substituter.SubstitutionFromDictionary(new Dictionary<Variable, Expr>()),
Substituter.SubstitutionFromDictionary(oldSubst),
lambda.Attributes);
if (0 < CommandLineOptions.Clo.VerifySnapshots &&
QKeyValue.FindStringAttribute(lambdaAttrs, "checksum") == null)
{
// Attach a dummy checksum to avoid issues in the dependency analysis.
var checksumAttr = new QKeyValue(lambda.tok, "checksum", new List<object> {"lambda expression"}, null);
if (lambdaAttrs == null)
{
lambdaAttrs = checksumAttr;
}
else
{
lambdaAttrs.AddLast(checksumAttr);
}
}
// this is ugly, the output will depend on hashing order
var subst = new Dictionary<Variable, Expr>();
var substFnAttrs = new Dictionary<Variable, Expr>();
var formals = new List<Variable>();
var callArgs = new List<Expr>();
var axCallArgs = new List<Expr>();
var dummies = new List<Variable>(lambda.Dummies);
var freeTypeVars = new List<TypeVariable>();
var fnTypeVarActuals = new List<Type /*!*/>();
var freshTypeVars = new List<TypeVariable>(); // these are only used in the lambda@n function's definition
// compute the free variables of the lambda expression, but with lambdaBody instead of lambda.Body
Set freeVars = new Set();
BinderExpr.ComputeBinderFreeVariables(lambda.TypeParameters, lambda.Dummies, lambdaBody, null, lambdaAttrs,
freeVars);
foreach (object o in freeVars)
{
// 'o' is either a Variable or a TypeVariable.
if (o is Variable)
{
var v = o as Variable;
var ti = new TypedIdent(v.TypedIdent.tok, v.TypedIdent.Name, v.TypedIdent.Type);
var f = new Formal(v.tok, ti, true);
formals.Add(f);
substFnAttrs.Add(v, new IdentifierExpr(f.tok, f));
var b = new BoundVariable(v.tok, ti);
dummies.Add(b);
if (callOldMapping.ContainsKey(v))
{
callArgs.Add(callOldMapping[v]);
}
else
{
callArgs.Add(new IdentifierExpr(v.tok, v));
}
Expr id = new IdentifierExpr(b.tok, b);
subst.Add(v, id);
axCallArgs.Add(id);
}
else
{
var tv = (TypeVariable) o;
freeTypeVars.Add(tv);
fnTypeVarActuals.Add(tv);
freshTypeVars.Add(new TypeVariable(tv.tok, tv.Name));
}
}
var sw = new System.IO.StringWriter();
var wr = new TokenTextWriter(sw, true);
lambda.Emit(wr);
string lam_str = sw.ToString();
FunctionCall fcall;
IToken tok = lambda.tok;
Formal res = new Formal(tok, new TypedIdent(tok, TypedIdent.NoName, cce.NonNull(lambda.Type)), false);
if (liftedLambdas.TryGetValue(lambda, out fcall))
{
if (CommandLineOptions.Clo.TraceVerify)
{
Console.WriteLine("Old lambda: {0}", lam_str);
}
}
else
{
if (CommandLineOptions.Clo.TraceVerify)
{
Console.WriteLine("New lambda: {0}", lam_str);
}
Function fn = new Function(tok, FreshLambdaFunctionName(), freshTypeVars, formals, res,
"auto-generated lambda function",
Substituter.Apply(Substituter.SubstitutionFromDictionary(substFnAttrs), lambdaAttrs));
fn.OriginalLambdaExprAsString = lam_str;
fcall = new FunctionCall(new IdentifierExpr(tok, fn.Name));
fcall.Func = fn; // resolve here
liftedLambdas[lambda] = fcall;
List<Expr /*!*/> selectArgs = new List<Expr /*!*/>();
foreach (Variable /*!*/ v in lambda.Dummies)
{
Contract.Assert(v != null);
selectArgs.Add(new IdentifierExpr(v.tok, v));
}
NAryExpr axcall = new NAryExpr(tok, fcall, axCallArgs);
axcall.Type = res.TypedIdent.Type;
axcall.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
NAryExpr select = Expr.Select(axcall, selectArgs);
select.Type = lambdaBody.Type;
List<Type /*!*/> selectTypeParamActuals = new List<Type /*!*/>();
List<TypeVariable> forallTypeVariables = new List<TypeVariable>();
foreach (TypeVariable /*!*/ tp in lambda.TypeParameters)
{
Contract.Assert(tp != null);
selectTypeParamActuals.Add(tp);
forallTypeVariables.Add(tp);
}
forallTypeVariables.AddRange(freeTypeVars);
select.TypeParameters = SimpleTypeParamInstantiation.From(lambda.TypeParameters, selectTypeParamActuals);
Expr bb = Substituter.Apply(Substituter.SubstitutionFromDictionary(subst), lambdaBody);
NAryExpr body = Expr.Eq(select, bb);
body.Type = Type.Bool;
body.TypeParameters = SimpleTypeParamInstantiation.EMPTY;
Trigger trig = new Trigger(select.tok, true, new List<Expr> {select});
lambdaFunctions.Add(fn);
lambdaAxioms.Add(new ForallExpr(tok, forallTypeVariables, dummies,
Substituter.Apply(Substituter.SubstitutionFromDictionary(subst), lambdaAttrs),
trig, body));
}
NAryExpr call = new NAryExpr(tok, fcall, callArgs);
call.Type = res.TypedIdent.Type;
call.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
return call;
}
public override Absy Visit(Absy node) {
//Contract.Requires(node != null);
Contract.Ensures(Contract.Result<Absy>() != null);
node = base.Visit(node);
LambdaExpr lambda = node as LambdaExpr;
if (lambda != null) {
IToken/*!*/ tok = lambda.tok;
Contract.Assert(tok != null);
Set freeVars = new Set();
lambda.ComputeFreeVariables(freeVars);
// this is ugly, the output will depend on hashing order
Dictionary<Variable, Expr> subst = new Dictionary<Variable, Expr>();
List<Variable> formals = new List<Variable>();
List<Expr> callArgs = new List<Expr>();
List<Expr> axCallArgs = new List<Expr>();
List<Variable> dummies = new List<Variable>(lambda.Dummies);
List<TypeVariable> freeTypeVars = new List<TypeVariable>();
List<Type/*!*/> fnTypeVarActuals = new List<Type/*!*/>();
List<TypeVariable> freshTypeVars = new List<TypeVariable>(); // these are only used in the lambda@n function's definition
foreach (object o in freeVars) {
// 'o' is either a Variable or a TypeVariable. Since the lambda desugaring happens only
// at the outermost level of a program (where there are no mutable variables) and, for
// procedure bodies, after the statements have been passified (when mutable variables have
// been replaced by immutable incarnations), we are interested only in BoundVar's and
// TypeVariable's.
BoundVariable v = o as BoundVariable;
if (v != null) {
TypedIdent ti = new TypedIdent(v.TypedIdent.tok, v.TypedIdent.Name, v.TypedIdent.Type);
Formal f = new Formal(v.tok, ti, true);
formals.Add(f);
BoundVariable b = new BoundVariable(v.tok, ti);
dummies.Add(b);
callArgs.Add(new IdentifierExpr(v.tok, v));
Expr/*!*/ id = new IdentifierExpr(f.tok, b);
Contract.Assert(id != null);
subst.Add(v, id);
axCallArgs.Add(id);
} else if (o is TypeVariable) {
TypeVariable tv = (TypeVariable)o;
freeTypeVars.Add(tv);
fnTypeVarActuals.Add(tv);
freshTypeVars.Add(new TypeVariable(tv.tok, tv.Name));
}
}
Formal res = new Formal(tok, new TypedIdent(tok, TypedIdent.NoName, cce.NonNull(lambda.Type)), false);
Function fn = new Function(tok, "lambda@" + lambdaid++, freshTypeVars, formals, res, "auto-generated lambda function", lambda.Attributes);
lambdaFunctions.Add(fn);
FunctionCall fcall = new FunctionCall(new IdentifierExpr(tok, fn.Name));
fcall.Func = fn; // resolve here
List<Expr/*!*/> selectArgs = new List<Expr/*!*/>();
foreach (Variable/*!*/ v in lambda.Dummies) {
Contract.Assert(v != null);
selectArgs.Add(new IdentifierExpr(v.tok, v));
}
NAryExpr axcall = new NAryExpr(tok, fcall, axCallArgs);
axcall.Type = res.TypedIdent.Type;
axcall.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
NAryExpr select = Expr.Select(axcall, selectArgs);
select.Type = lambda.Body.Type;
List<Type/*!*/> selectTypeParamActuals = new List<Type/*!*/>();
List<TypeVariable> forallTypeVariables = new List<TypeVariable>();
foreach (TypeVariable/*!*/ tp in lambda.TypeParameters) {
Contract.Assert(tp != null);
selectTypeParamActuals.Add(tp);
forallTypeVariables.Add(tp);
}
forallTypeVariables.AddRange(freeTypeVars);
select.TypeParameters = SimpleTypeParamInstantiation.From(lambda.TypeParameters, selectTypeParamActuals);
Expr bb = Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), lambda.Body);
NAryExpr body = Expr.Eq(select, bb);
body.Type = Type.Bool;
body.TypeParameters = SimpleTypeParamInstantiation.EMPTY;
Trigger trig = new Trigger(select.tok, true, new List<Expr> { select });
lambdaAxioms.Add(new ForallExpr(tok, forallTypeVariables, dummies, lambda.Attributes, trig, body));
NAryExpr call = new NAryExpr(tok, fcall, callArgs);
call.Type = res.TypedIdent.Type;
call.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
return call;
}
return node;
}
