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//-----------------------------------------------------------------------------
//
// Copyright (C) Microsoft Corporation. All Rights Reserved.
//
//-----------------------------------------------------------------------------
using System;
using System.Text;
using System.IO;
using System.Collections;
using System.Collections.Generic;
using Microsoft.Contracts;
using Microsoft.Basetypes;
using Microsoft.Boogie.VCExprAST;
// Ensure that no formulas (expressions of type boolean that are not
// just a variable) occur with terms (expressions of some other
// type). This is done by introducing let-binders for boolean
// variables.
namespace Microsoft.Boogie.VCExprAST
{
public struct FlattenerState {
public readonly int Polarity;
public readonly bool InTerm;
public static FlattenerState INITIAL = new FlattenerState(1, false);
public FlattenerState(int polarity, bool inTerm) {
Polarity = polarity;
InTerm = inTerm;
}
public FlattenerState TogglePolarity { get {
return new FlattenerState(-Polarity, InTerm);
} }
public FlattenerState ZeroPolarity { get {
return new FlattenerState(0, InTerm);
} }
public FlattenerState EnterTerm { get {
return new FlattenerState(Polarity, true);
} }
}
//////////////////////////////////////////////////////////////////////////////
public class TermFormulaFlattener : MutatingVCExprVisitor<FlattenerState> {
public TermFormulaFlattener(VCExpressionGenerator! gen) {
base(gen);
}
private readonly IDictionary<VCExpr!, VCExprVar!>! Bindings =
new Dictionary<VCExpr!, VCExprVar!> ();
private int varNameCounter = 0;
public VCExpr! Flatten(VCExpr! expr) {
VCExpr! res = Mutate(expr, FlattenerState.INITIAL);
while (Bindings.Count > 0) {
List<VCExprLetBinding!>! letBindings = new List<VCExprLetBinding!> ();
foreach (KeyValuePair<VCExpr!, VCExprVar!> pair in Bindings)
letBindings.Add(Gen.LetBinding(pair.Value, pair.Key));
Bindings.Clear();
res = AddBindings(letBindings, res, FlattenerState.INITIAL);
}
return res;
}
private VCExprVar! GetVarFor(VCExpr! expr) requires expr.Type.IsBool; {
VCExprVar res;
if (!Bindings.TryGetValue(expr, out res)) {
string! name = "flt" + varNameCounter;
varNameCounter = varNameCounter + 1;
res = Gen.Variable(name, Type.Bool);
Bindings.Add(expr, res);
}
return (!)res;
}
// Remove all let-bindings from the field bindings whose rhs
// contains any of the specified variables
private List<VCExprLetBinding!>!
RemoveBindingsWithVars(List<VCExprVar!>! boundVars,
List<TypeVariable!>! boundTypeVars) {
List<VCExprLetBinding!>! res = new List<VCExprLetBinding!> ();
FreeVariableCollector! coll = new FreeVariableCollector ();
foreach (KeyValuePair<VCExpr!, VCExprVar!> pair in Bindings) {
coll.Collect(pair.Key);
if (exists{VCExprVar! var in boundVars; coll.FreeTermVars.ContainsKey(var)} ||
exists{TypeVariable! var in boundTypeVars; coll.FreeTypeVars.Contains(var)})
res.Add(Gen.LetBinding(pair.Value, pair.Key));
coll.Reset();
}
foreach (VCExprLetBinding! b in res)
Bindings.Remove(b.E);
return res;
}
// Add bindings to a formula using an implication or
// conjunction. The bindings themselves will be flattened as well,
// which might introduce further bindings
private VCExpr! AddBindings(List<VCExprLetBinding!>! bindings,
VCExpr! body,
FlattenerState state)
requires body.Type.IsBool; {
List<VCExprLetBinding!>! mutatedBindings = FlattenBindings(bindings, state);
VCExpr! bindingEquations = Gen.AsEquations(mutatedBindings);
switch(state.Polarity) {
case 1:
return Gen.Implies(bindingEquations, body);
case -1:
return Gen.And(bindingEquations, body);
case 0:
// also add explicit quantifiers for the bound variables
List<VCExprVar!>! vars = new List<VCExprVar!> ();
foreach (VCExprLetBinding! binding in mutatedBindings)
vars.Add(binding.V);
return Gen.Forall(vars, new List<VCTrigger!>(),
Gen.Implies(bindingEquations, body));
}
assert false;
}
private List<VCExprLetBinding!>! FlattenBindings(List<VCExprLetBinding!>! bindings,
FlattenerState state) {
FlattenerState stateInBindings = state.ZeroPolarity;
List<VCExprLetBinding!>! mutatedBindings = new List<VCExprLetBinding!> ();
foreach (VCExprLetBinding! b in bindings)
mutatedBindings.Add(Gen.LetBinding(b.V, Mutate(b.E, stateInBindings)));
return mutatedBindings;
}
////////////////////////////////////////////////////////////////////////////
public override VCExpr! Visit(VCExprNAry! node, FlattenerState state) {
// track the polarity to know whether implications or conjunctions
// are to be introduced
if (node.Op.Equals(VCExpressionGenerator.NotOp))
return Gen.Not(Mutate(node[0], state.TogglePolarity));
if (node.Op.Equals(VCExpressionGenerator.ImpliesOp)) {
VCExpr! newArg0 = Mutate(node[0], state.TogglePolarity);
VCExpr! newArg1 = Mutate(node[1], state);
return Gen.Implies(newArg0, newArg1);
}
if (!node.Type.IsBool)
state = state.EnterTerm;
if (!node.Op.Equals(VCExpressionGenerator.AndOp) &&
!node.Op.Equals(VCExpressionGenerator.OrOp) &&
!(node.Op is VCExprLabelOp))
// standard is to set the polarity to 0 (fits most operators)
return base.Visit(node, state.ZeroPolarity);
return base.Visit(node, state);
}
public override VCExpr! Visit(VCExprQuantifier! node, FlattenerState state) {
if (state.InTerm)
return GetVarFor(node);
// we only flatten within the matrix of the quantified formula,
// not within the triggers (since SMT-solvers do not seem to
// appreciate triggers with let-binders)
VCExpr! newBody = Mutate(node.Body, state);
// Check whether any of the extracted terms contain variables
// bound by this quantifier. In this case, we have to add
// let-binders and remove the extracted terms
bool cont = true;
while (cont) {
List<VCExprLetBinding!>! localBindings =
RemoveBindingsWithVars(node.BoundVars, node.TypeParameters);
if (localBindings.Count > 0)
newBody = AddBindings(localBindings, newBody, state);
else
cont = false;
}
return Gen.Quantify(node.Quan, node.TypeParameters,
node.BoundVars, node.Triggers,
node.Infos, newBody);
}
public override VCExpr! Visit(VCExprLet! node, FlattenerState state) {
if (state.InTerm)
return GetVarFor(node);
VCExprLet! prelimRes = (VCExprLet!)base.Visit(node, state);
List<VCExprLetBinding!>! allBindings = new List<VCExprLetBinding!> ();
allBindings.AddRange(prelimRes);
// Check whether any of the extracted terms contain variables
// bound by this binder. In this case, we have to add
// let-binders and remove the extracted terms
bool cont = true;
while (cont) {
List<VCExprLetBinding!>! localBindings =
RemoveBindingsWithVars(prelimRes.BoundVars, new List<TypeVariable!> ());
if (localBindings.Count > 0)
allBindings.AddRange(FlattenBindings(localBindings, state));
else
cont = false;
}
return Gen.Let(allBindings, prelimRes.Body);
}
}
}
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