summaryrefslogtreecommitdiff
path: root/Source/Core/LambdaHelper.cs
blob: c884be3cba4e3afd6735bb942f30adbda90a230b (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
//-----------------------------------------------------------------------------
//
// Copyright (C) Microsoft Corporation.  All Rights Reserved.
//
//-----------------------------------------------------------------------------
namespace Microsoft.Boogie {

  using System;
  using System.IO;
  using System.Collections;
  using System.Collections.Generic;
  using System.Diagnostics;
  using System.Diagnostics.Contracts;
  using Set = GSet<object>;  // for the purposes here, "object" really means "either Variable or TypeVariable"

  public static class LambdaHelper {
    public static Program Desugar(Program program, out List<Expr/*!*/>/*!*/ axioms, out List<Function/*!*/>/*!*/ functions) {
      Contract.Requires(program != null);
      Contract.Ensures(cce.NonNullElements(Contract.ValueAtReturn(out functions)));
      Contract.Ensures(cce.NonNullElements(Contract.ValueAtReturn(out axioms)));
      Contract.Ensures(Contract.Result<Program>() != null);
      LambdaVisitor v = new LambdaVisitor();
      program = v.VisitProgram(program);
      axioms = v.lambdaAxioms;
      functions = v.lambdaFunctions;
      if (CommandLineOptions.Clo.TraceVerify) {
        Console.WriteLine("Desugaring of lambda expressions produced {0} functions and {1} axioms:", functions.Count, axioms.Count);
        TokenTextWriter wr = new TokenTextWriter("<console>", Console.Out, /*pretty=*/ false);
        foreach (Function f in functions) {
          f.Emit(wr, 0);
        }
        foreach (Expr ax in axioms) {
          ax.Emit(wr);
          Console.WriteLine();
        }
      }
      return program;
    }

    public static void ExpandLambdas(Program prog) {
      Contract.Requires(prog != null);
      List<Expr/*!*/>/*!*/ axioms;
      List<Function/*!*/>/*!*/ functions;

      Desugar(prog, out axioms, out functions);
      foreach (var f in functions) {
        prog.TopLevelDeclarations.Add(f);
      }
      foreach (var a in axioms) {
        prog.TopLevelDeclarations.Add(new Axiom(a.tok, a));
      }
    }

    private class LambdaVisitor : StandardVisitor {
      internal List<Expr/*!*/>/*!*/ lambdaAxioms = new List<Expr/*!*/>();
      internal List<Function/*!*/>/*!*/ lambdaFunctions = new List<Function/*!*/>();
      [ContractInvariantMethod]
      void ObjectInvariant() {
        Contract.Invariant(cce.NonNullElements(lambdaAxioms));
        Contract.Invariant(cce.NonNullElements(lambdaFunctions));
      }

      int lambdaid = 0;

      public override Expr VisitLambdaExpr(LambdaExpr lambda) {
        var baseResult = base.VisitLambdaExpr(lambda);
        lambda = baseResult as LambdaExpr;
        if (lambda == null) {
          return baseResult;  // apparently, the base visitor already turned the lambda into something else
        }

        // 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.SubstitutionFromHashtable(new Dictionary<Variable,Expr>()),
          Substituter.SubstitutionFromHashtable(oldSubst),
          lambda.Body);
        var lambdaAttrs = Substituter.ApplyReplacingOldExprs(
          Substituter.SubstitutionFromHashtable(new Dictionary<Variable, Expr>()),
          Substituter.SubstitutionFromHashtable(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> { "stable" }, 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, 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));
          }
        }

        IToken tok = lambda.tok;
        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",
          Substituter.Apply(Substituter.SubstitutionFromHashtable(substFnAttrs), lambdaAttrs));
        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 = 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.SubstitutionFromHashtable(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 });
        lambdaAxioms.Add(new ForallExpr(tok, forallTypeVariables, dummies,
          Substituter.Apply(Substituter.SubstitutionFromHashtable(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 Cmd VisitCallCmd(CallCmd node) {
        var baseResult = base.VisitCallCmd(node);
        node = baseResult as CallCmd;
        if (node == null) {
          return baseResult;  // apparently, the base visitor already turned the lambda into something else
        }
        // also visit the desugaring (which the StandardVisitor does not do)
        node.VisitDesugaring(this);
        return node;
      }
    }
  }

  class OldFinder : ReadOnlyVisitor
  {
    public readonly GSet<Variable> FreeOldVars = new GSet<Variable>();
    public override Expr VisitOldExpr(OldExpr node) {
      Set freeVars = new Set();
      node.Expr.ComputeFreeVariables(freeVars);
      foreach (var v in freeVars) {
        // Note, "v" is either a Variable or a TypeVariable
        if (v is Variable) {
          FreeOldVars.Add((Variable)v);
        }
      }
      return node;  // don't visit subexpressions, since ComputeFreeVariables has already gone through those
    }
    public override BinderExpr VisitBinderExpr(BinderExpr node) {
      base.VisitBinderExpr(node);
      // visit attributes, even though StandardVisitor does not do that (but maybe it should?)
      if (node.Attributes != null) {
        this.Visit(node.Attributes);
      }
      return node;
    }
  }

} // end namespace