path: root/Source/VCExpr/TypeErasureArguments.ssc

//-----------------------------------------------------------------------------
//
// 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;

// Erasure of types using explicit type parameters for functions

namespace Microsoft.Boogie.TypeErasure
{
  using Microsoft.Boogie.VCExprAST;
  using HFNS = Microsoft.Boogie.VCExprAST.HelperFuns;

  public class TypeAxiomBuilderArguments : TypeAxiomBuilderIntBoolU {

    public TypeAxiomBuilderArguments(VCExpressionGenerator! gen) {
      base(gen);
      Typed2UntypedFunctions = new Dictionary<Function!, Function!> ();
    }    

    // constructor to allow cloning
    [NotDelayed]
    internal TypeAxiomBuilderArguments(TypeAxiomBuilderArguments! builder) {
      Typed2UntypedFunctions =
        new Dictionary<Function!, Function!> (builder.Typed2UntypedFunctions);
      base(builder);

      MapTypeAbstracterAttr =
        builder.MapTypeAbstracterAttr == null ?
        null : new MapTypeAbstractionBuilderArguments(this, builder.Gen,
                                                      builder.MapTypeAbstracterAttr);
    }

    public override Object! Clone() {
      return new TypeAxiomBuilderArguments(this);
    }

    ///////////////////////////////////////////////////////////////////////////////    

    // generate axioms of the kind "forall x:U. {Int2U(U2Int(x))} Int2U(U2Int(x))==x"
    // (this makes use of the assumption that only well-typed terms are generated
    // by the SMT-solver, i.e., that U2Int is only applied to terms that actually
    // are of type int)
    protected override VCExpr! GenReverseCastAxiom(Function! castToU,
                                                   Function! castFromU) {
      List<VCTrigger!>! triggers;
      VCExprVar! var;
      VCExpr! eq = GenReverseCastEq(castToU, castFromU, out var, out triggers);
      return Gen.Forall(HelperFuns.ToList(var), triggers, "cast:" + castFromU.Name, eq);
    }

    protected override VCExpr! GenCastTypeAxioms(Function! castToU,
                                                 Function! castFromU) {
      // nothing
      return VCExpressionGenerator.True;
    }

    private MapTypeAbstractionBuilderArguments MapTypeAbstracterAttr = null;

    internal override MapTypeAbstractionBuilder! MapTypeAbstracter { get {
      if (MapTypeAbstracterAttr == null)
        MapTypeAbstracterAttr = new MapTypeAbstractionBuilderArguments (this, Gen);
      return MapTypeAbstracterAttr;
    } }

    protected override void AddVarTypeAxiom(VCExprVar! var, Type! originalType) {
      // no axioms are needed for variable or function types
    }

    ////////////////////////////////////////////////////////////////////////////
    // Symbols for representing functions

    // Globally defined functions
    private readonly IDictionary<Function!, Function!>! Typed2UntypedFunctions;

    public Function! Typed2Untyped(Function! fun) {
      Function res;
      if (!Typed2UntypedFunctions.TryGetValue(fun, out res)) {
        assert fun.OutParams.Length == 1;

        // if all of the parameters are int or bool, the function does
        // not have to be changed
        if (forall{Formal f in fun.InParams; UnchangedType(((!)f).TypedIdent.Type)} &&
            UnchangedType(((!)fun.OutParams[0]).TypedIdent.Type)) {
          res = fun;
        } else {
          Type[]! types = new Type [fun.TypeParameters.Length + fun.InParams.Length + 1];

          int i = 0;
          // the first arguments are the explicit type parameters
          for (int j = 0; j < fun.TypeParameters.Length; ++j) {
            types[i] = T;
            i = i + 1;
          }
          // followed by the actual parameters
          foreach (Variable! x in fun.InParams) {
            types[i] = TypeAfterErasure(x.TypedIdent.Type);
            i = i + 1;
          }

          types[types.Length - 1] = TypeAfterErasure(((!)fun.OutParams[0]).TypedIdent.Type);

          res = HelperFuns.BoogieFunction(fun.Name, types);
          res.Attributes = fun.Attributes;
        }

        Typed2UntypedFunctions.Add(fun, res);
      }
      return (!)res;
    }

  }

  //////////////////////////////////////////////////////////////////////////////

  internal class MapTypeAbstractionBuilderArguments : MapTypeAbstractionBuilder {

    private readonly TypeAxiomBuilderArguments! AxBuilderArguments;

    internal MapTypeAbstractionBuilderArguments(TypeAxiomBuilderArguments! axBuilder,
                                                VCExpressionGenerator! gen) {
      base(axBuilder, gen);
      this.AxBuilderArguments = axBuilder;
    }

    // constructor for cloning
    internal MapTypeAbstractionBuilderArguments(TypeAxiomBuilderArguments! axBuilder,
                                                VCExpressionGenerator! gen,
                                                MapTypeAbstractionBuilderArguments! builder) {
      base(axBuilder, gen, builder);
      this.AxBuilderArguments = axBuilder;
    }

    ////////////////////////////////////////////////////////////////////////////

    protected override void GenSelectStoreFunctions(MapType! abstractedType,
                                                    TypeCtorDecl! synonym,
                                                    out Function! select,
                                                    out Function! store) {
      string! baseName = synonym.Name;
      int typeParamNum = abstractedType.FreeVariables.Length +
                         abstractedType.TypeParameters.Length;
      int arity = typeParamNum + abstractedType.Arguments.Length;

      Type![]! selectTypes = new Type! [arity + 2];
      Type![]! storeTypes = new Type! [arity + 3];
      
      int i = 0;
      // Fill in the free variables and type parameters
      for (; i < typeParamNum; i++) {
        selectTypes[i] = AxBuilder.T;
        storeTypes[i] = AxBuilder.T;
      }
      // Fill in the map type
      selectTypes[i] = AxBuilder.U;
      storeTypes[i] = AxBuilder.U;
      i++;
      // Fill in the index types
      foreach (Type! type in abstractedType.Arguments)
      {
        if (CommandLineOptions.Clo.Monomorphize && AxBuilder.UnchangedType(type))
        {
			selectTypes[i] = type;
			storeTypes[i] = type;
		}
		else
		{
			selectTypes[i] = AxBuilder.U;
			storeTypes[i] = AxBuilder.U;
		}
		i++;
	  }
	  // Fill in the output type for select function which also happens 
	  // to be the type of the last argument to the store function
	  if (CommandLineOptions.Clo.Monomorphize && AxBuilder.UnchangedType(abstractedType.Result))
	  {
		selectTypes[i] = abstractedType.Result;
		storeTypes[i] = abstractedType.Result;
	  }
	  else
	  {
		selectTypes[i] = AxBuilder.U;
		storeTypes[i] = AxBuilder.U;
	  }
	  i++;
	  // Fill in the map type which is the output of the store function
      storeTypes[i] = AxBuilder.U;
	  NonNullType.AssertInitialized(selectTypes);
	  NonNullType.AssertInitialized(storeTypes);
	  
      select = HelperFuns.BoogieFunction(baseName + "Select", selectTypes);
      store = HelperFuns.BoogieFunction(baseName + "Store", storeTypes);

      AxBuilder.AddTypeAxiom(GenMapAxiom0(select, store, 
                 abstractedType.TypeParameters.Length, abstractedType.FreeVariables.Length));
      AxBuilder.AddTypeAxiom(GenMapAxiom1(select, store, 
                 abstractedType.TypeParameters.Length, abstractedType.FreeVariables.Length));
    }

    ///////////////////////////////////////////////////////////////////////////
    // The normal axioms of the theory of arrays (right now without extensionality)

    private VCExpr! Select(Function! select, List<VCExprVar!>! types,
                           VCExpr! map, List<VCExprVar!>! indexes) {
      List<VCExpr!>! selectArgs = new List<VCExpr!> ();
      selectArgs.AddRange(HelperFuns.ToVCExprList(types));
      selectArgs.Add(map);
      selectArgs.AddRange(HelperFuns.ToVCExprList(indexes));
      return Gen.Function(select, selectArgs);
    }

    private VCExpr! Store(Function! store, List<VCExprVar!>! types,
                          VCExpr! map, List<VCExprVar!>! indexes, VCExpr! val) {
      List<VCExpr!>! storeArgs = new List<VCExpr!> ();
      storeArgs.AddRange(HelperFuns.ToVCExprList(types));
      storeArgs.Add(map);
      storeArgs.AddRange(HelperFuns.ToVCExprList(indexes));
      storeArgs.Add(val);
      return Gen.Function(store, storeArgs);
    }

    private VCExpr! GenMapAxiom0(Function! select, Function! store,
                                 // bound type variables in the map type
                                 int mapTypeParamNum,
                                 // free type variables in the map
                                 // type (abstraction)
                                 int mapAbstractionVarNum) {
      int arity = select.InParams.Length - 1 - mapTypeParamNum - mapAbstractionVarNum;
      List<VCExprVar!>! types =
        HelperFuns.VarVector("t", mapTypeParamNum + mapAbstractionVarNum,
                             AxBuilder.T, Gen);
                             
      List<Type!> indexTypes = new List<Type!>();
      for (int i = mapTypeParamNum + mapAbstractionVarNum + 1; i < select.InParams.Length; i++)
      {
		indexTypes.Add(((!)select.InParams[i]).TypedIdent.Type);
	  }
      assert arity == indexTypes.Count;
      
      List<VCExprVar!>! indexes = HelperFuns.VarVector("x", indexTypes, Gen);

      VCExprVar! m = Gen.Variable("m", AxBuilder.U);
      VCExprVar! val = Gen.Variable("val", ((!)select.OutParams[0]).TypedIdent.Type);

      VCExpr! storeExpr = Store(store, types, m, indexes, val);
      VCExpr! selectExpr = Select(select, types, storeExpr, indexes);

      List<VCExprVar!>! quantifiedVars = new List<VCExprVar!> ();
      quantifiedVars.AddRange(types);
      quantifiedVars.Add(val);
      quantifiedVars.Add(m);
      quantifiedVars.AddRange(indexes);

      VCExpr! eq = Gen.Eq(selectExpr, val);
      return Gen.Forall(quantifiedVars, new List<VCTrigger!> (),
                        "mapAx0:" + select.Name, eq);
    }    

    private VCExpr! GenMapAxiom1(Function! select, Function! store, 
                                 // bound type variables in the map
                                 // type
                                 int mapTypeParamNum,
                                 // free type variables in the map
                                 // type (abstraction)
                                 int mapAbstractionVarNum) {
      int arity = select.InParams.Length - 1 - mapTypeParamNum - mapAbstractionVarNum;

      List<VCExprVar!>! freeTypeVars =
        HelperFuns.VarVector("u", mapAbstractionVarNum, AxBuilder.T, Gen);
      List<VCExprVar!>! boundTypeVars0 =
        HelperFuns.VarVector("s", mapTypeParamNum, AxBuilder.T, Gen);
      List<VCExprVar!>! boundTypeVars1 =
        HelperFuns.VarVector("t", mapTypeParamNum, AxBuilder.T, Gen);

      List<VCExprVar!>! types0 = new List<VCExprVar!> (boundTypeVars0);
      types0.AddRange(freeTypeVars);

      List<VCExprVar!>! types1 = new List<VCExprVar!> (boundTypeVars1);
      types1.AddRange(freeTypeVars);

      List<Type!> indexTypes = new List<Type!>();
      for (int i = mapTypeParamNum + mapAbstractionVarNum + 1; i < select.InParams.Length; i++)
      {
		indexTypes.Add(((!)select.InParams[i]).TypedIdent.Type);
	  }
      assert arity == indexTypes.Count;
      
      List<VCExprVar!>! indexes0 = HelperFuns.VarVector("x", indexTypes, Gen);
      List<VCExprVar!>! indexes1 = HelperFuns.VarVector("y", indexTypes, Gen);

      VCExprVar! m = Gen.Variable("m", AxBuilder.U);
      VCExprVar! val = Gen.Variable("val", ((!)select.OutParams[0]).TypedIdent.Type);

      VCExpr! storeExpr = Store(store, types0, m, indexes0, val);
      VCExpr! selectWithoutStoreExpr = Select(select, types1, m, indexes1);
      VCExpr! selectExpr = Select(select, types1, storeExpr, indexes1);

      VCExpr! selectEq = Gen.Eq(selectExpr, selectWithoutStoreExpr);

      List<VCExprVar!>! quantifiedVars = new List<VCExprVar!> ();
      quantifiedVars.AddRange(freeTypeVars);
      quantifiedVars.AddRange(boundTypeVars0);
      quantifiedVars.AddRange(boundTypeVars1);
      quantifiedVars.Add(val);
      quantifiedVars.Add(m);
      quantifiedVars.AddRange(indexes0);
      quantifiedVars.AddRange(indexes1);

      List<VCTrigger!>! triggers = new List<VCTrigger!> ();

      // different value arguments or different type arguments are sufficient
      // to conclude that that value of the map at some point (after an update)
      // has not changed

      List<VCExpr!>! indexEqs = new List<VCExpr!> ();
      for (int i = 0; i < mapTypeParamNum; ++i)
        indexEqs.Add(Gen.Eq(boundTypeVars0[i], boundTypeVars1[i]));
      for (int i = 0; i < arity; ++i)
        indexEqs.Add(Gen.Eq(indexes0[i], indexes1[i]));

      VCExpr! axiom = VCExpressionGenerator.True;
      int n = 0;
      foreach (VCExpr! indexesEq in indexEqs) {
        VCExpr! matrix = Gen.Or(indexesEq, selectEq);
        VCExpr! conjunct = Gen.Forall(quantifiedVars, triggers,
                                      "mapAx1:" + select.Name + ":" + n, matrix);
        axiom = Gen.AndSimp(axiom, conjunct);
        n = n + 1;
      }

      return axiom;
    }
  }

  //////////////////////////////////////////////////////////////////////////////

  public class TypeEraserArguments : TypeEraser {

    private readonly TypeAxiomBuilderArguments! AxBuilderArguments;

    private OpTypeEraser OpEraserAttr = null;
    protected override OpTypeEraser! OpEraser { get {
      if (OpEraserAttr == null)
        OpEraserAttr = new OpTypeEraserArguments(this, AxBuilderArguments, Gen);
      return OpEraserAttr;
    } }

    public TypeEraserArguments(TypeAxiomBuilderArguments! axBuilder,
                               VCExpressionGenerator! gen) {
      base(axBuilder, gen);
      this.AxBuilderArguments = axBuilder;
    }

    ////////////////////////////////////////////////////////////////////////////

    public override VCExpr! Visit(VCExprQuantifier! node,
                                  VariableBindings! oldBindings) {
      VariableBindings! bindings = oldBindings.Clone();
      
      // bound term variables are replaced with bound term variables
      // typed in a simpler way
      List<VCExprVar!>! newBoundVars =
        BoundVarsAfterErasure(node.BoundVars, bindings);

      // type variables are replaced with ordinary quantified variables
      GenBoundVarsForTypeParams(node.TypeParameters, newBoundVars, bindings);
      VCExpr! newNode = HandleQuantifier(node, newBoundVars, bindings);

      if (!(newNode is VCExprQuantifier) || !IsUniversalQuantifier(node))
        return newNode;

      VariableBindings! bindings2;
      if (!RedoQuantifier(node, (VCExprQuantifier)newNode, node.BoundVars, oldBindings,
                          out bindings2, out newBoundVars))
        return newNode;

      GenBoundVarsForTypeParams(node.TypeParameters, newBoundVars, bindings2);
      return HandleQuantifier(node, newBoundVars, bindings2);
    }

    private void GenBoundVarsForTypeParams(List<TypeVariable!>! typeParams,
                                           List<VCExprVar!>! newBoundVars,
                                           VariableBindings! bindings) {
      foreach (TypeVariable! tvar in typeParams) {
        VCExprVar! var = Gen.Variable(tvar.Name, AxBuilder.T);
        newBoundVars.Add(var);
        bindings.TypeVariableBindings.Add(tvar, var);
      }
    }

    private VCExpr! HandleQuantifier(VCExprQuantifier! node,
                                     List<VCExprVar!>! newBoundVars,
                                     VariableBindings! bindings) {
      List<VCTrigger!>! newTriggers = MutateTriggers(node.Triggers, bindings);
      VCExpr! newBody = Mutate(node.Body, bindings);
      newBody = AxBuilder.Cast(newBody, Type.Bool);

      if (newBoundVars.Count == 0)  // might happen that no bound variables are left
        return newBody;
      return Gen.Quantify(node.Quan, new List<TypeVariable!> (), newBoundVars,
                          newTriggers, node.Infos, newBody);
    }
  }

  //////////////////////////////////////////////////////////////////////////////

  public class OpTypeEraserArguments : OpTypeEraser {

    protected readonly TypeAxiomBuilderArguments! AxBuilderArguments;

    public OpTypeEraserArguments(TypeEraserArguments! eraser,
                                 TypeAxiomBuilderArguments! axBuilder,
                                 VCExpressionGenerator! gen) {
      base(eraser, axBuilder, gen);
      this.AxBuilderArguments = axBuilder;
    }

    ////////////////////////////////////////////////////////////////////////////

    private VCExpr! AssembleOpExpression(OpTypesPair opTypes,
                                         IEnumerable<VCExpr!>! oldArgs,
                                         VariableBindings! bindings) {
      // UGLY: the code for tracking polarities should be factored out
      int oldPolarity = Eraser.Polarity;
      Eraser.Polarity = 0;

      List<VCExpr!>! newArgs = new List<VCExpr!> ();
      // explicit type parameters
      foreach (Type! t in opTypes.Types)
        newArgs.Add(AxBuilder.Type2Term(t, bindings.TypeVariableBindings));
      
      // and the actual value parameters
      Function! newFun = ((VCExprBoogieFunctionOp)opTypes.Op).Func;
                          // ^ we only allow this operator at this point
      int i = opTypes.Types.Count;
      foreach (VCExpr! arg in oldArgs) {
        newArgs.Add(AxBuilder.Cast(Eraser.Mutate(arg, bindings),
                                   ((!)newFun.InParams[i]).TypedIdent.Type));
        i = i + 1;
      }

      Eraser.Polarity = oldPolarity;
      return Gen.Function(opTypes.Op, newArgs);
    }

    // for the time being, we store both the types of the arguments and the explicit
    // type parameters (for most operators, this is more than actually necessary)
    private OpTypesPair OriginalOpTypes(VCExprNAry! node) {
      List<Type!>! originalTypes = new List<Type!> ();
      foreach (VCExpr! expr in node)
        originalTypes.Add(expr.Type);
      originalTypes.AddRange(node.TypeArguments);
      return new OpTypesPair (node.Op, originalTypes);
    }

    private VCExpr! EqualTypes(Type! t0, Type! t1, VariableBindings! bindings) {
      if (t0.Equals(t1))
        return VCExpressionGenerator.True;
      VCExpr! t0Expr = AxBuilder.Type2Term(t0, bindings.TypeVariableBindings);
      VCExpr! t1Expr = AxBuilder.Type2Term(t1, bindings.TypeVariableBindings);
      return Gen.Eq(t0Expr, t1Expr);
    }

    ///////////////////////////////////////////////////////////////////////////

    public override VCExpr! VisitEqOp       (VCExprNAry! node, VariableBindings! bindings) {
      // we also have to state that the types are equal, because the
      // translation does not contain any information about the
      // relationship between values and types
      return Gen.AndSimp(base.VisitEqOp(node, bindings),
                         EqualTypes(node[0].Type, node[1].Type, bindings));
    }

    public override VCExpr! VisitNeqOp      (VCExprNAry! node, VariableBindings! bindings) {
      // we also have to state that the types are (un)equal, because the
      // translation does not contain any information about the
      // relationship between values and types
      return Gen.OrSimp(base.VisitNeqOp(node, bindings),
                        Gen.Not(EqualTypes(node[0].Type, node[1].Type, bindings)));
    }

    public override VCExpr! VisitSubtypeOp  (VCExprNAry! node, VariableBindings! bindings) {
      // UGLY: the code for tracking polarities should be factored out
      int oldPolarity = Eraser.Polarity;
      Eraser.Polarity = 0;

      VCExpr! res =
        Gen.Function(VCExpressionGenerator.Subtype3Op,
                     AxBuilder.Type2Term(node[0].Type,
                                         bindings.TypeVariableBindings),
                     AxBuilder.Cast(Eraser.Mutate(node[0], bindings),
                                    AxBuilder.U),
                     AxBuilder.Cast(Eraser.Mutate(node[1], bindings),
                                    AxBuilder.U));

      Eraser.Polarity = oldPolarity;
      return res;
    }
    
    public override VCExpr! VisitSelectOp   (VCExprNAry! node, VariableBindings! bindings) {
      OpTypesPair originalOpTypes = OriginalOpTypes(node);
      OpTypesPair newOpTypes;

      if (!NewOpCache.TryGetValue(originalOpTypes, out newOpTypes)) {
        MapType! rawType = node[0].Type.AsMap;
        TypeSeq! abstractionInstantiation;
        Function! select =
          AxBuilder.MapTypeAbstracter.Select(rawType, out abstractionInstantiation);

        newOpTypes = TypesPairForSelectStore(node, select, abstractionInstantiation);
        NewOpCache.Add(originalOpTypes, newOpTypes);
      }

      return AssembleOpExpression(newOpTypes, node, bindings);
    }

    public override VCExpr! VisitStoreOp    (VCExprNAry! node, VariableBindings! bindings) {
      OpTypesPair originalOpTypes = OriginalOpTypes(node);
      OpTypesPair newOpTypes;

      if (!NewOpCache.TryGetValue(originalOpTypes, out newOpTypes)) {
        MapType! rawType = node[0].Type.AsMap;
        TypeSeq! abstractionInstantiation;
        Function! store =
          AxBuilder.MapTypeAbstracter.Store(rawType, out abstractionInstantiation);

        newOpTypes = TypesPairForSelectStore(node, store, abstractionInstantiation);
        NewOpCache.Add(originalOpTypes, newOpTypes);
      }

      return AssembleOpExpression(newOpTypes, node, bindings);
    }

    private OpTypesPair TypesPairForSelectStore(VCExprNAry! node, Function! untypedOp,
                                                // instantiation of the abstract map type parameters
                                                TypeSeq! abstractionInstantiation) {
      List<Type!>! inferredTypeArgs = new List<Type!> ();
      foreach (Type! t in node.TypeArguments)
//        inferredTypeArgs.Add(AxBuilder.MapTypeAbstracter.AbstractMapTypeRecursively(t));
        inferredTypeArgs.Add(t);
      foreach (Type! t in abstractionInstantiation)
        inferredTypeArgs.Add(t);

      assert untypedOp.InParams.Length == inferredTypeArgs.Count + node.Arity;
      return new OpTypesPair (Gen.BoogieFunctionOp(untypedOp), inferredTypeArgs);
    }

    ///////////////////////////////////////////////////////////////////////////

    public override VCExpr! VisitBoogieFunctionOp (VCExprNAry! node, VariableBindings! bindings) {
      OpTypesPair originalOpTypes = OriginalOpTypes(node);
      OpTypesPair newOpTypes;

      if (!NewOpCache.TryGetValue(originalOpTypes, out newOpTypes)) {
        Function! oriFun = ((VCExprBoogieFunctionOp)node.Op).Func;

        List<Type!>! inferredTypeArgs = new List<Type!> ();
        foreach (Type! t in node.TypeArguments)
//          inferredTypeArgs.Add(AxBuilder.MapTypeAbstracter.AbstractMapTypeRecursively(t));
          inferredTypeArgs.Add(t);

        VCExprOp! newOp = Gen.BoogieFunctionOp(AxBuilderArguments.Typed2Untyped(oriFun));
        newOpTypes = new OpTypesPair (newOp, inferredTypeArgs);

        NewOpCache.Add(originalOpTypes, newOpTypes);
      }

      return AssembleOpExpression(newOpTypes, node, bindings);
    }

    ///////////////////////////////////////////////////////////////////////////

    // cache from the typed operators to the untyped operators with
    // explicit type arguments. the keys are pairs of the typed
    // operator and the actual types of the argument expressions, the
    // values are pairs of the new operators and the types that have
    // to be given as explicit type arguments
    private readonly IDictionary<OpTypesPair, OpTypesPair>! NewOpCache =
      new Dictionary<OpTypesPair, OpTypesPair>();

    private struct OpTypesPair {
      public readonly VCExprOp! Op;
      public readonly List<Type!>! Types;

      public OpTypesPair(VCExprOp! op, List<Type!>! types) {
        this.Op = op;
        this.Types = types;
        this.HashCode = HFNS.PolyHash(op.GetHashCode(), 17, types);
      }

      [Pure][Reads(ReadsAttribute.Reads.Nothing)]
      public override bool Equals(object that) {
        if (that is OpTypesPair) {
          OpTypesPair thatPair = (OpTypesPair)that;
          return this.Op.Equals(thatPair.Op) &&
            HFNS.SameElements(this.Types, thatPair.Types);
        }
        return false;
      }

      private readonly int HashCode;

      [Pure]
      public override int GetHashCode() {
        return HashCode;
      }
    }
  }

}