path: root/Source/Dafny/DafnyAst.ssc

//-----------------------------------------------------------------------------
//
// Copyright (C) Microsoft Corporation.  All Rights Reserved.
//
//-----------------------------------------------------------------------------
using System;
using System.Collections.Generic;
using Microsoft.Contracts;

namespace Microsoft.Dafny
{
  public class Program {
    public readonly string! Name;
    public readonly List<ClassDecl!>! Classes;
    public Program(string! name, [Captured] List<ClassDecl!>! classes) {
      Name = name;
      Classes = classes;
    }
  }
  
  public class Attributes {
    public readonly string! Name;
    /*Frozen*/ public readonly List<Argument!>! Args;
    public readonly Attributes Prev;
    
    public Attributes(string! name, [Captured] List<Argument!>! args, Attributes prev)
    {
      Name = name;
      Args = args;
      Prev = prev;
    }
    
    public class Argument {
      public readonly string S;
      public readonly Expression E;
      invariant (S == null) != (E == null);
      
      public Argument(string! s) {
        S = s;
      }
      public Argument(Expression! e) {
        E = e;
      }
    }
  }
  
  // ------------------------------------------------------------------------------------------------------
  
  public abstract class Type {
    public static readonly BoolType! Bool = new BoolType();
    public static readonly IntType! Int = new IntType();
    /// <summary>
    /// Used in error situations in order to reduce further error messages.
    /// </summary>
    [Pure(false)]
    public static Type! Flexible {
      get { return new InferredTypeProxy(); }
    }
    
    public bool IsRefType {
      get {
        if (this is ObjectType) {
          return true;
        } else {
          ClassType ct = this as ClassType;
          return ct != null && ct.ResolvedParam == null;
        }
      }
    }
    public bool IsTypeParameter {
      get
        ensures result ==> this is ClassType && ((ClassType)this).ResolvedParam != null;
      {
        ClassType ct = this as ClassType;
        return ct != null && ct.ResolvedParam != null;
      }
    }
  }
  
  public abstract class BasicType : Type {
  }
  
  public class BoolType : BasicType {
    [Pure] public override string! ToString() {
      return "bool";
    }
  }
  
  public class IntType : BasicType {
    [Pure] public override string! ToString() {
      return "int";
    }
  }
  
  public class ObjectType : BasicType {
    [Pure] public override string! ToString() {
      return "object";
    }
  }
  
  public abstract class CollectionType : Type {
    public readonly Type! Arg;
    public CollectionType(Type! arg) {
      this.Arg = arg;
    }
  }
  
  public class SetType : CollectionType {
    public SetType(Type! arg) {
      base(arg);
    }
    [Pure] public override string! ToString() {
      assume Arg.IsPeerConsistent;
      return "set<" + Arg + ">";
    }
  }
  
  public class SeqType : CollectionType {
    public SeqType(Type! arg) {
      base(arg);
    }
    [Pure] public override string! ToString() {
      assume Arg.IsPeerConsistent;
      return "seq<" + Arg + ">";
    }
  }

  public class ClassType : Type {
    public readonly Token! tok;
    public readonly string! Name;
    [Rep] public readonly List<Type!>! TypeArgs;
    
    public ClassDecl ResolvedClass;  // filled in by resolution, if Name denotes a class and TypeArgs match the type parameters of that class
    public TypeParameter ResolvedParam;  // filled in by resolution, if Name denotes an enclosing type parameter and TypeArgs is the empty list
    
    public ClassType(Token! tok, string! name, [Captured] List<Type!>! typeArgs) {
      this.tok = tok;
      this.Name = name;
      this.TypeArgs = typeArgs;
    }
    
    /// <summary>
    /// This constructor constructs a resolved class type
    /// </summary>
    public ClassType(Token! tok, string! name, ClassDecl! cd, [Captured] List<Type!>! typeArgs) {
      this.tok = tok;
      this.Name = name;
      this.TypeArgs = typeArgs;
      this.ResolvedClass = cd;
    }
    
    /// <summary>
    /// This constructor constructs a resolved type parameter
    /// </summary>
    public ClassType(Token! tok, string! name, TypeParameter! tp) {
      this.tok = tok;
      this.Name = name;
      this.TypeArgs = new List<Type!>();
      this.ResolvedParam = tp;
    }
    
    /// <summary>
    /// If type denotes a resolved class type, then return that class type.
    /// Otherwise, return null.
    /// </summary>
    public static ClassType DenotesClass(Type! type)
      ensures result != null ==> result.ResolvedClass != null;
    {
      while (true)
        invariant type.IsPeerConsistent;
      {
        TypeProxy pt = type as TypeProxy;
        if (pt != null && pt.T != null) {
          type = pt.T;
          assume type.IsPeerConsistent;
        } else {
          break;
        }
      }
      ClassType ct = type as ClassType;
      if (ct != null && ct.ResolvedClass != null) {
        return ct;
      } else {
        return null;
      }
    }
    
    [Pure] public override string! ToString() {
      string s = Name;
      if (TypeArgs.Count != 0) {
        string sep = "<";
        foreach (Type t in TypeArgs) {
          assume t.IsPeerConsistent;
          s += sep + t;
          sep = ",";
        }
        s += ">";
      }
      return s;
    }
  }
  
  public abstract class TypeProxy : Type {
    public Type T;  // filled in during resolution
    internal TypeProxy() { }
    
    [Pure] public override string! ToString() {
      assume T == null || T.IsPeerConsistent;
      return T == null ? "?" : T.ToString();
    }
  }
  
  public abstract class UnrestrictedTypeProxy : TypeProxy { }
  
  /// <summary>
  /// This proxy stands for any type.
  /// </summary>  
  public class InferredTypeProxy : UnrestrictedTypeProxy {
  }
  
  /// <summary>
  /// This proxy stands for any type, but it originates from an instantiated type parameter.
  /// </summary>  
  public class ParamTypeProxy : UnrestrictedTypeProxy {
    TypeParameter! orig;
    public ParamTypeProxy(TypeParameter! orig) {
      this.orig = orig;
    }
  }
  
  public abstract class RestrictedTypeProxy : TypeProxy {
    /// <summary>
    /// The OrderID is used to simplify the unification code.  Each restricted type proxy should use its
    /// own OrderID.
    /// </summary>
    public abstract int OrderID { get; }
  }
  
  /// <summary>
  /// This proxy stands for object or any class type.
  /// </summary>  
  public class ObjectTypeProxy : RestrictedTypeProxy {
    public override int OrderID { get { return 0; } }
  }
  
  /// <summary>
  /// This proxy stands for object or any class type or a set or sequence of object or a class type.
  /// </summary>
  public class ObjectsTypeProxy : RestrictedTypeProxy {
    public override int OrderID { get { return 1; } }
  }
  
  /// <summary>
  /// This proxy stands for either:
  ///     set(Arg) or seq(Arg)
  /// </summary>  
  public class CollectionTypeProxy : RestrictedTypeProxy {
    public readonly Type! Arg;
    public CollectionTypeProxy(Type! arg) {
      Arg = arg;
    }
    public override int OrderID { get { return 2; } }
  }

  /// <summary>
  /// This proxy stands for either:
  ///     int or set or seq
  /// if AllowSeq, or:
  ///     int or set
  /// if !AllowSeq.
  /// </summary>  
  public class OperationTypeProxy : RestrictedTypeProxy {
    public readonly bool AllowSeq;
    public OperationTypeProxy(bool allowSeq) {
      AllowSeq = allowSeq;
    }
    public override int OrderID { get { return 3; } }
  }
  
  // ------------------------------------------------------------------------------------------------------
  
  public abstract class Declaration {
    public Token! tok;
    public readonly string! Name;
    public readonly Attributes Attributes;
    
    public Declaration(Token! tok, string! name, Attributes attributes) {
      this.tok = tok;
      this.Name = name;
      this.Attributes = attributes;
    }
  }
  
  public class TypeParameter : Declaration {
    public interface ParentType { }
    [Peer] ParentType parent;
    public ParentType Parent {
      get {
        return parent;
      }
      [param: Captured]
      set
        requires Parent == null;  // set it only once
        requires value != null;
        // BUGBUG:  The following line is a workaround to tell the verifier that 'value' is not of an Immutable type.
        // A proper solution would be to be able to express that in the program (in a specification or attribute) or
        // to be able to declare 'parent' as [PeerOrImmutable].
        requires value is ClassDecl || value is Function || value is Method;
        modifies parent;
      {
        parent = value;
      }
    }
    public TypeParameter(Token! tok, string! name) {
      base(tok, name, null);
    }
  }
  
  public class ClassDecl : Declaration, TypeParameter.ParentType {
    public List<TypeParameter!>! TypeArgs;
    public List<MemberDecl!>! Members;
    
    public ClassDecl(Token! tok, string! name, List<TypeParameter!>! typeArgs, [Captured] List<MemberDecl!>! members, Attributes attributes) {
      TypeArgs = typeArgs;
      Members = members;
      base(tok, name, attributes);
    }
  }
  
  public abstract class MemberDecl : Declaration {
    public ClassDecl EnclosingClass;  // filled in during resolution
    
    public MemberDecl(Token! tok, string! name, Attributes attributes) {
      base(tok, name, attributes);
    }
    /// <summary>
    /// Returns className+"."+memberName.  Available only after resolution.
    /// </summary>
    public string! FullName {
      get
        requires EnclosingClass != null;
      {
        return EnclosingClass.Name + "." + Name;
      }
    }
  }
  
  public class Field : MemberDecl {
    public readonly Type! Type;
    
    public Field(Token! tok, string! name, Type! type, Attributes attributes) {
      Type = type;
      base(tok, name, attributes);
    }
  }
  
  public interface IVariable {
    string! Name { get; }
    string! UniqueName { get; }
    Type! Type { get; }
    bool IsMutable { get; }
  }
  
  public abstract class NonglobalVariable : IVariable {
    public readonly Token! tok;
    readonly string! name;
    public string! Name { get { return name; } }
    readonly int varId = varIdCount++;
    public string! UniqueName { get { return name + "#" + varId; } }
    Type! type;
    [Pure(false)]  // TODO: if Type gets the status of [Frozen], then this attribute is not needed
    public Type! Type { get {
      assume type.IsPeerConsistent;
      while (true)
        invariant type.IsPeerConsistent;
      {
        TypeProxy t = type as TypeProxy;
        if (t != null && t.T != null) {
          type = t.T;
          assume type.IsPeerConsistent;
        } else {
          return type;
        }
      }
    } }
    public abstract bool IsMutable { get; }
    
    public NonglobalVariable(Token! tok, string! name, Type! type) {
      this.tok = tok;
      this.name = name;
      this.type = type;
    }
    
    internal static int varIdCount;  // this varIdCount is used for both NonglobalVariable's and VarDecl's.
  }
  
  public class Formal : NonglobalVariable {
    public readonly bool InParam;  // true to in-parameter, false for out-parameter
    public override bool IsMutable { get { return !InParam; } }
    
    public Formal(Token! tok, string! name, Type! type, bool inParam) {
      InParam = inParam;
      base(tok, name, type);
    }
  }
  
  public class BoundVar : NonglobalVariable {
    public override bool IsMutable { get { return false; } }
    
    public BoundVar(Token! tok, string! name, Type! type) {
      base(tok, name, type);
    }
  }
  
  public class Function : MemberDecl, TypeParameter.ParentType {
    public readonly bool Use;
    public readonly List<TypeParameter!>! TypeArgs;
    public readonly List<Formal!>! Formals;
    public readonly Type! ResultType;
    public readonly List<Expression!>! Req;
    public readonly List<Expression!>! Reads;
    public readonly Expression Body;  // an extended expression
    
    public Function(Token! tok, string! name, bool use, [Captured] List<TypeParameter!>! typeArgs, [Captured] List<Formal!>! formals, Type! resultType,
                    List<Expression!>! req, List<Expression!>! reads, Expression body, Attributes attributes) {
      this.Use = use;
      this.TypeArgs = typeArgs;
      this.Formals = formals;
      this.ResultType = resultType;
      this.Req = req;
      this.Reads = reads;
      this.Body = body;
      base(tok, name, attributes);
    }
  }
  
  public class Method : MemberDecl, TypeParameter.ParentType {
    public readonly List<TypeParameter!>! TypeArgs;
    public readonly List<Formal!>! Ins;
    public readonly List<Formal!>! Outs;
    public readonly List<MaybeFreeExpression!>! Req;
    public readonly List<Expression!>! Mod;
    public readonly List<MaybeFreeExpression!>! Ens;
    public readonly Statement Body;
    
    public Method(Token! tok, string! name,
                  [Captured] List<TypeParameter!>! typeArgs,
                  [Captured] List<Formal!>! ins, [Captured] List<Formal!>! outs,
                  [Captured] List<MaybeFreeExpression!>! req, [Captured] List<Expression!>! mod, [Captured] List<MaybeFreeExpression!>! ens,
                  [Captured] Statement body,
                  Attributes attributes) {
      this.TypeArgs = typeArgs;
      this.Ins = ins;
      this.Outs = outs;
      this.Req = req;
      this.Mod = mod;
      this.Ens = ens;
      this.Body = body;
      base(tok, name, attributes);
    }
  }
  
  // ------------------------------------------------------------------------------------------------------
  
  public abstract class Statement {
    public readonly Token! Tok;
    public Statement(Token! tok) {
      this.Tok = tok;
    }
  }
  
  public abstract class PredicateStmt : Statement {
    [Peer] public readonly Expression! Expr;
    [Captured]
    public PredicateStmt(Token! tok, Expression! expr)
      ensures Owner.Same(this, expr);
    {
      base(tok);
      Owner.AssignSame(this, expr);
      this.Expr = expr;
    }
  }
  
  public class AssertStmt : PredicateStmt {
    [Captured]
    public AssertStmt(Token! tok, Expression! expr)
      ensures Owner.Same(this, expr);
    {
      base(tok, expr);
    }
  }
  
  public class AssumeStmt : PredicateStmt {
    [Captured]
    public AssumeStmt(Token! tok, Expression! expr)
      ensures Owner.Same(this, expr);
    {
      base(tok, expr);
    }
  }
  
  public class UseStmt : PredicateStmt {
    [Captured]
    public UseStmt(Token! tok, Expression! expr)
      ensures Owner.Same(this, expr);
    {
      base(tok, expr);
    }
    [Peer] private FunctionCallExpr fce;
    /// <summary>
    /// This method assumes the statement has been successfully resolved.
    /// </summary>
    [Pure(false)]
    public FunctionCallExpr! FunctionCallExpr {
      get {
        if (fce == null) {
          Expression expr = Expr;
          while (true)
            invariant Owner.Same(this, expr);
          {
            if (expr is OldExpr) {
              expr = ((OldExpr)expr).E;
            } else {
              break;
            }
          }
          assume expr is FunctionCallExpr;
          fce = (FunctionCallExpr)expr;
        }
        return fce;
      }
    }
    public bool EvalInOld {
      get {
        return Expr is OldExpr;
      }
    }
  }
  
  public class LabelStmt : Statement {
    public readonly string! Label;
    public LabelStmt(Token! tok, string! label) {
      this.Label = label;
      base(tok);
    }
  }
  
  public class BreakStmt : Statement {
    public readonly string TargetLabel;
    public Statement TargetStmt;  // filled in during resolution
    
    public BreakStmt(Token! tok, string targetLabel) {
      this.TargetLabel = targetLabel;
      base(tok);
    }
  }
  
  public class ReturnStmt : Statement {
    public ReturnStmt(Token! tok) {
      base(tok);
    }
  }
  
  public abstract class AssignmentRhs {
    internal AssignmentRhs() { }
  }
  
  public abstract class DeterminedAssignmentRhs : AssignmentRhs {
    internal DeterminedAssignmentRhs() { }
  }
  
  public class ExprRhs : DeterminedAssignmentRhs {
    public readonly Expression! Expr;
    public ExprRhs(Expression! expr) {
      Expr = expr;
    }
  }
  
  public class TypeRhs : DeterminedAssignmentRhs {
    public readonly Type! Type;
    public TypeRhs(Type! type) {
      Type = type;
    }
  }
  
  public class HavocRhs : AssignmentRhs {
  }

  public class AssignStmt : Statement {
    public readonly Expression! Lhs;
    public readonly AssignmentRhs! Rhs;
    public AssignStmt(Token! tok, Expression! lhs, Expression! rhs) {  // ordinary assignment statement
      this.Lhs = lhs;
      this.Rhs = new ExprRhs(rhs);
      base(tok);
    }
    public AssignStmt(Token! tok, Expression! lhs, Type! type) {  // alloc statement
      this.Lhs = lhs;
      this.Rhs = new TypeRhs(type);
      base(tok);
    }
    public AssignStmt(Token! tok, Expression! lhs) {  // havoc
      this.Lhs = lhs;
      this.Rhs = new HavocRhs();
      base(tok);
    }
  }
  
  public class VarDecl : Statement, IVariable {
    readonly string! name;
    public string! Name { get { return name; } }
    readonly int varId = NonglobalVariable.varIdCount++;
    public string! UniqueName { get { return name + "#" + varId; } }
    public readonly Type OptionalType;  // this is the type mentioned in the declaration, if any
    internal Type type;  // this is the declared or inferred type of the variable; it is non-null after resolution (even if resolution fails)
    [Pure(false)]
    public Type! Type { get {
      assume type != null;  /* we assume object has been resolved */
      assume type.IsPeerConsistent;
      while (true)
        invariant type != null && type.IsPeerConsistent;
      {
        TypeProxy t = type as TypeProxy;
        if (t != null && t.T != null) {
          type = t.T;
          assume type.IsPeerConsistent;
        } else {
          return type;
        }
      }
    } }
    public bool IsMutable { get { return true; } }

    public readonly DeterminedAssignmentRhs Rhs;
    invariant OptionalType != null || Rhs != null;
    
    public VarDecl(Token! tok, string! name, Type type, DeterminedAssignmentRhs rhs)
      requires type != null || rhs != null;
    {
      this.name = name;
      this.OptionalType = type;
      this.Rhs = rhs;
      base(tok);
    }
  }
  
  public class CallStmt : Statement {
    public readonly List<IdentifierExpr!>! Lhs;
    public readonly Expression! Receiver;
    public readonly string! MethodName;
    public readonly List<Expression!>! Args;
    public Method Method;  // filled in by resolution
    
    public CallStmt(Token! tok, List<IdentifierExpr!>! lhs, Expression! receiver, string! methodName, List<Expression!>! args) {
      this.Lhs = lhs;
      this.Receiver = receiver;
      this.MethodName = methodName;
      this.Args = args;
      base(tok);
    }
  }
  
  public class BlockStmt : Statement {
    public readonly List<Statement!>! Body;
    public BlockStmt(Token! tok, [Captured] List<Statement!>! body) {
      this.Body = body;
      base(tok);
    }
  }
  
  public class IfStmt : Statement {
    public readonly Expression Guard;
    public readonly Statement! Thn;
    public readonly Statement Els;
    invariant Els == null || Els is BlockStmt || Els is IfStmt;
    
    public IfStmt(Token! tok, Expression guard, Statement! thn, Statement els)
      requires els == null || els is BlockStmt || els is IfStmt;
    {
      this.Guard = guard;
      this.Thn = thn;
      this.Els = els;
      base(tok);
    }
  }

  public class WhileStmt : Statement {
    public readonly Expression Guard;
    public readonly List<MaybeFreeExpression!>! Invariants;
    public readonly List<Expression!>! Decreases;
    public readonly Statement! Body;
    
    public WhileStmt(Token! tok, Expression guard,
                     List<MaybeFreeExpression!>! invariants, List<Expression!>! decreases,
                     Statement! body) {
      this.Guard = guard;
      this.Invariants = invariants;
      this.Decreases = decreases;
      this.Body = body;
      base(tok);
    }
  }
  
  public class ForeachStmt : Statement {
    public readonly BoundVar! BoundVar;
    public readonly Expression! Collection;
    public readonly Expression! Range;
    public readonly List<PredicateStmt!>! BodyPrefix;
    public readonly AssignStmt BodyAssign;
    
    public ForeachStmt(Token! tok, BoundVar! boundVar, Expression! collection, Expression! range, List<PredicateStmt!>! bodyPrefix, AssignStmt bodyAssign) {
      this.BoundVar = boundVar;
      this.Collection = collection;
      this.Range = range;
      this.BodyPrefix = bodyPrefix;
      this.BodyAssign = bodyAssign;
      base(tok);
    }
  }
  
  // ------------------------------------------------------------------------------------------------------
  
  public abstract class Expression {
    public readonly Token! tok;
    protected Type type;
    public Type Type {  // filled in during resolution
      [Verify(false)]  // TODO: how do we allow Type.get to modify type and still be [Pure]?
      [Additive]  // validity of proper subclasses is not required
      get
        ensures type == null ==> result == null;  // useful in conjunction with postcondition of constructor
      {
        while (true) {
          TypeProxy t = type as TypeProxy;
          if (t != null && t.T != null) {
            type = t.T;
          } else {
            assume type == null || type.IsPeerConsistent;
            return type;
          }
        }
      }
      [NoDefaultContract]  // no particular validity of 'this' is required, except that it not be committed
      set
        requires this.IsValid;
        requires Type == null;  // set it only once
        requires value != null && value.IsPeerConsistent;
        modifies type;
      {
        type = value;
        while (true) {
          TypeProxy t = type as TypeProxy;
          if (t != null && t.T != null) {
            type = t.T;
          } else {
            return;
          }
        }
      }
    }
    
    public Expression(Token! tok)
      ensures type == null;  // we would have liked to have written Type==null, but that's not admissible or provable
    {
      this.tok = tok;
    }
  }
  
  public class LiteralExpr : Expression {
    public readonly object Value;
    
    public static bool IsTrue(Expression! e) {
      if (e is LiteralExpr) {
        LiteralExpr le = (LiteralExpr)e;
        return le.Value is bool && (bool)le.Value;
      } else {
        return false;
      }
    }
    
    public LiteralExpr(Token! tok) {  // represents the Dafny literal "null"
      this.Value = null;
      base(tok);
    }
    
    public LiteralExpr(Token! tok, int n)
      requires 0 <= n;
    {
      this.Value = n;
      base(tok);
    }
    
    public LiteralExpr(Token! tok, bool b) {
      this.Value = b;
      base(tok);
    }
  }
  
  public class ThisExpr : Expression {
    public ThisExpr(Token! tok) {
      base(tok);
    }
  }
  
  public class ImplicitThisExpr : ThisExpr {
    public ImplicitThisExpr(Token! tok) {
      base(tok);
    }
  }
  
  public class IdentifierExpr : Expression {
    public readonly string! Name;
    public IVariable Var;  // filled in by resolution

    public IdentifierExpr(Token! tok, string! name) {
      Name = name;
      base(tok);
    }
  }

  public abstract class DisplayExpression : Expression {
    public readonly List<Expression!>! Elements;
    public DisplayExpression(Token! tok, List<Expression!>! elements) {
      Elements = elements;
      base(tok);
    }
  }
    
  public class SetDisplayExpr : DisplayExpression {
    public SetDisplayExpr(Token! tok, List<Expression!>! elements) {
      base(tok, elements);
    }
  }
    
  public class SeqDisplayExpr : DisplayExpression {
    public SeqDisplayExpr(Token! tok, List<Expression!>! elements) {
      base(tok, elements);
    }
  }
    
  public class FieldSelectExpr : Expression {
    public readonly Expression! Obj;
    public readonly string! FieldName;
    public Field Field;  // filled in by resolution
    
    public FieldSelectExpr(Token! tok, Expression! obj, string! fieldName) {
      this.Obj = obj;
      this.FieldName = fieldName;
      base(tok);
    }
  }
  
  public class SeqSelectExpr : Expression {
    public readonly bool SelectOne;  // false means select a range
    public readonly Expression! Seq;
    public readonly Expression E0;
    public readonly Expression E1;
    invariant SelectOne ==> E1 == null;
    invariant E0 != null || E1 != null;
    
    public SeqSelectExpr(Token! tok, bool selectOne, Expression! seq, Expression e0, Expression e1)
      requires selectOne ==> e1 == null;
      requires e0 != null || e1 != null;
    {
      SelectOne = selectOne;
      Seq = seq;
      E0 = e0;
      E1 = e1;
      base(tok);
    }
  }

  public class FunctionCallExpr : Expression {
    public readonly string! Name;
    [Peer] public readonly Expression! Receiver;
    [Peer] public readonly List<Expression!>! Args;
    public Function Function;  // filled in by resolution
    
    [Captured]
    public FunctionCallExpr(Token! tok, string! fn, Expression! receiver, [Captured] List<Expression!>! args)
      ensures type == null;
      ensures Owner.Same(this, receiver);
    {
      base(tok);
      this.Name = fn;
      Owner.AssignSame(this, receiver);
      this.Receiver = receiver;
      this.Args = args;
    }
  }
  
  /// <summary>
  /// UseExpr's are used only temporarily during translation.
  /// </summary>
  public class UseExpr : FunctionCallExpr {
    [NotDelayed] [Captured]
    public UseExpr(FunctionCallExpr! fce)
      requires fce.Function != null && fce.Function.Use;
    {
      base(fce.tok, fce.Name, fce.Receiver, new List<Expression!>(fce.Args));
      this.Function = fce.Function;
      assume Type.Bool.IsPeerConsistent;  // This would follow from BoolType being an Immutable type, or from Type.Bool being [Frozen]
      this.Type = Type.Bool;
    }
  }
  
  public class OldExpr : Expression {
    [Peer] public readonly Expression! E;
    [Captured]
    public OldExpr(Token! tok, Expression! expr) {
      base(tok);
      Owner.AssignSame(this, expr);
      E = expr;
    }
  }

  public class FreshExpr : Expression {
    public readonly Expression! E;
    public FreshExpr(Token! tok, Expression! expr) {
      E = expr;
      base(tok);
    }
  }
  
  public class UnaryExpr : Expression {
    public enum Opcode { Not, SeqLength }
    public readonly Opcode Op;
    public readonly Expression! E;
    
    public UnaryExpr(Token! tok, Opcode op, Expression! e) {
      this.Op = op;
      this.E = e;
      base(tok);
    }
  }
  
  public class BinaryExpr : Expression {
    public enum Opcode { Iff, Imp, And, Or,
                         Eq, Neq, Lt, Le, Ge, Gt,
                         Disjoint, In,
                         Add, Sub, Mul, Div, Mod }
    public readonly Opcode Op;
    public enum ResolvedOpcode {
      // logical operators
      Iff, Imp, And, Or,
      // non-collection types
      EqCommon, NeqCommon,
      // integers
      Lt, Le, Ge, Gt, Add, Sub, Mul, Div, Mod,
      // sets
      SetEq, SetNeq, ProperSubset, Subset, Superset, ProperSuperset, Disjoint, InSet,
      Union, Intersection, SetDifference,
      // sequences
      SeqEq, SeqNeq, ProperPrefix, Prefix, Concat, InSeq
    }
    public ResolvedOpcode ResolvedOp;  // filled in by resolution
                                 
    public static string! OpcodeString(Opcode op) {
      switch (op) {
        case Opcode.Iff:  return "<==>";
        case Opcode.Imp:  return "==>";
        case Opcode.And:  return "&&";
        case Opcode.Or:  return "||";
        case Opcode.Eq:  return "==";
        case Opcode.Lt:  return "<";
        case Opcode.Gt:  return ">";
        case Opcode.Le:  return "<=";
        case Opcode.Ge:  return ">=";
        case Opcode.Neq:  return "!=";
        case Opcode.Disjoint:  return "!!";
        case Opcode.In:  return "in";
        case Opcode.Add:  return "+";
        case Opcode.Sub:  return "-";
        case Opcode.Mul:  return "*";
        case Opcode.Div:  return "/";
        case Opcode.Mod:  return "%";
        default:
          assert false;  // unexpected operator
      }
    }
    public readonly Expression! E0;
    public readonly Expression! E1;
    
    public BinaryExpr(Token! tok, Opcode op, Expression! e0, Expression! e1) {
      this.Op = op;
      this.E0 = e0;
      this.E1 = e1;
      base(tok);
    }
  }
  
  public abstract class QuantifierExpr : Expression {
    public readonly List<BoundVar!>! BoundVars;
    public readonly Expression! Body;
    public readonly Triggers Trigs;
    public readonly Attributes Attributes;
    
    public QuantifierExpr(Token! tok, List<BoundVar!>! bvars, Expression! body, Triggers trigs, Attributes attrs) {
      this.BoundVars = bvars;
      this.Body = body;
      this.Trigs = trigs;
      this.Attributes = attrs;
      base(tok);
    }
  }
  
  public class Triggers {
    public readonly List<Expression!>! Terms;
    public readonly Triggers Prev;
    
    public Triggers(List<Expression!>! terms, Triggers prev) {
      this.Terms = terms;
      this.Prev = prev;
    }
  }
  
  public class ForallExpr : QuantifierExpr {
    public ForallExpr(Token! tok, List<BoundVar!>! bvars, Expression! body, Triggers trig, Attributes attrs) {
      base(tok, bvars, body, trig, attrs);
    }
  }
  
  public class ExistsExpr : QuantifierExpr {
    public ExistsExpr(Token! tok, List<BoundVar!>! bvars, Expression! body, Triggers trig, Attributes attrs) {
      base(tok, bvars, body, trig, attrs);
    }
  }
  
  public class ITEExpr : Expression {  // an ITEExpr is an "extended expression" and is only allowed in certain places
    public readonly Expression! Test;
    public readonly Expression! Thn;
    public readonly Expression! Els;
    
    public ITEExpr(Token! tok, Expression! test, Expression! thn, Expression! els) {
      this.Test = test;
      this.Thn = thn;
      this.Els = els;
      base(tok);
    }
  }
  
  public class MaybeFreeExpression {
    public readonly Expression! E;
    public readonly bool IsFree;
    public MaybeFreeExpression(Expression! e, bool isFree) {
      E = e;
      IsFree = isFree;
    }
  }
}