path: root/Source/Dafny/Resolver.ssc

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

namespace Microsoft.Dafny {
  public class Resolver {
    public int ErrorCount = 0;
    void Error(Token! tok, string! msg, params object[] args) {
      ConsoleColor col = Console.ForegroundColor;
      Console.ForegroundColor = ConsoleColor.Red;
      Console.WriteLine("{0}({1},{2}): Error: {3}",
          tok.filename, tok.line, tok.col-1,
          string.Format(msg, args));
      Console.ForegroundColor = col;
      ErrorCount++;
    }
    void Error(Declaration! d, string! msg, params object[] args) {
      Error(d.tok, msg, args);
    }
    void Error(Statement! s, string! msg, params object[] args) {
      Error(s.Tok, msg, args);
    }
    void Error(NonglobalVariable! v, string! msg, params object[] args) {
      Error(v.tok, msg, args);
    }
    void Error(Expression! e, string! msg, params object[] args) {
      Error(e.tok, msg, args);
    }
    
    readonly Dictionary<string!,TopLevelDecl!>! classes = new Dictionary<string!,TopLevelDecl!>();
    readonly Dictionary<ClassDecl!,Dictionary<string!,MemberDecl!>!>! classMembers = new Dictionary<ClassDecl!,Dictionary<string!,MemberDecl!>!>();
    readonly Dictionary<DatatypeDecl!,Dictionary<string!,DatatypeCtor!>!>! datatypeCtors = new Dictionary<DatatypeDecl!,Dictionary<string!,DatatypeCtor!>!>();

    public void ResolveProgram(Program! prog) {
      foreach (TopLevelDecl d in prog.Classes) {
        // register the class/datatype name
        if (classes.ContainsKey(d.Name)) {
          Error(d, "Duplicate name of top-level declaration: {0}", d.Name);
        } else {
          classes.Add(d.Name, d);
        }

        if (d is ClassDecl) {
          ClassDecl cl = (ClassDecl)d;
          
          // register the names of the class members
          Dictionary<string!,MemberDecl!> members = new Dictionary<string!,MemberDecl!>();
          classMembers.Add(cl, members);
        
          foreach (MemberDecl m in cl.Members) {
            if (members.ContainsKey(m.Name)) {
              Error(m, "Duplicate member name: {0}", m.Name);
            } else {
              members.Add(m.Name, m);
            }
          }
        } else {
          DatatypeDecl dt = (DatatypeDecl)d;

          // register the names of the constructors
          Dictionary<string!,DatatypeCtor!> ctors = new Dictionary<string!,DatatypeCtor!>();
          datatypeCtors.Add(dt, ctors);
        
          foreach (DatatypeCtor ctor in dt.Ctors) {
            if (ctors.ContainsKey(ctor.Name)) {
              Error(ctor, "Duplicate datatype constructor name: {0}", ctor.Name);
            } else {
              ctors.Add(ctor.Name, ctor);
            }
          }
        }
      }

      // resolve each class
      foreach (TopLevelDecl d in prog.Classes) {
        allTypeParameters.PushMarker();
        ResolveTypeParameters(d.TypeArgs, true, d);
        if (d is ClassDecl) {
          ResolveClassMemberTypes((ClassDecl)d);
        } else {
          ResolveCtorTypes((DatatypeDecl)d);
        }
        allTypeParameters.PopMarker();
      }
      foreach (TopLevelDecl d in prog.Classes) {
        allTypeParameters.PushMarker();
        ResolveTypeParameters(d.TypeArgs, false, d);
        if (d is ClassDecl) {
          ResolveClassMemberBodies((ClassDecl)d);
        } else {
          assert d is DatatypeDecl;
          // nothing else to do (but there will be something to do here if constructors can have preconditions)
        }
        allTypeParameters.PopMarker();
      }
    }
    
    ClassDecl currentClass;
    readonly Scope<TypeParameter>! allTypeParameters = new Scope<TypeParameter>();
    readonly Scope<IVariable>! scope = new Scope<IVariable>();
    readonly Scope<Statement>! labeledStatements = new Scope<Statement>();
    
    /// <summary>
    /// Assumes type parameters have already been pushed
    /// </summary>
    void ResolveClassMemberTypes(ClassDecl! cl)
      requires currentClass == null;
      ensures currentClass == null;
    {
      currentClass = cl;
      foreach (MemberDecl member in cl.Members) {
        member.EnclosingClass = cl;
        if (member is Field) {
          ResolveType(((Field)member).Type);
          
        } else if (member is Function) {
          Function f = (Function)member;
          allTypeParameters.PushMarker();
          ResolveTypeParameters(f.TypeArgs, true, f);
          ResolveFunctionSignature(f);
          allTypeParameters.PopMarker();

        } else if (member is Method) {
          Method m = (Method)member;
          allTypeParameters.PushMarker();
          ResolveTypeParameters(m.TypeArgs, true, m);
          ResolveMethodSignature(m);
          allTypeParameters.PopMarker();

        } else {
          assert false;  // unexpected member type
        }
      }
      currentClass = null;
    }

    /// <summary>
    /// Assumes type parameters have already been pushed, and that all types in class members have been resolved
    /// </summary>
    void ResolveClassMemberBodies(ClassDecl! cl)
      requires currentClass == null;
      ensures currentClass == null;
    {
      ResolveAttributes(cl.Attributes, false);
      currentClass = cl;
      foreach (MemberDecl member in cl.Members) {
        ResolveAttributes(member.Attributes, false);
        if (member is Field) {
          // nothing more to do
          
        } else if (member is Function) {
          Function f = (Function)member;
          allTypeParameters.PushMarker();
          ResolveTypeParameters(f.TypeArgs, false, f);
          ResolveFunction(f);
          allTypeParameters.PopMarker();

        } else if (member is Method) {
          Method m = (Method)member;
          allTypeParameters.PushMarker();
          ResolveTypeParameters(m.TypeArgs, false, m);
          ResolveMethod(m);
          allTypeParameters.PopMarker();

        } else {
          assert false;  // unexpected member type
        }
      }
      currentClass = null;
    }

    /// <summary>
    /// Assumes type parameters have already been pushed
    /// </summary>
    void ResolveCtorTypes(DatatypeDecl! dt)
    {
      foreach (DatatypeCtor ctor in dt.Ctors) {
        ctor.EnclosingDatatype = dt;

        allTypeParameters.PushMarker();
        ResolveTypeParameters(ctor.TypeArgs, true, ctor);
        ResolveCtorSignature(ctor);
        allTypeParameters.PopMarker();
      }
    }

    void ResolveAttributes(Attributes attrs, bool twoState) {
      // order does not matter for resolution, so resolve them in reverse order
      for (; attrs != null; attrs = attrs.Prev) {
        foreach (Attributes.Argument aa in attrs.Args) {
          if (aa.E != null) {
            ResolveExpression(aa.E, twoState);
          }
        }
      }
    }
        
    void ResolveTriggers(Triggers trigs, bool twoState) {
      // order does not matter for resolution, so resolve them in reverse order
      for (; trigs != null; trigs = trigs.Prev) {
        foreach (Expression e in trigs.Terms) {
          ResolveExpression(e, twoState);
        }
      }
    }
        
    void ResolveTypeParameters(List<TypeParameter!>! tparams, bool emitErrors, TypeParameter.ParentType! parent) {
      // push non-duplicated type parameter names
      foreach (TypeParameter tp in tparams) {
        if (emitErrors) {
          // we're seeing this TypeParameter for the first time
          tp.Parent = parent;
        }
        if (!allTypeParameters.Push(tp.Name, tp) && emitErrors) {
          Error(tp, "Duplicate type-parameter name: {0}", tp.Name);
        }
      }
    }
    
    /// <summary>
    /// Assumes type parameters have already been pushed
    /// </summary>
    void ResolveFunctionSignature(Function! f) {
      scope.PushMarker();
      foreach (Formal p in f.Formals) {
        if (!scope.Push(p.Name, p)) {
          Error(p, "Duplicate parameter name: {0}", p.Name);
        }
        ResolveType(p.Type);
      }
      ResolveType(f.ResultType);
      scope.PopMarker();
    }

    /// <summary>
    /// Assumes type parameters have already been pushed
    /// </summary>
    void ResolveFunction(Function! f) {
      scope.PushMarker();
      if (f.IsClass) {
        scope.AllowInstance = false;
      }
      foreach (Formal p in f.Formals) {
        scope.Push(p.Name, p);
      }
      foreach (Expression r in f.Req) {
        ResolveExpression(r, false);
        assert r.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(r.Type, Type.Bool)) {
          Error(r, "Precondition must be a boolean (got {0})", r.Type);
        }
      }
      foreach (Expression r in f.Reads) {
        ResolveExpression(r, false);
        Type t = r.Type;
        assert t != null;  // follows from postcondition of ResolveExpression
        if (t is CollectionType) {
          t = ((CollectionType)t).Arg;
        }
        if (t is ObjectType) {
          // fine
        } else if (UserDefinedType.DenotesClass(t) != null) {
          // fine
        } else {
          Error(r, "a reads-clause expression must denote an object or a collection of objects (instead got {0})", r.Type);
        }
      }
      foreach (Expression r in f.Decreases) {
        ResolveExpression(r, false);
        // any type is fine
      }
      if (f.Body != null) {
        ResolveExpression(f.Body, false);
        assert f.Body.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(f.Body.Type, f.ResultType)) {
          Error(f, "Function body type mismatch (expected {0}, got {1})", f.ResultType, f.Body.Type);
        }
      }
      scope.PopMarker();
    }
    
    /// <summary>
    /// Assumes type parameters have already been pushed
    /// </summary>
    void ResolveMethodSignature(Method! m) {
      scope.PushMarker();
      // resolve in-parameters
      foreach (Formal p in m.Ins) {
        if (!scope.Push(p.Name, p)) {
          Error(p, "Duplicate parameter name: {0}", p.Name);
        }
        ResolveType(p.Type);
      }
      // resolve out-parameters
      foreach (Formal p in m.Outs) {
        if (!scope.Push(p.Name, p)) {
          Error(p, "Duplicate parameter name: {0}", p.Name);
        }
        ResolveType(p.Type);
      }
      scope.PopMarker();
    }
    
    /// <summary>
    /// Assumes type parameters have already been pushed
    /// </summary>
    void ResolveMethod(Method! m) {
      // Add in-parameters to the scope, but don't care about any duplication errors, since they have already been reported
      scope.PushMarker();
      if (m.IsClass) {
        scope.AllowInstance = false;
      }
      foreach (Formal p in m.Ins) {
        scope.Push(p.Name, p);
      }
      
      // Start resolving specification...
      foreach (MaybeFreeExpression e in m.Req) {
        ResolveExpression(e.E, false);
        assert e.E.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(e.E.Type, Type.Bool)) {
          Error(e.E, "Precondition must be a boolean (got {0})", e.E.Type);
        }
      }
      foreach (Expression e in m.Mod) {
        ResolveExpression(e, false);
        Type t = e.Type;
        assert t != null;  // follows from postcondition of ResolveExpression
        if (t is CollectionType) {
          t = ((CollectionType)t).Arg;
        }
        if (t is ObjectType) {
          // fine
        } else if (UserDefinedType.DenotesClass(t) != null) {
          // fine
        } else {
          Error(e, "a modifies-clause expression must denote an object or a collection of objects (instead got {0})", e.Type);
        }
      }
      
      // Add out-parameters to the scope, but don't care about any duplication errors, since they have already been reported
      foreach (Formal p in m.Outs) {
        scope.Push(p.Name, p);
      }

      // ... continue resolving specification
      foreach (MaybeFreeExpression e in m.Ens) {
        ResolveExpression(e.E, true);
        assert e.E.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(e.E.Type, Type.Bool)) {
          Error(e.E, "Postcondition must be a boolean (got {0})", e.E.Type);
        }
      }
      
      // Resolve body
      if (m.Body != null) {
        ResolveStatement(m.Body);
      }
      
      scope.PopMarker();
    }
    
    /// <summary>
    /// Assumes type parameters have already been pushed
    /// </summary>
    void ResolveCtorSignature(DatatypeCtor! ctor) {
      scope.PushMarker();
      foreach (Formal p in ctor.Formals) {
        if (!scope.Push(p.Name, p)) {
          Error(p, "Duplicate parameter name: {0}", p.Name);
        }
        ResolveType(p.Type);
      }
      scope.PopMarker();
    }

    public void ResolveType(Type! type) {
      if (type is BasicType) {
        // nothing to resolve
      } else if (type is CollectionType) {
        ResolveType(((CollectionType)type).Arg);
      } else if (type is UserDefinedType) {
        UserDefinedType t = (UserDefinedType)type;
        foreach (Type tt in t.TypeArgs) {
          ResolveType(tt);
        }
        TypeParameter tp = allTypeParameters.Find(t.Name);
        if (tp != null) {
          if (t.TypeArgs.Count == 0) {
            t.ResolvedParam = tp;
          } else {
            Error(t.tok, "Type parameter expects no type arguments: {0}", t.Name);
          }
        } else {
          TopLevelDecl d;
          if (!classes.TryGetValue(t.Name, out d)) {
            Error(t.tok, "Undeclared top-level type or type parameter: {0}", t.Name);
          } else if (((!)d).TypeArgs.Count == t.TypeArgs.Count) {
            t.ResolvedClass = d;
          } else {
            Error(t.tok, "Wrong number of type arguments ({0} instead of {1}) passed to class/datatype: {2}", t.TypeArgs.Count, d.TypeArgs.Count, t.Name);
          }
        }
      
      } else if (type is TypeProxy) {
        TypeProxy t = (TypeProxy)type;
        if (t.T != null) {
          ResolveType(t.T);
        }
        
      } else {
        assert false;  // unexpected type
      }
    }
    
    public bool UnifyTypes(Type! a, Type! b) {
      while (a is TypeProxy) {
        TypeProxy proxy = (TypeProxy)a;
        if (proxy.T == null) {
          // merge a and b; to avoid cycles, first get to the bottom of b
          while (b is TypeProxy && ((TypeProxy)b).T != null) {
            b = ((TypeProxy)b).T;
          }
          return AssignProxy(proxy, b);
        } else {
          a = proxy.T;
        }
      }
      
      while (b is TypeProxy) {
        TypeProxy proxy = (TypeProxy)b;
        if (proxy.T == null) {
          // merge a and b (we have already got to the bottom of a)
          return AssignProxy(proxy, a);
        } else {
          b = proxy.T;
        }
      }
      
#if !NO_CHEAP_OBJECT_WORKAROUND
      if (a is ObjectType || b is ObjectType) {  // TODO: remove this temporary hack
        // allow anything with object; this is BOGUS
        return true;
      }
#endif
      // Now, a and b are non-proxies and stand for the same things as the original a and b, respectively.
      
      if (a is BoolType) {
        return b is BoolType;
      } else if (a is IntType) {
        return b is IntType;
      } else if (a is ObjectType) {
        return b is ObjectType;
      } else if (a is SetType) {
        return b is SetType && UnifyTypes(((SetType)a).Arg, ((SetType)b).Arg);
      } else if (a is SeqType) {
        return b is SeqType && UnifyTypes(((SeqType)a).Arg, ((SeqType)b).Arg);
      } else if (a is UserDefinedType) {
        if (!(b is UserDefinedType)) {
          return false;
        }
        UserDefinedType aa = (UserDefinedType)a;
        UserDefinedType bb = (UserDefinedType)b;
        if (aa.ResolvedClass != null && aa.ResolvedClass == bb.ResolvedClass) {
          // these are both resolved class/datatype types
          assert aa.TypeArgs.Count == bb.TypeArgs.Count;
          bool successSoFar = true;
          for (int i = 0; i < aa.TypeArgs.Count; i++) {
            if (!UnifyTypes(aa.TypeArgs[i], bb.TypeArgs[i])) {
              successSoFar = false;
            }
          }
          return successSoFar;
        } else if (aa.ResolvedParam != null && aa.ResolvedParam == bb.ResolvedParam) {
          // these are both resolved type parameters
          assert aa.TypeArgs.Count == 0 && bb.TypeArgs.Count == 0;
          return true;
        } else {
          // something is wrong; either aa or bb wasn't properly resolved, or they don't unify
          return false;
        }
        
      } else {
        assert false;  // unexpected type
      }
    }
    
    bool AssignProxy(TypeProxy! proxy, Type! t)
      requires proxy.T == null;
      requires t is TypeProxy ==> ((TypeProxy)t).T == null;
      modifies proxy.T, ((TypeProxy)t).T;  // might also change t.T if t is a proxy
      ensures result ==> proxy == t || proxy.T != null || (t is TypeProxy && ((TypeProxy)t).T != null);
    {
      if (proxy == t) {
        // they are already in the same equivalence class
        return true;
      
      } else if (proxy is UnrestrictedTypeProxy) {
        // it's fine to redirect proxy to t (done below)
        
      } else if (t is UnrestrictedTypeProxy) {
          // merge proxy and t by redirecting t to proxy, rather than the other way around
          ((TypeProxy)t).T = proxy;
          return true;
      
      } else if (t is RestrictedTypeProxy) {
        // Both proxy and t are restricted type proxies.  To simplify unification, order proxy and t
        // according to their types.
        RestrictedTypeProxy r0 = (RestrictedTypeProxy)proxy;
        RestrictedTypeProxy r1 = (RestrictedTypeProxy)t;
        if (r0.OrderID <= r1.OrderID) {
          return AssignRestrictedProxies(r0, r1);
        } else {
          return AssignRestrictedProxies(r1, r0);
        }
      
      // In the remaining cases, proxy is a restricted proxy and t is a non-proxy
      } else if (proxy is ObjectTypeProxy) {
        if (t is ObjectType || UserDefinedType.DenotesClass(t) != null) {
          // all is fine, proxy can be redirected to t
        } else {
          return false;
        }
      
      } else if (proxy is ObjectsTypeProxy) {
        if (t is ObjectType || UserDefinedType.DenotesClass(t) != null) {
          // all is good
        } else if (t is CollectionType) {
          proxy.T = new CollectionTypeProxy(new ObjectTypeProxy());
          return UnifyTypes(proxy.T, t);
        }
        
      } else if (proxy is CollectionTypeProxy) {
        CollectionTypeProxy collProxy = (CollectionTypeProxy)proxy;
        if (t is CollectionType) {
          if (!UnifyTypes(collProxy.Arg, ((CollectionType)t).Arg)) {
            return false;
          }
        } else {
          return false;
        }
        
      } else if (proxy is OperationTypeProxy) {
        OperationTypeProxy opProxy = (OperationTypeProxy)proxy;
        if (t is IntType || t is SetType || (opProxy.AllowSeq && t is SeqType)) {
          // this is the expected case
        } else {
          return false;
        }
        
      } else {
        assert false;  // unexpected proxy type
      }
      
      // do the merge
      proxy.T = t;
      return true;
    }
    
    bool AssignRestrictedProxies(RestrictedTypeProxy! a, RestrictedTypeProxy! b)
      requires a != b;
      requires a.T == null && b.T == null;
      requires a.OrderID <= b.OrderID;
      modifies a.T, b.T;
      ensures result ==> a.T != null || b.T != null;
    {
      if (a is ObjectTypeProxy) {
        if (b is ObjectTypeProxy) {
          // all is fine
          a.T = b;
          return true;
        } else if (b is ObjectsTypeProxy) {
          // unify a and b by redirecting b to a, since a gives the stronger requirement
          b.T = a;
          return true;
        } else {
          return false;
        }
        
      } else if (a is ObjectsTypeProxy) {
        if (b is ObjectsTypeProxy) {
          // fine
          a.T = b;
          return true;
        } else if (b is CollectionTypeProxy) {
          // fine provided b's collection-element-type can be unified with object or a class type
          a.T = new ObjectTypeProxy();
          return UnifyTypes(a.T, ((CollectionTypeProxy)b).Arg);
        } else if (b is OperationTypeProxy) {
          // fine; restrict a to sets of object/class, and restrict b to set/seq of object/class
          if (((OperationTypeProxy)b).AllowSeq) {
            a.T = new CollectionTypeProxy(new ObjectTypeProxy());
            b.T = a.T;
          } else {
            a.T = new SetType(new ObjectTypeProxy());
            b.T = a.T;
          }
          return true;
        } else {
          assert false;  // unexpected restricted-proxy type
        }
          
      } else if (a is CollectionTypeProxy) {
        if (b is CollectionTypeProxy) {
          a.T = b;
          return UnifyTypes(((CollectionTypeProxy)a).Arg, ((CollectionTypeProxy)b).Arg);
        } else if (b is OperationTypeProxy) {
          if (((OperationTypeProxy)b).AllowSeq) {
            b.T = a;  // a is a stronger constraint than b
          } else {
            // a says set<T>,seq<T> and b says int,set; the intersection is set<T>
            a.T = new SetType(((CollectionTypeProxy)a).Arg);
            b.T = a.T;
          }
          return true;
        } else {
          assert false;  // unexpected restricted-proxy type
        }
        
      } else if (a is OperationTypeProxy) {
        assert b is OperationTypeProxy;  // else we we have unexpected restricted-proxy type
        if (((OperationTypeProxy)a).AllowSeq ==> ((OperationTypeProxy)b).AllowSeq) {
          b.T = a;
        } else {
          a.T = b;  // b has the stronger requirement
        }
        return true;
        
      } else {
        assert false;  // unexpected restricted-proxy type
      }
    }
    
    public void ResolveStatement(Statement! stmt)
      requires !(stmt is LabelStmt);  // these should be handled inside lists of statements
    {
      if (stmt is UseStmt) {
        UseStmt s = (UseStmt)stmt;
        ResolveExpression(s.Expr, true);
        assert s.Expr.Type != null;  // follows from postcondition of ResolveExpression
        Expression expr = s.Expr;
        while (true) {
          if (expr is OldExpr) {
            expr = ((OldExpr)expr).E;
          } else {
            break;
          }
        }
        FunctionCallExpr fce = expr as FunctionCallExpr;
        if (fce == null || fce.Function == null || !fce.Function.IsUse) {
          Error(s.Expr, "use statement must indicate a function declared as use");
        }
      } else if (stmt is PredicateStmt) {
        PredicateStmt s = (PredicateStmt)stmt;
        ResolveExpression(s.Expr, true);
        assert s.Expr.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(s.Expr.Type, Type.Bool)) {
          Error(s.Expr, "condition is expected to be of type {0}, but is {1}", Type.Bool, s.Expr.Type);
        }
        
      } else if (stmt is BreakStmt) {
        BreakStmt s = (BreakStmt)stmt;
        if (s.TargetLabel != null) {
          Statement target = labeledStatements.Find(s.TargetLabel);
          if (target == null) {
            Error(s, "break label is undefined or not in scope: {0}", s.TargetLabel);
          } else {
            s.TargetStmt = target;
          }
        }
      
      } else if (stmt is ReturnStmt) {
        // nothing to resolve
        
      } else if (stmt is AssignStmt) {
        AssignStmt s = (AssignStmt)stmt;
        ResolveExpression(s.Lhs, true);
        assert s.Lhs.Type != null;  // follows from postcondition of ResolveExpression
        // check that LHS denotes a mutable variable or a field
        if (s.Lhs is IdentifierExpr) {
          IVariable var = ((IdentifierExpr)s.Lhs).Var;
          if (var == null) {
            // the LHS didn't resolve correctly; some error would already have been reported
          } else if (!var.IsMutable) {
            Error(stmt, "LHS of assignment must denote a mutable variable or field");
          }
        } else if (s.Lhs is FieldSelectExpr) {
          // LHS is fine, but restrict the RHS to ExprRhs
          if (!(s.Rhs is ExprRhs)) {
            Error(stmt, "Assignment to field must have an expression RHS; try using a temporary local variable");
          }
        } else {
          Error(stmt, "LHS of assignment must denote a mutable variable or field");
        }
        
        if (s.Rhs is ExprRhs) {
          ExprRhs rr = (ExprRhs)s.Rhs;
          ResolveExpression(rr.Expr, true);
          assert rr.Expr.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(s.Lhs.Type, rr.Expr.Type)) {
            Error(stmt, "RHS (of type {0}) not assignable to LHS (of type {1})", rr.Expr.Type, s.Lhs.Type);
          }
        } else if (s.Rhs is TypeRhs) {
          TypeRhs rr = (TypeRhs)s.Rhs;
          ResolveType(rr.Type);
          if (!rr.Type.IsRefType) {
            Error(stmt, "new can be applied only to reference types (got {0})", rr.Type);
          } else if (!UnifyTypes(s.Lhs.Type, rr.Type)) {
            Error(stmt, "type {0} is not assignable to LHS (of type {1})", rr.Type, s.Lhs.Type);
          }
        } else if (s.Rhs is HavocRhs) {
          // nothing else to do
        } else {
          assert false;  // unexpected RHS
        }
        
      } else if (stmt is VarDecl) {
        VarDecl s = (VarDecl)stmt;
        if (s.OptionalType != null) {
          ResolveType(s.OptionalType);
          s.type = s.OptionalType;
        }
        if (s.Rhs != null) {
          Type! rhsType;
          if (s.Rhs is ExprRhs) {
            ExprRhs rr = (ExprRhs)s.Rhs;
            ResolveExpression(rr.Expr, true);
            assert rr.Expr.Type != null;  // follows from postcondition of ResolveExpression
            rhsType = rr.Expr.Type;
          } else if (s.Rhs is TypeRhs) {
            TypeRhs rr = (TypeRhs)s.Rhs;
            ResolveType(rr.Type);
            if (!rr.Type.IsRefType) {
              Error(stmt, "new can be applied only to reference types (got {0})", rr.Type);
            }
            rhsType = rr.Type;
          } else {
            assert false;  // unexpected RHS
          }
          if (s.OptionalType == null) {
            s.type = rhsType;
          } else if (!UnifyTypes(s.OptionalType, rhsType)) {
            Error(stmt, "initialization RHS (of type {0}) not assignable to variable (of type {1})", rhsType, s.OptionalType);
          }
        }
        // now that the declaration has been processed, add the name to the scope
        if (!scope.Push(s.Name, s)) {
          Error(s, "Duplicate local-variable name: {0}", s.Name);
        }
      
      } else if (stmt is CallStmt) {
        CallStmt s = (CallStmt)stmt;
        
        // resolve any local variables declared here
        foreach (VarDecl local in s.NewVars) {
          ResolveStatement(local);
        }
        
        // resolve left-hand side
        Dictionary<string!,object> lhsNameSet = new Dictionary<string!,object>();
        foreach (IdentifierExpr lhs in s.Lhs) {
          ResolveExpression(lhs, true);
          if (lhsNameSet.ContainsKey(lhs.Name)) {
            Error(s, "Duplicate variable in left-hand side of call statement: {0}", lhs.Name);
          } else {
            lhsNameSet.Add(lhs.Name, null);
          }
        }
        // resolve receiver
        ResolveReceiver(s.Receiver, true);
        assert s.Receiver.Type != null;  // follows from postcondition of ResolveExpression
        // resolve arguments
        foreach (Expression e in s.Args) {
          ResolveExpression(e, true);
        }
        
        // resolve the method name
        UserDefinedType ctype;
        MemberDecl member = ResolveMember(s.Tok, s.Receiver.Type, s.MethodName, out ctype);
        if (member == null) {
          // error has already been reported by ResolveMember
        } else if (!(member is Method)) {
          Error(s, "member {0} in class {1} does not refer to a method", s.MethodName, ((!)ctype).Name);
        } else {
          Method method = (Method)member;
          s.Method = method;
          if (method.Ins.Count != s.Args.Count) {
            Error(s, "wrong number of method arguments (got {0}, expected {1})", s.Args.Count, method.Ins.Count);
          } else if (method.Outs.Count != s.Lhs.Count) {
            Error(s, "wrong number of method result arguments (got {0}, expected {1})", s.Lhs.Count, method.Outs.Count);
          } else {
            assert ctype != null;  // follows from postcondition of ResolveMember
            if (!scope.AllowInstance && !method.IsClass && s.Receiver is ThisExpr) {
              // The call really needs an instance, but that instance is given as 'this', which is not
              // available in this context.  For more details, see comment in the resolution of a
              // FunctionCallExpr.
              Error(s.Receiver, "'this' is not allowed in a 'class' context");
            }
            // build the type substitution map
            Dictionary<TypeParameter!,Type!> subst = new Dictionary<TypeParameter!,Type!>();
            for (int i = 0; i < ctype.TypeArgs.Count; i++) {
              subst.Add(((!)ctype.ResolvedClass).TypeArgs[i], ctype.TypeArgs[i]);
            }
            foreach (TypeParameter p in method.TypeArgs) {
              subst.Add(p, new ParamTypeProxy(p));
            }
            // type check the arguments
            for (int i = 0; i < method.Ins.Count; i++) {
              Type st = SubstType(method.Ins[i].Type, subst);
              if (!UnifyTypes((!)s.Args[i].Type, st)) {
                Error(s, "incorrect type of method in-parameter {0} (expected {1}, got {2})", i, st, s.Args[i].Type);
              }
            }
            for (int i = 0; i < method.Outs.Count; i++) {
              Type st = SubstType(method.Outs[i].Type, subst);
              if (!UnifyTypes((!)s.Lhs[i].Type, st)) {
                Error(s, "incorrect type of method out-parameter {0} (expected {1}, got {2})", i, st, s.Lhs[i].Type);
              }
            }
          }
        }
        
      } else if (stmt is BlockStmt) {
        scope.PushMarker();
        int labelsToPop = 0;
        foreach (Statement ss in ((BlockStmt)stmt).Body) {
          if (ss is LabelStmt) {
            LabelStmt ls = (LabelStmt)ss;
            labeledStatements.PushMarker();
            bool b = labeledStatements.Push(ls.Label, ls);
            assert b;  // since we just pushed a marker, we expect the Push to succeed
            labelsToPop++;
          } else {
            ResolveStatement(ss);
            for (; 0 < labelsToPop; labelsToPop--) { labeledStatements.PopMarker(); }
          }
        }
        for (; 0 < labelsToPop; labelsToPop--) { labeledStatements.PopMarker(); }
        scope.PopMarker();
      
      } else if (stmt is IfStmt) {
        IfStmt s = (IfStmt)stmt;
        if (s.Guard != null) {
          ResolveExpression(s.Guard, true);
          assert s.Guard.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(s.Guard.Type, Type.Bool)) {
            Error(s.Guard, "condition is expected to be of type {0}, but is {1}", Type.Bool, s.Guard.Type);
          }
        }
        ResolveStatement(s.Thn);
        if (s.Els != null) {
          ResolveStatement(s.Els);
        }
      
      } else if (stmt is WhileStmt) {
        WhileStmt s = (WhileStmt)stmt;
        if (s.Guard != null) {
          ResolveExpression(s.Guard, true);
          assert s.Guard.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(s.Guard.Type, Type.Bool)) {
            Error(s.Guard, "condition is expected to be of type {0}, but is {1}", Type.Bool, s.Guard.Type);
          }
        }
        foreach (MaybeFreeExpression inv in s.Invariants) {
          ResolveExpression(inv.E, true);
          assert inv.E.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(inv.E.Type, Type.Bool)) {
            Error(inv.E, "invariant is expected to be of type {0}, but is {1}", Type.Bool, inv.E.Type);
          }
        }
        foreach (Expression e in s.Decreases) {
          ResolveExpression(e, true);
          // any type is fine
        }
        ResolveStatement(s.Body);
      
      } else if (stmt is ForeachStmt) {
        ForeachStmt s = (ForeachStmt)stmt;
        scope.PushMarker();
        bool b = scope.Push(s.BoundVar.Name, s.BoundVar);
        assert b;  // since we just pushed a marker, we expect the Push to succeed
        ResolveType(s.BoundVar.Type);
        
        ResolveExpression(s.Collection, true);
        assert s.Collection.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(s.Collection.Type, new CollectionTypeProxy(s.BoundVar.Type))) {
          Error(s.Collection, "The type is expected to be a collection of {0} (instead got {1})", s.BoundVar.Type, s.Collection.Type);
        }
        
        ResolveExpression(s.Range, true);
        assert s.Range.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(s.Range.Type, Type.Bool)) {
          Error(s.Range, "range condition is expected to be of type {0}, but is {1}", Type.Bool, s.Range.Type);
        }
        
        foreach (PredicateStmt ss in s.BodyPrefix) {
          ResolveStatement(ss);
        }
        if (s.BodyAssign != null) {
          ResolveStatement(s.BodyAssign);
          // check for correct usage of BoundVar in LHS and RHS of this assignment
          FieldSelectExpr lhs = s.BodyAssign.Lhs as FieldSelectExpr;
          IdentifierExpr obj = lhs == null ? null : lhs.Obj as IdentifierExpr;
          if (obj != null && obj.Var == s.BoundVar) {
            // exemplary!
          } else {
            Error(s, "assignment inside foreach must assign to a field of the bound variable of the foreach statement");
          }
        }
        scope.PopMarker();
      
      } else {
        assert false;
      }
    }

    MemberDecl ResolveMember(Token! tok, Type! receiverType, string! memberName, out UserDefinedType ctype)
      ensures result != null ==> ctype != null && ctype.ResolvedClass != null;
    {
      ctype = UserDefinedType.DenotesClass(receiverType);
      if (ctype == null) {
        Error(tok, "receiver (of type {0}) must be of a class type", receiverType);
      } else {
        assert ctype.ResolvedClass is ClassDecl;  // follows from postcondition of DenotesClass
        assert ctype.TypeArgs.Count == ctype.ResolvedClass.TypeArgs.Count;  // follows from the fact that ctype was resolved
        MemberDecl member;
        if (!classMembers[(ClassDecl)ctype.ResolvedClass].TryGetValue(memberName, out member)) {
          Error(tok, "member {0} does not exist in class {1}", memberName, ctype.Name);
        } else {
          return (!)member;
        }
      }
      ctype = null;
      return null;
    }

    Type! SubstType(Type! type, Dictionary<TypeParameter!,Type!>! subst) {
      if (type is BasicType) {
        return type;
      } else if (type is CollectionType) {
        CollectionType t = (CollectionType)type;
        Type arg = SubstType(t.Arg, subst);
        if (arg == t.Arg) {
          return type;
        } else if (type is SetType) {
          return new SetType(arg);
        } else if (type is SeqType) {
          return new SeqType(arg);
        } else {
          assert false;  // unexpected collection type
        }
      } else if (type is UserDefinedType) {
        UserDefinedType t = (UserDefinedType)type;
        if (t.ResolvedParam != null) {
          assert t.TypeArgs.Count == 0;
          Type s;
          if (subst.TryGetValue(t.ResolvedParam, out s)) {
            return (!)s;
          } else {
            return type;
          }
        } else if (t.ResolvedClass != null) {
          List<Type!> newArgs = null;  // allocate it lazily
          for (int i = 0; i < t.TypeArgs.Count; i++) {
            Type p = t.TypeArgs[i];
            Type s = SubstType(p, subst);
            if (s != p && newArgs == null) {
              // lazily construct newArgs
              newArgs = new List<Type!>();
              for (int j = 0; j < i; j++) {
                newArgs.Add(t.TypeArgs[j]);
              }
            }
            if (newArgs != null) {
              newArgs.Add(s);
            }
          }
          if (newArgs == null) {
            // there were no substitutions
            return type;
          } else {
            return new UserDefinedType(t.tok, t.Name, t.ResolvedClass, newArgs);
          }
        } else {
          // there's neither a resolved param nor a resolved class, which means the UserDefinedType wasn't
          // properly resolved; just return it
          return type;
        }
      } else if (type is TypeProxy) {
        TypeProxy t = (TypeProxy)type;
        if (t.T == null) {
          return type;
        } else {
          // bypass the proxy
          return SubstType(t.T, subst);
        }
      } else {
        assert false;  // unexpected type
      }
    }

    public static UserDefinedType! GetThisType(Token! tok, ClassDecl! cl) {
      List<Type!> args = new List<Type!>();
      foreach (TypeParameter tp in cl.TypeArgs) {
        args.Add(new UserDefinedType(tok, tp.Name, tp));
      }
      return new UserDefinedType(tok, cl.Name, cl, args);
    }
    
    /// <summary>
    /// "twoState" implies that "old" and "fresh" expressions are allowed
    /// </summary>
    void ResolveExpression(Expression! expr, bool twoState)
      requires currentClass != null;
      ensures expr.Type != null;
    {
      if (expr.Type != null) {
        // expression has already been resovled
        return;
      }
      
      // The following cases will resolve the subexpressions and will attempt to assign a type of expr.  However, if errors occur
      // and it cannot be determined what the type of expr is, then it is fine to leave expr.Type as null.  In that case, the end
      // of this method will assign proxy type to the expression, which reduces the number of error messages that are produced
      // while type checking the rest of the program.
      
      if (expr is LiteralExpr) {
        LiteralExpr e = (LiteralExpr)expr;
        if (e.Value == null) {
          e.Type = new ObjectTypeProxy();
        } else if (e.Value is BigInteger) {
          e.Type = Type.Int;
        } else if (e.Value is bool) {
          e.Type = Type.Bool;
        } else {
          assert false;  // unexpected literal type
        }
        
      } else if (expr is ThisExpr) {
        if (!scope.AllowInstance) {
          Error(expr, "'this' is not allowed in a 'class' context");
        }
        expr.Type = GetThisType(expr.tok, currentClass);  // do this regardless of scope.AllowInstance, for better error reporting
        
      } else if (expr is IdentifierExpr) {
        IdentifierExpr e = (IdentifierExpr)expr;
        e.Var = scope.Find(e.Name);
        if (e.Var == null) {
          Error(expr, "Identifier does not denote a local variable, parameter, or bound variable: {0}", e.Name);
        } else {
          expr.Type = e.Var.Type;
        }
      
      } else if (expr is DatatypeValue) {
        DatatypeValue dtv = (DatatypeValue)expr;
        TopLevelDecl d;
        if (!classes.TryGetValue(dtv.DatatypeName, out d)) {
          Error(expr.tok, "Undeclared datatype: {0}", dtv.DatatypeName);
        } else if (!(d is DatatypeDecl)) {
          Error(expr.tok, "Expected datatype, found class: {0}", dtv.DatatypeName);
        } else {
          // this resolution is a little special, in that the syntax shows only the base name, not its instantiation (which is inferred)
          DatatypeDecl dt = (DatatypeDecl)d;
          List<Type!> gt = new List<Type!>(dt.TypeArgs.Count);
          Dictionary<TypeParameter!,Type!> subst = new Dictionary<TypeParameter!,Type!>();
          for (int i = 0; i < dt.TypeArgs.Count; i++) {
            Type t = new InferredTypeProxy();
            gt.Add(t);
            subst.Add(dt.TypeArgs[i], t);
          }
          expr.Type = new UserDefinedType(dtv.tok, dtv.DatatypeName, gt);
          ResolveType(expr.Type);
          
          DatatypeCtor ctor;
          if (!datatypeCtors[dt].TryGetValue(dtv.MemberName, out ctor)) {
            Error(expr.tok, "undeclared constructor {0} in datatype {1}", dtv.MemberName, dtv.DatatypeName);
          } else {
            assert ctor != null;  // follows from postcondition of TryGetValue
            dtv.Ctor = ctor;
            if (ctor.Formals.Count != dtv.Arguments.Count) {
              Error(expr.tok, "wrong number of arguments to datatype constructor {0} (found {1}, expected {2})", dtv.DatatypeName, dtv.Arguments.Count, ctor.Formals.Count);
            }
            // add the constructor's own type parameters to the substitution map
            foreach (TypeParameter p in ctor.TypeArgs) {
              subst.Add(p, new ParamTypeProxy(p));
            }
          }
          int j = 0;
          foreach (Expression arg in dtv.Arguments) {
            ResolveExpression(arg, twoState);
            assert arg.Type != null;  // follows from postcondition of ResolveExpression
            if (ctor != null && j < ctor.Formals.Count) {
              Type st = SubstType(ctor.Formals[j].Type, subst);
              if (!UnifyTypes(arg.Type, st)) {
                Error(arg.tok, "incorrect type of datatype constructor argument (found {0}, expected {1})", arg.Type, st);
              }
            }
            j++;
          }
        }
        
      } else if (expr is DisplayExpression) {
        DisplayExpression e = (DisplayExpression)expr;
        Type elementType = new InferredTypeProxy();
        foreach (Expression ee in e.Elements) {
          ResolveExpression(ee, twoState);
          assert ee.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(elementType, ee.Type)) {
            Error(ee, "All elements of display must be of the same type (got {0}, but type of previous elements is {1})", ee.Type, elementType); 
          }
        }
        if (expr is SetDisplayExpr) {
          expr.Type = new SetType(elementType);
        } else {
          expr.Type = new SeqType(elementType);
        }
        
      } else if (expr is FieldSelectExpr) {
        FieldSelectExpr e = (FieldSelectExpr)expr;
        ResolveExpression(e.Obj, twoState);
        assert e.Obj.Type != null;  // follows from postcondition of ResolveExpression
        UserDefinedType ctype;
        MemberDecl member = ResolveMember(expr.tok, e.Obj.Type, e.FieldName, out ctype);
        if (member == null) {
          // error has already been reported by ResolveMember
        } else if (!(member is Field)) {
          Error(expr, "member {0} in class {1} does not refer to a field", e.FieldName, ((!)ctype).Name);
        } else {
          assert ctype != null && ctype.ResolvedClass != null;  // follows from postcondition of ResolveMember
          e.Field = (Field)member;
          // build the type substitution map
          Dictionary<TypeParameter!,Type!> subst = new Dictionary<TypeParameter!,Type!>();
          for (int i = 0; i < ctype.TypeArgs.Count; i++) {
            subst.Add(ctype.ResolvedClass.TypeArgs[i], ctype.TypeArgs[i]);
          }
          e.Type = SubstType(e.Field.Type, subst);
        }
      
      } else if (expr is SeqSelectExpr) {
        SeqSelectExpr e = (SeqSelectExpr)expr;
        bool seqErr = false;
        ResolveExpression(e.Seq, twoState);
        assert e.Seq.Type != null;  // follows from postcondition of ResolveExpression
        Type elementType = new InferredTypeProxy();
        if (!UnifyTypes(e.Seq.Type, new SeqType(elementType))) {
          Error(expr, "sequence selection requires a sequence (got {0})", e.Seq.Type);
          seqErr = true;
        }
        if (e.E0 != null) {
          ResolveExpression(e.E0, twoState);
          assert e.E0.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(e.E0.Type, Type.Int)) {
            Error(e.E0, "sequence selection requires integer indices (got {0})", e.E0.Type);
          }
        }
        if (e.E1 != null) {
          ResolveExpression(e.E1, twoState);
          assert e.E1.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(e.E1.Type, Type.Int)) {
            Error(e.E1, "sequence selection requires integer indices (got {0})", e.E1.Type);
          }
        }
        if (!seqErr) {
          if (e.SelectOne) {
            expr.Type = elementType;
          } else {
            expr.Type = e.Seq.Type;
          }
        }
        
      } else if (expr is SeqUpdateExpr) {
        SeqUpdateExpr e = (SeqUpdateExpr)expr;
        bool seqErr = false;
        ResolveExpression(e.Seq, twoState);
        assert e.Seq.Type != null;  // follows from postcondition of ResolveExpression
        Type elementType = new InferredTypeProxy();
        if (!UnifyTypes(e.Seq.Type, new SeqType(elementType))) {
          Error(expr, "sequence update requires a sequence (got {0})", e.Seq.Type);
          seqErr = true;
        }
        ResolveExpression(e.Index, twoState);
        assert e.Index.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(e.Index.Type, Type.Int)) {
          Error(e.Index, "sequence update requires integer index (got {0})", e.Index.Type);
        }
        ResolveExpression(e.Value, twoState);
        assert e.Value.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(e.Value.Type, elementType)) {
          Error(e.Value, "sequence update requires the value to have the element type of the sequence (got {0})", e.Value.Type);
        }
        if (!seqErr) {
          expr.Type = e.Seq.Type;
        }
        
      } else if (expr is FunctionCallExpr) {
        FunctionCallExpr e = (FunctionCallExpr)expr;
        ResolveReceiver(e.Receiver, twoState);
        assert e.Receiver.Type != null;  // follows from postcondition of ResolveExpression
        UserDefinedType ctype;
        MemberDecl member = ResolveMember(expr.tok, e.Receiver.Type, e.Name, out ctype);
        if (member == null) {
          // error has already been reported by ResolveMember
        } else if (!(member is Function)) {
          Error(expr, "member {0} in class {1} does not refer to a function", e.Name, ((!)ctype).Name);
        } else {
          Function function = (Function)member;
          e.Function = function;
          if (function.Formals.Count != e.Args.Count) {
            Error(expr, "wrong number of function arguments (got {0}, expected {1})", e.Args.Count, function.Formals.Count);
          } else {
            assert ctype != null;  // follows from postcondition of ResolveMember
            if (!scope.AllowInstance && !function.IsClass && e.Receiver is ThisExpr) {
              // The call really needs an instance, but that instance is given as 'this', which is not
              // available in this context.  In most cases, occurrences of 'this' inside e.Receiver would
              // have been caught in the recursive call to resolve e.Receiver, but not the specific case
              // of e.Receiver being 'this' (explicitly or implicitly), for that case needs to be allowed
              // in the event that a class function calls another class function (and note that we need the
              // type of the receiver in order to find the method, so we could not have made this check
              // earlier).
              Error(e.Receiver, "'this' is not allowed in a 'class' context");
            }
            // build the type substitution map
            Dictionary<TypeParameter!,Type!> subst = new Dictionary<TypeParameter!,Type!>();
            for (int i = 0; i < ctype.TypeArgs.Count; i++) {
              subst.Add(((!)ctype.ResolvedClass).TypeArgs[i], ctype.TypeArgs[i]);
            }
            foreach (TypeParameter p in function.TypeArgs) {
              subst.Add(p, new ParamTypeProxy(p));
            }
            // type check the arguments
            for (int i = 0; i < function.Formals.Count; i++) {
              Expression farg = e.Args[i];
              ResolveExpression(farg, twoState);
              assert farg.Type != null;  // follows from postcondition of ResolveExpression
              Type s = SubstType(function.Formals[i].Type, subst);
              if (!UnifyTypes(farg.Type, s)) {
                Error(expr, "incorrect type of function argument {0} (expected {1}, got {2})", i, s, farg.Type);
              }
            }
            expr.Type = SubstType(function.ResultType, subst);
          }
        }
        
      } else if (expr is OldExpr) {
        OldExpr e = (OldExpr)expr;
        if (!twoState) {
          Error(expr, "old expressions are not allowed in this context");
        }
        ResolveExpression(e.E, twoState);
        expr.Type = e.E.Type;
        
      } else if (expr is FreshExpr) {
        FreshExpr e = (FreshExpr)expr;
        if (!twoState) {
          Error(expr, "fresh expressions are not allowed in this context");
        }
        ResolveExpression(e.E, twoState);
        // the type of e.E must be either an object or a collection of objects
        Type t = e.E.Type;
        assert t != null;  // follows from postcondition of ResolveExpression
        if (t is CollectionType) {
          t = ((CollectionType)t).Arg;
        }
        if (t is ObjectType) {
          // fine
        } else if (UserDefinedType.DenotesClass(t) != null) {
          // fine
        } else {
          Error(expr, "the argument of a fresh expression must denote an object or a collection of objects (instead got {0})", e.E.Type);
        }
        expr.Type = Type.Bool;
        
      } else if (expr is UnaryExpr) {
        UnaryExpr e = (UnaryExpr)expr;
        ResolveExpression(e.E, twoState);
        assert e.E.Type != null;  // follows from postcondition of ResolveExpression
        switch (e.Op) {
          case UnaryExpr.Opcode.Not:
            if (!UnifyTypes(e.E.Type, Type.Bool)) {
              Error(expr, "logical negation expects a boolean argument (instead got {0})", e.E.Type);
            }
            expr.Type = Type.Bool;
            break;
          case UnaryExpr.Opcode.SeqLength:
            if (!UnifyTypes(e.E.Type, new SeqType(new InferredTypeProxy()))) {
              Error(expr, "sequence-length operator expects a sequence argument (instead got {0})", e.E.Type);
            }
            expr.Type = Type.Int;
            break;
          default:
            assert false;  // unexpected unary operator
        }
        
      } else if (expr is BinaryExpr) {
        BinaryExpr e = (BinaryExpr)expr;
        ResolveExpression(e.E0, twoState);
        assert e.E0.Type != null;  // follows from postcondition of ResolveExpression
        ResolveExpression(e.E1, twoState);
        assert e.E1.Type != null;  // follows from postcondition of ResolveExpression
        switch (e.Op) {
          case BinaryExpr.Opcode.Iff:
          case BinaryExpr.Opcode.Imp:
          case BinaryExpr.Opcode.And:
          case BinaryExpr.Opcode.Or:
            if (!UnifyTypes(e.E0.Type, Type.Bool)) {
              Error(expr, "first argument to {0} must be of type bool (instead got {1})", BinaryExpr.OpcodeString(e.Op), e.E0.Type);
            }
            if (!UnifyTypes(e.E1.Type, Type.Bool)) {
              Error(expr, "second argument to {0} must be of type bool (instead got {1})", BinaryExpr.OpcodeString(e.Op), e.E1.Type);
            }
            expr.Type = Type.Bool;
            break;
          
          case BinaryExpr.Opcode.Eq:
          case BinaryExpr.Opcode.Neq:
            if (!UnifyTypes(e.E0.Type, e.E1.Type)) {
              Error(expr, "arguments must have the same type (got {0} and {1})", e.E0.Type, e.E1.Type);
            }
            expr.Type = Type.Bool;
            break;
          
          case BinaryExpr.Opcode.Disjoint:
            if (!UnifyTypes(e.E0.Type, new SetType(new InferredTypeProxy()))) {
              Error(expr, "arguments must be of a set type (got {0})", e.E0.Type);
            }
            if (!UnifyTypes(e.E0.Type, e.E1.Type)) {
              Error(expr, "arguments must have the same type (got {0} and {1})", e.E0.Type, e.E1.Type);
            }
            expr.Type = Type.Bool;
            break;
          
          case BinaryExpr.Opcode.Lt:
          case BinaryExpr.Opcode.Le:
          case BinaryExpr.Opcode.Add:
            {
              bool err = false;
              if (!UnifyTypes(e.E0.Type, new OperationTypeProxy(true))) {
                Error(expr, "arguments to {0} must be int or a collection type (instead got {1})", BinaryExpr.OpcodeString(e.Op), e.E0.Type);
                err = true;
              }
              if (!UnifyTypes(e.E1.Type, e.E0.Type)) {
                Error(expr, "arguments to {0} must have the same type (got {1} and {2})", BinaryExpr.OpcodeString(e.Op), e.E0.Type, e.E1.Type);
                err = true;
              }
              if (e.Op != BinaryExpr.Opcode.Add) {
                expr.Type = Type.Bool;
              } else if (!err) {
                expr.Type = e.E0.Type;
              }
            }
            break;
          
          case BinaryExpr.Opcode.Sub:
          case BinaryExpr.Opcode.Mul:
          case BinaryExpr.Opcode.Gt:
          case BinaryExpr.Opcode.Ge:
            {
              bool err = false;
              if (!UnifyTypes(e.E0.Type, new OperationTypeProxy(false))) {
                Error(expr, "arguments to {0} must be int or a set (instead got {1})", BinaryExpr.OpcodeString(e.Op), e.E0.Type);
                err = true;
              }
              if (!UnifyTypes(e.E1.Type, e.E0.Type)) {
                Error(expr, "arguments to {0} must have the same type (got {1} and {2})", BinaryExpr.OpcodeString(e.Op), e.E0.Type, e.E1.Type);
                err = true;
              }
              if (e.Op == BinaryExpr.Opcode.Gt || e.Op == BinaryExpr.Opcode.Ge) {
                expr.Type = Type.Bool;
              } else if (!err) {
                expr.Type = e.E0.Type;
              }
            }
            break;

          case BinaryExpr.Opcode.In:
          case BinaryExpr.Opcode.NotIn:
            if (!UnifyTypes(e.E1.Type, new CollectionTypeProxy(e.E0.Type))) {
              Error(expr, "second argument to {0} must be a set or sequence of type {1} (instead got {2})", BinaryExpr.OpcodeString(e.Op), e.E0.Type, e.E1.Type);
            }
            expr.Type = Type.Bool;
            break;
            
          case BinaryExpr.Opcode.Div:
          case BinaryExpr.Opcode.Mod:
            if (!UnifyTypes(e.E0.Type, Type.Int)) {
              Error(expr, "first argument to {0} must be of type int (instead got {1})", BinaryExpr.OpcodeString(e.Op), e.E0.Type);
            }
            if (!UnifyTypes(e.E1.Type, Type.Int)) {
              Error(expr, "second argument to {0} must be of type int (instead got {1})", BinaryExpr.OpcodeString(e.Op), e.E1.Type);
            }
            expr.Type = Type.Int;
            break;
          
          default:
            assert false;  // unexpected operator
        }
        e.ResolvedOp = ResolveOp(e.Op, e.E1.Type);
        
      } else if (expr is QuantifierExpr) {
        QuantifierExpr e = (QuantifierExpr)expr;
        scope.PushMarker();
        foreach (BoundVar v in e.BoundVars) {
          if (!scope.Push(v.Name, v)) {
            Error(v, "Duplicate parameter name: {0}", v.Name);
          }
          ResolveType(v.Type);
        }
        ResolveExpression(e.Body, twoState);
        assert e.Body.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(e.Body.Type, Type.Bool)) {
          Error(expr, "body of quantifier must be of type bool (instead got {0})", e.Body.Type);
        }
        // Since the body is more likely to infer the types of the bound variables, resolve it
        // first (above) and only then resolve the attributes and triggers (below).
        ResolveAttributes(e.Attributes, twoState);
        ResolveTriggers(e.Trigs, twoState);
        scope.PopMarker();
        expr.Type = Type.Bool;
        
      } else if (expr is WildcardExpr) {
        expr.Type = new SetType(new ObjectType());
        
      } else if (expr is ITEExpr) {
        ITEExpr e = (ITEExpr)expr;
        ResolveExpression(e.Test, twoState);
        assert e.Test.Type != null;  // follows from postcondition of ResolveExpression
        ResolveExpression(e.Thn, twoState);
        assert e.Thn.Type != null;  // follows from postcondition of ResolveExpression
        ResolveExpression(e.Els, twoState);
        assert e.Els.Type != null;  // follows from postcondition of ResolveExpression
        if (!UnifyTypes(e.Test.Type, Type.Bool)) {
          Error(expr, "guard condition in if-then-else expression must be a boolean (instead got {0})", e.Test.Type);
        }
        if (UnifyTypes(e.Thn.Type, e.Els.Type)) {
          expr.Type = e.Thn.Type;
        } else {
          Error(expr, "the two branches of an if-then-else expression must have the same type (got {0} and {1})", e.Thn.Type, e.Els.Type);
        }
      
      } else if (expr is MatchExpr) {
        MatchExpr me = (MatchExpr)expr;
        assert !twoState;  // currently, match expressions are allowed only at the outermost level of function bodies
        ResolveExpression(me.Source, twoState);
        assert me.Source.Type != null;  // follows from postcondition of ResolveExpression
        UserDefinedType sourceType = null;
        DatatypeDecl dtd = null;
        Dictionary<TypeParameter!,Type!> subst = new Dictionary<TypeParameter!,Type!>();
        if (me.Source.Type.IsDatatype) {
          sourceType = (UserDefinedType)me.Source.Type;
          dtd = (DatatypeDecl!)sourceType.ResolvedClass;
        }
        Dictionary<string!,DatatypeCtor!> ctors;
        if (dtd == null) {
          Error(me.Source, "the type of the match source expression must be a datatype");
          ctors = null;
        } else {
          assert sourceType != null;  // dtd and sourceType are set together above
          ctors = datatypeCtors[dtd];
          assert ctors != null;  // dtd should have been inserted into datatypeCtors during a previous resolution stage
          
          IdentifierExpr ie = me.Source as IdentifierExpr;
          if (ie == null || !(ie.Var is Formal)) {
            Error(me.Source.tok, "match source expression must be a formal parameter of the enclosing function");
          }
          
          // build the type-parameter substitution map for this use of the datatype
          for (int i = 0; i < dtd.TypeArgs.Count; i++) {
            subst.Add(dtd.TypeArgs[i], sourceType.TypeArgs[i]);
          }
        }
        
        Dictionary<string!,object> memberNamesUsed = new Dictionary<string!,object>();  // this is really a set
        expr.Type = new InferredTypeProxy();
        foreach (MatchCase mc in me.Cases) {
          DatatypeCtor ctor = null;
          if (ctors != null) {
            assert dtd != null;
            if (!ctors.TryGetValue(mc.Id, out ctor)) {
              Error(mc.tok, "member {0} does not exist in datatype {1}", mc.Id, dtd.Name);
            } else {
              assert ctor != null;  // follows from postcondition of TryGetValue
              mc.Ctor = ctor;
              if (ctor.Formals.Count != mc.Arguments.Count) {
                Error(mc.tok, "member {0} has wrong number of formals (found {1}, expected {2})", mc.Arguments.Count, ctor.Formals.Count);
              }
              if (memberNamesUsed.ContainsKey(mc.Id)) {
                Error(mc.tok, "member {0} appears in more than one case", mc.Id);
              } else {
                memberNamesUsed.Add(mc.Id, null);  // add mc.Id to the set of names used
              }
            }
          }
          scope.PushMarker();
          if (ctor != null) {
            // add the constructor's own type parameters to the substitution map
            foreach (TypeParameter p in ctor.TypeArgs) {
              subst.Add(p, new ParamTypeProxy(p));
            }
          }
          int i = 0;
          foreach (BoundVar v in mc.Arguments) {
            if (!scope.Push(v.Name, v)) {
              Error(v, "Duplicate parameter name: {0}", v.Name);
            }
            ResolveType(v.Type);
            if (ctor != null && i < ctor.Formals.Count) {
              Type st = SubstType(ctor.Formals[i].Type, subst);
              if (!UnifyTypes(v.Type, st)) {
                Error(expr, "the declared type of the formal ({0}) does not agree with the corresponding type in the constructor's signature ({1})", v.Type, st);
              }
            }
            i++;
          }
          ResolveExpression(mc.Body, twoState);
          assert mc.Body.Type != null;  // follows from postcondition of ResolveExpression
          if (!UnifyTypes(expr.Type, mc.Body.Type)) {
            Error(mc.Body.tok, "type of case bodies do not agree (found {0}, previous types {1})", mc.Body.Type, expr.Type);
          }
          scope.PopMarker();
        }
        if (dtd != null && memberNamesUsed.Count != dtd.Ctors.Count) {
          Error(expr, "match expression does not cover all constructors");
        }
        
      } else {
        assert false;  // unexpected expression
      }

      if (expr.Type == null) {
        // some resolution error occurred
        expr.Type = Type.Flexible;
      }
    }
    
    void ResolveReceiver(Expression! expr, bool twoState)
      requires currentClass != null;
      ensures expr.Type != null;
    {
      if (expr is ThisExpr) {
        // Allow 'this' here, regardless of scope.AllowInstance.  The caller is responsible for
        // making sure 'this' does not really get used when it's not available.
        expr.Type = GetThisType(expr.tok, currentClass);
      } else {
        ResolveExpression(expr, twoState);
      }
    }
    
    /// <summary>
    /// Note: this method is allowed to be called even if "type" does not make sense for "op", as might be the case if
    /// resolution of the binary expression failed.  If so, an arbitrary resolved opcode is returned.
    /// </summary>
    BinaryExpr.ResolvedOpcode ResolveOp(BinaryExpr.Opcode op, Type! operandType) {
      switch (op) {
        case BinaryExpr.Opcode.Iff:  return BinaryExpr.ResolvedOpcode.Iff;
        case BinaryExpr.Opcode.Imp:  return BinaryExpr.ResolvedOpcode.Imp;
        case BinaryExpr.Opcode.And:  return BinaryExpr.ResolvedOpcode.And;
        case BinaryExpr.Opcode.Or:  return BinaryExpr.ResolvedOpcode.Or;
        case BinaryExpr.Opcode.Eq:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.SetEq;
          } else if (operandType is SeqType) {
            return BinaryExpr.ResolvedOpcode.SeqEq;
          } else {
            return BinaryExpr.ResolvedOpcode.EqCommon;
          }
        case BinaryExpr.Opcode.Neq:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.SetNeq;
          } else if (operandType is SeqType) {
            return BinaryExpr.ResolvedOpcode.SeqNeq;
          } else {
            return BinaryExpr.ResolvedOpcode.NeqCommon;
          }
        case BinaryExpr.Opcode.Disjoint:  return BinaryExpr.ResolvedOpcode.Disjoint;
        case BinaryExpr.Opcode.Lt:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.ProperSubset;
          } else if (operandType is SeqType) {
            return BinaryExpr.ResolvedOpcode.ProperPrefix;
          } else {
            return BinaryExpr.ResolvedOpcode.Lt;
          }
        case BinaryExpr.Opcode.Le:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.Subset;
          } else if (operandType is SeqType) {
            return BinaryExpr.ResolvedOpcode.Prefix;
          } else {
            return BinaryExpr.ResolvedOpcode.Le;
          }
        case BinaryExpr.Opcode.Add:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.Union;
          } else if (operandType is SeqType) {
            return BinaryExpr.ResolvedOpcode.Concat;
          } else {
            return BinaryExpr.ResolvedOpcode.Add;
          }
        case BinaryExpr.Opcode.Sub:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.SetDifference;
          } else {
            return BinaryExpr.ResolvedOpcode.Sub;
          }
        case BinaryExpr.Opcode.Mul:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.Intersection;
          } else {
            return BinaryExpr.ResolvedOpcode.Mul;
          }
        case BinaryExpr.Opcode.Gt:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.ProperSuperset;
          } else {
            return BinaryExpr.ResolvedOpcode.Gt;
          }
        case BinaryExpr.Opcode.Ge:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.Superset;
          } else {
            return BinaryExpr.ResolvedOpcode.Ge;
          }
        case BinaryExpr.Opcode.In:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.InSet;
          } else {
            return BinaryExpr.ResolvedOpcode.InSeq;
          }
        case BinaryExpr.Opcode.NotIn:
          if (operandType is SetType) {
            return BinaryExpr.ResolvedOpcode.NotInSet;
          } else {
            return BinaryExpr.ResolvedOpcode.NotInSeq;
          }
        case BinaryExpr.Opcode.Div:  return BinaryExpr.ResolvedOpcode.Div;
        case BinaryExpr.Opcode.Mod:  return BinaryExpr.ResolvedOpcode.Mod;
        default:
          assert false;  // unexpected operator
      }
    }
  }
    
  class Scope<Thing> where Thing : class {
    [Rep] readonly List<string>! names = new List<string>();  // a null means a marker
    [Rep] readonly List<Thing?>! things = new List<Thing?>();
    invariant names.Count == things.Count;
    int scopeSizeWhereInstancesWereDisallowed = -1;
    invariant -1 <= scopeSizeWhereInstancesWereDisallowed && scopeSizeWhereInstancesWereDisallowed <= names.Count;
    
    public bool AllowInstance {
      get { return scopeSizeWhereInstancesWereDisallowed == -1; }
      set
        requires AllowInstance && !value;  // only allowed to change from true to false (that's all that's currently needed in Dafny); Pop is what can make the change in the other direction
      {
        scopeSizeWhereInstancesWereDisallowed = names.Count;
      }
    }

    public void PushMarker() {
      names.Add(null);
      things.Add(null);
    }
    
    public void PopMarker() {
      int n = names.Count;
      while (true) {
        n--;
        if (names[n] == null) {
          break;
        }
      }
      names.RemoveRange(n, names.Count - n);
      things.RemoveRange(n, things.Count - n);
      if (names.Count < scopeSizeWhereInstancesWereDisallowed) {
        scopeSizeWhereInstancesWereDisallowed = -1;
      }
    }
    
    // Pushes name-->var association and returns "true", if name has not already been pushed since the last marker.
    // If name already has been pushed since the last marker, does nothing and returns "false".
    public bool Push(string! name, Thing! thing) {
      if (Find(name, true) != null) {
        return false;
      } else {
        names.Add(name);
        things.Add(thing);
        return true;
      }
    }
    
    Thing? Find(string! name, bool topScopeOnly) {
      for (int n = names.Count; 0 <= --n; ) {
        if (names[n] == null) {
          if (topScopeOnly) {
            return null;  // no present
          }
        } else if (names[n] == name) {
          Thing t = things[n];
          assert t != null;
          return t;
        }
      }
      return null;  // not present
    }
    
    public Thing? Find(string! name) {
      return Find(name, false);
    }
  }
}