path: root/Source/AIFramework/CommonFunctionSymbols.ssc

//-----------------------------------------------------------------------------
//
// Copyright (C) Microsoft Corporation.  All Rights Reserved.
//
//-----------------------------------------------------------------------------
namespace Microsoft.AbstractInterpretationFramework
{
    using Microsoft.Contracts;
    using System.Collections;
    using Microsoft.SpecSharp.Collections;
	using Microsoft.Basetypes;

    /// <summary>
    ///  A basic class for function symbols.
    /// </summary>
    public class FunctionSymbol : IFunctionSymbol
    {
        private readonly string! display;
        private readonly AIType! typ;

        public FunctionSymbol(AIType! typ)
        : this("FunctionSymbol", typ)
        {
        }

        internal FunctionSymbol(string! display, AIType! typ)
        {
            this.display = display;
            this.typ = typ;
            //            base();
        }

//        public AIType! AIType { [Pure][Reads(ReadsAttribute.Reads.Owned)] get { return typ; } }
        public AIType! AIType { [Pure][Reads(ReadsAttribute.Reads.Owned)] get { return typ; } }

        [NoDefaultContract]
        [Pure][Reads(ReadsAttribute.Reads.Owned)]
        public override string! ToString()
        {
            return display;
        }

    }
    
    /// <summary>
    ///  A class for integer constants.
    /// </summary>
    public class IntSymbol : FunctionSymbol
    {
        public readonly BigNum Value;
        
        /// <summary>
        /// The intention is that this constructor be called only from the Int.Const method.
        /// </summary>
        internal IntSymbol(BigNum x)
        : base((!)x.ToString(), Int.Type)
        {
            this.Value = x;
        }

        [Pure][Reads(ReadsAttribute.Reads.Nothing)]
        public override bool Equals(object other)
        {
            IntSymbol isym = other as IntSymbol;
            return isym != null && isym.Value.Equals(this.Value);
        }
        
        [Pure][Reads(ReadsAttribute.Reads.Owned)]
        public override int GetHashCode()
        {
            return Value.GetHashCode();
        }
    }

    /// <summary>
    ///  A class for bitvector constants.
    /// </summary>
    public class BvSymbol : FunctionSymbol
    {
        public readonly BigNum Value;
        public readonly int Bits;
        
        /// <summary>
        /// The intention is that this constructor be called only from the Int.Const method.
        /// </summary>
        internal BvSymbol(BigNum x, int y)
        : base(x + "bv" + y, Bv.Type)
        {
            this.Value = x;
            this.Bits = y;
        }

        [Pure][Reads(ReadsAttribute.Reads.Nothing)]
        public override bool Equals(object other)
        {
            BvSymbol isym = other as BvSymbol;
            return isym != null && isym.Value == this.Value && isym.Bits == this.Bits;
        }
        
        [Pure][Reads(ReadsAttribute.Reads.Owned)]
        public override int GetHashCode()
        {
            unchecked {
              return Value.GetHashCode() ^ Bits;
            }
        }
    }

    public class DoubleSymbol : FunctionSymbol
    {
        public readonly double Value;
        
        /// <summary>
        /// The intention is that this constructor be called only from the Double.Const method.
        /// </summary>
        internal DoubleSymbol(double x)
        : base((!)x.ToString(), Double.Type)
        {
            this.Value = x;
        }
        
        [Pure][Reads(ReadsAttribute.Reads.Nothing)]
        public override bool Equals(object other)
        {
            DoubleSymbol dsym = other as DoubleSymbol;
            return dsym != null && dsym.Value == this.Value;
        }

        [Pure][Reads(ReadsAttribute.Reads.Owned)] 
        public override int GetHashCode()
        {
            return Value.GetHashCode();
        }
    }

    /// <summary>
    ///  Function symbol based on a string.  Uses the string equality for determining equality
    ///  of symbol.
    /// </summary>
    public class NamedSymbol : FunctionSymbol
    {
        public string! Value { [NoDefaultContract] get { return (!) this.ToString(); } }

        public NamedSymbol(string! symbol, AIType! typ)
        : base(symbol, typ)
        {
        }

        [NoDefaultContract]
        [Pure][Reads(ReadsAttribute.Reads.Nothing)]
        public override bool Equals(object other)
        {
            NamedSymbol nsym = other as NamedSymbol;
            return nsym != null && this.Value.Equals(nsym.Value);
        }

        [NoDefaultContract]
        [Pure][Reads(ReadsAttribute.Reads.Owned)] 
        public override int GetHashCode()
        {
            return Value.GetHashCode();
        }
    }

    //
    // In the following, the classes like Value and Prop serve two
    // roles.  The primary role is to be the base types for AIType. 
    // The only objects of these classes are the representative
    // objects that denote an AIType, which are given by the
    // "Type" property.  Subtypes in the AIType language are
    // encoded by subclassing.  This yields some "higher-orderness"
    // for checking subtyping in the AIType language, by using
    // the Spec#/C# subclassing checks.
    //
    // The other role is simply as a module for collecting like function
    // symbols.
    //

    //-------------------------- Terms ----------------------------------

    /// <summary>
    ///  A class with the equality symbol and the ValueType.Type.
    /// </summary>
    public class Value : AIType
    {
        private static readonly AIType! valtype = new Value();
        public static AIType! Type { get { return valtype; } }

        private static readonly FunctionType[]! funtypeCache = new FunctionType[5];
        public static FunctionType! FunctionType(int inParameterCount)
            requires 0 <= inParameterCount;
            // ensures result.Arity == inParameterCount;
        {
            FunctionType result;
            if (inParameterCount < funtypeCache.Length) {
                result = funtypeCache[inParameterCount];
                if (result != null) {
                    return result;
                }
            }
            AIType[] signature = new AIType[1 + inParameterCount];
            for (int i = 0; i < signature.Length; i++) {
                signature[i] = valtype;
            }
            result = new FunctionType(signature);
            if (inParameterCount < funtypeCache.Length) {
                funtypeCache[inParameterCount] = result;
            }
            return result;
        }

        [Once] private static AIType! binreltype;
        private static AIType! BinrelType {
          get {
            if (binreltype == null) {
              binreltype = new FunctionType(Type, Type, Prop.Type);
            }
            return binreltype;
          }
        }

        [Once] private static FunctionSymbol! _eq;
        public static FunctionSymbol! Eq {
          get {
            if (_eq == null) {
              _eq = new FunctionSymbol("=", BinrelType);
            }
            return _eq;
          }
        }
        [Once] private static FunctionSymbol! _neq;
        public static FunctionSymbol! Neq {
          get {
            if (_neq == null) {
              _neq = new FunctionSymbol("!=", BinrelType);
            }
            return _neq;
          }
        }
        [Once] private static FunctionSymbol! _subtype;
        public static FunctionSymbol! Subtype {
          get {
            if (_subtype == null) {
              _subtype = new FunctionSymbol("<:", BinrelType);
            }
            return _subtype;
          }
        }

        [Once] private static AIType! typeof_type;
        private static AIType! TypeofType {
          get {
            if (typeof_type == null) {
              typeof_type = new FunctionType(Ref.Type, Type);
            }
            return typeof_type;
          }
        }
        [Once] private static FunctionSymbol! _typeof;
        public static FunctionSymbol! Typeof {
          get {
            if (_typeof == null) {
              _typeof = new FunctionSymbol("typeof", TypeofType);
            }
            return _typeof;
          }
        }

        /// <summary>
        /// Value should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        protected Value() { }
 
    }

    public class Int : Value
    {
        private static readonly AIType! inttype = new Int();
        public static AIType! Type { get { return inttype; } }
        
        private static readonly AIType! unaryinttype = new FunctionType(Type, Type);
        private static readonly AIType! bininttype = new FunctionType(Type, Type, Type);
        private static readonly AIType! relationtype = new FunctionType(Type, Type, Prop.Type);

        private static readonly FunctionSymbol! _negate = new FunctionSymbol("~", unaryinttype);
        private static readonly FunctionSymbol! _add = new FunctionSymbol("+", bininttype);
        private static readonly FunctionSymbol! _sub = new FunctionSymbol("-", bininttype);
        private static readonly FunctionSymbol! _mul = new FunctionSymbol("*", bininttype);
        private static readonly FunctionSymbol! _div = new FunctionSymbol("/", bininttype);
        private static readonly FunctionSymbol! _mod = new FunctionSymbol("%", bininttype);
        private static readonly FunctionSymbol! _atmost = new FunctionSymbol("<=", relationtype);
        private static readonly FunctionSymbol! _less = new FunctionSymbol("<", relationtype);
        private static readonly FunctionSymbol! _greater = new FunctionSymbol(">", relationtype);
        private static readonly FunctionSymbol! _atleast = new FunctionSymbol(">=", relationtype);

        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Negate { get { return _negate; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Add { get { return _add; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Sub { get { return _sub; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Mul { get { return _mul; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Div { get { return _div; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Mod { get { return _mod; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! AtMost { get { return _atmost; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Less { get { return _less; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Greater { get { return _greater; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! AtLeast { get { return _atleast; } }

        public static IntSymbol! Const(BigNum x)
        {
            // We could cache things here, but for now we don't.
            return new IntSymbol(x);
        }

        /// <summary>
        /// Int should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        private Int() { }
    }

    public class Double : Value
    {
        private static readonly AIType! doubletype = new Double();
        public static AIType! Type { get { return doubletype; } }
        
        public static DoubleSymbol! Const(double x)
        {
            // We could cache things here, but for now we don't.
            return new DoubleSymbol(x);
        }

        /// <summary>
        /// Double should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        private Double() { }
    }

    public class Bv : Value
    {
        private static readonly AIType! bvtype = new Bv();
        public static AIType! Type { get { return bvtype; } }
        
        private static readonly AIType! unaryinttype = new FunctionType(Type, Type);
        private static readonly AIType! bininttype = new FunctionType(Type, Type, Type);
        private static readonly AIType! relationtype = new FunctionType(Type, Type, Prop.Type);

        private static readonly FunctionSymbol! _negate = new FunctionSymbol("~", unaryinttype);
        private static readonly FunctionSymbol! _add = new FunctionSymbol("+", bininttype);
        private static readonly FunctionSymbol! _sub = new FunctionSymbol("-", bininttype);
        private static readonly FunctionSymbol! _mul = new FunctionSymbol("*", bininttype);
        private static readonly FunctionSymbol! _div = new FunctionSymbol("/", bininttype);
        private static readonly FunctionSymbol! _mod = new FunctionSymbol("%", bininttype);
        private static readonly FunctionSymbol! _concat = new FunctionSymbol("$concat", bininttype);
        private static readonly FunctionSymbol! _extract = new FunctionSymbol("$extract", unaryinttype);
        private static readonly FunctionSymbol! _atmost = new FunctionSymbol("<=", relationtype);
        private static readonly FunctionSymbol! _less = new FunctionSymbol("<", relationtype);
        private static readonly FunctionSymbol! _greater = new FunctionSymbol(">", relationtype);
        private static readonly FunctionSymbol! _atleast = new FunctionSymbol(">=", relationtype);

        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Negate { get { return _negate; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Add { get { return _add; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Sub { get { return _sub; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Mul { get { return _mul; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Div { get { return _div; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Mod { get { return _mod; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! AtMost { get { return _atmost; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Less { get { return _less; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Greater { get { return _greater; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! AtLeast { get { return _atleast; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Extract { get { return _extract; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Concat { get { return _concat; } }

        public static BvSymbol! Const(BigNum x, int y)
        {
            // We could cache things here, but for now we don't.
            return new BvSymbol(x, y);
        }

        /// <summary>
        /// Int should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        private Bv() { }
    }

    public class Ref : Value
    {
        private static readonly AIType! reftype = new Ref();
        public static AIType! Type { get { return reftype; } }

        private static readonly FunctionSymbol! _null = new FunctionSymbol("null", Type);

        public static FunctionSymbol! Null { get { return _null; } }

        /// <summary>
        /// Ref should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        private Ref() { }
    }

    public class HeapStructure : Value
    {
        private static readonly AIType! reftype = new HeapStructure();
        public static AIType! Type { get { return reftype; } }
        


        /// <summary>
        /// HeapStructure should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        private HeapStructure() { }
    }

    public class FieldName : Value
    {
        private static readonly AIType! fieldnametype = new FieldName();
        public static AIType! Type { get { return fieldnametype; } }

        private static readonly FunctionSymbol! _allocated = new FunctionSymbol("$allocated", FieldName.Type);
        public static FunctionSymbol! Allocated { get { return _allocated; } }

        /// <summary>
        /// Is this a boolean field that monotonically goes from false to true?
        /// </summary>
        public static bool IsBooleanMonotonicallyWeakening(IFunctionSymbol! f)
        {
            return f.Equals(Allocated);
        }

        /// <summary>
        /// FieldName should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        private FieldName() { }
    }

    public class Heap : Value
    {
        private static readonly AIType! heaptype = new Heap();
        public static AIType! Type { get { return heaptype; } }

        // the types in the following, select1, select2, are hard-coded; 
        // these types may not always be appropriate
        private static readonly FunctionSymbol! _select1 = new FunctionSymbol("sel1",
            // Heap x FieldName -> Prop
            new FunctionType(Type, FieldName.Type, Prop.Type)
        );
        public static FunctionSymbol! Select1 { get { return _select1; } }

        private static readonly FunctionSymbol! _select2 = new FunctionSymbol("sel2",
            // Heap x Ref x FieldName -> Value
            new FunctionType(Type, Ref.Type, FieldName.Type, Value.Type)
        );
        public static FunctionSymbol! Select2 { get { return _select2; } }

        // the types in the following, store1, store2, are hard-coded; 
        // these types may not always be appropriate
        private static readonly FunctionSymbol! _update1 = new FunctionSymbol("upd1",
            // Heap x FieldName x Value -> Heap
            new FunctionType(Type, FieldName.Type, Value.Type, Type)
        );
        public static FunctionSymbol! Update1 { get { return _update1; } }

        private static readonly FunctionSymbol! _update2 = new FunctionSymbol("upd2",
            // Heap x Ref x FieldName x Value -> Heap
            new FunctionType(Type, Ref.Type, FieldName.Type, Value.Type, Type)
        );
        public static FunctionSymbol! Update2 { get { return _update2; } }

        private static readonly FunctionSymbol! _unsupportedHeapOp =
            new FunctionSymbol("UnsupportedHeapOp",
            // Heap x FieldName -> Prop
            new FunctionType(Type, FieldName.Type, Prop.Type)
        );
        public static FunctionSymbol! UnsupportedHeapOp { get { return _unsupportedHeapOp; } }

        /// <summary>
        /// Heap should not be instantiated from the outside, except perhaps in
        /// subclasses.
        /// </summary>
        private Heap() { }
    }

//    public class List : Value
//    {
//        private static IDictionary/*<AIType!,AIType!>*/! lists = new Hashtable();
//        public static AIType! Type(AIType! typeParameter)
//        {
//            if (lists.Contains(typeParameter))
//                return lists[typeParameter];
//            else
//            {
//                AIType! result = new List(typeParameter);
//                lists[typeParameter] = result;
//                return result;
//            }
//        }
//
//        private static IDictionary/*<AIType!,AIType!>*/! nils = new Hashtable();
//        public static FunctionSymbol! Nil(AIType! typeParameter)
//        {
//            if (nils.Contains(typeParameter))
//                return nils[typeParameter];
//            else
//            {
//                FunctionSymbol! result = new FunctionSymbol(Type(typeParameter));
//                nils[typeParameter] = result;
//                return result;
//            }
//        }
//
//        private static IDictionary/*<AIType!,AIType!>*/! cons = new Hashtable();
//        public static FunctionSymbol! Cons(AIType! typeParameter)
//        {
//            if (cons.Contains(typeParameter))
//                return cons[typeParameter];
//            else
//            {
//                FunctionSymbol! result = new FunctionSymbol(
//                    new FunctionType(typeParameter, Type(typeParameter), Type(typeParameter))
//                );
//                cons[typeParameter] = result;
//                return result;
//            }
//        }
//
//        private AIType! typeParameter;
//        public AIType! TypeParameter { get { return typeParameter; } }
//
//        /// <summary>
//        /// List should not be instantiated from the outside.
//        /// </summary>
//        private List(AIType! typeParameter)
//        {
//            this.typeParameter = typeParameter;
//        }
//    }
//
//    public class Pair : Value
//    {
//        private static IDictionary! pairs = new Hashtable();
//        public static AIType! Type(AIType! type1, AIType! type2)
//        {
//            Microsoft.AbstractInterpretationFramework.Collections.Pair typpair
//                = new Microsoft.AbstractInterpretationFramework.Collections.Pair(type1, type2);
//
//            if (pairs.Contains(typpair))
//                return pairs[typpair];
//            else
//            {
//                AIType! result = new Pair(type1, type2);
//                pairs[typpair] = result;
//                return result;
//            }
//        }
//
//        private static IDictionary! constructs = new Hashtable();
//        public static FunctionSymbol! Pair(AIType! type1, AIType! type2)
//        {
//            Microsoft.AbstractInterpretationFramework.Collections.Pair typpair
//                = new Microsoft.AbstractInterpretationFramework.Collections.Pair(type1, type2);
//
//            if (constructs.Contains(typpair))
//                return constructs[typpair];
//            else
//            {
//                FunctionSymbol! result = new FunctionSymbol(
//                    new FunctionType(type1, type2, Type(type1, type2))
//                );
//                constructs[typpair] = result;
//                return result;
//            }
//        }
//
//        protected AIType! type1;
//        protected AIType! type2;
//
//        public AIType! Type1 { get { return type1; } }
//        public AIType! Type2 { get { return type2; } }
//
//        /// <summary>
//        /// Pair should not be instantiated from the outside, except by subclasses.
//        /// </summary>
//        protected Pair(AIType! type1, AIType! type2)
//        {
//            this.type1 = type1;
//            this.type2 = type2;
//        }
//    }

    //-------------------------- Propositions ---------------------------


    /// <summary>
    ///  A class with global propositional symbols and the Prop.Type.
    /// </summary>
    public sealed class Prop : AIType
    {
        private static readonly AIType! proptype = new Prop();
        public static AIType! Type { get { return proptype; } }

        private static readonly AIType! unaryproptype = new FunctionType(Type, Type);
        private static readonly AIType! binproptype = new FunctionType(Type, Type, Type);
        private static readonly AIType! quantifiertype =
            new FunctionType(new FunctionType(Value.Type, Type), Type);

        private static readonly FunctionSymbol! _false = new FunctionSymbol("false", Type);
        private static readonly FunctionSymbol! _true = new FunctionSymbol("true", Type);
        private static readonly FunctionSymbol! _not = new FunctionSymbol("!", unaryproptype);
        private static readonly FunctionSymbol! _and = new FunctionSymbol("/\\", binproptype);
        private static readonly FunctionSymbol! _or = new FunctionSymbol("\\/", binproptype);
        private static readonly FunctionSymbol! _implies = new FunctionSymbol("==>", binproptype);
        private static readonly FunctionSymbol! _exists = new FunctionSymbol("Exists", quantifiertype);
        private static readonly FunctionSymbol! _forall = new FunctionSymbol("Forall", quantifiertype);


        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! False { get { return _false; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! True { get { return _true; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Not { get { return _not; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! And { [Pure] get { return _and; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Or { get { return _or; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Implies { get { return _implies; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Exists { get { return _exists; } }
        [Pure][Reads(ReadsAttribute.Reads.Nothing)] public static FunctionSymbol! Forall { get { return _forall; } }


        /// <summary>
        ///  Prop should not be instantiated from the outside.
        /// </summary>
        private Prop() { }



        //
        // Utility Methods
        //
        
        public static IExpr! SimplifiedAnd(IPropExprFactory! factory, IExpr! e0, IExpr! e1)
        {
            IFunApp fun0 = e0 as IFunApp;
            if (fun0 != null)
            {
                if (fun0.FunctionSymbol.Equals(Prop.True))
                {
                    return e1;
                }
                else if (fun0.FunctionSymbol.Equals(Prop.False))
                {
                    return e0;
                }
            }
            
            IFunApp fun1 = e1 as IFunApp;
            if (fun1 != null)
            {
                if (fun1.FunctionSymbol.Equals(Prop.True))
                {
                    return e0;
                }
                else if (fun1.FunctionSymbol.Equals(Prop.False))
                {
                    return e1;
                }
            }
            
            return factory.And(e0, e1);
        }
        
        public static IExpr! SimplifiedAnd(IPropExprFactory! factory, IEnumerable/*<IExpr!>*/! exprs)
        {
            IExpr! result = factory.True;
            foreach (IExpr! conjunct in exprs)
            {
                result = SimplifiedAnd(factory, result, conjunct);
            }
            return result;
        }

        public static IExpr! SimplifiedOr(IPropExprFactory! factory, IExpr! e0, IExpr! e1)
        {
            IFunApp fun0 = e0 as IFunApp;
            if (fun0 != null)
            {
                if (fun0.FunctionSymbol.Equals(Prop.False))
                {
                    return e1;
                }
                else if (fun0.FunctionSymbol.Equals(Prop.True))
                {
                    return e0;
                }
            }
            
            IFunApp fun1 = e1 as IFunApp;
            if (fun1 != null)
            {
                if (fun1.FunctionSymbol.Equals(Prop.False))
                {
                    return e0;
                }
                else if (fun1.FunctionSymbol.Equals(Prop.True))
                {
                    return e1;
                }
            }
            
            return factory.Or(e0, e1);
        }
        
        public static IExpr! SimplifiedOr(IPropExprFactory! factory, IEnumerable/*<IExpr!>*/! exprs)
        {
            IExpr! result = factory.False;
            foreach (IExpr! disj in exprs)
            {
                result = SimplifiedOr(factory, result, disj);
            }
            return result;
        }



        /// <summary>
        ///  Break top-level conjuncts into a list of sub-expressions.
        /// </summary>
        /// <param name="e">The expression to examine.</param>
        /// <returns>A list of conjuncts.</returns>
        internal static IList/*<IExpr!>*/! BreakConjuncts(IExpr! e)
          ensures forall{ IExpr sub in result; sub is IFunApp ==> !((IFunApp) sub).FunctionSymbol.Equals(Prop.And) };
        {
            return BreakJuncts(e, Prop.And);
        }

        /// <summary>
        ///  Break top-level disjuncts into a list of sub-expressions.
        /// </summary>
        /// <param name="e">The expression to examine.</param>
        /// <returns>A list of conjuncts.</returns>
        internal static IList/*<IExpr!>*/! BreakDisjuncts(IExpr! e)
          ensures forall{ IExpr sub in result; sub is IFunApp ==> !((IFunApp) sub).FunctionSymbol.Equals(Prop.Or) };
        {
            return BreakJuncts(e, Prop.Or);
        }
        
        private static IList/*<IExpr!>*/! BreakJuncts(IExpr! e, IFunctionSymbol! sym)
          ensures forall{ IExpr sub in result; sub is IFunApp ==> !((IFunApp) sub).FunctionSymbol.Equals(sym) };
        {
            ArrayList/*<IExpr!>*/! result = new ArrayList();

            IFunApp f = e as IFunApp;
            if (f != null)
            {
                // If it is a sym, go down into sub-expressions.
                if (f.FunctionSymbol.Equals(sym))
                {
                    foreach (IExpr! arg in f.Arguments)
                    {
                        result.AddRange(BreakJuncts(arg,sym));
                    }
                }
                // Otherwise, stop.
                else
                {
                    result.Add(e);
                }
            }
            else
            {
                result.Add(e);
            }

            return result;
        }
    }

    /// <summary>
    /// A callback to produce a function body given the bound variable.
    /// </summary>
    /// <param name="var">The bound variable to use.</param>
    /// <returns>The function body.</returns>
    public delegate IExpr! FunctionBody(IVariable! var);

    /// <summary>
    ///  An interface for constructing propositional expressions.
    /// 
    ///  This interface should be implemented by the client.  An implementation of
    ///  of this class should generally be used as a singleton object.
    /// </summary>
    public interface IPropExprFactory
    {
        IFunApp! False { get /*ensures result.FunctionSymbol.Equals(Prop.False);*/; }
        IFunApp! True { get /*ensures result.FunctionSymbol.Equals(Prop.True);*/; }

        IFunApp! Not(IExpr! p) /*ensures result.FunctionSymbol.Equals(Prop.Not);*/;

        IFunApp! And(IExpr! p, IExpr! q) /*ensures result.FunctionSymbol.Equals(Prop.And);*/;
        IFunApp! Or(IExpr! p, IExpr! q) /*ensures result.FunctionSymbol.Equals(Prop.Or);*/;
        
        IFunApp! Implies(IExpr! p, IExpr! q) /*ensures result.FunctionSymbol.Equals(Prop.Implies);*/;
    }
    
    /// <summary>
    /// Like IPropExprFactory, but also with quantifiers.
    /// </summary>
    public interface IQuantPropExprFactory : IPropExprFactory {
        /// <summary>
        /// Produce an existential given the lambda-expression.
        /// </summary>
        /// <param name="p">The lambda-expression.</param>
        /// <returns>The existential.</returns>
        IFunApp! Exists(IFunction! p) /*ensures result.FunctionSymbol.Equals(Prop.Exists);*/;
        IFunApp! Forall(IFunction! p) /*ensures result.FunctionSymbol.Equals(Prop.Forall);*/;

        /// <summary>
        /// Produce an existential given a callback that can produce a function body given the
        /// bound variable to use.  The implementer of this method is responsible for generating
        /// a fresh new variable to pass to the FunctionBody callback to use as the bound variable.
        /// </summary>
        /// <param name="body">The function body callback.</param>
        /// <returns>The existential.</returns>
        IFunApp! Exists(AIType paramType, FunctionBody! body) /*ensures result.FunctionSymbol.Equals(Prop.Exists);*/;
        IFunApp! Forall(AIType paramType, FunctionBody! body) /*ensures result.FunctionSymbol.Equals(Prop.Forall);*/;
    }

    /// <summary>
    ///  An interface for constructing value expressions.
    /// 
    ///  This interface should be implemented by the client.  An implementation of
    ///  of this class should generally be used as a singleton object.
    /// </summary>
    public interface IValueExprFactory
    {
        IFunApp! Eq(IExpr! e0, IExpr! e1) /*ensures result.FunctionSymbol.Equals(Value.Eq);*/;
        IFunApp! Neq(IExpr! e0, IExpr! e1) /*ensures result.FunctionSymbol.Equals(Value.Neq);*/;
    }

    /// <summary>
    ///  An interface for constructing value expressions having to with null.
    /// 
    ///  This interface should be implemented by the client.  An implementation of
    ///  of this class should generally be used as a singleton object.
    /// </summary>
    public interface INullnessFactory
    {
        IFunApp! Eq(IExpr! e0, IExpr! e1) /*ensures result.FunctionSymbol.Equals(Value.Eq);*/;
        IFunApp! Neq(IExpr! e0, IExpr! e1) /*ensures result.FunctionSymbol.Equals(Value.Neq);*/;
        IFunApp! Null { get; /*ensures result.FunctionSymbol.Equals(Ref.Null);*/ }
    }

    /// <summary>
    ///  An interface for constructing integer expressions.
    /// 
    ///  This interface should be implemented by the client.  An implementation of
    ///  of this class should generally be used as a singleton object.
    /// </summary>
    public interface IIntExprFactory : IValueExprFactory
    {
        IFunApp! Const(BigNum i) /*ensures result.FunctionSymbol.Equals(new IntSymbol(i));*/;
    }

    /// <summary>
    ///  An interface for constructing linear integer expressions.
    /// 
    ///  This interface should be implemented by the client.  An implementation of
    ///  of this class should generally be used as a singleton object.
    /// </summary>
    public interface ILinearExprFactory : IIntExprFactory
    {
        IFunApp! AtMost(IExpr! e0, IExpr! e1) /*ensures result.FunctionSymbol.Equals(Value.AtMost);*/;
        IFunApp! Add(IExpr! e0, IExpr! e1) /*ensures result.FunctionSymbol.Equals(Value.Add);*/;
        /// <summary>
        /// If "var" is null, returns an expression representing r.
        /// Otherwise, returns an expression representing r*var.
        /// </summary>
        IExpr! Term(Microsoft.Basetypes.Rational r, IVariable var);

        IFunApp! False { get /*ensures result.FunctionSymbol.Equals(Prop.False);*/; }
        IFunApp! True { get /*ensures result.FunctionSymbol.Equals(Prop.True);*/; }
        IFunApp! And(IExpr! p, IExpr! q) /*ensures result.FunctionSymbol.Equals(Prop.And);*/;
    }

    /// <summary>
    ///  An interface for constructing type expressions and performing some type operations.
    ///  The types are assumed to be arranged in a rooted tree.
    ///
    ///  This interface should be implemented by the client.  An implementation of
    ///  of this class should generally be used as a singleton object.
    /// </summary>
    public interface ITypeExprFactory
    {
        /// <summary>
        /// Returns an expression denoting the top of the type hierarchy.
        /// </summary>
        IExpr! RootType { get; }

        /// <summary>
        /// Returns true iff "t" denotes a type constant.
        /// </summary>
        [Pure][Reads(ReadsAttribute.Reads.Owned)]
        bool IsTypeConstant(IExpr! t);

        /// <summary>
        /// Returns true iff t0 and t1 are types such that t0 and t1 are equal.
        /// </summary>
        [Pure][Reads(ReadsAttribute.Reads.Owned)]
        bool IsTypeEqual(IExpr! t0, IExpr! t1);

        /// <summary>
        /// Returns true iff t0 and t1 are types such that t0 is a subtype of t1.
        /// </summary>
        [Pure][Reads(ReadsAttribute.Reads.Owned)]
        bool IsSubType(IExpr! t0, IExpr! t1);

        /// <summary>
        /// Returns the most derived supertype of both "t0" and "t1".  A precondition is
        /// that "t0" and "t1" both represent types.
        /// </summary>
        IExpr! JoinTypes(IExpr! t0, IExpr! t1);

        IFunApp! IsExactlyA(IExpr! e, IExpr! type) /*requires IsTypeConstant(type); ensures result.FunctionSymbol.Equals(Value.Eq);*/;
        IFunApp! IsA(IExpr! e, IExpr! type) /*requires IsTypeConstant(type); ensures result.FunctionSymbol.Equals(Value.Subtype);*/;
    }

}