path: root/Source/AIFramework/MultiLattice.ssc

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

    using Microsoft.Boogie;    
    using ISet = Microsoft.Boogie.Set;


    /// <summary>
    ///  The cartesian product lattice.
    /// </summary>
    public class MultiLattice : Lattice, IEnumerable
    {
        internal class Elt : Element
        {
            public /*MaybeNull*/Element[] elementPerLattice;

            public Elt(int domainCount, bool isBottom)
            {
                this.elementPerLattice = (domainCount == 0 && isBottom) ? null : new Element[domainCount];
            }
            
            private Elt(Elt! other)
            {
                Element[] otherEPL = other.elementPerLattice;
                if (otherEPL != null)
                {
                    Element[] newEPL = new Element[otherEPL.Length];
                    for (int i = 0; i < newEPL.Length; i++)
                    {
                        newEPL[i] = (Element) ((!)otherEPL[i]).Clone();
                    }
                    this.elementPerLattice = newEPL;          
                }
            }
            
            public override Element! Clone()
            {
                return new Elt(this);
            }

            [Pure]
            public override string! ToString()
            {
//                string s = "MultiLattice+Elt{";
//                string sep = "";
//                Element[] epl = this.elementPerLattice;
//                if (epl != null)
//                {
//                    foreach (Element! e in epl)
//                    {
//                        s += sep + e.ToString();
//                        sep = ", ";
//                    }
//                }
//                return s + "}";
                if (elementPerLattice == null) return "";
                System.Text.StringBuilder buffer = new System.Text.StringBuilder();
                for (int i = 0; i < this.Count; i++)
                {
                    if (i > 0) buffer.Append("; ");
                    buffer.AppendFormat("{0}", elementPerLattice[i]);
                }
                return buffer.ToString();
            }

            public override void Dump(string! msg) {
                System.Console.WriteLine("MultiLattice.Elt.Dump({0})", msg);
                Element[] epl = this.elementPerLattice;
                if (epl != null) {
                    foreach (Element! e in epl) {
                        e.Dump(msg);
                    }
                }
            }
            
            [Pure]
            public override ICollection<IVariable!>! FreeVariables()
            {
                List<IVariable!>! list = new List<IVariable!>();
                for (int i = 0; i < this.Count; i++)
                {
                    list.AddRange(((!)this[i]).FreeVariables());
                }
                return (!)list.AsReadOnly();
            }

            public static Elt! Top(ArrayList/*<Lattice>*/! lattices)
            {
                Elt multiValue = new Elt(lattices.Count, false);
                for (int i = 0; i < lattices.Count; i++)
                {
                    Lattice d = (Lattice!)lattices[i];
                    multiValue[d.Index] = d.Top;
                }
                Debug.Assert(multiValue.IsValid);
                return multiValue;
            }


            public static Elt! Bottom(ArrayList/*<Lattice>*/! lattices)
            {
                Elt multiValue = new Elt(lattices.Count, true);
                for (int i = 0; i < lattices.Count; i++)
                {
                    Lattice d = (Lattice!)lattices[i];
                    multiValue[d.Index] = d.Bottom;
                }
                Debug.Assert(multiValue.IsValid);
                return multiValue;
            }

            public bool IsValid
            {
                get
                {
                    if (this.elementPerLattice == null) { return true; /*bottom*/ }

                    Element[] epl = this.elementPerLattice;
                    for (int i = 0; i < epl.Length; i++)
                    {
                        if (epl[i] == null) { return false; }
                    }
                    return true;
                }
            }

            public int Count { get { return this.elementPerLattice == null ? 0 : this.elementPerLattice.Length; } }

            public bool Contains(int i) { return 0 <= i && i < this.Count; }

            public Element this[int i] // just syntactic sugar
            {
                get { Element[] epl = this.elementPerLattice; return epl == null ? null : epl[i]; }
                set { Element[] epl = this.elementPerLattice; if (epl == null) return; epl[i] = value; }
            }

        } // class



        ArrayList/*<Lattice>*/! lattices = new ArrayList();

        private readonly IPropExprFactory! propExprFactory;


        public MultiLattice(IPropExprFactory! propExprFactory, IValueExprFactory! valueExprFactory)
            : base(valueExprFactory)
        {
            this.propExprFactory = propExprFactory;
            // base(valueExprFactory);
        }

        

        public void AddLattice(Lattice lattice) { this.lattices.Add(lattice); }

        private Lattice! SubLattice(int i) { return (Lattice!)this.lattices[i]; }


        public override Element! Top { get { return Elt.Top(this.lattices); } }

        public override Element! Bottom { get { return Elt.Bottom(this.lattices); } }




        public override bool IsBottom(Element! element)
        {
            Elt e = (Elt)element;
            // The program is errorneous/nonterminating if any subdomain knows it is.
            //
            if (e.elementPerLattice == null) { return true; }
            for (int i = 0; i < e.Count; i++) { if (SubLattice(i).IsBottom((!)e[i])) { return true; } }
            return false;
        }

        public override bool IsTop(Element! element)
        {
            Elt e = (Elt)element;
            if (e.elementPerLattice == null) { return false; }
            // The multidomain knows nothing about the program only if no subdomain
            // knows anything about it.
            //
            for (int i = 0; i < e.Count; i++) { if (!SubLattice(i).IsTop((!)e[i])) { return false; } }
            return true;
        }

        protected override bool AtMost(Element! first, Element! second)
        {
            Elt a = (Elt)first;
            Elt b = (Elt)second;

            for (int i = 0; i < a.Count; i++)
            {
                Element thisElement = (!) a[i];
                Element thatElement = (!) b[i];
                if (thisElement.GetType() != thatElement.GetType())
                {
                    throw new System.InvalidOperationException(
                      "AtMost called on MultiDomain objects with different lattices"
                      );
                }
                if (!SubLattice(i).LowerThan(thisElement, thatElement)) { return false; }
            }
            return true;
        }
        
        protected override bool AtMost(Element! first, ICombineNameMap! firstToResult, Element! second, ICombineNameMap! secondToResult)
        {
            Elt a = (Elt)first;
            Elt b = (Elt)second;

            for (int i = 0; i < a.Count; i++)
            {
                Element thisElement = (!) a[i];
                Element thatElement = (!) b[i];
                if (thisElement.GetType() != thatElement.GetType())
                {
                    throw new System.InvalidOperationException(
                      "AtMost called on MultiDomain objects with different lattices"
                      );
                }
                if (!SubLattice(i).LowerThan(thisElement, firstToResult, thatElement, secondToResult)) { return false; }
            }
            return true;
        }


        private enum CombineOp { Meet, Join, Widen }
        
        private Element! Combine(Element! first, ICombineNameMap/*?*/ firstToResult, Element! second, ICombineNameMap/*?*/ secondToResult, CombineOp c)
        {
            Elt a = (Elt)first;
            Elt b = (Elt)second;

            int unionCount = System.Math.Max(a.Count, b.Count);
            Elt combined = new Elt(unionCount, IsBottom(a) && IsBottom(b));
            for (int i = 0; i < unionCount; i++)
            {
                bool thisExists = a.Contains(i);
                bool thatExists = b.Contains(i);

                if (thisExists && thatExists)
                {
                    Lattice.Element suba = a[i];
                    Lattice.Element subb = b[i];
                    assert suba != null && subb != null;
                    
                    switch (c)
                    {
                      case CombineOp.Meet:
                        combined[i] = SubLattice(i).Meet(suba, subb);
                        break;
                      case CombineOp.Join:
                        if (firstToResult != null && secondToResult != null)
                            combined[i] = SubLattice(i).Join(suba, firstToResult, subb, secondToResult);
                        else
                            combined[i] = SubLattice(i).Join(suba, subb);
                        break;
                      case CombineOp.Widen:
                        if (firstToResult != null && secondToResult != null)
                            combined[i] = SubLattice(i).Widen(suba, firstToResult, subb, secondToResult);
                        else
                            combined[i] = SubLattice(i).Widen(suba, subb);
                        break;
                    }
                }
                else if (thisExists)
                {
                    combined[i] = a[i];
                }
                else
                {
                    combined[i] = b[i];
                }
            }
            Debug.Assert(combined.IsValid);
            return combined;
        }

        public override Element! NontrivialJoin(Element! a, Element! b) { return this.Combine(a, null, b, null, CombineOp.Join); }

        public override Element! NontrivialJoin(Element! a, ICombineNameMap! aToResult, Element! b, ICombineNameMap! bToResult) { return this.Combine(a, aToResult, b, bToResult, CombineOp.Join); }

        public override Element! NontrivialMeet(Element! a, Element! b) { return this.Combine(a, null, b, null, CombineOp.Meet); }

        public override Element! Widen(Element! a, Element! b) { return this.Combine(a, null, b, null, CombineOp.Widen); }

        public override Element! Widen(Element! a, ICombineNameMap! aToResult, Element! b, ICombineNameMap! bToResult) { return this.Combine(a, aToResult, b, bToResult, CombineOp.Widen); }

        public override Element! Eliminate(Element! element, IVariable! variable)
        {
            Elt e = (Elt)element;
            if (IsBottom(e))
            {
                return e;
            }
            Elt newValue = new Elt(e.Count, false);
            for (int i = 0; i < this.lattices.Count; i++)
            {
                newValue[i] = SubLattice(i).Eliminate((!) e[i], variable);
            }
            return newValue;
        }


        public override Element! Constrain(Element! element, IExpr! expr)
        {
            Elt e = (Elt)element;
            if (IsBottom(e))
            {
                return e;
            }
            Elt newValue = new Elt(e.Count, false);
            for (int i = 0; i < this.lattices.Count; i++)
            {
                newValue[i] = SubLattice(i).Constrain((!)e[i], expr);
            }
            return newValue;
        }


        public override Element! Rename(Element! element, IVariable! oldName, IVariable! newName)
        {
            Elt e = (Elt)element;
            if (IsBottom(e))
            {
                return e;
            }
            Elt newValue = new Elt(e.Count, false);
            for (int i = 0; i < this.lattices.Count; i++)
            {
                newValue[i] = SubLattice(i).Rename((!)e[i], oldName, newName);
            }
            return newValue;
        }


        public override bool Understands(IFunctionSymbol! f, IList! args)
        {
            bool result = false;

            for (int i = 0; i < this.lattices.Count; i++)
            {
                result = (result || SubLattice(i).Understands(f, args));
            }

            return result;
        }


        public override string! ToString(Element! element)
        {
            Elt e = (Elt)element;
            return e.ToString();
        }


        public override IExpr! ToPredicate(Element! element)
        {
            Elt e = (Elt)element;
            
            IExpr result = propExprFactory.True;
            for (int i = 0; i < e.Count; i++)
            {
                IExpr conjunct = SubLattice(i).ToPredicate((!)e[i]);
                assert conjunct != null;

                result = Prop.SimplifiedAnd(propExprFactory, conjunct, result);
            }
            return result;
        }
        
        /// <summary>
        ///  Return an expression that is equivalent to the given expression that does not
        ///  contain the given variable according to the lattice element and queryable.
        /// 
        ///  Simply asks each sublattice to try to generate an equivalent expression.  We
        ///  do not try to combine information to infer new equivalences here.
        /// </summary>
        /// <param name="e">The lattice element.</param>
        /// <param name="q">A queryable for asking addtional information.</param>
        /// <param name="expr">The expression to find an equivalent expression.</param>
        /// <param name="var">The variable to eliminate.</param>
        /// <returns>
        /// An equivalent expression to <paramref name="expr"/> without <paramref name="var"/>
        /// or null if not possible.
        /// </returns>
        public override IExpr/*?*/ EquivalentExpr(Element! element, IQueryable! q, IExpr! expr, IVariable! var, Set/*<IVariable!>*/! prohibitedVars)
        {
            Elt! e = (Elt!)element;

            for (int i = 0; i < e.Count; i++)
            {
                IExpr equivexpr = SubLattice(i).EquivalentExpr((!)e[i], q, expr, var, prohibitedVars);

                if (equivexpr != null)
                    return equivexpr;
            }

            return null;
        }


        public override Answer CheckPredicate(Element! element, IExpr! pred)
        {
            Elt! e = (Elt!)element;

            for (int i = 0; i < e.Count; i++)
            {
                Answer ans = SubLattice(i).CheckPredicate((!)e[i], pred);

                if (ans == Answer.Yes || ans == Answer.No)
                    return ans;
            }

            return Answer.Maybe;
        }


        public override Answer CheckVariableDisequality(Element! element, IVariable! var1, IVariable! var2)
        {
            Elt! e = (Elt!)element;

            for (int i = 0; i < e.Count; i++)
            {
                Answer ans = SubLattice(i).CheckVariableDisequality((!)e[i], var1, var2);

                if (ans == Answer.Yes || ans == Answer.No)
                    return ans;
            }

            return Answer.Maybe;
        }



        public override void Validate()
        {
            base.Validate();
            foreach (Lattice! l in lattices)
            {
                l.Validate();
            }
        }

        /// <summary>
        ///  The enumeration over a MultiLattice is its sublattices.
        /// </summary>
        /// <returns>An enumerator over the sublattices.</returns>
        [Pure] [GlobalAccess(false)] [Escapes(true,false)]
        public IEnumerator/*<Lattice!>*/! GetEnumerator()
        {
            return lattices.GetEnumerator();
        }

        /// <summary>
        ///  Return an enumerable over a mapping of sublattices to the their corresponding
        ///  lattice elements given a MultiLattice element.
        /// </summary>
        /// <param name="element">The MultiLattice element.</param>
        /// <returns>
        /// An enumerable that yields an IDictionaryEnumerator over the
        /// (Lattice, Lattice.Element) pairs.
        /// </returns>
        public IEnumerable! Subelements(Element! element)
        {
            return new SubelementsEnumerable(this, (Elt!) element);
        }

        /// <summary>
        ///  An enumerator over the sublattices and elements.
        /// </summary>
        private sealed class SubelementsEnumerable : IEnumerable
        {
            private sealed class SubelementsEnumerator : IDictionaryEnumerator
            {
                private readonly IEnumerator/*<Lattice!>*/! multiLatticeIter;
                private readonly IEnumerator/*<Lattice.Element!>*/! multiElementIter;

                public SubelementsEnumerator(MultiLattice! multiLattice, Elt! multiElement)
                  requires multiElement.elementPerLattice != null;
                {
                    this.multiLatticeIter = multiLattice.lattices.GetEnumerator();
                    this.multiElementIter = multiElement.elementPerLattice.GetEnumerator();
                    // base();
                }

                public DictionaryEntry Entry
                {
                    get
                    {
                        return new DictionaryEntry((!)multiLatticeIter.Current, multiElementIter.Current);
                    }
                }

                public object Key
                {
                    get
                    {
                        return multiLatticeIter.Current;
                    }
                }

                public object Value
                {
                    get
                    {
                        return multiElementIter.Current;
                    }
                }

                public object Current
                {
                    get
                    {
                        return this.Entry;
                    }
                }

                public bool MoveNext()
                {
                    return multiLatticeIter.MoveNext() && multiElementIter.MoveNext();
                }

                public void Reset()
                {
                    multiLatticeIter.Reset();
                    multiElementIter.Reset();
                }
            }

            private MultiLattice! multiLattice;
            private Elt! multiElement;
            
            public SubelementsEnumerable(MultiLattice! multiLattice, Elt! multiElement)
            {
                this.multiLattice = multiLattice;
                this.multiElement = multiElement;
                // base();
            }

            [Pure] [GlobalAccess(false)] [Escapes(true,false)]
            public IEnumerator! GetEnumerator()
            {
                return new SubelementsEnumerator(multiLattice, multiElement);
            }
        }


    }
}