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Java example source code file (Infer.java)

This example Java source code file (Infer.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

inapplicablemethodexception, incorporationbinaryop, inferencecontext, inferenceexception, integer, list, listbuffer, node, override, pair, set, type, undetvar, util, warner

The Infer.java Java example source code

/*
 * Copyright (c) 1999, 2013, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package com.sun.tools.javac.comp;

import com.sun.tools.javac.tree.JCTree;
import com.sun.tools.javac.tree.JCTree.JCTypeCast;
import com.sun.tools.javac.tree.TreeInfo;
import com.sun.tools.javac.util.*;
import com.sun.tools.javac.util.JCDiagnostic.DiagnosticPosition;
import com.sun.tools.javac.util.List;
import com.sun.tools.javac.code.*;
import com.sun.tools.javac.code.Type.*;
import com.sun.tools.javac.code.Type.UndetVar.InferenceBound;
import com.sun.tools.javac.code.Symbol.*;
import com.sun.tools.javac.comp.DeferredAttr.AttrMode;
import com.sun.tools.javac.comp.Infer.GraphSolver.InferenceGraph;
import com.sun.tools.javac.comp.Infer.GraphSolver.InferenceGraph.Node;
import com.sun.tools.javac.comp.Resolve.InapplicableMethodException;
import com.sun.tools.javac.comp.Resolve.VerboseResolutionMode;
import com.sun.tools.javac.util.GraphUtils.TarjanNode;

import java.util.ArrayList;
import java.util.Collections;
import java.util.EnumMap;
import java.util.EnumSet;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedHashSet;
import java.util.Map;
import java.util.Set;

import static com.sun.tools.javac.code.TypeTag.*;

/** Helper class for type parameter inference, used by the attribution phase.
 *
 *  <p>This is NOT part of any supported API.
 *  If you write code that depends on this, you do so at your own risk.
 *  This code and its internal interfaces are subject to change or
 *  deletion without notice.</b>
 */
public class Infer {
    protected static final Context.Key<Infer> inferKey =
        new Context.Key<Infer>();

    Resolve rs;
    Check chk;
    Symtab syms;
    Types types;
    JCDiagnostic.Factory diags;
    Log log;

    /** should the graph solver be used? */
    boolean allowGraphInference;

    public static Infer instance(Context context) {
        Infer instance = context.get(inferKey);
        if (instance == null)
            instance = new Infer(context);
        return instance;
    }

    protected Infer(Context context) {
        context.put(inferKey, this);

        rs = Resolve.instance(context);
        chk = Check.instance(context);
        syms = Symtab.instance(context);
        types = Types.instance(context);
        diags = JCDiagnostic.Factory.instance(context);
        log = Log.instance(context);
        inferenceException = new InferenceException(diags);
        Options options = Options.instance(context);
        allowGraphInference = Source.instance(context).allowGraphInference()
                && options.isUnset("useLegacyInference");
    }

    /** A value for prototypes that admit any type, including polymorphic ones. */
    public static final Type anyPoly = new JCNoType();

   /**
    * This exception class is design to store a list of diagnostics corresponding
    * to inference errors that can arise during a method applicability check.
    */
    public static class InferenceException extends InapplicableMethodException {
        private static final long serialVersionUID = 0;

        List<JCDiagnostic> messages = List.nil();

        InferenceException(JCDiagnostic.Factory diags) {
            super(diags);
        }

        @Override
        InapplicableMethodException setMessage() {
            //no message to set
            return this;
        }

        @Override
        InapplicableMethodException setMessage(JCDiagnostic diag) {
            messages = messages.append(diag);
            return this;
        }

        @Override
        public JCDiagnostic getDiagnostic() {
            return messages.head;
        }

        void clear() {
            messages = List.nil();
        }
    }

    protected final InferenceException inferenceException;

    // <editor-fold defaultstate="collapsed" desc="Inference routines">
    /**
     * Main inference entry point - instantiate a generic method type
     * using given argument types and (possibly) an expected target-type.
     */
    public Type instantiateMethod(Env<AttrContext> env,
                                  List<Type> tvars,
                                  MethodType mt,
                                  Attr.ResultInfo resultInfo,
                                  Symbol msym,
                                  List<Type> argtypes,
                                  boolean allowBoxing,
                                  boolean useVarargs,
                                  Resolve.MethodResolutionContext resolveContext,
                                  Warner warn) throws InferenceException {
        //-System.err.println("instantiateMethod(" + tvars + ", " + mt + ", " + argtypes + ")"); //DEBUG
        final InferenceContext inferenceContext = new InferenceContext(tvars);
        inferenceException.clear();
        try {
            DeferredAttr.DeferredAttrContext deferredAttrContext =
                        resolveContext.deferredAttrContext(msym, inferenceContext, resultInfo, warn);

            resolveContext.methodCheck.argumentsAcceptable(env, deferredAttrContext,
                    argtypes, mt.getParameterTypes(), warn);

            if (allowGraphInference &&
                    resultInfo != null &&
                    !warn.hasNonSilentLint(Lint.LintCategory.UNCHECKED)) {
                //inject return constraints earlier
                checkWithinBounds(inferenceContext, warn); //propagation
                Type newRestype = generateReturnConstraints(resultInfo, mt, inferenceContext);
                mt = (MethodType)types.createMethodTypeWithReturn(mt, newRestype);
                //propagate outwards if needed
                if (resultInfo.checkContext.inferenceContext().free(resultInfo.pt)) {
                    //propagate inference context outwards and exit
                    inferenceContext.dupTo(resultInfo.checkContext.inferenceContext());
                    deferredAttrContext.complete();
                    return mt;
                }
            }

            deferredAttrContext.complete();

            // minimize as yet undetermined type variables
            if (allowGraphInference) {
                inferenceContext.solve(warn);
            } else {
                inferenceContext.solveLegacy(true, warn, LegacyInferenceSteps.EQ_LOWER.steps); //minimizeInst
            }

            mt = (MethodType)inferenceContext.asInstType(mt);

            if (!allowGraphInference &&
                    inferenceContext.restvars().nonEmpty() &&
                    resultInfo != null &&
                    !warn.hasNonSilentLint(Lint.LintCategory.UNCHECKED)) {
                generateReturnConstraints(resultInfo, mt, inferenceContext);
                inferenceContext.solveLegacy(false, warn, LegacyInferenceSteps.EQ_UPPER.steps); //maximizeInst
                mt = (MethodType)inferenceContext.asInstType(mt);
            }

            if (resultInfo != null && rs.verboseResolutionMode.contains(VerboseResolutionMode.DEFERRED_INST)) {
                log.note(env.tree.pos, "deferred.method.inst", msym, mt, resultInfo.pt);
            }

            // return instantiated version of method type
            return mt;
        } finally {
            if (resultInfo != null || !allowGraphInference) {
                inferenceContext.notifyChange();
            } else {
                inferenceContext.notifyChange(inferenceContext.boundedVars());
            }
        }
    }

    /**
     * Generate constraints from the generic method's return type. If the method
     * call occurs in a context where a type T is expected, use the expected
     * type to derive more constraints on the generic method inference variables.
     */
    Type generateReturnConstraints(Attr.ResultInfo resultInfo,
            MethodType mt, InferenceContext inferenceContext) {
        Type from = mt.getReturnType();
        if (mt.getReturnType().containsAny(inferenceContext.inferencevars) &&
                resultInfo.checkContext.inferenceContext() != emptyContext) {
            from = types.capture(from);
            //add synthetic captured ivars
            for (Type t : from.getTypeArguments()) {
                if (t.hasTag(TYPEVAR) && ((TypeVar)t).isCaptured()) {
                    inferenceContext.addVar((TypeVar)t);
                }
            }
        }
        Type qtype1 = inferenceContext.asFree(from);
        Type to = returnConstraintTarget(qtype1, resultInfo.pt);
        Assert.check(allowGraphInference || !resultInfo.checkContext.inferenceContext().free(to),
                "legacy inference engine cannot handle constraints on both sides of a subtyping assertion");
        //we need to skip capture?
        Warner retWarn = new Warner();
        if (!resultInfo.checkContext.compatible(qtype1, resultInfo.checkContext.inferenceContext().asFree(to), retWarn) ||
                //unchecked conversion is not allowed in source 7 mode
                (!allowGraphInference && retWarn.hasLint(Lint.LintCategory.UNCHECKED))) {
            throw inferenceException
                    .setMessage("infer.no.conforming.instance.exists",
                    inferenceContext.restvars(), mt.getReturnType(), to);
        }
        return from;
    }

    Type returnConstraintTarget(Type from, Type to) {
        if (from.hasTag(VOID)) {
            return syms.voidType;
        } else if (to.hasTag(NONE)) {
            return from.isPrimitive() ? from : syms.objectType;
        } else if (from.hasTag(UNDETVAR) && to.isPrimitive()) {
            if (!allowGraphInference) {
                //if legacy, just return boxed type
                return types.boxedClass(to).type;
            }
            //if graph inference we need to skip conflicting boxed bounds...
            UndetVar uv = (UndetVar)from;
            for (Type t : uv.getBounds(InferenceBound.EQ, InferenceBound.LOWER)) {
                Type boundAsPrimitive = types.unboxedType(t);
                if (boundAsPrimitive == null) continue;
                if (types.isConvertible(boundAsPrimitive, to)) {
                    //effectively skip return-type constraint generation (compatibility)
                    return syms.objectType;
                }
            }
            return types.boxedClass(to).type;
        } else {
            return to;
        }
    }

    /**
      * Infer cyclic inference variables as described in 15.12.2.8.
      */
    private void instantiateAsUninferredVars(List<Type> vars, InferenceContext inferenceContext) {
        ListBuffer<Type> todo = new ListBuffer<>();
        //step 1 - create fresh tvars
        for (Type t : vars) {
            UndetVar uv = (UndetVar)inferenceContext.asFree(t);
            List<Type> upperBounds = uv.getBounds(InferenceBound.UPPER);
            if (Type.containsAny(upperBounds, vars)) {
                TypeSymbol fresh_tvar = new TypeVariableSymbol(Flags.SYNTHETIC, uv.qtype.tsym.name, null, uv.qtype.tsym.owner);
                fresh_tvar.type = new TypeVar(fresh_tvar, types.makeCompoundType(uv.getBounds(InferenceBound.UPPER)), null);
                todo.append(uv);
                uv.inst = fresh_tvar.type;
            } else if (upperBounds.nonEmpty()) {
                uv.inst = types.glb(upperBounds);
            } else {
                uv.inst = syms.objectType;
            }
        }
        //step 2 - replace fresh tvars in their bounds
        List<Type> formals = vars;
        for (Type t : todo) {
            UndetVar uv = (UndetVar)t;
            TypeVar ct = (TypeVar)uv.inst;
            ct.bound = types.glb(inferenceContext.asInstTypes(types.getBounds(ct)));
            if (ct.bound.isErroneous()) {
                //report inference error if glb fails
                reportBoundError(uv, BoundErrorKind.BAD_UPPER);
            }
            formals = formals.tail;
        }
    }

    /**
     * Compute a synthetic method type corresponding to the requested polymorphic
     * method signature. The target return type is computed from the immediately
     * enclosing scope surrounding the polymorphic-signature call.
     */
    Type instantiatePolymorphicSignatureInstance(Env<AttrContext> env,
                                            MethodSymbol spMethod,  // sig. poly. method or null if none
                                            Resolve.MethodResolutionContext resolveContext,
                                            List<Type> argtypes) {
        final Type restype;

        //The return type for a polymorphic signature call is computed from
        //the enclosing tree E, as follows: if E is a cast, then use the
        //target type of the cast expression as a return type; if E is an
        //expression statement, the return type is 'void' - otherwise the
        //return type is simply 'Object'. A correctness check ensures that
        //env.next refers to the lexically enclosing environment in which
        //the polymorphic signature call environment is nested.

        switch (env.next.tree.getTag()) {
            case TYPECAST:
                JCTypeCast castTree = (JCTypeCast)env.next.tree;
                restype = (TreeInfo.skipParens(castTree.expr) == env.tree) ?
                    castTree.clazz.type :
                    syms.objectType;
                break;
            case EXEC:
                JCTree.JCExpressionStatement execTree =
                        (JCTree.JCExpressionStatement)env.next.tree;
                restype = (TreeInfo.skipParens(execTree.expr) == env.tree) ?
                    syms.voidType :
                    syms.objectType;
                break;
            default:
                restype = syms.objectType;
        }

        List<Type> paramtypes = Type.map(argtypes, new ImplicitArgType(spMethod, resolveContext.step));
        List<Type> exType = spMethod != null ?
            spMethod.getThrownTypes() :
            List.of(syms.throwableType); // make it throw all exceptions

        MethodType mtype = new MethodType(paramtypes,
                                          restype,
                                          exType,
                                          syms.methodClass);
        return mtype;
    }
    //where
        class ImplicitArgType extends DeferredAttr.DeferredTypeMap {

            public ImplicitArgType(Symbol msym, Resolve.MethodResolutionPhase phase) {
                rs.deferredAttr.super(AttrMode.SPECULATIVE, msym, phase);
            }

            public Type apply(Type t) {
                t = types.erasure(super.apply(t));
                if (t.hasTag(BOT))
                    // nulls type as the marker type Null (which has no instances)
                    // infer as java.lang.Void for now
                    t = types.boxedClass(syms.voidType).type;
                return t;
            }
        }

    /**
      * This method is used to infer a suitable target SAM in case the original
      * SAM type contains one or more wildcards. An inference process is applied
      * so that wildcard bounds, as well as explicit lambda/method ref parameters
      * (where applicable) are used to constraint the solution.
      */
    public Type instantiateFunctionalInterface(DiagnosticPosition pos, Type funcInterface,
            List<Type> paramTypes, Check.CheckContext checkContext) {
        if (types.capture(funcInterface) == funcInterface) {
            //if capture doesn't change the type then return the target unchanged
            //(this means the target contains no wildcards!)
            return funcInterface;
        } else {
            Type formalInterface = funcInterface.tsym.type;
            InferenceContext funcInterfaceContext =
                    new InferenceContext(funcInterface.tsym.type.getTypeArguments());

            Assert.check(paramTypes != null);
            //get constraints from explicit params (this is done by
            //checking that explicit param types are equal to the ones
            //in the functional interface descriptors)
            List<Type> descParameterTypes = types.findDescriptorType(formalInterface).getParameterTypes();
            if (descParameterTypes.size() != paramTypes.size()) {
                checkContext.report(pos, diags.fragment("incompatible.arg.types.in.lambda"));
                return types.createErrorType(funcInterface);
            }
            for (Type p : descParameterTypes) {
                if (!types.isSameType(funcInterfaceContext.asFree(p), paramTypes.head)) {
                    checkContext.report(pos, diags.fragment("no.suitable.functional.intf.inst", funcInterface));
                    return types.createErrorType(funcInterface);
                }
                paramTypes = paramTypes.tail;
            }

            try {
                funcInterfaceContext.solve(funcInterfaceContext.boundedVars(), types.noWarnings);
            } catch (InferenceException ex) {
                checkContext.report(pos, diags.fragment("no.suitable.functional.intf.inst", funcInterface));
            }

            List<Type> actualTypeargs = funcInterface.getTypeArguments();
            for (Type t : funcInterfaceContext.undetvars) {
                UndetVar uv = (UndetVar)t;
                if (uv.inst == null) {
                    uv.inst = actualTypeargs.head;
                }
                actualTypeargs = actualTypeargs.tail;
            }

            Type owntype = funcInterfaceContext.asInstType(formalInterface);
            if (!chk.checkValidGenericType(owntype)) {
                //if the inferred functional interface type is not well-formed,
                //or if it's not a subtype of the original target, issue an error
                checkContext.report(pos, diags.fragment("no.suitable.functional.intf.inst", funcInterface));
            }
            return owntype;
        }
    }
    // </editor-fold>

    // <editor-fold defaultstate="collapsed" desc="Bound checking">
    /**
     * Check bounds and perform incorporation
     */
    void checkWithinBounds(InferenceContext inferenceContext,
                             Warner warn) throws InferenceException {
        MultiUndetVarListener mlistener = new MultiUndetVarListener(inferenceContext.undetvars);
        List<Type> saved_undet = inferenceContext.save();
        try {
            while (true) {
                mlistener.reset();
                if (!allowGraphInference) {
                    //in legacy mode we lack of transitivity, so bound check
                    //cannot be run in parallel with other incoprporation rounds
                    for (Type t : inferenceContext.undetvars) {
                        UndetVar uv = (UndetVar)t;
                        IncorporationStep.CHECK_BOUNDS.apply(uv, inferenceContext, warn);
                    }
                }
                for (Type t : inferenceContext.undetvars) {
                    UndetVar uv = (UndetVar)t;
                    //bound incorporation
                    EnumSet<IncorporationStep> incorporationSteps = allowGraphInference ?
                            incorporationStepsGraph : incorporationStepsLegacy;
                    for (IncorporationStep is : incorporationSteps) {
                        if (is.accepts(uv, inferenceContext)) {
                            is.apply(uv, inferenceContext, warn);
                        }
                    }
                }
                if (!mlistener.changed || !allowGraphInference) break;
            }
        }
        finally {
            mlistener.detach();
            if (incorporationCache.size() == MAX_INCORPORATION_STEPS) {
                inferenceContext.rollback(saved_undet);
            }
            incorporationCache.clear();
        }
    }
    //where
        /**
         * This listener keeps track of changes on a group of inference variable
         * bounds. Note: the listener must be detached (calling corresponding
         * method) to make sure that the underlying inference variable is
         * left in a clean state.
         */
        class MultiUndetVarListener implements UndetVar.UndetVarListener {

            boolean changed;
            List<Type> undetvars;

            public MultiUndetVarListener(List<Type> undetvars) {
                this.undetvars = undetvars;
                for (Type t : undetvars) {
                    UndetVar uv = (UndetVar)t;
                    uv.listener = this;
                }
            }

            public void varChanged(UndetVar uv, Set<InferenceBound> ibs) {
                //avoid non-termination
                if (incorporationCache.size() < MAX_INCORPORATION_STEPS) {
                    changed = true;
                }
            }

            void reset() {
                changed = false;
            }

            void detach() {
                for (Type t : undetvars) {
                    UndetVar uv = (UndetVar)t;
                    uv.listener = null;
                }
            }
        };

        /** max number of incorporation rounds */
        static final int MAX_INCORPORATION_STEPS = 100;

    /**
     * This enumeration defines an entry point for doing inference variable
     * bound incorporation - it can be used to inject custom incorporation
     * logic into the basic bound checking routine
     */
    enum IncorporationStep {
        /**
         * Performs basic bound checking - i.e. is the instantiated type for a given
         * inference variable compatible with its bounds?
         */
        CHECK_BOUNDS() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                uv.substBounds(inferenceContext.inferenceVars(), inferenceContext.instTypes(), infer.types);
                infer.checkCompatibleUpperBounds(uv, inferenceContext);
                if (uv.inst != null) {
                    Type inst = uv.inst;
                    for (Type u : uv.getBounds(InferenceBound.UPPER)) {
                        if (!isSubtype(inst, inferenceContext.asFree(u), warn, infer)) {
                            infer.reportBoundError(uv, BoundErrorKind.UPPER);
                        }
                    }
                    for (Type l : uv.getBounds(InferenceBound.LOWER)) {
                        if (!isSubtype(inferenceContext.asFree(l), inst, warn, infer)) {
                            infer.reportBoundError(uv, BoundErrorKind.LOWER);
                        }
                    }
                    for (Type e : uv.getBounds(InferenceBound.EQ)) {
                        if (!isSameType(inst, inferenceContext.asFree(e), infer)) {
                            infer.reportBoundError(uv, BoundErrorKind.EQ);
                        }
                    }
                }
            }
            @Override
            boolean accepts(UndetVar uv, InferenceContext inferenceContext) {
                //applies to all undetvars
                return true;
            }
        },
        /**
         * Check consistency of equality constraints. This is a slightly more aggressive
         * inference routine that is designed as to maximize compatibility with JDK 7.
         * Note: this is not used in graph mode.
         */
        EQ_CHECK_LEGACY() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                Type eq = null;
                for (Type e : uv.getBounds(InferenceBound.EQ)) {
                    Assert.check(!inferenceContext.free(e));
                    if (eq != null && !isSameType(e, eq, infer)) {
                        infer.reportBoundError(uv, BoundErrorKind.EQ);
                    }
                    eq = e;
                    for (Type l : uv.getBounds(InferenceBound.LOWER)) {
                        Assert.check(!inferenceContext.free(l));
                        if (!isSubtype(l, e, warn, infer)) {
                            infer.reportBoundError(uv, BoundErrorKind.BAD_EQ_LOWER);
                        }
                    }
                    for (Type u : uv.getBounds(InferenceBound.UPPER)) {
                        if (inferenceContext.free(u)) continue;
                        if (!isSubtype(e, u, warn, infer)) {
                            infer.reportBoundError(uv, BoundErrorKind.BAD_EQ_UPPER);
                        }
                    }
                }
            }
        },
        /**
         * Check consistency of equality constraints.
         */
        EQ_CHECK() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type e : uv.getBounds(InferenceBound.EQ)) {
                    if (e.containsAny(inferenceContext.inferenceVars())) continue;
                    for (Type u : uv.getBounds(InferenceBound.UPPER)) {
                        if (!isSubtype(e, inferenceContext.asFree(u), warn, infer)) {
                            infer.reportBoundError(uv, BoundErrorKind.BAD_EQ_UPPER);
                        }
                    }
                    for (Type l : uv.getBounds(InferenceBound.LOWER)) {
                        if (!isSubtype(inferenceContext.asFree(l), e, warn, infer)) {
                            infer.reportBoundError(uv, BoundErrorKind.BAD_EQ_LOWER);
                        }
                    }
                }
            }
        },
        /**
         * Given a bound set containing {@code alpha <: T} and {@code alpha :> S}
         * perform {@code S <: T} (which could lead to new bounds).
         */
        CROSS_UPPER_LOWER() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type b1 : uv.getBounds(InferenceBound.UPPER)) {
                    for (Type b2 : uv.getBounds(InferenceBound.LOWER)) {
                        isSubtype(inferenceContext.asFree(b2), inferenceContext.asFree(b1), warn , infer);
                    }
                }
            }
        },
        /**
         * Given a bound set containing {@code alpha <: T} and {@code alpha == S}
         * perform {@code S <: T} (which could lead to new bounds).
         */
        CROSS_UPPER_EQ() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type b1 : uv.getBounds(InferenceBound.UPPER)) {
                    for (Type b2 : uv.getBounds(InferenceBound.EQ)) {
                        isSubtype(inferenceContext.asFree(b2), inferenceContext.asFree(b1), warn, infer);
                    }
                }
            }
        },
        /**
         * Given a bound set containing {@code alpha :> S} and {@code alpha == T}
         * perform {@code S <: T} (which could lead to new bounds).
         */
        CROSS_EQ_LOWER() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type b1 : uv.getBounds(InferenceBound.EQ)) {
                    for (Type b2 : uv.getBounds(InferenceBound.LOWER)) {
                        isSubtype(inferenceContext.asFree(b2), inferenceContext.asFree(b1), warn, infer);
                    }
                }
            }
        },
        /**
         * Given a bound set containing {@code alpha == S} and {@code alpha == T}
         * perform {@code S == T} (which could lead to new bounds).
         */
        CROSS_EQ_EQ() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type b1 : uv.getBounds(InferenceBound.EQ)) {
                    for (Type b2 : uv.getBounds(InferenceBound.EQ)) {
                        if (b1 != b2) {
                            isSameType(inferenceContext.asFree(b2), inferenceContext.asFree(b1), infer);
                        }
                    }
                }
            }
        },
        /**
         * Given a bound set containing {@code alpha <: beta} propagate lower bounds
         * from alpha to beta; also propagate upper bounds from beta to alpha.
         */
        PROP_UPPER() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type b : uv.getBounds(InferenceBound.UPPER)) {
                    if (inferenceContext.inferenceVars().contains(b)) {
                        UndetVar uv2 = (UndetVar)inferenceContext.asFree(b);
                        if (uv2.isCaptured()) continue;
                        //alpha <: beta
                        //0. set beta :> alpha
                        addBound(InferenceBound.LOWER, uv2, inferenceContext.asInstType(uv.qtype), infer);
                        //1. copy alpha's lower to beta's
                        for (Type l : uv.getBounds(InferenceBound.LOWER)) {
                            addBound(InferenceBound.LOWER, uv2, inferenceContext.asInstType(l), infer);
                        }
                        //2. copy beta's upper to alpha's
                        for (Type u : uv2.getBounds(InferenceBound.UPPER)) {
                            addBound(InferenceBound.UPPER, uv, inferenceContext.asInstType(u), infer);
                        }
                    }
                }
            }
        },
        /**
         * Given a bound set containing {@code alpha :> beta} propagate lower bounds
         * from beta to alpha; also propagate upper bounds from alpha to beta.
         */
        PROP_LOWER() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type b : uv.getBounds(InferenceBound.LOWER)) {
                    if (inferenceContext.inferenceVars().contains(b)) {
                        UndetVar uv2 = (UndetVar)inferenceContext.asFree(b);
                        if (uv2.isCaptured()) continue;
                        //alpha :> beta
                        //0. set beta <: alpha
                        addBound(InferenceBound.UPPER, uv2, inferenceContext.asInstType(uv.qtype), infer);
                        //1. copy alpha's upper to beta's
                        for (Type u : uv.getBounds(InferenceBound.UPPER)) {
                            addBound(InferenceBound.UPPER, uv2, inferenceContext.asInstType(u), infer);
                        }
                        //2. copy beta's lower to alpha's
                        for (Type l : uv2.getBounds(InferenceBound.LOWER)) {
                            addBound(InferenceBound.LOWER, uv, inferenceContext.asInstType(l), infer);
                        }
                    }
                }
            }
        },
        /**
         * Given a bound set containing {@code alpha == beta} propagate lower/upper
         * bounds from alpha to beta and back.
         */
        PROP_EQ() {
            public void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn) {
                Infer infer = inferenceContext.infer();
                for (Type b : uv.getBounds(InferenceBound.EQ)) {
                    if (inferenceContext.inferenceVars().contains(b)) {
                        UndetVar uv2 = (UndetVar)inferenceContext.asFree(b);
                        if (uv2.isCaptured()) continue;
                        //alpha == beta
                        //0. set beta == alpha
                        addBound(InferenceBound.EQ, uv2, inferenceContext.asInstType(uv.qtype), infer);
                        //1. copy all alpha's bounds to beta's
                        for (InferenceBound ib : InferenceBound.values()) {
                            for (Type b2 : uv.getBounds(ib)) {
                                if (b2 != uv2) {
                                    addBound(ib, uv2, inferenceContext.asInstType(b2), infer);
                                }
                            }
                        }
                        //2. copy all beta's bounds to alpha's
                        for (InferenceBound ib : InferenceBound.values()) {
                            for (Type b2 : uv2.getBounds(ib)) {
                                if (b2 != uv) {
                                    addBound(ib, uv, inferenceContext.asInstType(b2), infer);
                                }
                            }
                        }
                    }
                }
            }
        };

        abstract void apply(UndetVar uv, InferenceContext inferenceContext, Warner warn);

        boolean accepts(UndetVar uv, InferenceContext inferenceContext) {
            return !uv.isCaptured();
        }

        boolean isSubtype(Type s, Type t, Warner warn, Infer infer) {
            return doIncorporationOp(IncorporationBinaryOpKind.IS_SUBTYPE, s, t, warn, infer);
        }

        boolean isSameType(Type s, Type t, Infer infer) {
            return doIncorporationOp(IncorporationBinaryOpKind.IS_SAME_TYPE, s, t, null, infer);
        }

        void addBound(InferenceBound ib, UndetVar uv, Type b, Infer infer) {
            doIncorporationOp(opFor(ib), uv, b, null, infer);
        }

        IncorporationBinaryOpKind opFor(InferenceBound boundKind) {
            switch (boundKind) {
                case EQ:
                    return IncorporationBinaryOpKind.ADD_EQ_BOUND;
                case LOWER:
                    return IncorporationBinaryOpKind.ADD_LOWER_BOUND;
                case UPPER:
                    return IncorporationBinaryOpKind.ADD_UPPER_BOUND;
                default:
                    Assert.error("Can't get here!");
                    return null;
            }
        }

        boolean doIncorporationOp(IncorporationBinaryOpKind opKind, Type op1, Type op2, Warner warn, Infer infer) {
            IncorporationBinaryOp newOp = infer.new IncorporationBinaryOp(opKind, op1, op2);
            Boolean res = infer.incorporationCache.get(newOp);
            if (res == null) {
                infer.incorporationCache.put(newOp, res = newOp.apply(warn));
            }
            return res;
        }
    }

    /** incorporation steps to be executed when running in legacy mode */
    EnumSet<IncorporationStep> incorporationStepsLegacy = EnumSet.of(IncorporationStep.EQ_CHECK_LEGACY);

    /** incorporation steps to be executed when running in graph mode */
    EnumSet<IncorporationStep> incorporationStepsGraph =
            EnumSet.complementOf(EnumSet.of(IncorporationStep.EQ_CHECK_LEGACY));

    /**
     * Three kinds of basic operation are supported as part of an incorporation step:
     * (i) subtype check, (ii) same type check and (iii) bound addition (either
     * upper/lower/eq bound).
     */
    enum IncorporationBinaryOpKind {
        IS_SUBTYPE() {
            @Override
            boolean apply(Type op1, Type op2, Warner warn, Types types) {
                return types.isSubtypeUnchecked(op1, op2, warn);
            }
        },
        IS_SAME_TYPE() {
            @Override
            boolean apply(Type op1, Type op2, Warner warn, Types types) {
                return types.isSameType(op1, op2);
            }
        },
        ADD_UPPER_BOUND() {
            @Override
            boolean apply(Type op1, Type op2, Warner warn, Types types) {
                UndetVar uv = (UndetVar)op1;
                uv.addBound(InferenceBound.UPPER, op2, types);
                return true;
            }
        },
        ADD_LOWER_BOUND() {
            @Override
            boolean apply(Type op1, Type op2, Warner warn, Types types) {
                UndetVar uv = (UndetVar)op1;
                uv.addBound(InferenceBound.LOWER, op2, types);
                return true;
            }
        },
        ADD_EQ_BOUND() {
            @Override
            boolean apply(Type op1, Type op2, Warner warn, Types types) {
                UndetVar uv = (UndetVar)op1;
                uv.addBound(InferenceBound.EQ, op2, types);
                return true;
            }
        };

        abstract boolean apply(Type op1, Type op2, Warner warn, Types types);
    }

    /**
     * This class encapsulates a basic incorporation operation; incorporation
     * operations takes two type operands and a kind. Each operation performed
     * during an incorporation round is stored in a cache, so that operations
     * are not executed unnecessarily (which would potentially lead to adding
     * same bounds over and over).
     */
    class IncorporationBinaryOp {

        IncorporationBinaryOpKind opKind;
        Type op1;
        Type op2;

        IncorporationBinaryOp(IncorporationBinaryOpKind opKind, Type op1, Type op2) {
            this.opKind = opKind;
            this.op1 = op1;
            this.op2 = op2;
        }

        @Override
        public boolean equals(Object o) {
            if (!(o instanceof IncorporationBinaryOp)) {
                return false;
            } else {
                IncorporationBinaryOp that = (IncorporationBinaryOp)o;
                return opKind == that.opKind &&
                        types.isSameType(op1, that.op1, true) &&
                        types.isSameType(op2, that.op2, true);
            }
        }

        @Override
        public int hashCode() {
            int result = opKind.hashCode();
            result *= 127;
            result += types.hashCode(op1);
            result *= 127;
            result += types.hashCode(op2);
            return result;
        }

        boolean apply(Warner warn) {
            return opKind.apply(op1, op2, warn, types);
        }
    }

    /** an incorporation cache keeps track of all executed incorporation-related operations */
    Map<IncorporationBinaryOp, Boolean> incorporationCache =
            new HashMap<IncorporationBinaryOp, Boolean>();

    /**
     * Make sure that the upper bounds we got so far lead to a solvable inference
     * variable by making sure that a glb exists.
     */
    void checkCompatibleUpperBounds(UndetVar uv, InferenceContext inferenceContext) {
        List<Type> hibounds =
                Type.filter(uv.getBounds(InferenceBound.UPPER), new BoundFilter(inferenceContext));
        Type hb = null;
        if (hibounds.isEmpty())
            hb = syms.objectType;
        else if (hibounds.tail.isEmpty())
            hb = hibounds.head;
        else
            hb = types.glb(hibounds);
        if (hb == null || hb.isErroneous())
            reportBoundError(uv, BoundErrorKind.BAD_UPPER);
    }
    //where
        protected static class BoundFilter implements Filter<Type> {

            InferenceContext inferenceContext;

            public BoundFilter(InferenceContext inferenceContext) {
                this.inferenceContext = inferenceContext;
            }

            @Override
            public boolean accepts(Type t) {
                return !t.isErroneous() && !inferenceContext.free(t) &&
                        !t.hasTag(BOT);
            }
        };

    /**
     * This enumeration defines all possible bound-checking related errors.
     */
    enum BoundErrorKind {
        /**
         * The (uninstantiated) inference variable has incompatible upper bounds.
         */
        BAD_UPPER() {
            @Override
            InapplicableMethodException setMessage(InferenceException ex, UndetVar uv) {
                return ex.setMessage("incompatible.upper.bounds", uv.qtype,
                        uv.getBounds(InferenceBound.UPPER));
            }
        },
        /**
         * An equality constraint is not compatible with an upper bound.
         */
        BAD_EQ_UPPER() {
            @Override
            InapplicableMethodException setMessage(InferenceException ex, UndetVar uv) {
                return ex.setMessage("incompatible.eq.upper.bounds", uv.qtype,
                        uv.getBounds(InferenceBound.EQ), uv.getBounds(InferenceBound.UPPER));
            }
        },
        /**
         * An equality constraint is not compatible with a lower bound.
         */
        BAD_EQ_LOWER() {
            @Override
            InapplicableMethodException setMessage(InferenceException ex, UndetVar uv) {
                return ex.setMessage("incompatible.eq.lower.bounds", uv.qtype,
                        uv.getBounds(InferenceBound.EQ), uv.getBounds(InferenceBound.LOWER));
            }
        },
        /**
         * Instantiated inference variable is not compatible with an upper bound.
         */
        UPPER() {
            @Override
            InapplicableMethodException setMessage(InferenceException ex, UndetVar uv) {
                return ex.setMessage("inferred.do.not.conform.to.upper.bounds", uv.inst,
                        uv.getBounds(InferenceBound.UPPER));
            }
        },
        /**
         * Instantiated inference variable is not compatible with a lower bound.
         */
        LOWER() {
            @Override
            InapplicableMethodException setMessage(InferenceException ex, UndetVar uv) {
                return ex.setMessage("inferred.do.not.conform.to.lower.bounds", uv.inst,
                        uv.getBounds(InferenceBound.LOWER));
            }
        },
        /**
         * Instantiated inference variable is not compatible with an equality constraint.
         */
        EQ() {
            @Override
            InapplicableMethodException setMessage(InferenceException ex, UndetVar uv) {
                return ex.setMessage("inferred.do.not.conform.to.eq.bounds", uv.inst,
                        uv.getBounds(InferenceBound.EQ));
            }
        };

        abstract InapplicableMethodException setMessage(InferenceException ex, UndetVar uv);
    }

    /**
     * Report a bound-checking error of given kind
     */
    void reportBoundError(UndetVar uv, BoundErrorKind bk) {
        throw bk.setMessage(inferenceException, uv);
    }
    // </editor-fold>

    // <editor-fold defaultstate="collapsed" desc="Inference engine">
    /**
     * Graph inference strategy - act as an input to the inference solver; a strategy is
     * composed of two ingredients: (i) find a node to solve in the inference graph,
     * and (ii) tell th engine when we are done fixing inference variables
     */
    interface GraphStrategy {

        /**
         * A NodeNotFoundException is thrown whenever an inference strategy fails
         * to pick the next node to solve in the inference graph.
         */
        public static class NodeNotFoundException extends RuntimeException {
            private static final long serialVersionUID = 0;

            InferenceGraph graph;

            public NodeNotFoundException(InferenceGraph graph) {
                this.graph = graph;
            }
        }
        /**
         * Pick the next node (leaf) to solve in the graph
         */
        Node pickNode(InferenceGraph g) throws NodeNotFoundException;
        /**
         * Is this the last step?
         */
        boolean done();
    }

    /**
     * Simple solver strategy class that locates all leaves inside a graph
     * and picks the first leaf as the next node to solve
     */
    abstract class LeafSolver implements GraphStrategy {
        public Node pickNode(InferenceGraph g) {
            if (g.nodes.isEmpty()) {
                //should not happen
                throw new NodeNotFoundException(g);
            };
            return g.nodes.get(0);
        }

        boolean isSubtype(Type s, Type t, Warner warn, Infer infer) {
            return doIncorporationOp(IncorporationBinaryOpKind.IS_SUBTYPE, s, t, warn, infer);
        }

        boolean isSameType(Type s, Type t, Infer infer) {
            return doIncorporationOp(IncorporationBinaryOpKind.IS_SAME_TYPE, s, t, null, infer);
        }

        void addBound(InferenceBound ib, UndetVar uv, Type b, Infer infer) {
            doIncorporationOp(opFor(ib), uv, b, null, infer);
        }

        IncorporationBinaryOpKind opFor(InferenceBound boundKind) {
            switch (boundKind) {
                case EQ:
                    return IncorporationBinaryOpKind.ADD_EQ_BOUND;
                case LOWER:
                    return IncorporationBinaryOpKind.ADD_LOWER_BOUND;
                case UPPER:
                    return IncorporationBinaryOpKind.ADD_UPPER_BOUND;
                default:
                    Assert.error("Can't get here!");
                    return null;
            }
        }

        boolean doIncorporationOp(IncorporationBinaryOpKind opKind, Type op1, Type op2, Warner warn, Infer infer) {
            IncorporationBinaryOp newOp = infer.new IncorporationBinaryOp(opKind, op1, op2);
            Boolean res = infer.incorporationCache.get(newOp);
            if (res == null) {
                infer.incorporationCache.put(newOp, res = newOp.apply(warn));
            }
            return res;
        }
    }

    /**
     * This solver uses an heuristic to pick the best leaf - the heuristic
     * tries to select the node that has maximal probability to contain one
     * or more inference variables in a given list
     */
    abstract class BestLeafSolver extends LeafSolver {

        /** list of ivars of which at least one must be solved */
        List<Type> varsToSolve;

        BestLeafSolver(List<Type> varsToSolve) {
            this.varsToSolve = varsToSolve;
        }

        /**
         * Computes a path that goes from a given node to the leafs in the graph.
         * Typically this will start from a node containing a variable in
         * {@code varsToSolve}. For any given path, the cost is computed as the total
         * number of type-variables that should be eagerly instantiated across that path.
         */
        Pair<List computeTreeToLeafs(Node n) {
            Pair<List cachedPath = treeCache.get(n);
            if (cachedPath == null) {
                //cache miss
                if (n.isLeaf()) {
                    //if leaf, stop
                    cachedPath = new Pair<List(List.of(n), n.data.length());
                } else {
                    //if non-leaf, proceed recursively
                    Pair<List path = new Pair, Integer>(List.of(n), n.data.length());
                    for (Node n2 : n.getAllDependencies()) {
                        if (n2 == n) continue;
                        Pair<List subpath = computeTreeToLeafs(n2);
                        path = new Pair<List(
                                path.fst.prependList(subpath.fst),
                                path.snd + subpath.snd);
                    }
                    cachedPath = path;
                }
                //save results in cache
                treeCache.put(n, cachedPath);
            }
            return cachedPath;
        }

        /** cache used to avoid redundant computation of tree costs */
        final Map<Node, Pair> treeCache =
                new HashMap<Node, Pair>();

        /** constant value used to mark non-existent paths */
        final Pair<List noPath =
                new Pair<List(null, Integer.MAX_VALUE);

        /**
         * Pick the leaf that minimize cost
         */
        @Override
        public Node pickNode(final InferenceGraph g) {
            treeCache.clear(); //graph changes at every step - cache must be cleared
            Pair<List bestPath = noPath;
            for (Node n : g.nodes) {
                if (!Collections.disjoint(n.data, varsToSolve)) {
                    Pair<List path = computeTreeToLeafs(n);
                    //discard all paths containing at least a node in the
                    //closure computed above
                    if (path.snd < bestPath.snd) {
                        bestPath = path;
                    }
                }
            }
            if (bestPath == noPath) {
                //no path leads there
                throw new NodeNotFoundException(g);
            }
            return bestPath.fst.head;
        }
    }

    /**
     * The inference process can be thought of as a sequence of steps. Each step
     * instantiates an inference variable using a subset of the inference variable
     * bounds, if certain condition are met. Decisions such as the sequence in which
     * steps are applied, or which steps are to be applied are left to the inference engine.
     */
    enum InferenceStep {

        /**
         * Instantiate an inference variables using one of its (ground) equality
         * constraints
         */
        EQ(InferenceBound.EQ) {
            @Override
            Type solve(UndetVar uv, InferenceContext inferenceContext) {
                return filterBounds(uv, inferenceContext).head;
            }
        },
        /**
         * Instantiate an inference variables using its (ground) lower bounds. Such
         * bounds are merged together using lub().
         */
        LOWER(InferenceBound.LOWER) {
            @Override
            Type solve(UndetVar uv, InferenceContext inferenceContext) {
                Infer infer = inferenceContext.infer();
                List<Type> lobounds = filterBounds(uv, inferenceContext);
                //note: lobounds should have at least one element
                Type owntype = lobounds.tail.tail == null  ? lobounds.head : infer.types.lub(lobounds);
                if (owntype.isPrimitive() || owntype.hasTag(ERROR)) {
                    throw infer.inferenceException
                        .setMessage("no.unique.minimal.instance.exists",
                                    uv.qtype, lobounds);
                } else {
                    return owntype;
                }
            }
        },
        /**
         * Infer uninstantiated/unbound inference variables occurring in 'throws'
         * clause as RuntimeException
         */
        THROWS(InferenceBound.UPPER) {
            @Override
            public boolean accepts(UndetVar t, InferenceContext inferenceContext) {
                if ((t.qtype.tsym.flags() & Flags.THROWS) == 0) {
                    //not a throws undet var
                    return false;
                }
                if (t.getBounds(InferenceBound.EQ, InferenceBound.LOWER, InferenceBound.UPPER)
                            .diff(t.getDeclaredBounds()).nonEmpty()) {
                    //not an unbounded undet var
                    return false;
                }
                Infer infer = inferenceContext.infer();
                for (Type db : t.getDeclaredBounds()) {
                    if (t.isInterface()) continue;
                    if (infer.types.asSuper(infer.syms.runtimeExceptionType, db.tsym) != null) {
                        //declared bound is a supertype of RuntimeException
                        return true;
                    }
                }
                //declared bound is more specific then RuntimeException - give up
                return false;
            }

            @Override
            Type solve(UndetVar uv, InferenceContext inferenceContext) {
                return inferenceContext.infer().syms.runtimeExceptionType;
            }
        },
        /**
         * Instantiate an inference variables using its (ground) upper bounds. Such
         * bounds are merged together using glb().
         */
        UPPER(InferenceBound.UPPER) {
            @Override
            Type solve(UndetVar uv, InferenceContext inferenceContext) {
                Infer infer = inferenceContext.infer();
                List<Type> hibounds = filterBounds(uv, inferenceContext);
                //note: lobounds should have at least one element
                Type owntype = hibounds.tail.tail == null  ? hibounds.head : infer.types.glb(hibounds);
                if (owntype.isPrimitive() || owntype.hasTag(ERROR)) {
                    throw infer.inferenceException
                        .setMessage("no.unique.maximal.instance.exists",
                                    uv.qtype, hibounds);
                } else {
                    return owntype;
                }
            }
        },
        /**
         * Like the former; the only difference is that this step can only be applied
         * if all upper bounds are ground.
         */
        UPPER_LEGACY(InferenceBound.UPPER) {
            @Override
            public boolean accepts(UndetVar t, InferenceContext inferenceContext) {
                return !inferenceContext.free(t.getBounds(ib)) && !t.isCaptured();
            }

            @Override
            Type solve(UndetVar uv, InferenceContext inferenceContext) {
                return UPPER.solve(uv, inferenceContext);
            }
        },
        /**
         * Like the former; the only difference is that this step can only be applied
         * if all upper/lower bounds are ground.
         */
        CAPTURED(InferenceBound.UPPER) {
            @Override
            public boolean accepts(UndetVar t, InferenceContext inferenceContext) {
                return t.isCaptured() &&
                        !inferenceContext.free(t.getBounds(InferenceBound.UPPER, InferenceBound.LOWER));
            }

            @Override
            Type solve(UndetVar uv, InferenceContext inferenceContext) {
                Infer infer = inferenceContext.infer();
                Type upper = UPPER.filterBounds(uv, inferenceContext).nonEmpty() ?
                        UPPER.solve(uv, inferenceContext) :
                        infer.syms.objectType;
                Type lower = LOWER.filterBounds(uv, inferenceContext).nonEmpty() ?
                        LOWER.solve(uv, inferenceContext) :
                        infer.syms.botType;
                CapturedType prevCaptured = (CapturedType)uv.qtype;
                return new CapturedType(prevCaptured.tsym.name, prevCaptured.tsym.owner, upper, lower, prevCaptured.wildcard);
            }
        };

        final InferenceBound ib;

        InferenceStep(InferenceBound ib) {
            this.ib = ib;
        }

        /**
         * Find an instantiated type for a given inference variable within
         * a given inference context
         */
        abstract Type solve(UndetVar uv, InferenceContext inferenceContext);

        /**
         * Can the inference variable be instantiated using this step?
         */
        public boolean accepts(UndetVar t, InferenceContext inferenceContext) {
            return filterBounds(t, inferenceContext).nonEmpty() && !t.isCaptured();
        }

        /**
         * Return the subset of ground bounds in a given bound set (i.e. eq/lower/upper)
         */
        List<Type> filterBounds(UndetVar uv, InferenceContext inferenceContext) {
            return Type.filter(uv.getBounds(ib), new BoundFilter(inferenceContext));
        }
    }

    /**
     * This enumeration defines the sequence of steps to be applied when the
     * solver works in legacy mode. The steps in this enumeration reflect
     * the behavior of old inference routine (see JLS SE 7 15.12.2.7/15.12.2.8).
     */
    enum LegacyInferenceSteps {

        EQ_LOWER(EnumSet.of(InferenceStep.EQ, InferenceStep.LOWER)),
        EQ_UPPER(EnumSet.of(InferenceStep.EQ, InferenceStep.UPPER_LEGACY));

        final EnumSet<InferenceStep> steps;

        LegacyInferenceSteps(EnumSet<InferenceStep> steps) {
            this.steps = steps;
        }
    }

    /**
     * This enumeration defines the sequence of steps to be applied when the
     * graph solver is used. This order is defined so as to maximize compatibility
     * w.r.t. old inference routine (see JLS SE 7 15.12.2.7/15.12.2.8).
     */
    enum GraphInferenceSteps {

        EQ(EnumSet.of(InferenceStep.EQ)),
        EQ_LOWER(EnumSet.of(InferenceStep.EQ, InferenceStep.LOWER)),
        EQ_LOWER_THROWS_UPPER_CAPTURED(EnumSet.of(InferenceStep.EQ, InferenceStep.LOWER, InferenceStep.UPPER, InferenceStep.THROWS, InferenceStep.CAPTURED));

        final EnumSet<InferenceStep> steps;

        GraphInferenceSteps(EnumSet<InferenceStep> steps) {
            this.steps = steps;
        }
    }

    /**
     * There are two kinds of dependencies between inference variables. The basic
     * kind of dependency (or bound dependency) arises when a variable mention
     * another variable in one of its bounds. There's also a more subtle kind
     * of dependency that arises when a variable 'might' lead to better constraints
     * on another variable (this is typically the case with variables holding up
     * stuck expressions).
     */
    enum DependencyKind implements GraphUtils.DependencyKind {

        /** bound dependency */
        BOUND("dotted"),
        /** stuck dependency */
        STUCK("dashed");

        final String dotSyle;

        private DependencyKind(String dotSyle) {
            this.dotSyle = dotSyle;
        }

        @Override
        public String getDotStyle() {
            return dotSyle;
        }
    }

    /**
     * This is the graph inference solver - the solver organizes all inference variables in
     * a given inference context by bound dependencies - in the general case, such dependencies
     * would lead to a cyclic directed graph (hence the name); the dependency info is used to build
     * an acyclic graph, where all cyclic variables are bundled together. An inference
     * step corresponds to solving a node in the acyclic graph - this is done by
     * relying on a given strategy (see GraphStrategy).
     */
    class GraphSolver {

        InferenceContext inferenceContext;
        Map<Type, Set stuckDeps;
        Warner warn;

        GraphSolver(InferenceContext inferenceContext, Map<Type, Set stuckDeps, Warner warn) {
            this.inferenceContext = inferenceContext;
            this.stuckDeps = stuckDeps;
            this.warn = warn;
        }

        /**
         * Solve variables in a given inference context. The amount of variables
         * to be solved, and the way in which the underlying acyclic graph is explored
         * depends on the selected solver strategy.
         */
        void solve(GraphStrategy sstrategy) {
            checkWithinBounds(inferenceContext, warn); //initial propagation of bounds
            InferenceGraph inferenceGraph = new InferenceGraph(stuckDeps);
            while (!sstrategy.done()) {
                InferenceGraph.Node nodeToSolve = sstrategy.pickNode(inferenceGraph);
                List<Type> varsToSolve = List.from(nodeToSolve.data);
                List<Type> saved_undet = inferenceContext.save();
                try {
                    //repeat until all variables are solved
                    outer: while (Type.containsAny(inferenceContext.restvars(), varsToSolve)) {
                        //for each inference phase
                        for (GraphInferenceSteps step : GraphInferenceSteps.values()) {
                            if (inferenceContext.solveBasic(varsToSolve, step.steps)) {
                                checkWithinBounds(inferenceContext, warn);
                                continue outer;
                            }
                        }
                        //no progress
                        throw inferenceException.setMessage();
                    }
                }
                catch (InferenceException ex) {
                    //did we fail because of interdependent ivars?
                    inferenceContext.rollback(saved_undet);
                    instantiateAsUninferredVars(varsToSolve, inferenceContext);
                    checkWithinBounds(inferenceContext, warn);
                }
                inferenceGraph.deleteNode(nodeToSolve);
            }
        }

        /**
         * The dependencies between the inference variables that need to be solved
         * form a (possibly cyclic) graph. This class reduces the original dependency graph
         * to an acyclic version, where cyclic nodes are folded into a single 'super node'.
         */
        class InferenceGraph {

            /**
             * This class represents a node in the graph. Each node corresponds
             * to an inference variable and has edges (dependencies) on other
             * nodes. The node defines an entry point that can be used to receive
             * updates on the structure of the graph this node belongs to (used to
             * keep dependencies in sync).
             */
            class Node extends GraphUtils.TarjanNode<ListBuffer {

                /** map listing all dependencies (grouped by kind) */
                EnumMap<DependencyKind, Set deps;

                Node(Type ivar) {
                    super(ListBuffer.of(ivar));
                    this.deps = new EnumMap<DependencyKind, Set(DependencyKind.class);
                }

                @Override
                public GraphUtils.DependencyKind[] getSupportedDependencyKinds() {
                    return DependencyKind.values();
                }

                @Override
                public String getDependencyName(GraphUtils.Node<ListBuffer to, GraphUtils.DependencyKind dk) {
                    if (dk == DependencyKind.STUCK) return "";
                    else {
                        StringBuilder buf = new StringBuilder();
                        String sep = "";
                        for (Type from : data) {
                            UndetVar uv = (UndetVar)inferenceContext.asFree(from);
                            for (Type bound : uv.getBounds(InferenceBound.values())) {
                                if (bound.containsAny(List.from(to.data))) {
                                    buf.append(sep);
                                    buf.append(bound);
                                    sep = ",";
                                }
                            }
                        }
                        return buf.toString();
                    }
                }

                @Override
                public Iterable<? extends Node> getAllDependencies() {
                    return getDependencies(DependencyKind.values());
                }

                @Override
                public Iterable<? extends TarjanNode> getDependenciesByKind(GraphUtils.DependencyKind dk) {
                    return getDependencies((DependencyKind)dk);
                }

                /**
                 * Retrieves all dependencies with given kind(s).
                 */
                protected Set<Node> getDependencies(DependencyKind... depKinds) {
                    Set<Node> buf = new LinkedHashSet();
                    for (DependencyKind dk : depKinds) {
                        Set<Node> depsByKind = deps.get(dk);
                        if (depsByKind != null) {
                            buf.addAll(depsByKind);
                        }
                    }
                    return buf;
                }

                /**
                 * Adds dependency with given kind.
                 */
                protected void addDependency(DependencyKind dk, Node depToAdd) {
                    Set<Node> depsByKind = deps.get(dk);
                    if (depsByKind == null) {
                        depsByKind = new LinkedHashSet<Node>();
                        deps.put(dk, depsByKind);
                    }
                    depsByKind.add(depToAdd);
                }

                /**
                 * Add multiple dependencies of same given kind.
                 */
                protected void addDependencies(DependencyKind dk, Set<Node> depsToAdd) {
                    for (Node n : depsToAdd) {
                        addDependency(dk, n);
                    }
                }

                /**
                 * Remove a dependency, regardless of its kind.
                 */
                protected Set<DependencyKind> removeDependency(Node n) {
                    Set<DependencyKind> removedKinds = new HashSet<>();
                    for (DependencyKind dk : DependencyKind.values()) {
                        Set<Node> depsByKind = deps.get(dk);
                        if (depsByKind == null) continue;
                        if (depsByKind.remove(n)) {
                            removedKinds.add(dk);
                        }
                    }
                    return removedKinds;
                }

                /**
                 * Compute closure of a give node, by recursively walking
                 * through all its dependencies (of given kinds)
                 */
                protected Set<Node> closure(DependencyKind... depKinds) {
                    boolean progress = true;
                    Set<Node> closure = new HashSet();
                    closure.add(this);
                    while (progress) {
                        progress = false;
                        for (Node n1 : new HashSet<Node>(closure)) {
                            progress = closure.addAll(n1.getDependencies(depKinds));
                        }
                    }
                    return closure;
                }

                /**
                 * Is this node a leaf? This means either the node has no dependencies,
                 * or it just has self-dependencies.
                 */
                protected boolean isLeaf() {
                    //no deps, or only one self dep
                    Set<Node> allDeps = getDependencies(DependencyKind.BOUND, DependencyKind.STUCK);
                    if (allDeps.isEmpty()) return true;
                    for (Node n : allDeps) {
                        if (n != this) {
                            return false;
                        }
                    }
                    return true;
                }

                /**
                 * Merge this node with another node, acquiring its dependencies.
                 * This routine is used to merge all cyclic node together and
                 * form an acyclic graph.
                 */
                protected void mergeWith(List<? extends Node> nodes) {
                    for (Node n : nodes) {
                        Assert.check(n.data.length() == 1, "Attempt to merge a compound node!");
                        data.appendList(n.data);
                        for (DependencyKind dk : DependencyKind.values()) {
                            addDependencies(dk, n.getDependencies(dk));
                        }
                    }
                    //update deps
                    EnumMap<DependencyKind, Set deps2 = new EnumMap>(DependencyKind.class);
                    for (DependencyKind dk : DependencyKind.values()) {
                        for (Node d : getDependencies(dk)) {
                            Set<Node> depsByKind = deps2.get(dk);
                            if (depsByKind == null) {
                                depsByKind = new LinkedHashSet<Node>();
                                deps2.put(dk, depsByKind);
                            }
                            if (data.contains(d.data.first())) {
                                depsByKind.add(this);
                            } else {
                                depsByKind.add(d);
                            }
                        }
                    }
                    deps = deps2;
                }

                /**
                 * Notify all nodes that something has changed in the graph
                 * topology.
                 */
                private void graphChanged(Node from, Node to) {
                    for (DependencyKind dk : removeDependency(from)) {
                        if (to != null) {
                            addDependency(dk, to);
                        }
                    }
                }
            }

            /** the nodes in the inference graph */
            ArrayList<Node> nodes;

            InferenceGraph(Map<Type, Set optDeps) {
                initNodes(optDeps);
            }

            /**
             * Basic lookup helper for retrieving a graph node given an inference
             * variable type.
             */
            public Node findNode(Type t) {
                for (Node n : nodes) {
                    if (n.data.contains(t)) {
                        return n;
                    }
                }
                return null;
            }

            /**
             * Delete a node from the graph. This update the underlying structure
             * of the graph (including dependencies) via listeners updates.
             */
            public void deleteNode(Node n) {
                Assert.check(nodes.contains(n));
                nodes.remove(n);
                notifyUpdate(n, null);
            }

            /**
             * Notify all nodes of a change in the graph. If the target node is
             * {@code null} the source node is assumed to be removed.
             */
            void notifyUpdate(Node from, Node to) {
                for (Node n : nodes) {
                    n.graphChanged(from, to);
                }
            }

            /**
             * Create the graph nodes. First a simple node is created for every inference
             * variables to be solved. Then Tarjan is used to found all connected components
             * in the graph. For each component containing more than one node, a super node is
             * created, effectively replacing the original cyclic nodes.
             */
            void initNodes(Map<Type, Set stuckDeps) {
                //add nodes
                nodes = new ArrayList<Node>();
                for (Type t : inferenceContext.restvars()) {
                    nodes.add(new Node(t));
                }
                //add dependencies
                for (Node n_i : nodes) {
                    Type i = n_i.data.first();
                    Set<Type> optDepsByNode = stuckDeps.get(i);
                    for (Node n_j : nodes) {
                        Type j = n_j.data.first();
                        UndetVar uv_i = (UndetVar)inferenceContext.asFree(i);
                        if (Type.containsAny(uv_i.getBounds(InferenceBound.values()), List.of(j))) {
                            //update i's bound dependencies
                            n_i.addDependency(DependencyKind.BOUND, n_j);
                        }
                        if (optDepsByNode != null && optDepsByNode.contains(j)) {
                            //update i's stuck dependencies
                            n_i.addDependency(DependencyKind.STUCK, n_j);
                        }
                    }
                }
                //merge cyclic nodes
                ArrayList<Node> acyclicNodes = new ArrayList();
                for (List<? extends Node> conSubGraph : GraphUtils.tarjan(nodes)) {
                    if (conSubGraph.length() > 1) {
                        Node root = conSubGraph.head;
                        root.mergeWith(conSubGraph.tail);
                        for (Node n : conSubGraph) {
                            notifyUpdate(n, root);
                        }
                    }
                    acyclicNodes.add(conSubGraph.head);
                }
                nodes = acyclicNodes;
            }

            /**
             * Debugging: dot representation of this graph
             */
            String toDot() {
                StringBuilder buf = new StringBuilder();
                for (Type t : inferenceContext.undetvars) {
                    UndetVar uv = (UndetVar)t;
                    buf.append(String.format("var %s - upper bounds = %s, lower bounds = %s, eq bounds = %s\\n",
                            uv.qtype, uv.getBounds(InferenceBound.UPPER), uv.getBounds(InferenceBound.LOWER),
                            uv.getBounds(InferenceBound.EQ)));
                }
                return GraphUtils.toDot(nodes, "inferenceGraph" + hashCode(), buf.toString());
            }
        }
    }
    // </editor-fold>

    // <editor-fold defaultstate="collapsed" desc="Inference context">
    /**
     * Functional interface for defining inference callbacks. Certain actions
     * (i.e. subtyping checks) might need to be redone after all inference variables
     * have been fixed.
     */
    interface FreeTypeListener {
        void typesInferred(InferenceContext inferenceContext);
    }

    /**
     * An inference context keeps track of the set of variables that are free
     * in the current context. It provides utility methods for opening/closing
     * types to their corresponding free/closed forms. It also provide hooks for
     * attaching deferred post-inference action (see PendingCheck). Finally,
     * it can be used as an entry point for performing upper/lower bound inference
     * (see InferenceKind).
     */
     class InferenceContext {

        /** list of inference vars as undet vars */
        List<Type> undetvars;

        /** list of inference vars in this context */
        List<Type> inferencevars;

        java.util.Map<FreeTypeListener, List freeTypeListeners =
                new java.util.HashMap<FreeTypeListener, List();

        List<FreeTypeListener> freetypeListeners = List.nil();

        public InferenceContext(List<Type> inferencevars) {
            this.undetvars = Type.map(inferencevars, fromTypeVarFun);
            this.inferencevars = inferencevars;
        }
        //where
            Mapping fromTypeVarFun = new Mapping("fromTypeVarFunWithBounds") {
                // mapping that turns inference variables into undet vars
                public Type apply(Type t) {
                    if (t.hasTag(TYPEVAR)) {
                        TypeVar tv = (TypeVar)t;
                        if (tv.isCaptured()) {
                            return new CapturedUndetVar((CapturedType)tv, types);
                        } else {
                            return new UndetVar(tv, types);
                        }
                    } else {
                        return t.map(this);
                    }
                }
            };

        /**
         * add a new inference var to this inference context
         */
        void addVar(TypeVar t) {
            this.undetvars = this.undetvars.prepend(fromTypeVarFun.apply(t));
            this.inferencevars = this.inferencevars.prepend(t);
        }

        /**
         * returns the list of free variables (as type-variables) in this
         * inference context
         */
        List<Type> inferenceVars() {
            return inferencevars;
        }

        /**
         * returns the list of uninstantiated variables (as type-variables) in this
         * inference context
         */
        List<Type> restvars() {
            return filterVars(new Filter<UndetVar>() {
                public boolean accepts(UndetVar uv) {
                    return uv.inst == null;
                }
            });
        }

        /**
         * returns the list of instantiated variables (as type-variables) in this
         * inference context
         */
        List<Type> instvars() {
            return filterVars(new Filter<UndetVar>() {
                public boolean accepts(UndetVar uv) {
                    return uv.inst != null;
                }
            });
        }

        /**
         * Get list of bounded inference variables (where bound is other than
         * declared bounds).
         */
        final List<Type> boundedVars() {
            return filterVars(new Filter<UndetVar>() {
                public boolean accepts(UndetVar uv) {
                    return uv.getBounds(InferenceBound.UPPER)
                             .diff(uv.getDeclaredBounds())
                             .appendList(uv.getBounds(InferenceBound.EQ, InferenceBound.LOWER)).nonEmpty();
                }
            });
        }

        private List<Type> filterVars(Filter fu) {
            ListBuffer<Type> res = new ListBuffer<>();
            for (Type t : undetvars) {
                UndetVar uv = (UndetVar)t;
                if (fu.accepts(uv)) {
                    res.append(uv.qtype);
                }
            }
            return res.toList();
        }

        /**
         * is this type free?
         */
        final boolean free(Type t) {
            return t.containsAny(inferencevars);
        }

        final boolean free(List<Type> ts) {
            for (Type t : ts) {
                if (free(t)) return true;
            }
            return false;
        }

        /**
         * Returns a list of free variables in a given type
         */
        final List<Type> freeVarsIn(Type t) {
            ListBuffer<Type> buf = new ListBuffer<>();
            for (Type iv : inferenceVars()) {
                if (t.contains(iv)) {
                    buf.add(iv);
                }
            }
            return buf.toList();
        }

        final List<Type> freeVarsIn(List ts) {
            ListBuffer<Type> buf = new ListBuffer<>();
            for (Type t : ts) {
                buf.appendList(freeVarsIn(t));
            }
            ListBuffer<Type> buf2 = new ListBuffer<>();
            for (Type t : buf) {
                if (!buf2.contains(t)) {
                    buf2.add(t);
                }
            }
            return buf2.toList();
        }

        /**
         * Replace all free variables in a given type with corresponding
         * undet vars (used ahead of subtyping/compatibility checks to allow propagation
         * of inference constraints).
         */
        final Type asFree(Type t) {
            return types.subst(t, inferencevars, undetvars);
        }

        final List<Type> asFree(List ts) {
            ListBuffer<Type> buf = new ListBuffer<>();
            for (Type t : ts) {
                buf.append(asFree(t));
            }
            return buf.toList();
        }

        List<Type> instTypes() {
            ListBuffer<Type> buf = new ListBuffer<>();
            for (Type t : undetvars) {
                UndetVar uv = (UndetVar)t;
                buf.append(uv.inst != null ? uv.inst : uv.qtype);
            }
            return buf.toList();
        }

        /**
         * Replace all free variables in a given type with corresponding
         * instantiated types - if one or more free variable has not been
         * fully instantiated, it will still be available in the resulting type.
         */
        Type asInstType(Type t) {
            return types.subst(t, inferencevars, instTypes());
        }

        List<Type> asInstTypes(List ts) {
            ListBuffer<Type> buf = new ListBuffer<>();
            for (Type t : ts) {
                buf.append(asInstType(t));
            }
            return buf.toList();
        }

        /**
         * Add custom hook for performing post-inference action
         */
        void addFreeTypeListener(List<Type> types, FreeTypeListener ftl) {
            freeTypeListeners.put(ftl, freeVarsIn(types));
        }

        /**
         * Mark the inference context as complete and trigger evaluation
         * of all deferred checks.
         */
        void notifyChange() {
            notifyChange(inferencevars.diff(restvars()));
        }

        void notifyChange(List<Type> inferredVars) {
            InferenceException thrownEx = null;
            for (Map.Entry<FreeTypeListener, List entry :
                    new HashMap<FreeTypeListener, List(freeTypeListeners).entrySet()) {
                if (!Type.containsAny(entry.getValue(), inferencevars.diff(inferredVars))) {
                    try {
                        entry.getKey().typesInferred(this);
                        freeTypeListeners.remove(entry.getKey());
                    } catch (InferenceException ex) {
                        if (thrownEx == null) {
                            thrownEx = ex;
                        }
                    }
                }
            }
            //inference exception multiplexing - present any inference exception
            //thrown when processing listeners as a single one
            if (thrownEx != null) {
                throw thrownEx;
            }
        }

        /**
         * Save the state of this inference context
         */
        List<Type> save() {
            ListBuffer<Type> buf = new ListBuffer<>();
            for (Type t : undetvars) {
                UndetVar uv = (UndetVar)t;
                UndetVar uv2 = new UndetVar((TypeVar)uv.qtype, types);
                for (InferenceBound ib : InferenceBound.values()) {
                    for (Type b : uv.getBounds(ib)) {
                        uv2.addBound(ib, b, types);
                    }
                }
                uv2.inst = uv.inst;
                buf.add(uv2);
            }
            return buf.toList();
        }

        /**
         * Restore the state of this inference context to the previous known checkpoint
         */
        void rollback(List<Type> saved_undet) {
             Assert.check(saved_undet != null && saved_undet.length() == undetvars.length());
            //restore bounds (note: we need to preserve the old instances)
            for (Type t : undetvars) {
                UndetVar uv = (UndetVar)t;
                UndetVar uv_saved = (UndetVar)saved_undet.head;
                for (InferenceBound ib : InferenceBound.values()) {
                    uv.setBounds(ib, uv_saved.getBounds(ib));
                }
                uv.inst = uv_saved.inst;
                saved_undet = saved_undet.tail;
            }
        }

        /**
         * Copy variable in this inference context to the given context
         */
        void dupTo(final InferenceContext that) {
            that.inferencevars = that.inferencevars.appendList(inferencevars);
            that.undetvars = that.undetvars.appendList(undetvars);
            //set up listeners to notify original inference contexts as
            //propagated vars are inferred in new context
            for (Type t : inferencevars) {
                that.freeTypeListeners.put(new FreeTypeListener() {
                    public void typesInferred(InferenceContext inferenceContext) {
                        InferenceContext.this.notifyChange();
                    }
                }, List.of(t));
            }
        }

        private void solve(GraphStrategy ss, Warner warn) {
            solve(ss, new HashMap<Type, Set(), warn);
        }

        /**
         * Solve with given graph strategy.
         */
        private void solve(GraphStrategy ss, Map<Type, Set stuckDeps, Warner warn) {
            GraphSolver s = new GraphSolver(this, stuckDeps, warn);
            s.solve(ss);
        }

        /**
         * Solve all variables in this context.
         */
        public void solve(Warner warn) {
            solve(new LeafSolver() {
                public boolean done() {
                    return restvars().isEmpty();
                }
            }, warn);
        }

        /**
         * Solve all variables in the given list.
         */
        public void solve(final List<Type> vars, Warner warn) {
            solve(new BestLeafSolver(vars) {
                public boolean done() {
                    return !free(asInstTypes(vars));
                }
            }, warn);
        }

        /**
         * Solve at least one variable in given list.
         */
        public void solveAny(List<Type> varsToSolve, Map> optDeps, Warner warn) {
            solve(new BestLeafSolver(varsToSolve.intersect(restvars())) {
                public boolean done() {
                    return instvars().intersect(varsToSolve).nonEmpty();
                }
            }, optDeps, warn);
        }

        /**
         * Apply a set of inference steps
         */
        private boolean solveBasic(EnumSet<InferenceStep> steps) {
            return solveBasic(inferencevars, steps);
        }

        private boolean solveBasic(List<Type> varsToSolve, EnumSet steps) {
            boolean changed = false;
            for (Type t : varsToSolve.intersect(restvars())) {
                UndetVar uv = (UndetVar)asFree(t);
                for (InferenceStep step : steps) {
                    if (step.accepts(uv, this)) {
                        uv.inst = step.solve(uv, this);
                        changed = true;
                        break;
                    }
                }
            }
            return changed;
        }

        /**
         * Instantiate inference variables in legacy mode (JLS 15.12.2.7, 15.12.2.8).
         * During overload resolution, instantiation is done by doing a partial
         * inference process using eq/lower bound instantiation. During check,
         * we also instantiate any remaining vars by repeatedly using eq/upper
         * instantiation, until all variables are solved.
         */
        public void solveLegacy(boolean partial, Warner warn, EnumSet<InferenceStep> steps) {
            while (true) {
                boolean stuck = !solveBasic(steps);
                if (restvars().isEmpty() || partial) {
                    //all variables have been instantiated - exit
                    break;
                } else if (stuck) {
                    //some variables could not be instantiated because of cycles in
                    //upper bounds - provide a (possibly recursive) default instantiation
                    instantiateAsUninferredVars(restvars(), this);
                    break;
                } else {
                    //some variables have been instantiated - replace newly instantiated
                    //variables in remaining upper bounds and continue
                    for (Type t : undetvars) {
                        UndetVar uv = (UndetVar)t;
                        uv.substBounds(inferenceVars(), instTypes(), types);
                    }
                }
            }
            checkWithinBounds(this, warn);
        }

        private Infer infer() {
            //back-door to infer
            return Infer.this;
        }
    }

    final InferenceContext emptyContext = new InferenceContext(List.<Type>nil());
    // </editor-fold>
}

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