FunctionType.java

/*
 * Copyright 2013 The Closure Compiler Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package com.google.javascript.jscomp.newtypes;

import com.google.common.base.Preconditions;
import com.google.common.collect.ImmutableList;
import com.google.common.collect.ImmutableMap;
import com.google.common.collect.Iterables;
import com.google.common.collect.LinkedHashMultimap;
import com.google.common.collect.Multimap;
import java.util.Collection;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;
import java.util.Objects;

/**
 *
 * @author blickly@google.com (Ben Lickly)
 * @author dimvar@google.com (Dimitris Vardoulakis)
 */
public final class FunctionType {
  private final JSTypes commonTypes;
  private final ImmutableList<JSType> requiredFormals;
  private final ImmutableList<JSType> optionalFormals;
  private final JSType restFormals;
  private final JSType returnType;
  private final boolean isLoose;
  private final boolean isAbstract;
  private final ImmutableMap<String, JSType> outerVarPreconditions;
  // If this FunctionType is a constructor/interface, this field stores the
  // type of the instance.
  private final JSType nominalType;
  // If this FunctionType is a prototype method, this field stores the
  // type of the instance.
  private final JSType receiverType;
  // non-empty iff this function has an @template annotation
  private final ImmutableList<String> typeParameters;
  private static final boolean DEBUGGING = false;

  private FunctionType(
      JSTypes commonTypes,
      ImmutableList<JSType> requiredFormals,
      ImmutableList<JSType> optionalFormals,
      JSType restFormals,
      JSType retType,
      JSType nominalType,
      JSType receiverType,
      ImmutableMap<String, JSType> outerVars,
      ImmutableList<String> typeParameters,
      boolean isLoose,
      boolean isAbstract) {
    Preconditions.checkNotNull(commonTypes);
    this.commonTypes = commonTypes;
    this.requiredFormals = requiredFormals;
    this.optionalFormals = optionalFormals;
    this.restFormals = restFormals;
    this.returnType = retType;
    this.nominalType = nominalType;
    this.receiverType = receiverType;
    this.outerVarPreconditions = outerVars;
    this.typeParameters = typeParameters;
    this.isLoose = isLoose;
    this.isAbstract = isAbstract;
    checkValid();
  }

  // Only used to create TOP_FUNCTION and LOOSE_TOP_FUNCTION
  private FunctionType(JSTypes commonTypes, boolean isLoose) {
    Preconditions.checkNotNull(commonTypes);
    this.commonTypes = commonTypes;
    this.requiredFormals = null;
    this.optionalFormals = null;
    this.restFormals = null;
    this.returnType = null;
    this.nominalType = null;
    this.receiverType = null;
    this.outerVarPreconditions = null;
    this.typeParameters = ImmutableList.of();
    this.isLoose = isLoose;
    this.isAbstract = false;
  }

  void checkValid() {
    if (isTopFunction() || isQmarkFunction()) {
      return;
    }
    Preconditions.checkNotNull(requiredFormals,
        "null required formals for function: %s", this);
    for (JSType formal : requiredFormals) {
      Preconditions.checkNotNull(formal);
      // A loose function has bottom formals in the bwd direction of NTI.
      // See NTI#analyzeLooseCallNodeBwd.
      Preconditions.checkState(isLoose || !formal.isBottom());
    }
    Preconditions.checkNotNull(optionalFormals,
        "null optional formals for function: %s", this);
    for (JSType formal : optionalFormals) {
      Preconditions.checkNotNull(formal);
      Preconditions.checkState(!formal.isBottom());
    }
    Preconditions.checkState(restFormals == null || !restFormals.isBottom());
    Preconditions.checkNotNull(returnType);
  }

  JSTypes getCommonTypes() {
    return this.commonTypes;
  }

  public boolean isLoose() {
    return isLoose;
  }

  FunctionType withLoose() {
    if (isLoose()) {
      return this;
    }
    if (isTopFunction()) {
      return this.commonTypes.LOOSE_TOP_FUNCTION;
    }
    return new FunctionType(
        this.commonTypes,
        requiredFormals, optionalFormals, restFormals, returnType, nominalType,
        receiverType, outerVarPreconditions, typeParameters, true, isAbstract);
  }

  public boolean isAbstract() {
    return isAbstract;
  }

  public boolean isConstructorOfAbstractClass() {
    return isUniqueConstructor()
        && this.nominalType.getNominalTypeIfSingletonObj().isAbstractClass();
  }

  static FunctionType normalized(
      JSTypes commonTypes,
      List<JSType> requiredFormals,
      List<JSType> optionalFormals,
      JSType restFormals,
      JSType retType,
      JSType nominalType,
      JSType receiverType,
      Map<String, JSType> outerVars,
      ImmutableList<String> typeParameters,
      boolean isLoose,
      boolean isAbstract) {
    if (requiredFormals == null) {
      requiredFormals = ImmutableList.of();
    }
    if (optionalFormals == null) {
      optionalFormals = ImmutableList.of();
    }
    if (outerVars == null) {
      outerVars = ImmutableMap.of();
    }
    if (typeParameters == null) {
      typeParameters = ImmutableList.of();
    }
    if (restFormals != null) {
      // Remove trailing optional params w/ type equal to restFormals
      for (int i = optionalFormals.size() - 1; i >= 0; i--) {
        if (restFormals.equals(optionalFormals.get(i))) {
          optionalFormals.remove(i);
        } else {
          break;
        }
      }
    }
    return new FunctionType(
        commonTypes,
        ImmutableList.copyOf(requiredFormals),
        ImmutableList.copyOf(optionalFormals),
        restFormals, retType, nominalType, receiverType,
        ImmutableMap.copyOf(outerVars),
        typeParameters,
        isLoose,
        isAbstract);
  }

  static Map<String, FunctionType> createInitialFunctionTypes(JSTypes commonTypes) {
    LinkedHashMap<String, FunctionType> functions = new LinkedHashMap<>();
    functions.put(
        "QMARK_FUNCTION",
        FunctionType.normalized(
            commonTypes, null, null, commonTypes.UNKNOWN, commonTypes.UNKNOWN,
            null, null, null, null, true, false));
    functions.put(
        "BOTTOM_FUNCTION",
        FunctionType.normalized(
            commonTypes, null, null, null, commonTypes.BOTTOM, null, null, null, null, false,
            false));
    functions.put("TOP_FUNCTION", new FunctionType(commonTypes, false));
    functions.put("LOOSE_TOP_FUNCTION", new FunctionType(commonTypes, true));
    return functions;
  }

  public boolean isTopFunction() {
    return this == this.commonTypes.TOP_FUNCTION || this == this.commonTypes.LOOSE_TOP_FUNCTION;
  }

  private static NominalType getNominalTypeIfSingletonObj(JSType t) {
    return t == null ? null : t.getNominalTypeIfSingletonObj();
  }

  // Looser than the next two methods; also true for types like:
  // function(new:T) and function(new:(Foo|Bar))
  public boolean isSomeConstructorOrInterface() {
    return this.nominalType != null;
  }

  public boolean isUniqueConstructor() {
    NominalType nt = getNominalTypeIfSingletonObj(this.nominalType);
    return nt != null && nt.isClass();
  }

  public boolean isInterfaceDefinition() {
    NominalType nt = getNominalTypeIfSingletonObj(this.nominalType);
    return nt != null && nt.isInterface();
  }

  public JSType getSuperPrototype() {
    Preconditions.checkState(isUniqueConstructor());
    NominalType nt = getNominalTypeIfSingletonObj(this.nominalType);
    NominalType superClass = nt.getInstantiatedSuperclass();
    return superClass == null ? null : superClass.getPrototypePropertyOfCtor();
  }

  public boolean isQmarkFunction() {
    return this == this.commonTypes.QMARK_FUNCTION;
  }

  static boolean isInhabitable(FunctionType f) {
    return f == null || f != f.commonTypes.BOTTOM_FUNCTION;
  }

  public boolean hasRestFormals() {
    return restFormals != null;
  }

  public JSType getRestFormalsType() {
    Preconditions.checkNotNull(restFormals);
    return restFormals;
  }

  // 0-indexed
  // Returns null if argpos indexes past the arguments
  public JSType getFormalType(int argpos) {
    Preconditions.checkArgument(!isTopFunction());
    int numReqFormals = requiredFormals.size();
    if (argpos < numReqFormals) {
      Preconditions.checkState(null != requiredFormals.get(argpos));
      return requiredFormals.get(argpos);
    } else if (argpos < numReqFormals + optionalFormals.size()) {
      Preconditions.checkState(
          null != optionalFormals.get(argpos - numReqFormals));
      return optionalFormals.get(argpos - numReqFormals);
    } else {
      return restFormals;
    }
  }

  public JSType getReturnType() {
    Preconditions.checkArgument(!isTopFunction());
    return returnType;
  }

  public JSType getOuterVarPrecondition(String name) {
    Preconditions.checkArgument(!isTopFunction());
    return outerVarPreconditions.get(name);
  }

  public int getMinArity() {
    Preconditions.checkArgument(!isTopFunction());
    return requiredFormals.size();
  }

  public int getMaxArity() {
    Preconditions.checkArgument(!isTopFunction());
    if (restFormals != null) {
      return Integer.MAX_VALUE; // "Infinite" arity
    } else {
      return requiredFormals.size() + optionalFormals.size();
    }
  }

  public int getMaxArityWithoutRestFormals() {
    return requiredFormals.size() + optionalFormals.size();
  }

  public boolean isRequiredArg(int i) {
    return i < requiredFormals.size();
  }

  public boolean isOptionalArg(int i) {
    return i >= requiredFormals.size()
        && i < requiredFormals.size() + optionalFormals.size();
  }

  public JSType getInstanceTypeOfCtor() {
    if (!isGeneric()) {
      return this.nominalType;
    }
    return getNominalTypeIfSingletonObj(this.nominalType)
        .instantiateGenerics(this.commonTypes.MAP_TO_UNKNOWN).getInstanceAsJSType();
  }

  public JSType getThisType() {
    return this.receiverType != null ? this.receiverType : this.nominalType;
  }

  public FunctionType transformByCallProperty() {
    if (isTopFunction() || isQmarkFunction() || isLoose) {
      return this.commonTypes.QMARK_FUNCTION;
    }
    FunctionTypeBuilder builder = new FunctionTypeBuilder(this.commonTypes);
    builder.addReqFormal(fromReceiverToFirstFormal());
    for (JSType type : this.requiredFormals) {
      builder.addReqFormal(type);
    }
    for (JSType type : this.optionalFormals) {
      builder.addOptFormal(type);
    }
    builder.addRestFormals(this.restFormals);
    builder.addRetType(this.returnType);
    builder.addTypeParameters(this.typeParameters);
    builder.addAbstract(this.isAbstract);
    return builder.buildFunction();
  }

  // We only typecheck the receiver type for a .apply function. To typecheck all
  // arguments we either need tuple types or special handling in NTI to gather
  // the types inside the array.
  public FunctionType transformByApplyProperty() {
    if (isTopFunction() || isQmarkFunction() || isLoose) {
      return this.commonTypes.QMARK_FUNCTION;
    }
    if (isGeneric()) {
      return instantiateGenericsWithUnknown(this).transformByApplyProperty();
    }
    FunctionTypeBuilder builder = new FunctionTypeBuilder(this.commonTypes);
    builder.addReqFormal(fromReceiverToFirstFormal());
    builder.addOptFormal(JSType.join(
        this.commonTypes.getArrayInstance(), this.commonTypes.getArgumentsArrayType()));
    builder.addRetType(this.returnType);
    builder.addAbstract(this.isAbstract);
    return builder.buildFunction();
  }

  private JSType fromReceiverToFirstFormal() {
    if (this.receiverType == null) {
      return this.commonTypes.UNKNOWN;
    }
    NominalType nt = this.receiverType.getNominalTypeIfSingletonObj();
    if (nt == null || nt.isBuiltinObject()) {
      return this.receiverType;
    }
    if (nt.isGeneric()) {
      return nt.instantiateGenerics(this.commonTypes.MAP_TO_UNKNOWN).getInstanceAsJSType();
    }
    return nt.getInstanceAsJSType();
  }

  // Should only be used during GlobalTypeInfo.
  public DeclaredFunctionType toDeclaredFunctionType() {
    if (isQmarkFunction()) {
      return DeclaredFunctionType.qmarkFunctionDeclaration(this.commonTypes);
    }
    Preconditions.checkState(!isLoose(), "Loose function: %s", this);
    Preconditions.checkState(!isGeneric(), "Generic function: %s", this);
    FunctionTypeBuilder builder = new FunctionTypeBuilder(this.commonTypes);
    for (JSType type : this.requiredFormals) {
      builder.addReqFormal(type);
    }
    for (JSType type : this.optionalFormals) {
      builder.addOptFormal(type);
    }
    builder.addRestFormals(this.restFormals);
    builder.addRetType(this.returnType);
    builder.addNominalType(this.nominalType);
    builder.addReceiverType(this.receiverType);
    builder.addAbstract(this.isAbstract);
    return builder.buildDeclaration();
  }

  private static JSType nullAcceptingMeet(JSType t1, JSType t2) {
    if (t1 == null) {
      return t2;
    }
    if (t2 == null) {
      return t1;
    }
    JSType tmp = JSType.meet(t1, t2);
    return tmp.isBottom() ? null : tmp;
  }

  // TODO(dimvar): we need to clean up the combination of loose functions with
  // new: and/or this: types. Eg, this.nominalType doesn't appear at all.
  private static FunctionType looseJoin(FunctionType f1, FunctionType f2) {
    Preconditions.checkArgument(f1.isLoose() || f2.isLoose());

    FunctionTypeBuilder builder = new FunctionTypeBuilder(f1.commonTypes);
    int minRequiredArity = Math.min(f1.getMinArity(), f2.getMinArity());
    for (int i = 0; i < minRequiredArity; i++) {
      builder.addReqFormal(JSType.nullAcceptingJoin(
          f1.getFormalType(i), f2.getFormalType(i)));
    }
    int maxTotalArity = Math.max(
        f1.requiredFormals.size() + f1.optionalFormals.size(),
        f2.requiredFormals.size() + f2.optionalFormals.size());
    for (int i = minRequiredArity; i < maxTotalArity; i++) {
      JSType t = JSType.nullAcceptingJoin(f1.getFormalType(i), f2.getFormalType(i));
      if (t != null && t.isBottom()) {
        // We will add the optional formal of the loose function in the fwd
        // direction, when we have better type information.
        break;
      }
      builder.addOptFormal(t);
    }
    // Loose types never have varargs, because there is no way for that
    // information to make it to a function summary
    return builder.addRetType(
        JSType.nullAcceptingJoin(f1.returnType, f2.returnType))
        .addLoose().buildFunction();
  }

  public boolean isValidOverride(FunctionType other) {
    return isSubtypeOfHelper(other, false, SubtypeCache.create(), null);
  }

  // We want to warn about argument mismatch, so we don't consider a function
  // with N required arguments to have restFormals of type TOP.
  // But we allow joins (eg after an IF) to change arity, eg,
  // number->number \/ number,number->number = number,number->number

  boolean isSubtypeOf(FunctionType other, SubtypeCache subSuperMap) {
    return isSubtypeOfHelper(other, true, subSuperMap, null);
  }

  static void whyNotSubtypeOf(FunctionType f1, FunctionType f2,
      SubtypeCache subSuperMap, MismatchInfo[] boxedInfo) {
    Preconditions.checkArgument(boxedInfo.length == 1);
    f1.isSubtypeOfHelper(f2, true, subSuperMap, boxedInfo);
  }

  // When we write ...?, it has a special meaning, it is NOT a variable-arity
  // function with arguments of ? type. It means that we should not typecheck
  // the arguments, eg, we can use that to express the type: a constructor of
  // Foos with whatever arguments.
  private boolean acceptsAnyArguments() {
    return this.requiredFormals.isEmpty() && this.optionalFormals.isEmpty()
        && this.restFormals != null && this.restFormals.isUnknown();
  }

  private boolean isSubtypeOfHelper(FunctionType other, boolean checkThisType,
      SubtypeCache subSuperMap, MismatchInfo[] boxedInfo) {
    if (other.isTopFunction() ||
        other.isQmarkFunction() || this.isQmarkFunction()) {
      return true;
    }
    if (isTopFunction()) {
      return false;
    }
    // NOTE(dimvar): We never happen to call isSubtypeOf for loose functions.
    // If some analyzed program changes this, the preconditions check will tell
    // us so we can handle looseness correctly.
    Preconditions.checkState(!isLoose() && !other.isLoose());
    if (this.isGeneric()) {
      if (this.equals(other)) {
        return true;
      }
      // NOTE(dimvar): This is a bug. The code that triggers this should be rare
      // and the fix is not trivial, so for now we decided to not fix.
      // See unit tests in NewTypeInferenceTest#testGenericsSubtyping
      return instantiateGenericsWithUnknown(this)
          .isSubtypeOfHelper(other, checkThisType, subSuperMap, boxedInfo);
    }

    if (!other.acceptsAnyArguments()) {
      // The subtype must have an equal or smaller number of required formals
      if (requiredFormals.size() > other.requiredFormals.size()) {
        return false;
      }
      int otherMaxTotalArity =
          other.requiredFormals.size() + other.optionalFormals.size();
      for (int i = 0; i < otherMaxTotalArity; i++) {
        // contravariance in the arguments
        JSType thisFormal = getFormalType(i);
        JSType otherFormal = other.getFormalType(i);
        if (thisFormal != null
            && !thisFormal.isUnknown() && !otherFormal.isUnknown()
            && !otherFormal.isSubtypeOf(thisFormal, subSuperMap)) {
          if (boxedInfo != null) {
            boxedInfo[0] =
                MismatchInfo.makeArgTypeMismatch(i, otherFormal, thisFormal);
          }
          return false;
        }
      }

      if (other.restFormals != null) {
        int thisMaxTotalArity =
            this.requiredFormals.size() + this.optionalFormals.size();
        if (this.restFormals != null) {
          thisMaxTotalArity++;
        }
        for (int i = otherMaxTotalArity; i < thisMaxTotalArity; i++) {
          JSType thisFormal = getFormalType(i);
          JSType otherFormal = other.getFormalType(i);
          if (thisFormal != null
              && !thisFormal.isUnknown() && !otherFormal.isUnknown()
              && !otherFormal.isSubtypeOf(thisFormal, subSuperMap)) {
            return false;
          }
        }
      }
    }

    // covariance for the new: type
    if (this.nominalType == null && other.nominalType != null
        || this.nominalType != null && other.nominalType == null
        || this.nominalType != null && other.nominalType != null
           && !this.nominalType.isSubtypeOf(other.nominalType, subSuperMap)) {
      return false;
    }

    if (checkThisType) {
      // A function without @this can be a subtype of a function with @this.
      if (!this.commonTypes.allowMethodsAsFunctions
          && this.receiverType != null && other.receiverType == null) {
        return false;
      }
      if (this.receiverType != null && other.receiverType != null
          // Contravariance for the receiver type
          && !other.receiverType.isSubtypeOf(this.receiverType, subSuperMap)
          // NOTE(dimvar): Covariance for the receiver type.
          // Not correct, but allowed to make migration easier.
          // After bounded generics, we could probably drop support for this.
          && !this.receiverType.isSubtypeOf(other.receiverType, subSuperMap)) {
        return false;
      }
    }

    // covariance in the return type
    boolean areRetTypesSubtypes = this.returnType.isUnknown()
        || other.returnType.isUnknown()
        || this.returnType.isSubtypeOf(other.returnType, subSuperMap);
    if (boxedInfo != null) {
      boxedInfo[0] =
          MismatchInfo.makeRetTypeMismatch(other.returnType, this.returnType);
    }
    return areRetTypesSubtypes;
  }

  // Avoid using JSType#join if possible, to avoid creating new types
  private static JSType joinNominalTypes(JSType nt1, JSType nt2) {
    if (nt1 == null || nt2 == null) {
      return null;
    }
    NominalType n1 = getNominalTypeIfSingletonObj(nt1);
    NominalType n2 = getNominalTypeIfSingletonObj(nt2);
    if (n1 != null && n2 != null) {
      NominalType tmp = NominalType.pickSuperclass(n1, n2);
      if (tmp != null) {
        return tmp.getInstanceAsJSType();
      }
    }
    // One of the nominal types is non-standard; can't avoid the join
    return JSType.join(nt1, nt2);
  }

  // Avoid using JSType#meet if possible, to avoid creating new types
  private static JSType meetNominalTypes(JSType nt1, JSType nt2) {
    if (nt1 == null) {
      return nt2;
    }
    if (nt2 == null) {
      return nt1;
    }
    NominalType n1 = getNominalTypeIfSingletonObj(nt1);
    NominalType n2 = getNominalTypeIfSingletonObj(nt2);
    if (n1 != null && n2 != null) {
      NominalType tmp = NominalType.pickSubclass(n1, n2);
      return tmp == null ? null : tmp.getInstanceAsJSType();
    }
    // One of the nominal types is non-standard; can't avoid the meet
    return JSType.meet(nt1, nt2);
  }

  static FunctionType join(FunctionType f1, FunctionType f2) {
    if (f1 == null) {
      return f2;
    } else if (f2 == null || f1.equals(f2)) {
      return f1;
    } else if (f1.isQmarkFunction() || f2.isQmarkFunction()) {
      return f1.commonTypes.QMARK_FUNCTION;
    } else if (f1.isTopFunction() || f2.isTopFunction()) {
      return f1.commonTypes.TOP_FUNCTION;
    }

    if (f1.isLoose() || f2.isLoose()) {
      return looseJoin(f1, f2);
    }

    if (f1.isGeneric() && f2.isSubtypeOf(f1, SubtypeCache.create())) {
      return f1;
    } else if (f2.isGeneric() && f1.isSubtypeOf(f2, SubtypeCache.create())) {
      return f2;
    }

    // We lose precision for generic funs that are not in a subtype relation.
    if (f1.isGeneric()) {
      f1 = instantiateGenericsWithUnknown(f1);
    }
    if (f2.isGeneric()) {
      f2 = instantiateGenericsWithUnknown(f2);
    }

    JSTypes commonTypes = f1.commonTypes;
    FunctionTypeBuilder builder = new FunctionTypeBuilder(commonTypes);
    int maxRequiredArity = Math.max(
        f1.requiredFormals.size(), f2.requiredFormals.size());
    for (int i = 0; i < maxRequiredArity; i++) {
      JSType reqFormal = nullAcceptingMeet(f1.getFormalType(i), f2.getFormalType(i));
      if (reqFormal == null) {
        return commonTypes.BOTTOM_FUNCTION;
      }
      builder.addReqFormal(reqFormal);
    }
    int maxTotalArity = Math.max(
        f1.requiredFormals.size() + f1.optionalFormals.size(),
        f2.requiredFormals.size() + f2.optionalFormals.size());
    for (int i = maxRequiredArity; i < maxTotalArity; i++) {
      JSType optFormal = nullAcceptingMeet(f1.getFormalType(i), f2.getFormalType(i));
      if (optFormal == null) {
        return commonTypes.BOTTOM_FUNCTION;
      }
      builder.addOptFormal(optFormal);
    }
    if (f1.restFormals != null && f2.restFormals != null) {
      JSType newRestFormals = nullAcceptingMeet(f1.restFormals, f2.restFormals);
      if (newRestFormals == null) {
        return commonTypes.BOTTOM_FUNCTION;
      }
      builder.addRestFormals(newRestFormals);
    }
    builder.addRetType(JSType.join(f1.returnType, f2.returnType));
    builder.addNominalType(joinNominalTypes(f1.nominalType, f2.nominalType));
    builder.addReceiverType(meetNominalTypes(f1.receiverType, f2.receiverType));
    return builder.buildFunction();
  }

  FunctionType specialize(FunctionType other) {
    if (other == null
        || other.isQmarkFunction() || other.isTopFunction() || equals(other)
        || !isLoose()) {
      return this;
    }
    return isTopFunction() || isQmarkFunction()
        ? other.withLoose() : looseJoin(this, other);
  }

  static FunctionType meet(FunctionType f1, FunctionType f2) {
    if (f1 == null || f2 == null) {
      return null;
    } else if (f2.isTopFunction() || f1.equals(f2)) {
      return f1;
    } else if (f1.isTopFunction()) {
      return f2;
    }

    // War is peace, freedom is slavery, meet is join
    if (f1.isLoose() || f2.isLoose()) {
      return looseJoin(f1, f2);
    }

    if (f1.isGeneric() && f1.isSubtypeOf(f2, SubtypeCache.create())) {
      return f1;
    } else if (f2.isGeneric() && f2.isSubtypeOf(f1, SubtypeCache.create())) {
      return f2;
    }

    // We lose precision for generic funs that are not in a subtype relation.
    if (f1.isGeneric()) {
      f1 = instantiateGenericsWithUnknown(f1);
    }
    if (f2.isGeneric()) {
      f2 = instantiateGenericsWithUnknown(f2);
    }

    JSTypes commonTypes = f1.commonTypes;
    FunctionTypeBuilder builder = new FunctionTypeBuilder(commonTypes);
    int minRequiredArity = Math.min(
        f1.requiredFormals.size(), f2.requiredFormals.size());
    for (int i = 0; i < minRequiredArity; i++) {
      builder.addReqFormal(
          JSType.nullAcceptingJoin(f1.getFormalType(i), f2.getFormalType(i)));
    }
    int maxTotalArity = Math.max(
        f1.requiredFormals.size() + f1.optionalFormals.size(),
        f2.requiredFormals.size() + f2.optionalFormals.size());
    for (int i = minRequiredArity; i < maxTotalArity; i++) {
      JSType optFormalType =
          JSType.nullAcceptingJoin(f1.getFormalType(i), f2.getFormalType(i));
      if (optFormalType.isBottom()) {
        return commonTypes.BOTTOM_FUNCTION;
      }
      builder.addOptFormal(optFormalType);
    }
    if (f1.restFormals != null || f2.restFormals != null) {
      JSType restFormalsType =
          JSType.nullAcceptingJoin(f1.restFormals, f2.restFormals);
      if (restFormalsType.isBottom()) {
        return commonTypes.BOTTOM_FUNCTION;
      }
      builder.addRestFormals(restFormalsType);
    }
    JSType retType = JSType.meet(f1.returnType, f2.returnType);
    if (retType.isBottom()) {
      return commonTypes.BOTTOM_FUNCTION;
    }
    builder.addRetType(retType);
    // NOTE(dimvar): these two are not correct. We should be picking the
    // greatest lower bound of the types if they are incomparable.
    // Eg, this case arises when an interface extends multiple interfaces.
    // OTOH, it may be enough to detect that during GTI, and not implement the
    // more expensive methods (in NominalType or ObjectType).
    builder.addNominalType(meetNominalTypes(f1.nominalType, f2.nominalType));
    builder.addReceiverType(joinNominalTypes(f1.receiverType, f2.receiverType));
    return builder.buildFunction();
  }

  // We may consider true subtyping for deferred checks when the formal
  // parameter has a loose function type.
  boolean isLooseSubtypeOf(FunctionType f2) {
    Preconditions.checkState(this.isLoose() || f2.isLoose());
    if (this.isTopFunction() || f2.isTopFunction()) {
      return true;
    }
    int minRequiredArity =
        Math.min(this.requiredFormals.size(), f2.requiredFormals.size());
    for (int i = 0; i < minRequiredArity; i++) {
      if (!JSType.haveCommonSubtype(this.getFormalType(i), f2.getFormalType(i))) {
        return false;
      }
    }
    return JSType.haveCommonSubtype(this.getReturnType(), f2.getReturnType());
  }

  public boolean isGeneric() {
    return !typeParameters.isEmpty();
  }

  public List<String> getTypeParameters() {
    return typeParameters;
  }

  boolean unifyWithSubtype(FunctionType other, List<String> typeParameters,
      Multimap<String, JSType> typeMultimap, SubtypeCache subSuperMap) {
    Preconditions.checkState(this.typeParameters.isEmpty(),
        "Non-empty type parameters %s", this.typeParameters);
    Preconditions.checkState(this.outerVarPreconditions.isEmpty());
    Preconditions.checkState(this != this.commonTypes.TOP_FUNCTION);

    if (this == this.commonTypes.LOOSE_TOP_FUNCTION || other.isTopFunction() || other.isLoose()) {
      return true;
    }
    if (!acceptsAnyArguments()) {
      if (other.requiredFormals.size() > this.requiredFormals.size()) {
        return false;
      }
      int maxNonInfiniteArity = getMaxArityWithoutRestFormals();
      for (int i = 0; i < maxNonInfiniteArity; i++) {
        JSType thisFormal = getFormalType(i);
        JSType otherFormal = other.getFormalType(i);
        // NOTE(dimvar): The correct handling here would be to implement
        // unifyWithSupertype for JSType, ObjectType, etc, to handle the
        // contravariance here.
        // But it's probably an overkill to do, so instead we just do a subtype
        // check if unification fails. Same for restFormals and receiverType.
        // Altenatively, maybe the unifyWith function could handle both subtype
        // and supertype, and we'd catch type errors as invalid-argument-type
        // after unification. (Not sure this is correct, I'd have to try it.)
        if (otherFormal != null
            && !thisFormal.unifyWithSubtype(
                otherFormal, typeParameters, typeMultimap, subSuperMap)
            && !thisFormal.isSubtypeOf(otherFormal, SubtypeCache.create())) {
          return false;
        }
      }
      if (this.restFormals != null) {
        JSType otherRestFormals = other.getFormalType(maxNonInfiniteArity);
        if (otherRestFormals != null
            && !this.restFormals.unifyWithSubtype(
                otherRestFormals, typeParameters, typeMultimap, subSuperMap)
            && !this.restFormals.isSubtypeOf(
                otherRestFormals, SubtypeCache.create())) {
          return false;
        }
      }
    }

    if (nominalType == null && other.nominalType != null
        || nominalType != null && other.nominalType == null) {
      return false;
    }
    if (nominalType != null && !nominalType.unifyWithSubtype(
        other.nominalType, typeParameters, typeMultimap, subSuperMap)) {
      return false;
    }

    // If one of the two functions doesn't use THIS in the body, we can still
    // unify.
    if (this.receiverType != null && other.receiverType != null
        && !this.receiverType.unifyWithSubtype(
            other.receiverType, typeParameters, typeMultimap, subSuperMap)
        && !this.receiverType.isSubtypeOf(
            other.receiverType, SubtypeCache.create())) {
      return false;
    }

    return this.returnType.unifyWithSubtype(
        other.returnType, typeParameters, typeMultimap, subSuperMap);
  }

  private static FunctionType instantiateGenericsWithUnknown(FunctionType f) {
    if (!f.isGeneric()) {
      return f;
    }
    return f.instantiateGenerics(f.commonTypes.MAP_TO_UNKNOWN);
  }

  /**
   * Unify the two types symmetrically, given that we have already instantiated
   * the type variables of interest in {@code f1} and {@code f2}, treating
   * JSType.UNKNOWN as a "hole" to be filled.
   * @return The unified type, or null if unification fails
   */
  static FunctionType unifyUnknowns(FunctionType f1, FunctionType f2) {
    Preconditions.checkState(f1 != null || f2 != null);
    if (f1 == null || f2 == null) {
      return null;
    }
    if (!f1.typeParameters.isEmpty()) {
      f1 = instantiateGenericsWithUnknown(f1);
    }
    if (!f2.typeParameters.isEmpty()) {
      f2 = instantiateGenericsWithUnknown(f2);
    }
    Preconditions.checkState(!f1.isLoose() && !f2.isLoose());
    if (f1.equals(f2)) {
      return f1;
    }

    ImmutableList<JSType> formals1 = f1.requiredFormals;
    ImmutableList<JSType> formals2 = f2.requiredFormals;
    if (formals1.size() != formals2.size()) {
      return null;
    }
    FunctionTypeBuilder builder = new FunctionTypeBuilder(f1.commonTypes);
    int numReqFormals = formals1.size();
    for (int i = 0; i < numReqFormals; i++) {
      JSType t = JSType.unifyUnknowns(formals1.get(i), formals2.get(i));
      if (t == null) {
        return null;
      }
      builder.addReqFormal(t);
    }

    formals1 = f1.optionalFormals;
    formals2 = f2.optionalFormals;
    if (formals1.size() != formals2.size()) {
      return null;
    }
    int numOptFormals = formals1.size();
    for (int i = 0; i < numOptFormals; i++) {
      JSType t = JSType.unifyUnknowns(formals1.get(i), formals2.get(i));
      if (t == null) {
        return null;
      }
      builder.addOptFormal(t);
    }

    if (f1.restFormals == null && f2.restFormals != null
        || f1.restFormals != null && f2.restFormals == null) {
      return null;
    }
    if (f1.restFormals != null) {
      JSType t = JSType.unifyUnknowns(f1.restFormals, f2.restFormals);
      if (t == null) {
        return null;
      }
      builder.addRestFormals(t);
    }

    JSType t = JSType.unifyUnknowns(f1.returnType, f2.returnType);
    if (t == null) {
      return null;
    }
    builder.addRetType(t);

    // Don't unify unknowns in nominal types; it's going to be rare.
    if (!Objects.equals(f1.nominalType, f2.nominalType)) {
      return null;
    }
    builder.addNominalType(f1.nominalType);

    if (!Objects.equals(f1.receiverType, f2.receiverType)) {
      return null;
    }
    builder.addReceiverType(f1.receiverType);

    return builder.buildFunction();
  }

  // Avoid JSType#substituteGenerics if possible, to avoid creating new types.
  private static JSType substGenericsInNomType(JSType nt, Map<String, JSType> typeMap) {
    if (nt == null) {
      return null;
    }
    NominalType tmp = nt.getNominalTypeIfSingletonObj();
    if (tmp == null) {
      return nt.substituteGenerics(typeMap);
    }
    if (!tmp.isGeneric()) {
      return tmp.getInstanceAsJSType();
    }
    if (typeMap.isEmpty()) {
      return nt;
    }
    return JSType.fromObjectType(ObjectType.fromNominalType(
        tmp.instantiateGenerics(typeMap)));
  }

  private FunctionType substituteNominalGenerics(Map<String, JSType> typeMap) {
    if (typeMap.isEmpty()) {
      return this;
    }
    Map<String, JSType> reducedMap = typeMap;
    if (!this.commonTypes.MAP_TO_UNKNOWN.equals(typeMap)) {
      boolean foundShadowedTypeParam = false;
      for (String typeParam : this.typeParameters) {
        if (typeMap.containsKey(typeParam)) {
          foundShadowedTypeParam = true;
          break;
        }
      }
      if (foundShadowedTypeParam) {
        ImmutableMap.Builder<String, JSType> builder = ImmutableMap.builder();
        for (Map.Entry<String, JSType> entry : typeMap.entrySet()) {
          if (!typeParameters.contains(entry.getKey())) {
            builder.put(entry);
          }
        }
        reducedMap = builder.build();
      }
    }
    FunctionTypeBuilder builder = new FunctionTypeBuilder(this.commonTypes);
    for (JSType reqFormal : this.requiredFormals) {
      builder.addReqFormal(reqFormal.substituteGenerics(reducedMap));
    }
    for (JSType optFormal : this.optionalFormals) {
      builder.addOptFormal(optFormal.substituteGenerics(reducedMap));
    }
    if (this.restFormals != null) {
      builder.addRestFormals(restFormals.substituteGenerics(reducedMap));
    }
    builder.addRetType(this.returnType.substituteGenerics(reducedMap));
    if (isLoose()) {
      builder.addLoose();
    }
    builder.addNominalType(substGenericsInNomType(this.nominalType, typeMap));
    builder.addReceiverType(substGenericsInNomType(this.receiverType, typeMap));
    // TODO(blickly): Do we need instatiation here?
    for (String var : this.outerVarPreconditions.keySet()) {
      builder.addOuterVarPrecondition(var, this.outerVarPreconditions.get(var));
    }
    builder.addTypeParameters(this.typeParameters);
    return builder.buildFunction();
  }

  private FunctionType substituteParametricGenerics(Map<String, JSType> typeMap) {
    if (typeMap.isEmpty()) {
      return this;
    }
    FunctionTypeBuilder builder = new FunctionTypeBuilder(this.commonTypes);
    for (JSType reqFormal : this.requiredFormals) {
      builder.addReqFormal(reqFormal.substituteGenerics(typeMap));
    }
    for (JSType optFormal : this.optionalFormals) {
      builder.addOptFormal(optFormal.substituteGenerics(typeMap));
    }
    if (this.restFormals != null) {
      builder.addRestFormals(restFormals.substituteGenerics(typeMap));
    }
    builder.addRetType(this.returnType.substituteGenerics(typeMap));
    if (isLoose()) {
      builder.addLoose();
    }
    builder.addNominalType(substGenericsInNomType(this.nominalType, typeMap));
    if (this.receiverType != null) {
      // NOTE(dimvar):
      // We have no way of knowing if receiverType comes from an @this
      // annotation, or because this type represents a method.
      // In case 1, we would want to substitute in receiverType, in case 2 we
      // don't, it's a different scope for the type variables.
      // To properly track this we would need two separate fields instead of
      // just receiverType.
      // Instead, the IF test is a heuristic that works in most cases.
      // In the else branch, we are substituting incorrectly when receiverType
      // comes from a method declaration, but I have not been able to find a
      // test that exposes the bug.
      NominalType recvType = getNominalTypeIfSingletonObj(this.receiverType);
      if (recvType != null && recvType.isUninstantiatedGenericType()) {
        builder.addReceiverType(this.receiverType);
      } else {
        builder.addReceiverType(substGenericsInNomType(this.receiverType, typeMap));
      }
    }
    // TODO(blickly): Do we need instatiation here?
    for (String var : outerVarPreconditions.keySet()) {
      builder.addOuterVarPrecondition(var, outerVarPreconditions.get(var));
    }
    return builder.buildFunction();
  }

  /**
   * FunctionType#substituteGenerics is called while instantiating prototype
   * methods of generic nominal types.
   */
  FunctionType substituteGenerics(Map<String, JSType> concreteTypes) {
    if (!isGeneric() || this.commonTypes.MAP_TO_UNKNOWN.equals(concreteTypes)) {
      return substituteNominalGenerics(concreteTypes);
    }
    ImmutableMap.Builder<String, JSType> builder = ImmutableMap.builder();
    for (Map.Entry<String, JSType> concreteTypeEntry
             : concreteTypes.entrySet()) {
      if (!typeParameters.contains(concreteTypeEntry.getKey())) {
        builder.put(concreteTypeEntry);
      }
    }
    return substituteNominalGenerics(builder.build());
  }

  public FunctionType instantiateGenerics(Map<String, JSType> typeMap) {
    Preconditions.checkState(isGeneric());
    return substituteParametricGenerics(typeMap);
  }

  public FunctionType instantiateGenericsFromArgumentTypes(
      List<JSType> argTypes) {
    Preconditions.checkState(isGeneric());
    if (argTypes.size() < getMinArity() || argTypes.size() > getMaxArity()) {
      return null;
    }
    Multimap<String, JSType> typeMultimap = LinkedHashMultimap.create();
    for (int i = 0, size = argTypes.size(); i < size; i++) {
      if (!this.getFormalType(i)
          .unifyWithSubtype(argTypes.get(i), typeParameters, typeMultimap,
              SubtypeCache.create())) {
        return null;
      }
    }
    ImmutableMap.Builder<String, JSType> builder = ImmutableMap.builder();
    for (String typeParam : typeParameters) {
      Collection<JSType> types = typeMultimap.get(typeParam);
      if (types.size() != 1) {
        return null;
      }
      builder.put(typeParam, Iterables.getOnlyElement(types));
    }
    return substituteParametricGenerics(builder.build());
  }

  @Override
  public boolean equals(Object obj) {
    if (obj == null) {
      return false;
    }
    if (this == obj) {
      return true;
    }
    Preconditions.checkArgument(obj instanceof FunctionType, "obj is: %s", obj);
    FunctionType f2 = (FunctionType) obj;
    return Objects.equals(this.requiredFormals, f2.requiredFormals)
        && Objects.equals(this.optionalFormals, f2.optionalFormals)
        && Objects.equals(this.restFormals, f2.restFormals)
        && Objects.equals(this.returnType, f2.returnType)
        && Objects.equals(this.nominalType, f2.nominalType)
        && Objects.equals(this.receiverType, f2.receiverType);
  }

  @Override
  public int hashCode() {
    return Objects.hash(requiredFormals, optionalFormals, restFormals,
        returnType, nominalType, receiverType);
  }

  @Override
  public String toString() {
    return appendTo(new StringBuilder()).toString();
  }

  public StringBuilder appendTo(StringBuilder builder) {
    if (this == this.commonTypes.LOOSE_TOP_FUNCTION) {
      return builder.append("LOOSE_TOP_FUNCTION");
    } else if (this == this.commonTypes.TOP_FUNCTION) {
      return builder.append("TOP_FUNCTION");
    } else if (isQmarkFunction()) {
      return builder.append("Function");
    }
    builder.append("function(");
    if (nominalType != null) {
      builder.append("new:");
      builder.append(nominalType);
      builder.append(',');
    } else if (receiverType != null) {
      builder.append("this:");
      builder.append(receiverType);
      builder.append(',');
    }
    for (int i = 0; i < requiredFormals.size(); ++i) {
      requiredFormals.get(i).appendTo(builder);
      builder.append(',');
    }
    for (int i = 0; i < optionalFormals.size(); ++i) {
      optionalFormals.get(i).appendTo(builder);
      builder.append("=,");
    }
    if (restFormals != null) {
      builder.append("...");
      restFormals.appendTo(builder);
    }
    // Delete the trailing comma, if present
    if (builder.charAt(builder.length() - 1) == ',') {
      builder.deleteCharAt(builder.length() - 1);
    }
    builder.append(')');
    if (returnType != null) {
      builder.append(':');
      returnType.appendTo(builder);
    }
    if (isLoose()) {
      builder.append(" (loose)");
    }
    if (DEBUGGING && !outerVarPreconditions.isEmpty()) {
      builder.append("\tFV: {");
      boolean firstIteration = true;
      for (Map.Entry<String, JSType> entry : outerVarPreconditions.entrySet()) {
        if (!firstIteration) {
          builder.append(',');
        }
        builder.append(entry.getKey());
        builder.append('=');
        entry.getValue().appendTo(builder);
      }
      builder.append('}');
    }
    return builder;
  }
}