// Copyright (c) 2018, the Dart project authors.  Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

// @dart = 2.9

import '../ast.dart'
    show
        BottomType,
        Class,
        DartType,
        DynamicType,
        FunctionType,
        FutureOrType,
        InterfaceType,
        InvalidType,
        Library,
        NamedType,
        NeverType,
        NullType,
        Nullability,
        TypeParameter,
        TypeParameterType,
        Typedef,
        TypedefType,
        Variance,
        VoidType;

import '../type_algebra.dart' show Substitution, substitute;

import '../type_environment.dart' show SubtypeCheckMode, TypeEnvironment;

import '../util/graph.dart' show Graph, computeStrongComponents;

import '../visitor.dart' show DartTypeVisitor, DartTypeVisitor1;

import 'legacy_erasure.dart';

class TypeVariableGraph extends Graph<int> {
  List<int> vertices;
  List<TypeParameter> typeParameters;
  List<DartType> bounds;

  // `edges[i]` is the list of indices of type variables that reference the type
  // variable with the index `i` in their bounds.
  List<List<int>> edges;

  TypeVariableGraph(this.typeParameters, this.bounds) {
    assert(typeParameters.length == bounds.length);

    vertices = new List<int>.filled(typeParameters.length, null);
    Map<TypeParameter, int> typeParameterIndices = <TypeParameter, int>{};
    edges = new List<List<int>>.filled(typeParameters.length, null);
    for (int i = 0; i < vertices.length; i++) {
      vertices[i] = i;
      typeParameterIndices[typeParameters[i]] = i;
      edges[i] = <int>[];
    }

    for (int i = 0; i < vertices.length; i++) {
      OccurrenceCollectorVisitor collector =
          new OccurrenceCollectorVisitor(typeParameters.toSet());
      collector.visit(bounds[i]);
      for (TypeParameter typeParameter in collector.occurred) {
        edges[typeParameterIndices[typeParameter]].add(i);
      }
    }
  }

  Iterable<int> neighborsOf(int index) {
    return edges[index];
  }
}

class OccurrenceCollectorVisitor extends DartTypeVisitor {
  final Set<TypeParameter> typeParameters;
  Set<TypeParameter> occurred = new Set<TypeParameter>();

  OccurrenceCollectorVisitor(this.typeParameters);

  visit(DartType node) => node.accept(this);

  visitNamedType(NamedType node) {
    node.type.accept(this);
  }

  visitInvalidType(InvalidType node);
  visitDynamicType(DynamicType node);
  visitVoidType(VoidType node);

  visitInterfaceType(InterfaceType node) {
    for (DartType argument in node.typeArguments) {
      argument.accept(this);
    }
  }

  visitTypedefType(TypedefType node) {
    for (DartType argument in node.typeArguments) {
      argument.accept(this);
    }
  }

  visitFunctionType(FunctionType node) {
    for (TypeParameter typeParameter in node.typeParameters) {
      typeParameter.bound.accept(this);
      typeParameter.defaultType?.accept(this);
    }
    for (DartType parameter in node.positionalParameters) {
      parameter.accept(this);
    }
    for (NamedType namedParameter in node.namedParameters) {
      namedParameter.type.accept(this);
    }
    node.returnType.accept(this);
  }

  visitTypeParameterType(TypeParameterType node) {
    if (typeParameters.contains(node.parameter)) {
      occurred.add(node.parameter);
    }
  }
}

DartType instantiateToBounds(
    DartType type, Class objectClass, Library contextLibrary) {
  if (type is InterfaceType) {
    if (type.typeArguments.isEmpty) return type;
    for (DartType typeArgument in type.typeArguments) {
      // If at least one of the arguments is not dynamic, we assume that the
      // type is not raw and does not need instantiation of its type parameters
      // to their bounds.
      if (typeArgument is! DynamicType) {
        return type;
      }
    }
    return new InterfaceType.byReference(
        type.className,
        type.nullability,
        calculateBounds(
            type.classNode.typeParameters, objectClass, contextLibrary));
  }
  if (type is TypedefType) {
    if (type.typeArguments.isEmpty) return type;
    for (DartType typeArgument in type.typeArguments) {
      if (typeArgument is! DynamicType) {
        return type;
      }
    }
    return new TypedefType.byReference(
        type.typedefReference,
        type.nullability,
        calculateBounds(
            type.typedefNode.typeParameters, objectClass, contextLibrary));
  }
  return type;
}

/// Calculates bounds to be provided as type arguments in place of missing type
/// arguments on raw types with the given type parameters.
///
/// See the [description]
/// (https://github.com/dart-lang/sdk/blob/master/docs/language/informal/instantiate-to-bound.md)
/// of the algorithm for details.
List<DartType> calculateBounds(List<TypeParameter> typeParameters,
    Class objectClass, Library contextLibrary) {
  return calculateBoundsInternal(typeParameters, objectClass,
      isNonNullableByDefault: contextLibrary.isNonNullableByDefault);
}

List<DartType> calculateBoundsInternal(
    List<TypeParameter> typeParameters, Class objectClass,
    {bool isNonNullableByDefault}) {
  assert(isNonNullableByDefault != null);

  List<DartType> bounds =
      new List<DartType>.filled(typeParameters.length, null);
  for (int i = 0; i < typeParameters.length; i++) {
    DartType bound = typeParameters[i].bound;
    if (bound == null) {
      bound = const DynamicType();
    } else if (bound is InterfaceType && bound.classNode == objectClass) {
      DartType defaultType = typeParameters[i].defaultType;
      if (!(defaultType is InterfaceType &&
          defaultType.classNode == objectClass)) {
        bound = const DynamicType();
      }
    }
    bounds[i] = bound;
  }

  TypeVariableGraph graph = new TypeVariableGraph(typeParameters, bounds);
  List<List<int>> stronglyConnected = computeStrongComponents(graph);
  final DartType topType = const DynamicType();
  final DartType bottomType = isNonNullableByDefault
      ? const NeverType(Nullability.nonNullable)
      : const BottomType();
  for (List<int> component in stronglyConnected) {
    Map<TypeParameter, DartType> upperBounds = <TypeParameter, DartType>{};
    Map<TypeParameter, DartType> lowerBounds = <TypeParameter, DartType>{};
    for (int typeParameterIndex in component) {
      upperBounds[typeParameters[typeParameterIndex]] = topType;
      lowerBounds[typeParameters[typeParameterIndex]] = bottomType;
    }
    Substitution substitution =
        Substitution.fromUpperAndLowerBounds(upperBounds, lowerBounds);
    for (int typeParameterIndex in component) {
      bounds[typeParameterIndex] =
          substitution.substituteType(bounds[typeParameterIndex]);
    }
  }

  for (int i = 0; i < typeParameters.length; i++) {
    Map<TypeParameter, DartType> upperBounds = <TypeParameter, DartType>{};
    Map<TypeParameter, DartType> lowerBounds = <TypeParameter, DartType>{};
    upperBounds[typeParameters[i]] = bounds[i];
    lowerBounds[typeParameters[i]] = bottomType;
    Substitution substitution =
        Substitution.fromUpperAndLowerBounds(upperBounds, lowerBounds);
    for (int j = 0; j < typeParameters.length; j++) {
      bounds[j] = substitution.substituteType(bounds[j]);
    }
  }

  return bounds;
}

class TypeArgumentIssue {
  /// The index for type argument within the passed type arguments.
  final int index;

  /// The type argument that violated the bound.
  final DartType argument;

  /// The type parameter with the bound that was violated.
  final TypeParameter typeParameter;

  /// The enclosing type of the issue, that is, the one with [typeParameter].
  final DartType enclosingType;

  /// The type computed from [enclosingType] for the super-boundness check.
  ///
  /// This field can be null.  [invertedType] is supposed to enhance error
  /// messages, providing the auxiliary type for super-boundness checks for the
  /// user.  It is set to null if it's not helpful, for example, if
  /// [enclosingType] is well-bounded or is strictly required to be
  /// regular-bounded, so the super-boundness check is skipped.  It is set to
  /// null also if the inversion didn't change the type at all, and it's not
  /// helpful to show the same type to the user.
  DartType invertedType;

  TypeArgumentIssue(
      this.index, this.argument, this.typeParameter, this.enclosingType,
      {this.invertedType});

  int get hashCode {
    int hash = 0x3fffffff & index;
    hash = 0x3fffffff & (hash * 31 + (hash ^ argument.hashCode));
    hash = 0x3fffffff & (hash * 31 + (hash ^ typeParameter.hashCode));
    hash = 0x3fffffff & (hash * 31 + (hash ^ enclosingType.hashCode));
    return hash;
  }

  bool operator ==(Object other) {
    assert(other is TypeArgumentIssue);
    return other is TypeArgumentIssue &&
        index == other.index &&
        argument == other.argument &&
        typeParameter == other.typeParameter &&
        enclosingType == other.enclosingType;
  }

  String toString() {
    return "TypeArgumentIssue(index=${index}, argument=${argument}, "
        "typeParameter=${typeParameter}, enclosingType=${enclosingType}";
  }
}

// Finds type arguments that don't follow the rules of well-boundness.
//
// [bottomType] should be either Null or Never, depending on what should be
// taken for the bottom type at the call site.  The bottom type is used in the
// checks for super-boundness for construction of the auxiliary type.  For
// details see Dart Language Specification, Section 14.3.2 The Instantiation to
// Bound Algorithm.
// TODO(dmitryas):  Remove [typedefInstantiations] when type arguments passed to
// typedefs are preserved in the Kernel output.
List<TypeArgumentIssue> findTypeArgumentIssues(Library library, DartType type,
    TypeEnvironment typeEnvironment, SubtypeCheckMode subtypeCheckMode,
    {bool allowSuperBounded = false}) {
  List<TypeParameter> variables;
  List<DartType> arguments;
  List<TypeArgumentIssue> typedefRhsResult;

  if (type is FunctionType && type.typedefType != null) {
    // [type] is a function type that is an application of a parametrized
    // typedef.  We need to check both the l.h.s. and the r.h.s. of the
    // definition in that case.  For details, see [link]
    // (https://github.com/dart-lang/sdk/blob/master/docs/language/informal/super-bounded-types.md).
    FunctionType functionType = type;
    FunctionType cloned = new FunctionType(functionType.positionalParameters,
        functionType.returnType, functionType.nullability,
        namedParameters: functionType.namedParameters,
        typeParameters: functionType.typeParameters,
        requiredParameterCount: functionType.requiredParameterCount,
        typedefType: null);
    typedefRhsResult = findTypeArgumentIssues(
        library, cloned, typeEnvironment, subtypeCheckMode,
        allowSuperBounded: true);
    type = functionType.typedefType;
  }

  if (type is InterfaceType) {
    variables = type.classNode.typeParameters;
    arguments = type.typeArguments;
  } else if (type is TypedefType) {
    variables = type.typedefNode.typeParameters;
    arguments = type.typeArguments;
  } else if (type is FunctionType) {
    List<TypeArgumentIssue> result = null;

    for (TypeParameter parameter in type.typeParameters) {
      List<TypeArgumentIssue> parameterResult = findTypeArgumentIssues(
          library, parameter.bound, typeEnvironment, subtypeCheckMode,
          allowSuperBounded: true);
      if (result == null) {
        result = parameterResult;
      } else if (parameterResult != null) {
        result.addAll(parameterResult);
      }
    }

    for (DartType formal in type.positionalParameters) {
      List<TypeArgumentIssue> parameterResult = findTypeArgumentIssues(
          library, formal, typeEnvironment, subtypeCheckMode,
          allowSuperBounded: true);
      if (result == null) {
        result = parameterResult;
      } else if (parameterResult != null) {
        result.addAll(parameterResult);
      }
    }

    for (NamedType named in type.namedParameters) {
      List<TypeArgumentIssue> parameterResult = findTypeArgumentIssues(
          library, named.type, typeEnvironment, subtypeCheckMode,
          allowSuperBounded: true);
      if (result == null) {
        result = parameterResult;
      } else if (parameterResult != null) {
        result.addAll(parameterResult);
      }
    }

    {
      List<TypeArgumentIssue> returnTypeResult = findTypeArgumentIssues(
          library, type.returnType, typeEnvironment, subtypeCheckMode,
          allowSuperBounded: true);
      if (result == null) {
        result = returnTypeResult;
      } else if (returnTypeResult != null) {
        result.addAll(returnTypeResult);
      }
    }

    return result;
  } else if (type is FutureOrType) {
    variables = typeEnvironment.coreTypes.futureClass.typeParameters;
    arguments = <DartType>[type.typeArgument];
  } else {
    return null;
  }

  if (variables == null) return null;

  List<TypeArgumentIssue> result = null;
  List<TypeArgumentIssue> argumentsResult = null;

  Map<TypeParameter, DartType> substitutionMap =
      new Map<TypeParameter, DartType>.fromIterables(variables, arguments);
  for (int i = 0; i < arguments.length; ++i) {
    DartType argument = arguments[i];
    if (isGenericFunctionTypeOrAlias(argument)) {
      // Generic function types aren't allowed as type arguments either.
      result ??= <TypeArgumentIssue>[];
      result.add(new TypeArgumentIssue(i, argument, variables[i], type));
    } else if (variables[i].bound is! InvalidType) {
      DartType bound = substitute(variables[i].bound, substitutionMap);
      if (!library.isNonNullableByDefault) {
        bound = legacyErasure(bound);
      }
      if (!typeEnvironment.isSubtypeOf(argument, bound, subtypeCheckMode)) {
        result ??= <TypeArgumentIssue>[];
        result.add(new TypeArgumentIssue(i, argument, variables[i], type));
      }
    } else {
      // The bound is InvalidType so it's not checked, because an error was
      // reported already at the time of the creation of InvalidType.
    }

    List<TypeArgumentIssue> issues = findTypeArgumentIssues(
        library, argument, typeEnvironment, subtypeCheckMode,
        allowSuperBounded: true);
    if (issues != null) {
      argumentsResult ??= <TypeArgumentIssue>[];
      argumentsResult.addAll(issues);
    }
  }
  if (argumentsResult != null) {
    result ??= <TypeArgumentIssue>[];
    result.addAll(argumentsResult);
  }
  if (typedefRhsResult != null) {
    result ??= <TypeArgumentIssue>[];
    result.addAll(typedefRhsResult);
  }

  // [type] is regular-bounded.
  if (result == null) return null;
  if (!allowSuperBounded) return result;

  bool isCorrectSuperBounded = true;
  DartType invertedType =
      convertSuperBoundedToRegularBounded(library, typeEnvironment, type);

  // The auxiliary type is the same as [type].  At this point we know that
  // [type] is not regular-bounded, which means that the inverted type is also
  // not regular-bounded.  These two judgments together allow us to conclude
  // that [type] is not well-bounded.
  if (invertedType == null) return result;

  if (invertedType is InterfaceType) {
    variables = invertedType.classNode.typeParameters;
    arguments = invertedType.typeArguments;
  } else if (invertedType is TypedefType) {
    variables = invertedType.typedefNode.typeParameters;
    arguments = invertedType.typeArguments;
  } else if (invertedType is FutureOrType) {
    variables = typeEnvironment.coreTypes.futureClass.typeParameters;
    arguments = <DartType>[invertedType.typeArgument];
  }
  substitutionMap =
      new Map<TypeParameter, DartType>.fromIterables(variables, arguments);
  for (int i = 0; i < arguments.length; ++i) {
    DartType argument = arguments[i];
    if (isGenericFunctionTypeOrAlias(argument)) {
      // Generic function types aren't allowed as type arguments either.
      isCorrectSuperBounded = false;
    } else if (!typeEnvironment.isSubtypeOf(argument,
        substitute(variables[i].bound, substitutionMap), subtypeCheckMode)) {
      isCorrectSuperBounded = false;
    }
  }
  if (argumentsResult != null) {
    isCorrectSuperBounded = false;
  }
  if (typedefRhsResult != null) {
    isCorrectSuperBounded = false;
  }

  // The inverted type is regular-bounded, which means that [type] is
  // well-bounded.
  if (isCorrectSuperBounded) return null;

  // The inverted type isn't regular-bounded, but it's different from [type].
  // In this case we'll provide the programmer with the inverted type as a hint,
  // in case they were going for a super-bounded type and will benefit from that
  // information correcting the program.
  for (TypeArgumentIssue issue in result) {
    issue.invertedType = invertedType;
  }
  return result;
}

// Finds type arguments that don't follow the rules of well-boundness.
//
// [bottomType] should be either Null or Never, depending on what should be
// taken for the bottom type at the call site.  The bottom type is used in the
// checks for super-boundness for construction of the auxiliary type.  For
// details see Dart Language Specification, Section 14.3.2 The Instantiation to
// Bound Algorithm.
// TODO(dmitryas):  Remove [typedefInstantiations] when type arguments passed to
// typedefs are preserved in the Kernel output.
List<TypeArgumentIssue> findTypeArgumentIssuesForInvocation(
    Library library,
    List<TypeParameter> parameters,
    List<DartType> arguments,
    TypeEnvironment typeEnvironment,
    SubtypeCheckMode subtypeCheckMode,
    DartType bottomType,
    {Map<FunctionType, List<DartType>> typedefInstantiations}) {
  assert(arguments.length == parameters.length);
  assert(bottomType == const NeverType(Nullability.nonNullable) ||
      bottomType is NullType);
  List<TypeArgumentIssue> result;
  Map<TypeParameter, DartType> substitutionMap = <TypeParameter, DartType>{};
  for (int i = 0; i < arguments.length; ++i) {
    substitutionMap[parameters[i]] = arguments[i];
  }
  for (int i = 0; i < arguments.length; ++i) {
    DartType argument = arguments[i];
    if (argument is TypeParameterType && argument.promotedBound != null) {
      result ??= <TypeArgumentIssue>[];
      result.add(new TypeArgumentIssue(i, argument, parameters[i], null));
    } else if (isGenericFunctionTypeOrAlias(argument)) {
      // Generic function types aren't allowed as type arguments either.
      result ??= <TypeArgumentIssue>[];
      result.add(new TypeArgumentIssue(i, argument, parameters[i], null));
    } else if (parameters[i].bound is! InvalidType) {
      DartType bound = substitute(parameters[i].bound, substitutionMap);
      if (!library.isNonNullableByDefault) {
        bound = legacyErasure(bound);
      }
      if (!typeEnvironment.isSubtypeOf(argument, bound, subtypeCheckMode)) {
        result ??= <TypeArgumentIssue>[];
        result.add(new TypeArgumentIssue(i, argument, parameters[i], null));
      }
    }

    List<TypeArgumentIssue> issues = findTypeArgumentIssues(
        library, argument, typeEnvironment, subtypeCheckMode,
        allowSuperBounded: true);
    if (issues != null) {
      result ??= <TypeArgumentIssue>[];
      result.addAll(issues);
    }
  }
  return result;
}

String getGenericTypeName(DartType type) {
  if (type is InterfaceType) {
    return type.classNode.name;
  } else if (type is TypedefType) {
    return type.typedefNode.name;
  }
  return type.toString();
}

/// Replaces all covariant occurrences of `dynamic`, `Object`, and `void` with
/// [BottomType] and all contravariant occurrences of `Null` and [BottomType]
/// with `Object`.  Returns null if the converted type is the same as [type].
DartType convertSuperBoundedToRegularBounded(
    Library clientLibrary, TypeEnvironment typeEnvironment, DartType type,
    {int variance = Variance.covariant}) {
  bool flipTop;
  bool flipBottom;
  DartType topType;
  DartType bottomType;
  bool isTop;
  bool isBottom;
  if (clientLibrary.isNonNullableByDefault) {
    flipTop = variance != Variance.contravariant;
    flipBottom = variance == Variance.contravariant;
    topType = typeEnvironment.coreTypes.objectNullableRawType;
    bottomType = const NeverType(Nullability.nonNullable);
    isTop = typeEnvironment.coreTypes.isTop(type);
    isBottom = typeEnvironment.coreTypes.isBottom(type);
  } else {
    flipTop = variance == Variance.covariant;
    flipBottom = variance != Variance.covariant;
    topType = const DynamicType();
    bottomType = const NullType();
    isTop = type is DynamicType ||
        type is VoidType ||
        type is InterfaceType &&
            type.classNode == typeEnvironment.coreTypes.objectClass;
    isBottom = type is NullType || type is BottomType;
  }

  if (isTop && flipTop) {
    return bottomType;
  } else if (isBottom && flipBottom) {
    return topType;
  } else if (type is InterfaceType &&
      type.classNode.typeParameters.isNotEmpty) {
    assert(type.classNode.typeParameters.length == type.typeArguments.length);

    List<DartType> convertedTypeArguments = null;
    for (int i = 0; i < type.typeArguments.length; ++i) {
      DartType convertedTypeArgument = convertSuperBoundedToRegularBounded(
          clientLibrary, typeEnvironment, type.typeArguments[i],
          variance: variance);
      if (convertedTypeArgument != null) {
        convertedTypeArguments ??= new List<DartType>.of(type.typeArguments);
        convertedTypeArguments[i] = convertedTypeArgument;
      }
    }
    if (convertedTypeArguments == null) return null;
    return new InterfaceType(
        type.classNode, type.nullability, convertedTypeArguments);
  } else if (type is TypedefType &&
      type.typedefNode.typeParameters.isNotEmpty) {
    assert(type.typedefNode.typeParameters.length == type.typeArguments.length);

    List<DartType> convertedTypeArguments = null;
    for (int i = 0; i < type.typeArguments.length; i++) {
      // The implementation of instantiate-to-bound in legacy mode ignored the
      // variance of type parameters of the typedef.  This behavior is preserved
      // here in passing the 'variance' parameter unchanged in for legacy
      // libraries.
      DartType convertedTypeArgument = convertSuperBoundedToRegularBounded(
          clientLibrary, typeEnvironment, type.typeArguments[i],
          variance: clientLibrary.isNonNullableByDefault
              ? Variance.combine(
                  variance, type.typedefNode.typeParameters[i].variance)
              : variance);
      if (convertedTypeArgument != null) {
        convertedTypeArguments ??= new List<DartType>.of(type.typeArguments);
        convertedTypeArguments[i] = convertedTypeArgument;
      }
    }
    if (convertedTypeArguments == null) return null;
    return new TypedefType(
        type.typedefNode, type.nullability, convertedTypeArguments);
  } else if (type is FunctionType) {
    if (clientLibrary.isNonNullableByDefault && type.typedefType != null) {
      return convertSuperBoundedToRegularBounded(
          clientLibrary, typeEnvironment, type.typedefType,
          variance: variance);
    }

    DartType convertedReturnType = convertSuperBoundedToRegularBounded(
        clientLibrary, typeEnvironment, type.returnType,
        variance: variance);

    List<DartType> convertedPositionalParameters = null;
    for (int i = 0; i < type.positionalParameters.length; i++) {
      DartType convertedPositionalParameter =
          convertSuperBoundedToRegularBounded(
              clientLibrary, typeEnvironment, type.positionalParameters[i],
              variance: Variance.combine(variance, Variance.contravariant));
      if (convertedPositionalParameter != null) {
        convertedPositionalParameters ??=
            new List<DartType>.of(type.positionalParameters);
        convertedPositionalParameters[i] = convertedPositionalParameter;
      }
    }

    List<NamedType> convertedNamedParameters = null;
    for (int i = 0; i < type.namedParameters.length; i++) {
      NamedType convertedNamedParameter = new NamedType(
          type.namedParameters[i].name,
          convertSuperBoundedToRegularBounded(
              clientLibrary, typeEnvironment, type.namedParameters[i].type,
              variance: Variance.combine(variance, Variance.contravariant)),
          isRequired: type.namedParameters[i].isRequired);
      if (convertedNamedParameter != null) {
        convertedNamedParameters ??=
            new List<NamedType>.of(type.namedParameters);
        convertedNamedParameters[i] = convertedNamedParameter;
      }
    }

    List<TypeParameter> convertedTypeParameters = null;
    if (clientLibrary.isNonNullableByDefault &&
        type.typeParameters.isNotEmpty) {
      for (int i = 0; i < type.typeParameters.length; ++i) {
        DartType convertedBound = convertSuperBoundedToRegularBounded(
            clientLibrary, typeEnvironment, type.typeParameters[i].bound,
            variance: Variance.combine(variance, Variance.invariant));
        if (convertedBound != null) {
          if (convertedTypeParameters == null) {
            convertedTypeParameters = <TypeParameter>[];
            for (TypeParameter parameter in type.typeParameters) {
              convertedTypeParameters.add(new TypeParameter(parameter.name));
            }
          }
          convertedTypeParameters[i].bound = convertedBound;
        }
      }

      Map<TypeParameter, DartType> substitutionMap =
          <TypeParameter, DartType>{};
      for (int i = 0; i < type.typeParameters.length; ++i) {
        substitutionMap[type.typeParameters[i]] =
            new TypeParameterType.forAlphaRenaming(
                type.typeParameters[i], convertedTypeParameters[i]);
      }
      for (TypeParameter parameter in convertedTypeParameters) {
        parameter.bound = substitute(parameter.bound, substitutionMap);
      }
      List<DartType> defaultTypes = calculateBounds(convertedTypeParameters,
          typeEnvironment.coreTypes.objectClass, clientLibrary);
      for (int i = 0; i < convertedTypeParameters.length; ++i) {
        convertedTypeParameters[i].defaultType = defaultTypes[i];
      }

      if (convertedReturnType != null) {
        convertedReturnType = substitute(convertedReturnType, substitutionMap);
      }
      if (convertedPositionalParameters != null) {
        for (int i = 0; i < convertedPositionalParameters.length; ++i) {
          convertedPositionalParameters[i] =
              substitute(convertedPositionalParameters[i], substitutionMap);
        }
      }
      if (convertedNamedParameters != null) {
        for (int i = 0; i < convertedNamedParameters.length; ++i) {
          convertedNamedParameters[i] = new NamedType(
              convertedNamedParameters[i].name,
              substitute(convertedNamedParameters[i].type, substitutionMap),
              isRequired: convertedNamedParameters[i].isRequired);
        }
      }
    }

    if (convertedReturnType == null &&
        convertedPositionalParameters == null &&
        convertedNamedParameters == null &&
        convertedTypeParameters == null) {
      return null;
    }

    convertedReturnType ??= type.returnType;
    convertedPositionalParameters ??= type.positionalParameters;
    convertedNamedParameters ??= type.namedParameters;
    convertedTypeParameters ??= type.typeParameters;

    return new FunctionType(
        convertedPositionalParameters, convertedReturnType, type.nullability,
        namedParameters: convertedNamedParameters,
        typeParameters: type.typeParameters,
        requiredParameterCount: type.requiredParameterCount,
        typedefType: type.typedefType);
  } else if (type is FutureOrType) {
    DartType convertedTypeArgument = convertSuperBoundedToRegularBounded(
        clientLibrary, typeEnvironment, type.typeArgument,
        variance: variance);
    if (convertedTypeArgument == null) return null;
    return new FutureOrType(convertedTypeArgument, type.declaredNullability);
  }

  return null;
}

int computeVariance(TypeParameter typeParameter, DartType type,
    {Map<TypeParameter, Map<DartType, int>> computedVariances}) {
  computedVariances ??= new Map<TypeParameter, Map<DartType, int>>.identity();
  computedVariances[typeParameter] ??= new Map<DartType, int>.identity();

  int variance = computedVariances[typeParameter][type];
  if (variance != null) return variance;
  computedVariances[typeParameter][type] = VarianceCalculator._visitMarker;

  return computedVariances[typeParameter][type] =
      type.accept1(new VarianceCalculator(typeParameter), computedVariances);
}

class VarianceCalculator
    implements DartTypeVisitor1<int, Map<TypeParameter, Map<DartType, int>>> {
  final TypeParameter typeParameter;

  static const int _visitMarker = -2;

  VarianceCalculator(this.typeParameter);

  @override
  int defaultDartType(
      DartType node, Map<TypeParameter, Map<DartType, int>> computedVariances) {
    throw new StateError("Unhandled ${node.runtimeType} "
        "when computing variance of a type parameter.");
  }

  @override
  int visitTypeParameterType(TypeParameterType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    if (node.parameter == typeParameter) return Variance.covariant;
    return Variance.unrelated;
  }

  @override
  int visitInterfaceType(InterfaceType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    int result = Variance.unrelated;
    for (int i = 0; i < node.typeArguments.length; ++i) {
      result = Variance.meet(
          result,
          Variance.combine(
              node.classNode.typeParameters[i].variance,
              computeVariance(typeParameter, node.typeArguments[i],
                  computedVariances: computedVariances)));
    }
    return result;
  }

  @override
  int visitFutureOrType(FutureOrType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    return computeVariance(typeParameter, node.typeArgument,
        computedVariances: computedVariances);
  }

  @override
  int visitTypedefType(TypedefType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    int result = Variance.unrelated;
    for (int i = 0; i < node.typeArguments.length; ++i) {
      Typedef typedefNode = node.typedefNode;
      TypeParameter typedefTypeParameter = typedefNode.typeParameters[i];
      if (computedVariances.containsKey(typedefTypeParameter) &&
          computedVariances[typedefTypeParameter][typedefNode.type] ==
              _visitMarker) {
        throw new StateError("The typedef '${node.typedefNode.name}' "
            "has a reference to itself.");
      }

      result = Variance.meet(
          result,
          Variance.combine(
              computeVariance(typeParameter, node.typeArguments[i],
                  computedVariances: computedVariances),
              computeVariance(typedefTypeParameter, typedefNode.type,
                  computedVariances: computedVariances)));
    }
    return result;
  }

  @override
  int visitFunctionType(FunctionType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    int result = Variance.unrelated;
    result = Variance.meet(
        result,
        computeVariance(typeParameter, node.returnType,
            computedVariances: computedVariances));
    for (TypeParameter functionTypeParameter in node.typeParameters) {
      // If [typeParameter] is referenced in the bound at all, it makes the
      // variance of [typeParameter] in the entire type invariant.  The
      // invocation of the visitor below is made to simply figure out if
      // [typeParameter] occurs in the bound.
      if (computeVariance(typeParameter, functionTypeParameter.bound,
              computedVariances: computedVariances) !=
          Variance.unrelated) {
        result = Variance.invariant;
      }
    }
    for (DartType positionalType in node.positionalParameters) {
      result = Variance.meet(
          result,
          Variance.combine(
              Variance.contravariant,
              computeVariance(typeParameter, positionalType,
                  computedVariances: computedVariances)));
    }
    for (NamedType namedType in node.namedParameters) {
      result = Variance.meet(
          result,
          Variance.combine(
              Variance.contravariant,
              computeVariance(typeParameter, namedType.type,
                  computedVariances: computedVariances)));
    }
    return result;
  }

  @override
  int visitBottomType(BottomType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    return Variance.unrelated;
  }

  @override
  int visitNeverType(NeverType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    return Variance.unrelated;
  }

  @override
  int visitNullType(
      NullType node, Map<TypeParameter, Map<DartType, int>> computedVariances) {
    return Variance.unrelated;
  }

  @override
  int visitVoidType(
      VoidType node, Map<TypeParameter, Map<DartType, int>> computedVariances) {
    return Variance.unrelated;
  }

  @override
  int visitDynamicType(DynamicType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    return Variance.unrelated;
  }

  @override
  int visitInvalidType(InvalidType node,
      Map<TypeParameter, Map<DartType, int>> computedVariances) {
    return Variance.unrelated;
  }
}

bool isGenericFunctionTypeOrAlias(DartType type) {
  if (type is TypedefType) type = type.unalias;
  return type is FunctionType && type.typeParameters.isNotEmpty;
}