// Copyright (c) 2019, 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.

/// This library contains support for runtime type information.
library rti;

import 'dart:_foreign_helper'
    show
        getInterceptor,
        getJSArrayInteropRti,
        JS,
        JS_BUILTIN,
        JS_EMBEDDED_GLOBAL,
        JS_GET_FLAG,
        JS_GET_NAME,
        JS_STRING_CONCAT,
        RAW_DART_FUNCTION_REF;

import 'dart:_interceptors' show JSArray, JSUnmodifiableArray;

import 'dart:_js_names' show unmangleGlobalNameIfPreservedAnyways;

import 'dart:_js_embedded_names'
    show JsBuiltin, JsGetName, RtiUniverseFieldNames, RTI_UNIVERSE, TYPES;

import 'dart:_recipe_syntax';

/// An Rti object represents both a type (e.g `Map<int, String>`) and a type
/// environment (`Map<int, String>` binds `Map.K=int` and `Map.V=String`).
///
/// There is a single [Rti] class to help reduce polymorphism in the JavaScript
/// runtime. The class has a default constructor and no final fields so it can
/// be created before much of the runtime exists.
///
/// The fields are declared in an order that gets shorter minified names for the
/// more commonly used fields. (TODO: we should exploit the fact that an Rti
/// instance never appears in a dynamic context, so does not need field names to
/// be distinct from dynamic selectors).
///
class Rti {
  /// JavaScript method for 'as' check. The method is called from generated code,
  /// e.g. `o as T` generates something like `rtiForT._as(o)`.
  @pragma('dart2js:noElision')
  dynamic _as;

  /// JavaScript method for type check.  The method is called from generated
  /// code, e.g. parameter check for `T param` generates something like
  /// `rtiForT._check(param)`.
  @pragma('dart2js:noElision')
  dynamic _check;

  /// JavaScript method for 'is' test.  The method is called from generated
  /// code, e.g. `o is T` generates something like `rtiForT._is(o)`.
  @pragma('dart2js:noElision')
  dynamic _is;

  static void _setAsCheckFunction(Rti rti, fn) {
    rti._as = fn;
  }

  static void _setTypeCheckFunction(Rti rti, fn) {
    rti._check = fn;
  }

  static void _setIsTestFunction(Rti rti, fn) {
    rti._is = fn;
  }

  @pragma('dart2js:tryInline')
  static bool _isCheck(Rti rti, object) {
    return JS(
        'bool', '#.#(#)', rti, JS_GET_NAME(JsGetName.RTI_FIELD_IS), object);
  }

  /// Method called from generated code to evaluate a type environment recipe in
  /// `this` type environment.
  Rti _eval(recipe) {
    // TODO(sra): Clone the fast-path of _Universe.evalInEnvironment to here.
    return _rtiEval(this, _Utils.asString(recipe));
  }

  /// Method called from generated code to extend `this` type environment (an
  /// interface or binding Rti) with function type arguments (a singleton
  /// argument or tuple of arguments).
  Rti _bind(typeOrTuple) => _rtiBind(this, _castToRti(typeOrTuple));

  /// Method called from generated code to extend `this` type (as a singleton
  /// type environment) with function type arguments (a singleton argument or
  /// tuple of arguments).
  Rti _bind1(Rti typeOrTuple) => _rtiBind1(this, typeOrTuple);

  // Precomputed derived types. These fields are used to hold derived types that
  // are computed eagerly.
  // TODO(sra): Implement precomputed type optimizations.
  dynamic _precomputed1;
  dynamic _precomputed2;
  dynamic _precomputed3;
  dynamic _precomputed4;

  // The Type object corresponding to this Rti.
  Object _cachedRuntimeType;
  static _Type _getCachedRuntimeType(Rti rti) =>
      JS('_Type|Null', '#', rti._cachedRuntimeType);
  static void _setCachedRuntimeType(Rti rti, _Type type) {
    rti._cachedRuntimeType = type;
  }

  /// The kind of Rti `this` is, one of the kindXXX constants below.
  ///
  /// We don't use an enum since we need to create Rti objects very early.
  ///
  /// The zero initializer ensures dart2js type analysis considers [_kind] is
  /// non-nullable.
  Object /*int*/ _kind = 0;

  static int _getKind(Rti rti) => _Utils.asInt(rti._kind);
  static void _setKind(Rti rti, int kind) {
    rti._kind = kind;
  }

  // Terminal terms.
  static const kindNever = 1;
  static const kindDynamic = 2;
  static const kindVoid = 3; // TODO(sra): Use `dynamic` instead?
  static const kindAny = 4; // Dart1-style 'dynamic' for JS-interop.
  // Unary terms.
  static const kindStar = 5;
  static const kindQuestion = 6;
  static const kindFutureOr = 7;
  // More complex terms.
  static const kindInterface = 8;
  // A vector of type parameters from enclosing functions and closures.
  static const kindBinding = 9;
  static const kindFunction = 10;
  static const kindGenericFunction = 11;
  static const kindGenericFunctionParameter = 12;

  static bool _isUnionOfFunctionType(Rti rti) {
    int kind = Rti._getKind(rti);
    if (kind == kindStar || kind == kindQuestion || kind == kindFutureOr) {
      return _isUnionOfFunctionType(_castToRti(_getPrimary(rti)));
    }
    return kind == kindFunction || kind == kindGenericFunction;
  }

  /// Primary data associated with type.
  ///
  /// - Minified name of interface for interface types.
  /// - Underlying type for unary terms.
  /// - Class part of a type environment inside a generic class, or `null` for
  ///   type tuple.
  /// - Return type of a function type.
  /// - Underlying function type for a generic function.
  /// - de Bruijn index for a generic function parameter.
  dynamic _primary;

  static Object _getPrimary(Rti rti) => rti._primary;
  static void _setPrimary(Rti rti, value) {
    rti._primary = value;
  }

  /// Additional data associated with type.
  ///
  /// - The type arguments of an interface type.
  /// - The type arguments from enclosing functions and closures for a
  ///   kindBinding.
  /// - The [_FunctionParameters] of a function type.
  /// - The type parameter bounds of a generic function.
  dynamic _rest;

  static Object _getRest(Rti rti) => rti._rest;
  static void _setRest(Rti rti, value) {
    rti._rest = value;
  }

  static String _getInterfaceName(Rti rti) {
    assert(_getKind(rti) == kindInterface);
    return _Utils.asString(_getPrimary(rti));
  }

  static JSArray _getInterfaceTypeArguments(Rti rti) {
    // The array is a plain JavaScript Array, otherwise we would need the type
    // `JSArray<Rti>` to exist before we could create the type `JSArray<Rti>`.
    assert(_getKind(rti) == kindInterface);
    return JS('JSUnmodifiableArray', '#', _getRest(rti));
  }

  static Rti _getBindingBase(Rti rti) {
    assert(_getKind(rti) == kindBinding);
    return _castToRti(_getPrimary(rti));
  }

  static JSArray _getBindingArguments(Rti rti) {
    assert(_getKind(rti) == kindBinding);
    return JS('JSUnmodifiableArray', '#', _getRest(rti));
  }

  static Rti _getStarArgument(Rti rti) {
    assert(_getKind(rti) == kindStar);
    return _castToRti(_getPrimary(rti));
  }

  static Rti _getQuestionArgument(Rti rti) {
    assert(_getKind(rti) == kindQuestion);
    return _castToRti(_getPrimary(rti));
  }

  static Rti _getFutureOrArgument(Rti rti) {
    assert(_getKind(rti) == kindFutureOr);
    return _castToRti(_getPrimary(rti));
  }

  static Rti _getReturnType(Rti rti) {
    assert(_getKind(rti) == kindFunction);
    return _castToRti(_getPrimary(rti));
  }

  static _FunctionParameters _getFunctionParameters(Rti rti) {
    assert(_getKind(rti) == kindFunction);
    return JS('_FunctionParameters', '#', _getRest(rti));
  }

  static Rti _getGenericFunctionBase(Rti rti) {
    assert(_getKind(rti) == kindGenericFunction);
    return _castToRti(_getPrimary(rti));
  }

  static JSArray _getGenericFunctionBounds(Rti rti) {
    assert(_getKind(rti) == kindGenericFunction);
    return JS('JSUnmodifiableArray', '#', _getRest(rti));
  }

  static int _getGenericFunctionParameterIndex(Rti rti) {
    assert(_getKind(rti) == kindGenericFunctionParameter);
    return _Utils.asInt(_getPrimary(rti));
  }

  /// On [Rti]s that are type environments*, derived types are cached on the
  /// environment to ensure fast canonicalization. Ground-term types (i.e. not
  /// dependent on class or function type parameters) are cached in the
  /// universe. This field starts as `null` and the cache is created on demand.
  ///
  /// *Any Rti can be a type environment, since we use the type for a function
  /// type environment. The ambiguity between 'generic class is the environment'
  /// and 'generic class is a singleton type argument' is resolved by using
  /// different indexing in the recipe.
  Object _evalCache;

  static Object _getEvalCache(Rti rti) => rti._evalCache;
  static void _setEvalCache(Rti rti, value) {
    rti._evalCache = value;
  }

  /// On [Rti]s that are type environments*, extended environments are cached on
  /// the base environment to ensure fast canonicalization.
  ///
  /// This field starts as `null` and the cache is created on demand.
  ///
  /// *This is valid only on kindInterface and kindBinding Rtis. The ambiguity
  /// between 'generic class is the base environment' and 'generic class is a
  /// singleton type argument' is resolved [TBD] (either (1) a bind1 cache, or
  /// (2)using `env._eval("@<0>")._bind(args)` in place of `env._bind1(args)`).
  ///
  /// On [Rti]s that are generic function types, results of instantiation are
  /// cached on the generic function type to ensure fast repeated
  /// instantiations.
  Object _bindCache;

  static Object _getBindCache(Rti rti) => rti._bindCache;
  static void _setBindCache(Rti rti, value) {
    rti._bindCache = value;
  }

  static Rti allocate() {
    return new Rti();
  }

  Object _canonicalRecipe;

  static String _getCanonicalRecipe(Rti rti) {
    Object s = rti._canonicalRecipe;
    assert(_Utils.isString(s), 'Missing canonical recipe');
    return _Utils.asString(s);
  }

  static void _setCanonicalRecipe(Rti rti, String s) {
    rti._canonicalRecipe = s;
  }
}

class _FunctionParameters {
  // TODO(fishythefish): Support required named parameters.

  static _FunctionParameters allocate() => _FunctionParameters();

  Object _requiredPositional;
  static JSArray _getRequiredPositional(_FunctionParameters parameters) =>
      JS('JSUnmodifiableArray', '#', parameters._requiredPositional);
  static void _setRequiredPositional(
      _FunctionParameters parameters, Object requiredPositional) {
    parameters._requiredPositional = requiredPositional;
  }

  Object _optionalPositional;
  static JSArray _getOptionalPositional(_FunctionParameters parameters) =>
      JS('JSUnmodifiableArray', '#', parameters._optionalPositional);
  static void _setOptionalPositional(
      _FunctionParameters parameters, Object optionalPositional) {
    parameters._optionalPositional = optionalPositional;
  }

  /// These are alternating name/type pairs; that is, the optional named
  /// parameters of the function
  ///
  ///   void foo({int bar, double baz})
  ///
  /// would be encoded as ["bar", int, "baz", double], where the even indices are
  /// the name [String]s and the odd indices are the type [Rti]s.
  ///
  /// Invariant: These pairs are sorted by name in lexicographically ascending order.
  Object _optionalNamed;
  static JSArray _getOptionalNamed(_FunctionParameters parameters) =>
      JS('JSUnmodifiableArray', '#', parameters._optionalNamed);
  static void _setOptionalNamed(
      _FunctionParameters parameters, Object optionalNamed) {
    parameters._optionalNamed = optionalNamed;
  }
}

Object _theUniverse() => JS_EMBEDDED_GLOBAL('', RTI_UNIVERSE);

Rti _rtiEval(Rti environment, String recipe) {
  return _Universe.evalInEnvironment(_theUniverse(), environment, recipe);
}

Rti _rtiBind1(Rti environment, Rti types) {
  return _Universe.bind1(_theUniverse(), environment, types);
}

Rti _rtiBind(Rti environment, Rti types) {
  return _Universe.bind(_theUniverse(), environment, types);
}

/// Evaluate a ground-term type.
/// Called from generated code.
Rti findType(String recipe) {
  return _Universe.eval(_theUniverse(), recipe);
}

/// Evaluate a type recipe in the environment of an instance.
Rti evalInInstance(instance, String recipe) {
  return _rtiEval(instanceType(instance), recipe);
}

/// Returns [genericFunctionRti] with type parameters bound to those specified
/// by [instantiationRti].
///
/// [genericFunctionRti] must be an rti representation with a number of generic
/// type parameters matching the number of types provided by [instantiationRti].
///
/// Called from generated code.
@pragma('dart2js:noInline')
Rti instantiatedGenericFunctionType(
    Rti genericFunctionRti, Rti instantiationRti) {
  var bounds = Rti._getGenericFunctionBounds(genericFunctionRti);
  var typeArguments = Rti._getInterfaceTypeArguments(instantiationRti);
  assert(_Utils.arrayLength(bounds) == _Utils.arrayLength(typeArguments));

  var cache = Rti._getBindCache(genericFunctionRti);
  if (cache == null) {
    cache = JS('', 'new Map()');
    Rti._setBindCache(genericFunctionRti, cache);
  }
  String key = Rti._getCanonicalRecipe(instantiationRti);
  var probe = _Utils.mapGet(cache, key);
  if (probe != null) return _castToRti(probe);
  Rti rti = _instantiate(_theUniverse(),
      Rti._getGenericFunctionBase(genericFunctionRti), typeArguments, 0);
  _Utils.mapSet(cache, key, rti);
  return rti;
}

/// Substitutes [typeArguments] for generic function parameters in [rti].
///
/// Generic function parameters are de Bruijn indices counting up through the
/// parameters' scopes to index into [typeArguments].
///
/// [depth] is the number of subsequent generic function parameters that are in
/// scope. This is subtracted off the de Bruijn index for the type parameter to
/// arrive at an potential index into [typeArguments].
Rti _instantiate(universe, Rti rti, Object typeArguments, int depth) {
  int kind = Rti._getKind(rti);
  switch (kind) {
    case Rti.kindNever:
    case Rti.kindDynamic:
    case Rti.kindVoid:
    case Rti.kindAny:
      return rti;
    case Rti.kindStar:
      Rti baseType = _castToRti(Rti._getPrimary(rti));
      Rti instantiatedBaseType =
          _instantiate(universe, baseType, typeArguments, depth);
      if (_Utils.isIdentical(instantiatedBaseType, baseType)) return rti;
      return _Universe._lookupStarRti(universe, instantiatedBaseType);
    case Rti.kindQuestion:
      Rti baseType = _castToRti(Rti._getPrimary(rti));
      Rti instantiatedBaseType =
          _instantiate(universe, baseType, typeArguments, depth);
      if (_Utils.isIdentical(instantiatedBaseType, baseType)) return rti;
      return _Universe._lookupQuestionRti(universe, instantiatedBaseType);
    case Rti.kindFutureOr:
      Rti baseType = _castToRti(Rti._getPrimary(rti));
      Rti instantiatedBaseType =
          _instantiate(universe, baseType, typeArguments, depth);
      if (_Utils.isIdentical(instantiatedBaseType, baseType)) return rti;
      return _Universe._lookupFutureOrRti(universe, instantiatedBaseType);
    case Rti.kindInterface:
      Object interfaceTypeArguments = Rti._getInterfaceTypeArguments(rti);
      Object instantiatedInterfaceTypeArguments = _instantiateArray(
          universe, interfaceTypeArguments, typeArguments, depth);
      if (_Utils.isIdentical(
          instantiatedInterfaceTypeArguments, interfaceTypeArguments))
        return rti;
      return _Universe._lookupInterfaceRti(universe, Rti._getInterfaceName(rti),
          instantiatedInterfaceTypeArguments);
    case Rti.kindBinding:
      Rti base = Rti._getBindingBase(rti);
      Rti instantiatedBase = _instantiate(universe, base, typeArguments, depth);
      Object arguments = Rti._getBindingArguments(rti);
      Object instantiatedArguments =
          _instantiateArray(universe, arguments, typeArguments, depth);
      if (_Utils.isIdentical(instantiatedBase, base) &&
          _Utils.isIdentical(instantiatedArguments, arguments)) return rti;
      return _Universe._lookupBindingRti(
          universe, instantiatedBase, instantiatedArguments);
    case Rti.kindFunction:
      Rti returnType = Rti._getReturnType(rti);
      Rti instantiatedReturnType =
          _instantiate(universe, returnType, typeArguments, depth);
      _FunctionParameters functionParameters = Rti._getFunctionParameters(rti);
      _FunctionParameters instantiatedFunctionParameters =
          _instantiateFunctionParameters(
              universe, functionParameters, typeArguments, depth);
      if (_Utils.isIdentical(instantiatedReturnType, returnType) &&
          _Utils.isIdentical(
              instantiatedFunctionParameters, functionParameters)) return rti;
      return _Universe._lookupFunctionRti(
          universe, instantiatedReturnType, instantiatedFunctionParameters);
    case Rti.kindGenericFunction:
      Object bounds = Rti._getGenericFunctionBounds(rti);
      depth += _Utils.arrayLength(bounds);
      Object instantiatedBounds =
          _instantiateArray(universe, bounds, typeArguments, depth);
      Rti base = Rti._getGenericFunctionBase(rti);
      Rti instantiatedBase = _instantiate(universe, base, typeArguments, depth);
      if (_Utils.isIdentical(instantiatedBounds, bounds) &&
          _Utils.isIdentical(instantiatedBase, base)) return rti;
      return _Universe._lookupGenericFunctionRti(
          universe, instantiatedBase, instantiatedBounds);
    case Rti.kindGenericFunctionParameter:
      int index = Rti._getGenericFunctionParameterIndex(rti);
      if (index < depth) return null;
      return _castToRti(_Utils.arrayAt(typeArguments, index - depth));
    default:
      throw AssertionError(
          'Attempted to instantiate unexpected RTI kind $kind');
  }
}

Object _instantiateArray(
    universe, Object rtiArray, Object typeArguments, int depth) {
  bool changed = false;
  int length = _Utils.arrayLength(rtiArray);
  Object result = JS('', '[]');
  for (int i = 0; i < length; i++) {
    Rti rti = _castToRti(_Utils.arrayAt(rtiArray, i));
    Rti instantiatedRti = _instantiate(universe, rti, typeArguments, depth);
    if (!_Utils.isIdentical(instantiatedRti, rti)) {
      changed = true;
    }
    _Utils.arrayPush(result, instantiatedRti);
  }
  return changed ? result : rtiArray;
}

Object _instantiateNamed(
    universe, Object namedArray, Object typeArguments, int depth) {
  bool changed = false;
  int length = _Utils.arrayLength(namedArray);
  assert(length.isEven);
  Object result = JS('', '[]');
  for (int i = 0; i < length; i += 2) {
    String name = _Utils.asString(_Utils.arrayAt(namedArray, i));
    Rti rti = _castToRti(_Utils.arrayAt(namedArray, i + 1));
    Rti instantiatedRti = _instantiate(universe, rti, typeArguments, depth);
    if (!_Utils.isIdentical(instantiatedRti, rti)) {
      changed = true;
    }
    _Utils.arrayPush(result, name);
    _Utils.arrayPush(result, instantiatedRti);
  }
  return changed ? result : namedArray;
}

// TODO(fishythefish): Support required named parameters.
_FunctionParameters _instantiateFunctionParameters(universe,
    _FunctionParameters functionParameters, Object typeArguments, int depth) {
  Object requiredPositional =
      _FunctionParameters._getRequiredPositional(functionParameters);
  Object instantiatedRequiredPositional =
      _instantiateArray(universe, requiredPositional, typeArguments, depth);
  Object optionalPositional =
      _FunctionParameters._getOptionalPositional(functionParameters);
  Object instantiatedOptionalPositional =
      _instantiateArray(universe, optionalPositional, typeArguments, depth);
  Object optionalNamed =
      _FunctionParameters._getOptionalNamed(functionParameters);
  Object instantiatedOptionalNamed =
      _instantiateNamed(universe, optionalNamed, typeArguments, depth);
  if (_Utils.isIdentical(instantiatedRequiredPositional, requiredPositional) &&
      _Utils.isIdentical(instantiatedOptionalPositional, optionalPositional) &&
      _Utils.isIdentical(instantiatedOptionalNamed, optionalNamed))
    return functionParameters;
  _FunctionParameters result = _FunctionParameters.allocate();
  _FunctionParameters._setRequiredPositional(
      result, instantiatedRequiredPositional);
  _FunctionParameters._setOptionalPositional(
      result, instantiatedOptionalPositional);
  _FunctionParameters._setOptionalNamed(result, instantiatedOptionalNamed);
  return result;
}

bool _isClosure(object) => _Utils.instanceOf(object,
    JS_BUILTIN('depends:none;effects:none;', JsBuiltin.dartClosureConstructor));

/// Returns the structural function [Rti] of [closure].
/// Called from generated code.
Rti closureFunctionType(closure) {
  var signatureName = JS_GET_NAME(JsGetName.SIGNATURE_NAME);
  var signature = JS('', '#[#]', closure, signatureName);
  if (signature != null) {
    if (JS('bool', 'typeof # == "number"', signature)) {
      return getTypeFromTypesTable(_Utils.asInt(signature));
    }
    return _castToRti(JS('', '#[#]()', closure, signatureName));
  }
  return null;
}

// Subclasses of Closure are synthetic classes. The synthetic classes all
// extend a 'normal' class (Closure, BoundClosure, StaticClosure), so make
// them appear to be the superclass.
// TODO(sra): Can this be done less expensively, e.g. by putting $ti on the
// prototype of Closure/BoundClosure/StaticClosure classes?
Rti _closureInterfaceType(closure) {
  var rti = JS('', r'#[#]', closure, JS_GET_NAME(JsGetName.RTI_NAME));
  return rti != null
      ? _castToRti(rti)
      : _instanceTypeFromConstructor(
          JS('', '#.__proto__.__proto__.constructor', closure));
}

/// Returns the Rti type of [object]. Closures have both an interface type
/// (Closures implement `Function`) and a structural function type. Uses
/// [testRti] to choose the appropriate type.
///
/// Called from generated code.
Rti instanceOrFunctionType(object, Rti testRti) {
  if (Rti._isUnionOfFunctionType(testRti)) {
    if (_isClosure(object)) {
      // If [testRti] is e.g. `FutureOr<Action>` (where `Action` is some
      // function type), we don't need to worry about the `Future<Action>`
      // branch because closures can't be `Future`s.
      Rti rti = closureFunctionType(object);
      if (rti != null) return rti;
    }
  }
  return instanceType(object);
}

/// Returns the Rti type of [object].
/// Called from generated code.
Rti instanceType(object) {
  if (_isClosure(object)) return _closureInterfaceType(object);
  return _nonClosureInstanceType(object);
}

Rti _nonClosureInstanceType(object) {
  // TODO(sra): Add specializations of this method. One possible way is to
  // arrange that the interceptor has a _getType method that is injected into
  // DartObject, Interceptor and JSArray. Then this method can be replaced-by
  // `getInterceptor(o)._getType(o)`, allowing interceptor optimizations to
  // select the specialization.

  if (_Utils.instanceOf(
      object,
      JS_BUILTIN(
          'depends:none;effects:none;', JsBuiltin.dartObjectConstructor))) {
    return _instanceType(object);
  }

  if (_Utils.isArray(object)) {
    return _arrayInstanceType(object);
  }

  var interceptor = getInterceptor(object);
  return _instanceTypeFromConstructor(JS('', '#.constructor', interceptor));
}

/// Returns the Rti type of JavaScript Array [object].
/// Called from generated code.
Rti _arrayInstanceType(object) {
  // TODO(sra): Do we need to protect against an Array passed between two Dart
  // programs loaded into the same JavaScript isolate (e.g. via JS-interop).
  // FWIW, the legacy rti has this problem too. Perhaps JSArrays should use a
  // program-local `symbol` for the type field.
  var rti = JS('', r'#[#]', object, JS_GET_NAME(JsGetName.RTI_NAME));
  return rti != null ? _castToRti(rti) : _castToRti(getJSArrayInteropRti());
}

/// Returns the Rti type of user-defined class [object].
/// [object] must not be an intercepted class or a closure.
/// Called from generated code.
Rti _instanceType(object) {
  var rti = JS('', r'#[#]', object, JS_GET_NAME(JsGetName.RTI_NAME));
  return rti != null
      ? _castToRti(rti)
      : _instanceTypeFromConstructor(JS('', '#.constructor', object));
}

String instanceTypeName(object) {
  Rti rti = instanceType(object);
  return _rtiToString(rti, null);
}

Rti _instanceTypeFromConstructor(constructor) {
  // TODO(sra): Cache Rti on constructor.
  return findType(JS('String', '#.name', constructor));
}

/// Returns the structural function type of [object], or `null` if the object is
/// not a closure.
Rti _instanceFunctionType(object) =>
    _isClosure(object) ? closureFunctionType(object) : null;

/// Returns Rti from types table. The types table is initialized with recipe
/// strings.
Rti getTypeFromTypesTable(/*int*/ _index) {
  int index = _Utils.asInt(_index);
  var table = JS_EMBEDDED_GLOBAL('', TYPES);
  var type = _Utils.arrayAt(table, index);
  if (_Utils.isString(type)) {
    Rti rti = findType(_Utils.asString(type));
    _Utils.arraySetAt(table, index, rti);
    return rti;
  }
  return _castToRti(type);
}

Type getRuntimeType(object) {
  Rti rti = _instanceFunctionType(object) ?? _nonClosureInstanceType(object);
  return createRuntimeType(rti);
}

/// Called from generated code.
Type createRuntimeType(Rti rti) {
  _Type type = Rti._getCachedRuntimeType(rti);
  if (type != null) return type;
  // TODO(https://github.com/dart-lang/language/issues/428) For NNBD transition,
  // canonicalization may be needed. It might be possible to generate a
  // star-free recipe from the canonical recipe and evaluate that.
  type = _Type(rti);
  Rti._setCachedRuntimeType(rti, type);
  return type;
}

/// Called from generated code in the constant pool.
Type typeLiteral(String recipe) {
  return createRuntimeType(findType(recipe));
}

/// Implementation of [Type] based on Rti.
class _Type implements Type {
  final Rti _rti;
  int _hashCode;

  _Type(this._rti);

  int get hashCode => _hashCode ??= Rti._getCanonicalRecipe(_rti).hashCode;

  @pragma('dart2js:noInline')
  bool operator ==(other) {
    return (other is _Type) && identical(_rti, other._rti);
  }

  @override
  String toString() => _rtiToString(_rti, null);
}

/// Called from generated code.
bool _generalIsTestImplementation(object) {
  // This static method is installed on an Rti object as a JavaScript instance
  // method. The Rti object is 'this'.
  Rti testRti = _castToRti(JS('', 'this'));
  Rti objectRti = instanceOrFunctionType(object, testRti);
  return isSubtype(_theUniverse(), objectRti, testRti);
}

/// Called from generated code.
_generalAsCheckImplementation(object) {
  if (object == null) return object;
  // This static method is installed on an Rti object as a JavaScript instance
  // method. The Rti object is 'this'.
  Rti testRti = _castToRti(JS('', 'this'));
  if (Rti._isCheck(testRti, object)) return object;

  Rti objectRti = instanceOrFunctionType(object, testRti);
  String message =
      _Error.compose(object, objectRti, _rtiToString(testRti, null));
  throw _CastError.fromMessage(message);
}

/// Called from generated code.
_generalTypeCheckImplementation(object) {
  if (object == null) return object;
  // This static method is installed on an Rti object as a JavaScript instance
  // method. The Rti object is 'this'.
  Rti testRti = _castToRti(JS('', 'this'));
  if (Rti._isCheck(testRti, object)) return object;

  Rti objectRti = instanceOrFunctionType(object, testRti);
  String message =
      _Error.compose(object, objectRti, _rtiToString(testRti, null));
  throw _TypeError.fromMessage(message);
}

/// Called from generated code.
checkTypeBound(Rti type, Rti bound, variable) {
  if (isSubtype(_theUniverse(), type, bound)) return type;
  String message = "Type '${_rtiToString(type, null)}'"
      " is not a subtype of type '${_rtiToString(bound, null)}'"
      " of '${_Utils.asString(variable)}'";
  throw _TypeError.fromMessage(message);
}

/// Base class to _CastError and _TypeError.
class _Error extends Error {
  final String _message;
  _Error(this._message);

  static String compose(object, objectRti, checkedTypeDescription) {
    String objectDescription = Error.safeToString(object);
    objectRti ??= instanceType(object);
    String objectTypeDescription = _rtiToString(objectRti, null);
    return "${objectDescription}:"
        " type '${objectTypeDescription}'"
        " is not a subtype of type '${checkedTypeDescription}'";
  }

  @override
  String toString() => _message;
}

class _CastError extends _Error implements CastError {
  _CastError.fromMessage(String message) : super('CastError: $message');

  factory _CastError.forType(object, String type) {
    return _CastError.fromMessage(_Error.compose(object, null, type));
  }
}

class _TypeError extends _Error implements TypeError {
  _TypeError.fromMessage(String message) : super('TypeError: $message');

  factory _TypeError.forType(object, String type) {
    return _TypeError.fromMessage(_Error.compose(object, null, type));
  }

  @override
  String get message => _message;
}

// Specializations.
//
// Specializations can be placed on Rti objects as the _as, _check and _is
// 'methods'. They can also be called directly called from generated code.

/// Specialization for 'is bool'.
/// Called from generated code.
bool _isBool(object) {
  return true == object || false == object;
}

/// Specialization for 'as bool?'.
/// Called from generated code.
bool /*?*/ _asBoolNullable(object) {
  if (_isBool(object)) return _Utils.asBool(object);
  if (object == null) return object;
  throw _CastError.forType(object, 'bool');
}

/// Specialization for check on 'bool?'.
/// Called from generated code.
bool /*?*/ _checkBoolNullable(object) {
  if (_isBool(object)) return _Utils.asBool(object);
  if (object == null) return object;
  throw _TypeError.forType(object, 'bool');
}

/// Specialization for 'as double?'.
/// Called from generated code.
double /*?*/ _asDoubleNullable(object) {
  if (_isNum(object)) return _Utils.asDouble(object);
  if (object == null) return object;
  throw _CastError.forType(object, 'double');
}

/// Specialization for check on 'double?'.
/// Called from generated code.
double /*?*/ _checkDoubleNullable(object) {
  if (_isNum(object)) return _Utils.asDouble(object);
  if (object == null) return object;
  throw _TypeError.forType(object, 'double');
}

/// Specialization for 'is int'.
/// Called from generated code.
bool _isInt(object) {
  return JS('bool', 'typeof # == "number"', object) &&
      JS('bool', 'Math.floor(#) === #', object, object);
}

/// Specialization for 'as int?'.
/// Called from generated code.
int /*?*/ _asIntNullable(object) {
  if (_isInt(object)) return _Utils.asInt(object);
  if (object == null) return object;
  throw _CastError.forType(object, 'int');
}

/// Specialization for check on 'int?'.
/// Called from generated code.
int /*?*/ _checkIntNullable(object) {
  if (_isInt(object)) return _Utils.asInt(object);
  if (object == null) return object;
  throw _TypeError.forType(object, 'int');
}

/// Specialization for 'is num' and 'is double'.
/// Called from generated code.
bool _isNum(object) {
  return JS('bool', 'typeof # == "number"', object);
}

/// Specialization for 'as num?'.
/// Called from generated code.
num /*?*/ _asNumNullable(object) {
  if (_isNum(object)) return _Utils.asNum(object);
  if (object == null) return object;
  throw _CastError.forType(object, 'num');
}

/// Specialization for check on 'num?'.
/// Called from generated code.
num /*?*/ _checkNumNullable(object) {
  if (_isNum(object)) return _Utils.asNum(object);
  if (object == null) return object;
  throw _TypeError.forType(object, 'num');
}

/// Specialization for 'is String'.
/// Called from generated code.
bool _isString(object) {
  return JS('bool', 'typeof # == "string"', object);
}

/// Specialization for 'as String?'.
/// Called from generated code.
String /*?*/ _asStringNullable(object) {
  if (_isString(object)) return _Utils.asString(object);
  if (object == null) return object;
  throw _CastError.forType(object, 'String');
}

/// Specialization for check on 'String?'.
/// Called from generated code.
String /*?*/ _checkStringNullable(object) {
  if (_isString(object)) return _Utils.asString(object);
  if (object == null) return object;
  throw _TypeError.forType(object, 'String');
}

String _rtiArrayToString(Object array, List<String> genericContext) {
  String s = '', sep = '';
  for (int i = 0; i < _Utils.arrayLength(array); i++) {
    s += sep +
        _rtiToString(_castToRti(_Utils.arrayAt(array, i)), genericContext);
    sep = ', ';
  }
  return s;
}

String _functionRtiToString(Rti functionType, List<String> genericContext,
    {Object bounds = null}) {
  String typeParametersText = '';
  int outerContextLength;

  if (bounds != null) {
    int boundsLength = _Utils.arrayLength(bounds);
    if (genericContext == null) {
      genericContext = <String>[];
    } else {
      outerContextLength = genericContext.length;
    }
    int offset = genericContext.length;
    for (int i = boundsLength; i > 0; i--) {
      genericContext.add('T${offset + i}');
    }

    String typeSep = '';
    typeParametersText = '<';
    for (int i = 0; i < boundsLength; i++) {
      typeParametersText += typeSep;
      typeParametersText += genericContext[genericContext.length - 1 - i];
      Rti boundRti = _castToRti(_Utils.arrayAt(bounds, i));
      if (!isTopType(boundRti)) {
        typeParametersText +=
            ' extends ' + _rtiToString(boundRti, genericContext);
      }
      typeSep = ', ';
    }
    typeParametersText += '>';
  }

  // TODO(fishythefish): Support required named parameters.
  Rti returnType = Rti._getReturnType(functionType);
  _FunctionParameters parameters = Rti._getFunctionParameters(functionType);
  var requiredPositional =
      _FunctionParameters._getRequiredPositional(parameters);
  int requiredPositionalLength = _Utils.arrayLength(requiredPositional);
  var optionalPositional =
      _FunctionParameters._getOptionalPositional(parameters);
  int optionalPositionalLength = _Utils.arrayLength(optionalPositional);
  var optionalNamed = _FunctionParameters._getOptionalNamed(parameters);
  int optionalNamedLength = _Utils.arrayLength(optionalNamed);
  assert(optionalPositionalLength == 0 || optionalNamedLength == 0);

  String returnTypeText = _rtiToString(returnType, genericContext);

  String argumentsText = '';
  String sep = '';
  for (int i = 0; i < requiredPositionalLength; i++) {
    argumentsText += sep +
        _rtiToString(
            _castToRti(_Utils.arrayAt(requiredPositional, i)), genericContext);
    sep = ', ';
  }

  if (optionalPositionalLength > 0) {
    argumentsText += sep + '[';
    sep = '';
    for (int i = 0; i < optionalPositionalLength; i++) {
      argumentsText += sep +
          _rtiToString(_castToRti(_Utils.arrayAt(optionalPositional, i)),
              genericContext);
      sep = ', ';
    }
    argumentsText += ']';
  }

  if (optionalNamedLength > 0) {
    argumentsText += sep + '{';
    sep = '';
    for (int i = 0; i < optionalNamedLength; i += 2) {
      argumentsText += sep +
          _rtiToString(_castToRti(_Utils.arrayAt(optionalNamed, i + 1)),
              genericContext) +
          ' ' +
          _Utils.asString(_Utils.arrayAt(optionalNamed, i));
      sep = ', ';
    }
    argumentsText += '}';
  }

  if (outerContextLength != null) {
    // Pop all of the generic type parameters.
    JS('', '#.length = #', genericContext, outerContextLength);
  }

  // TODO(fishythefish): Below is the same format as the VM. Change to:
  //
  //     return '${returnTypeText} Function${typeParametersText}(${argumentsText})';
  //
  return '${typeParametersText}(${argumentsText}) => ${returnTypeText}';
}

String _rtiToString(Rti rti, List<String> genericContext) {
  int kind = Rti._getKind(rti);

  if (kind == Rti.kindDynamic) return 'dynamic';
  if (kind == Rti.kindVoid) return 'void';
  if (kind == Rti.kindNever) return 'Never';
  if (kind == Rti.kindAny) return 'any';

  if (kind == Rti.kindStar) {
    Rti starArgument = Rti._getStarArgument(rti);
    return '${_rtiToString(starArgument, genericContext)}*';
  }

  if (kind == Rti.kindQuestion) {
    Rti questionArgument = Rti._getQuestionArgument(rti);
    return '${_rtiToString(questionArgument, genericContext)}?';
  }

  if (kind == Rti.kindFutureOr) {
    Rti futureOrArgument = Rti._getFutureOrArgument(rti);
    return 'FutureOr<${_rtiToString(futureOrArgument, genericContext)}>';
  }

  if (kind == Rti.kindInterface) {
    String name = Rti._getInterfaceName(rti);
    name = _unminifyOrTag(name);
    var arguments = Rti._getInterfaceTypeArguments(rti);
    if (arguments.length != 0) {
      name += '<' + _rtiArrayToString(arguments, genericContext) + '>';
    }
    return name;
  }

  if (kind == Rti.kindFunction) {
    return _functionRtiToString(rti, genericContext);
  }

  if (kind == Rti.kindGenericFunction) {
    Rti baseFunctionType = Rti._getGenericFunctionBase(rti);
    Object bounds = Rti._getGenericFunctionBounds(rti);
    return _functionRtiToString(baseFunctionType, genericContext,
        bounds: bounds);
  }

  if (kind == Rti.kindGenericFunctionParameter) {
    int index = Rti._getGenericFunctionParameterIndex(rti);
    return genericContext[genericContext.length - 1 - index];
  }

  return '?';
}

String _unminifyOrTag(String rawClassName) {
  String preserved = unmangleGlobalNameIfPreservedAnyways(rawClassName);
  if (preserved != null) return preserved;
  return JS_GET_FLAG('MINIFIED') ? 'minified:$rawClassName' : rawClassName;
}

String _rtiArrayToDebugString(Object array) {
  String s = '[', sep = '';
  for (int i = 0; i < _Utils.arrayLength(array); i++) {
    s += sep + _rtiToDebugString(_castToRti(_Utils.arrayAt(array, i)));
    sep = ', ';
  }
  return s + ']';
}

String functionParametersToString(_FunctionParameters parameters) {
  // TODO(fishythefish): Support required named parameters.
  String s = '(', sep = '';
  var requiredPositional =
      _FunctionParameters._getRequiredPositional(parameters);
  int requiredPositionalLength = _Utils.arrayLength(requiredPositional);
  var optionalPositional =
      _FunctionParameters._getOptionalPositional(parameters);
  int optionalPositionalLength = _Utils.arrayLength(optionalPositional);
  var optionalNamed = _FunctionParameters._getOptionalNamed(parameters);
  int optionalNamedLength = _Utils.arrayLength(optionalNamed);
  assert(optionalPositionalLength == 0 || optionalNamedLength == 0);

  for (int i = 0; i < requiredPositionalLength; i++) {
    s += sep +
        _rtiToDebugString(_castToRti(_Utils.arrayAt(requiredPositional, i)));
    sep = ', ';
  }

  if (optionalPositionalLength > 0) {
    s += sep + '[';
    sep = '';
    for (int i = 0; i < optionalPositionalLength; i++) {
      s += sep +
          _rtiToDebugString(_castToRti(_Utils.arrayAt(optionalPositional, i)));
      sep = ', ';
    }
    s += ']';
  }

  if (optionalNamedLength > 0) {
    s += sep + '{';
    sep = '';
    for (int i = 0; i < optionalNamedLength; i += 2) {
      s += sep +
          _rtiToDebugString(_castToRti(_Utils.arrayAt(optionalNamed, i + 1))) +
          ' ' +
          _Utils.asString(_Utils.arrayAt(optionalNamed, i));
      sep = ', ';
    }
    s += '}';
  }

  return s + ')';
}

String _rtiToDebugString(Rti rti) {
  int kind = Rti._getKind(rti);

  if (kind == Rti.kindDynamic) return 'dynamic';
  if (kind == Rti.kindVoid) return 'void';
  if (kind == Rti.kindNever) return 'Never';
  if (kind == Rti.kindAny) return 'any';

  if (kind == Rti.kindStar) {
    Rti starArgument = Rti._getStarArgument(rti);
    return 'star(${_rtiToDebugString(starArgument)})';
  }

  if (kind == Rti.kindQuestion) {
    Rti questionArgument = Rti._getQuestionArgument(rti);
    return 'question(${_rtiToDebugString(questionArgument)})';
  }

  if (kind == Rti.kindFutureOr) {
    Rti futureOrArgument = Rti._getFutureOrArgument(rti);
    return 'FutureOr(${_rtiToDebugString(futureOrArgument)})';
  }

  if (kind == Rti.kindInterface) {
    String name = Rti._getInterfaceName(rti);
    var arguments = Rti._getInterfaceTypeArguments(rti);
    if (_Utils.arrayLength(arguments) == 0) {
      return 'interface("$name")';
    } else {
      return 'interface("$name", ${_rtiArrayToDebugString(arguments)})';
    }
  }

  if (kind == Rti.kindBinding) {
    Rti base = Rti._getBindingBase(rti);
    var arguments = Rti._getBindingArguments(rti);
    return 'binding(${_rtiToDebugString(base)}, ${_rtiArrayToDebugString(arguments)})';
  }

  if (kind == Rti.kindFunction) {
    Rti returnType = Rti._getReturnType(rti);
    _FunctionParameters parameters = Rti._getFunctionParameters(rti);
    return 'function(${_rtiToDebugString(returnType)}, ${functionParametersToString(parameters)})';
  }

  if (kind == Rti.kindGenericFunction) {
    Rti baseFunctionType = Rti._getGenericFunctionBase(rti);
    Object bounds = Rti._getGenericFunctionBounds(rti);
    return 'genericFunction(${_rtiToDebugString(baseFunctionType)}, ${_rtiArrayToDebugString(bounds)})';
  }

  if (kind == Rti.kindGenericFunctionParameter) {
    int index = Rti._getGenericFunctionParameterIndex(rti);
    return 'genericFunctionParameter($index)';
  }

  return 'other(kind=$kind)';
}

/// Class of static methods for the universe of Rti objects.
///
/// The universe is the manager object for the Rti instances.
///
/// The universe itself is allocated at startup before any types or Dart objects
/// can be created, so it does not have a Dart type.
class _Universe {
  _Universe._() {
    throw UnimplementedError('_Universe is static methods only');
  }

  @pragma('dart2js:noInline')
  static Object create() {
    // This needs to be kept in sync with `FragmentEmitter.createRtiUniverse` in
    // `fragment_emitter.dart`.
    return JS(
        '',
        '{'
            '#: new Map(),'
            '#: {},'
            '#: [],' // shared empty array.
            '}',
        RtiUniverseFieldNames.evalCache,
        RtiUniverseFieldNames.typeRules,
        RtiUniverseFieldNames.sharedEmptyArray);
  }

  // Field accessors.

  static evalCache(universe) =>
      JS('', '#.#', universe, RtiUniverseFieldNames.evalCache);

  static Object typeRules(universe) =>
      JS('', '#.#', universe, RtiUniverseFieldNames.typeRules);

  static Object findRule(universe, String targetType) =>
      JS('', '#.#', typeRules(universe), targetType);

  static void addRules(universe, rules) {
    // TODO(fishythefish): Use `Object.assign()` when IE11 is deprecated.
    var keys = JS('JSArray', 'Object.keys(#)', rules);
    int length = _Utils.arrayLength(keys);
    Object ruleset = typeRules(universe);
    for (int i = 0; i < length; i++) {
      String targetType = _Utils.asString(_Utils.arrayAt(keys, i));
      JS('', '#[#] = #[#]', ruleset, targetType, rules, targetType);
    }
  }

  static Object sharedEmptyArray(universe) =>
      JS('JSArray', '#.#', universe, RtiUniverseFieldNames.sharedEmptyArray);

  /// Evaluates [recipe] in the global environment.
  static Rti eval(Object universe, String recipe) {
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, recipe);
    if (probe != null) return _castToRti(probe);
    Rti rti = _parseRecipe(universe, null, recipe);
    _cacheSet(cache, recipe, rti);
    return rti;
  }

  static Rti evalInEnvironment(
      Object universe, Rti environment, String recipe) {
    var cache = Rti._getEvalCache(environment);
    if (cache == null) {
      cache = JS('', 'new Map()');
      Rti._setEvalCache(environment, cache);
    }
    var probe = _cacheGet(cache, recipe);
    if (probe != null) return _castToRti(probe);
    Rti rti = _parseRecipe(universe, environment, recipe);
    _cacheSet(cache, recipe, rti);
    return rti;
  }

  static Rti bind(Object universe, Rti environment, Rti argumentsRti) {
    var cache = Rti._getBindCache(environment);
    if (cache == null) {
      cache = JS('', 'new Map()');
      Rti._setBindCache(environment, cache);
    }
    String argumentsRecipe = Rti._getCanonicalRecipe(argumentsRti);
    var probe = _cacheGet(cache, argumentsRecipe);
    if (probe != null) return _castToRti(probe);
    var argumentsArray;
    if (Rti._getKind(argumentsRti) == Rti.kindBinding) {
      argumentsArray = Rti._getBindingArguments(argumentsRti);
    } else {
      argumentsArray = JS('', '[#]', argumentsRti);
    }
    Rti rti = _lookupBindingRti(universe, environment, argumentsArray);
    _cacheSet(cache, argumentsRecipe, rti);
    return rti;
  }

  static Rti bind1(Object universe, Rti environment, Rti argumentsRti) {
    throw UnimplementedError('_Universe.bind1');
  }

  static Rti evalTypeVariable(Object universe, Rti environment, String name) {
    if (Rti._getKind(environment) == Rti.kindBinding) {
      environment = Rti._getBindingBase(environment);
    }

    assert(Rti._getKind(environment) == Rti.kindInterface);
    String interfaceName = Rti._getInterfaceName(environment);
    Object rule = _Universe.findRule(universe, interfaceName);
    assert(rule != null);
    String recipe = TypeRule.lookupTypeVariable(rule, name);
    return _Universe.evalInEnvironment(universe, environment, recipe);
  }

  static _cacheGet(cache, key) => JS('', '#.get(#)', cache, key);
  static void _cacheSet(cache, key, value) {
    JS('', '#.set(#, #)', cache, key, value);
  }

  static Rti _parseRecipe(Object universe, Object environment, String recipe) {
    Object parser = _Parser.create(universe, environment, recipe);
    Rti rti = _Parser.parse(parser);
    if (rti != null) return rti;
    throw UnimplementedError('_Universe._parseRecipe("$recipe")');
  }

  static Rti _finishRti(Object universe, Rti rti) {
    // Enter fresh Rti in global table under it's canonical recipe.
    String key = Rti._getCanonicalRecipe(rti);
    _cacheSet(evalCache(universe), key, rti);

    // Set up methods to perform type tests.

    // TODO(sra): Find better way to install specializations. Perhaps the
    // installed version should replace itself with the specialization.
    var checkFn = RAW_DART_FUNCTION_REF(_generalTypeCheckImplementation);
    var asFn = RAW_DART_FUNCTION_REF(_generalAsCheckImplementation);
    var isFn = RAW_DART_FUNCTION_REF(_generalIsTestImplementation);

    if (JS_GET_NAME(JsGetName.INT_RECIPE) == key) {
      isFn = RAW_DART_FUNCTION_REF(_isInt);
    } else if (JS_GET_NAME(JsGetName.DOUBLE_RECIPE) == key) {
      isFn = RAW_DART_FUNCTION_REF(_isNum);
    } else if (JS_GET_NAME(JsGetName.NUM_RECIPE) == key) {
      isFn = RAW_DART_FUNCTION_REF(_isNum);
    } else if (JS_GET_NAME(JsGetName.STRING_RECIPE) == key) {
      isFn = RAW_DART_FUNCTION_REF(_isString);
    } else if (JS_GET_NAME(JsGetName.BOOL_RECIPE) == key) {
      isFn = RAW_DART_FUNCTION_REF(_isBool);
    }

    Rti._setAsCheckFunction(rti, asFn);
    Rti._setTypeCheckFunction(rti, checkFn);
    Rti._setIsTestFunction(rti, isFn);
    return rti;
  }

  // For each kind of Rti there are three methods:
  //
  // * `lookupXXX` which takes the component parts and returns an existing Rti
  //   object if it exists.
  // * `canonicalRecipeOfXXX` that returns the compositional canonical recipe
  //   for the proposed type.
  // * `createXXX` to create the type if it does not exist.

  static String _canonicalRecipeOfDynamic() => Recipe.pushDynamicString;
  static String _canonicalRecipeOfVoid() => Recipe.pushVoidString;
  static String _canonicalRecipeOfNever() =>
      Recipe.pushNeverExtensionString + Recipe.extensionOpString;
  static String _canonicalRecipeOfAny() =>
      Recipe.pushAnyExtensionString + Recipe.extensionOpString;

  static String _canonicalRecipeOfStar(Rti baseType) =>
      Rti._getCanonicalRecipe(baseType) + Recipe.wrapStarString;
  static String _canonicalRecipeOfQuestion(Rti baseType) =>
      Rti._getCanonicalRecipe(baseType) + Recipe.wrapQuestionString;
  static String _canonicalRecipeOfFutureOr(Rti baseType) =>
      Rti._getCanonicalRecipe(baseType) + Recipe.wrapFutureOrString;

  static String _canonicalRecipeOfGenericFunctionParameter(int index) =>
      '$index' + Recipe.genericFunctionTypeParameterIndexString;

  static Rti _lookupDynamicRti(universe) {
    return _lookupTerminalRti(
        universe, Rti.kindDynamic, _canonicalRecipeOfDynamic());
  }

  static Rti _lookupVoidRti(universe) {
    return _lookupTerminalRti(universe, Rti.kindVoid, _canonicalRecipeOfVoid());
  }

  static Rti _lookupNeverRti(universe) {
    return _lookupTerminalRti(
        universe, Rti.kindNever, _canonicalRecipeOfNever());
  }

  static Rti _lookupAnyRti(universe) {
    return _lookupTerminalRti(universe, Rti.kindAny, _canonicalRecipeOfAny());
  }

  static Rti _lookupTerminalRti(universe, int kind, String canonicalRecipe) {
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, canonicalRecipe);
    if (probe != null) return _castToRti(probe);
    return _createTerminalRti(universe, kind, canonicalRecipe);
  }

  static Rti _createTerminalRti(universe, int kind, String canonicalRecipe) {
    Rti rti = Rti.allocate();
    Rti._setKind(rti, kind);
    Rti._setCanonicalRecipe(rti, canonicalRecipe);
    return _finishRti(universe, rti);
  }

  static Rti _lookupStarRti(universe, Rti baseType) => _lookupUnaryRti(
      universe, Rti.kindStar, baseType, _canonicalRecipeOfStar(baseType));

  static Rti _lookupQuestionRti(universe, Rti baseType) => _lookupUnaryRti(
      universe,
      Rti.kindQuestion,
      baseType,
      _canonicalRecipeOfQuestion(baseType));

  static Rti _lookupFutureOrRti(universe, Rti baseType) => _lookupUnaryRti(
      universe,
      Rti.kindFutureOr,
      baseType,
      _canonicalRecipeOfFutureOr(baseType));

  static Rti _lookupUnaryRti(
      universe, int kind, Rti baseType, String canonicalRecipe) {
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, canonicalRecipe);
    if (probe != null) return _castToRti(probe);
    return _createUnaryRti(universe, kind, baseType, canonicalRecipe);
  }

  static Rti _createUnaryRti(
      universe, int kind, Rti baseType, String canonicalRecipe) {
    Rti rti = Rti.allocate();
    Rti._setKind(rti, kind);
    Rti._setPrimary(rti, baseType);
    Rti._setCanonicalRecipe(rti, canonicalRecipe);
    return _finishRti(universe, rti);
  }

  static Rti _lookupGenericFunctionParameterRti(universe, int index) {
    String canonicalRecipe = _canonicalRecipeOfGenericFunctionParameter(index);
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, canonicalRecipe);
    if (probe != null) return _castToRti(probe);
    return _createGenericFunctionParameterRti(universe, index, canonicalRecipe);
  }

  static Rti _createGenericFunctionParameterRti(
      universe, int index, String canonicalRecipe) {
    Rti rti = Rti.allocate();
    Rti._setKind(rti, Rti.kindGenericFunctionParameter);
    Rti._setPrimary(rti, index);
    Rti._setCanonicalRecipe(rti, canonicalRecipe);
    return _finishRti(universe, rti);
  }

  static String _canonicalRecipeJoin(Object arguments) {
    String s = '', sep = '';
    int length = _Utils.arrayLength(arguments);
    for (int i = 0; i < length; i++) {
      Rti argument = _castToRti(_Utils.arrayAt(arguments, i));
      String subrecipe = Rti._getCanonicalRecipe(argument);
      s += sep + subrecipe;
      sep = Recipe.separatorString;
    }
    return s;
  }

  static String _canonicalRecipeJoinNamed(Object arguments) {
    String s = '', sep = '';
    int length = _Utils.arrayLength(arguments);
    assert(length.isEven);
    for (int i = 0; i < length; i += 2) {
      String name = _Utils.asString(_Utils.arrayAt(arguments, i));
      Rti type = _castToRti(_Utils.arrayAt(arguments, i + 1));
      String subrecipe = Rti._getCanonicalRecipe(type);
      s += sep + name + Recipe.nameSeparatorString + subrecipe;
      sep = Recipe.separatorString;
    }
    return s;
  }

  static String _canonicalRecipeOfInterface(String name, Object arguments) {
    assert(_Utils.isString(name));
    String s = _Utils.asString(name);
    int length = _Utils.arrayLength(arguments);
    if (length != 0) {
      s += Recipe.startTypeArgumentsString +
          _canonicalRecipeJoin(arguments) +
          Recipe.endTypeArgumentsString;
    }
    return s;
  }

  static Rti _lookupInterfaceRti(
      Object universe, String name, Object arguments) {
    String key = _canonicalRecipeOfInterface(name, arguments);
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, key);
    if (probe != null) return _castToRti(probe);
    return _createInterfaceRti(universe, name, arguments, key);
  }

  static Rti _createInterfaceRti(
      Object universe, String name, Object typeArguments, String key) {
    Rti rti = Rti.allocate();
    Rti._setKind(rti, Rti.kindInterface);
    Rti._setPrimary(rti, name);
    Rti._setRest(rti, typeArguments);
    Rti._setCanonicalRecipe(rti, key);
    return _finishRti(universe, rti);
  }

  static String _canonicalRecipeOfBinding(Rti base, Object arguments) {
    String s = Rti._getCanonicalRecipe(base);
    s += Recipe
        .toTypeString; // TODO(sra): Omit when base encoding is Rti without ToType.
    s += Recipe.startTypeArgumentsString +
        _canonicalRecipeJoin(arguments) +
        Recipe.endTypeArgumentsString;
    return s;
  }

  /// [arguments] becomes owned by the created Rti.
  static Rti _lookupBindingRti(Object universe, Rti base, Object arguments) {
    Rti newBase = base;
    Object newArguments = arguments;
    if (Rti._getKind(base) == Rti.kindBinding) {
      newBase = Rti._getBindingBase(base);
      newArguments =
          _Utils.arrayConcat(Rti._getBindingArguments(base), arguments);
    }
    String key = _canonicalRecipeOfBinding(newBase, newArguments);
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, key);
    if (probe != null) return _castToRti(probe);
    return _createBindingRti(universe, newBase, newArguments, key);
  }

  static Rti _createBindingRti(
      Object universe, Rti base, Object arguments, String key) {
    Rti rti = Rti.allocate();
    Rti._setKind(rti, Rti.kindBinding);
    Rti._setPrimary(rti, base);
    Rti._setRest(rti, arguments);
    Rti._setCanonicalRecipe(rti, key);
    return _finishRti(universe, rti);
  }

  static String _canonicalRecipeOfFunction(
          Rti returnType, _FunctionParameters parameters) =>
      Rti._getCanonicalRecipe(returnType) +
      _canonicalRecipeOfFunctionParameters(parameters);

  // TODO(fishythefish): Support required named parameters.
  static String _canonicalRecipeOfFunctionParameters(
      _FunctionParameters parameters) {
    var requiredPositional =
        _FunctionParameters._getRequiredPositional(parameters);
    int requiredPositionalLength = _Utils.arrayLength(requiredPositional);
    var optionalPositional =
        _FunctionParameters._getOptionalPositional(parameters);
    int optionalPositionalLength = _Utils.arrayLength(optionalPositional);
    var optionalNamed = _FunctionParameters._getOptionalNamed(parameters);
    int optionalNamedLength = _Utils.arrayLength(optionalNamed);
    assert(optionalPositionalLength == 0 || optionalNamedLength == 0);

    String recipe = Recipe.startFunctionArgumentsString +
        _canonicalRecipeJoin(requiredPositional);

    if (optionalPositionalLength > 0) {
      String sep = requiredPositionalLength > 0 ? Recipe.separatorString : '';
      recipe += sep +
          Recipe.startOptionalGroupString +
          _canonicalRecipeJoin(optionalPositional) +
          Recipe.endOptionalGroupString;
    }

    if (optionalNamedLength > 0) {
      String sep = requiredPositionalLength > 0 ? Recipe.separatorString : '';
      recipe += sep +
          Recipe.startNamedGroupString +
          _canonicalRecipeJoinNamed(optionalNamed) +
          Recipe.endNamedGroupString;
    }

    return recipe + Recipe.endFunctionArgumentsString;
  }

  static Rti _lookupFunctionRti(
      Object universe, Rti returnType, _FunctionParameters parameters) {
    String key = _canonicalRecipeOfFunction(returnType, parameters);
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, key);
    if (probe != null) return _castToRti(probe);
    return _createFunctionRti(universe, returnType, parameters, key);
  }

  static Rti _createFunctionRti(Object universe, Rti returnType,
      _FunctionParameters parameters, String canonicalRecipe) {
    Rti rti = Rti.allocate();
    Rti._setKind(rti, Rti.kindFunction);
    Rti._setPrimary(rti, returnType);
    Rti._setRest(rti, parameters);
    Rti._setCanonicalRecipe(rti, canonicalRecipe);
    return _finishRti(universe, rti);
  }

  static String _canonicalRecipeOfGenericFunction(
          Rti baseFunctionType, Object bounds) =>
      Rti._getCanonicalRecipe(baseFunctionType) +
      Recipe.startTypeArgumentsString +
      _canonicalRecipeJoin(bounds) +
      Recipe.endTypeArgumentsString;

  static Rti _lookupGenericFunctionRti(
      Object universe, Rti baseFunctionType, Object bounds) {
    String key = _canonicalRecipeOfGenericFunction(baseFunctionType, bounds);
    var cache = evalCache(universe);
    var probe = _cacheGet(cache, key);
    if (probe != null) return _castToRti(probe);
    return _createGenericFunctionRti(universe, baseFunctionType, bounds, key);
  }

  static Rti _createGenericFunctionRti(Object universe, Rti baseFunctionType,
      Object bounds, String canonicalRecipe) {
    Rti rti = Rti.allocate();
    Rti._setKind(rti, Rti.kindGenericFunction);
    Rti._setPrimary(rti, baseFunctionType);
    Rti._setRest(rti, bounds);
    Rti._setCanonicalRecipe(rti, canonicalRecipe);
    return _finishRti(universe, rti);
  }
}

/// Class of static methods implementing recipe parser.
///
/// The recipe is a sequence of operations on a stack machine. The operations
/// are described below using the format
///
///      operation: stack elements before --- stack elements after
///
/// integer:  --- integer-value
///
/// identifier:  --- string-value
///
/// identifier-with-one-period:  --- type-variable-value
///
///   Period may be in any position, including first and last e.g. `.x`.
///
/// ',':  ---
///
///   Ignored. Used to separate elements.
///
/// ';': item  ---  ToType(item)
///
///   Used to separate elements.
///
/// '@': --- dynamicType
///
/// '~': --- voidType
///
/// '?':  type  ---  type?
///
/// '&':  0  ---  NeverType
/// '&':  1  ---  anyType
///
///   Escape op-code with small integer values for encoding rare operations.
///
/// '<':  --- position
///
///   Saves (pushes) position register, sets position register to end of stack.
///
/// '>':  name saved-position type ... type  ---  name<type, ..., type>
/// '>':  type saved-position type ... type  ---  binding(type, type, ..., type)
///
///   When first element is a String: Creates interface type from string 'name'
///   and the types pushed since the position register was last set. The types
///   are converted with a ToType operation. Restores position register to
///   previous saved value.
///
///   When first element is an Rti: Creates binding Rti wrapping the first
///   element. Binding Rtis are flattened: if the first element is a binding
///   Rti, the new binding Rti has the concatentation of the first element
///   bindings and new type.
///
///
/// The ToType operation coerces an item to an Rti. This saves encoding looking
/// up simple interface names and indexed variables.
///
///   ToType(string): Creates an interface Rti for the non-generic class.
///   ToType(integer): Indexes into the environment.
///   ToType(Rti): Same Rti
///
///
/// Notes on enviroments and indexing.
///
/// To avoid creating a binding Rti for a single function type parameter, the
/// type is passed without creating a 1-tuple object. This means that the
/// interface Rti for, say, `Map<num,dynamic>` serves as two environments with
/// different shapes. It is a class environment (K=num, V=dynamic) and a simple
/// 1-tuple environment. This is supported by index '0' refering to the whole
/// type, and '1 and '2' refering to K and V positionally:
///
///     interface("Map", [num,dynamic])
///     0                 1   2
///
/// Thus the type expression `List<K>` encodes as `List<1>` and in this
/// environment evaluates to `List<num>`. `List<Map<K,V>>` could be encoded as
/// either `List<0>` or `List<Map<1,2>>` (and in this environment evaluates to
/// `List<Map<num,dynamic>>`).
///
/// When `Map<num,dynamic>` is combined with a binding `<int,bool>` (e.g. inside
/// the instance method `Map<K,V>.cast<RK,RV>()`), '0' refers to the base object
/// of the binding, and then the numbering counts the bindings followed by the
/// class parameters.
///
///     binding(interface("Map", [num,dynamic]), [int, bool])
///             0                 3   4           1    2
///
/// Any environment can be reconstructed via a recipe. The above enviroment for
/// method `cast` can be constructed as the ground term
/// `Map<num,dynamic><int,bool>`, or (somewhat pointlessly) reconstructed via
/// `0<1,2>` or `Map<3,4><1,2>`. The ability to construct an environment
/// directly rather than via `bind` calls is used in folding sequences of `eval`
/// and `bind` calls.
///
/// While a single type parameter is passed as the type, multiple type
/// parameters are passed as a tuple. Tuples are encoded as a binding with an
/// ignored base. `dynamic` can be used as the base, giving an encoding like
/// `@<int,bool>`.
///
/// Bindings flatten, so `@<int><bool><num>` is the same as `@<int,bool,num>`.
///
/// The base of a binding does not have to have type parameters. Consider
/// `CodeUnits`, which mixes in `ListMixin<int>`. The environment inside of
/// `ListMixin.fold` (from the call `x.codeUnits.fold<bool>(...)`) would be
///
///     binding(interface("CodeUnits", []), [bool])
///
/// This can be encoded as `CodeUnits;<bool>` (note the `;` to force ToType to
/// avoid creating an interface type Rti with a single class type
/// argument). Metadata about the supertypes is used to resolve the recipe
/// `ListMixin.E` to `int`.

class _Parser {
  _Parser._() {
    throw UnimplementedError('_Parser is static methods only');
  }

  /// Creates a parser object for parsing a recipe against an environment in a
  /// universe.
  ///
  /// Marked as no-inline so the object literal is not cloned by inlining.
  @pragma('dart2js:noInline')
  static Object create(Object universe, Object environment, String recipe) {
    return JS(
        '',
        '{'
            'u:#,' // universe
            'e:#,' // environment
            'r:#,' // recipe
            's:[],' // stack
            'p:0,' // position of sequence start.
            '}',
        universe,
        environment,
        recipe);
  }

  // Field accessors for the parser.
  static Object universe(Object parser) => JS('', '#.u', parser);
  static Rti environment(Object parser) => JS('Rti', '#.e', parser);
  static String recipe(Object parser) => JS('String', '#.r', parser);
  static Object stack(Object parser) => JS('', '#.s', parser);
  static int position(Object parser) => JS('int', '#.p', parser);
  static void setPosition(Object parser, int p) {
    JS('', '#.p = #', parser, p);
  }

  static int charCodeAt(String s, int i) => JS('int', '#.charCodeAt(#)', s, i);
  static void push(Object stack, Object value) {
    JS('', '#.push(#)', stack, value);
  }

  static Object pop(Object stack) => JS('', '#.pop()', stack);

  static Rti parse(Object parser) {
    String source = _Parser.recipe(parser);
    Object stack = _Parser.stack(parser);
    int i = 0;
    while (i < source.length) {
      int ch = charCodeAt(source, i);
      if (Recipe.isDigit(ch)) {
        i = handleDigit(i + 1, ch, source, stack);
      } else if (Recipe.isIdentifierStart(ch)) {
        i = handleIdentifer(parser, i, source, stack, false);
      } else if (ch == Recipe.period) {
        i = handleIdentifer(parser, i, source, stack, true);
      } else {
        i++;
        switch (ch) {
          case Recipe.separator:
            break;

          case Recipe.nameSeparator:
            break;

          case Recipe.toType:
            push(stack,
                toType(universe(parser), environment(parser), pop(stack)));
            break;

          case Recipe.genericFunctionTypeParameterIndex:
            push(stack,
                toGenericFunctionParameter(universe(parser), pop(stack)));
            break;

          case Recipe.pushDynamic:
            push(stack, _Universe._lookupDynamicRti(universe(parser)));
            break;

          case Recipe.pushVoid:
            push(stack, _Universe._lookupVoidRti(universe(parser)));
            break;

          case Recipe.startTypeArguments:
            pushStackFrame(parser, stack);
            break;

          case Recipe.endTypeArguments:
            handleTypeArguments(parser, stack);
            break;

          case Recipe.extensionOp:
            handleExtendedOperations(parser, stack);
            break;

          case Recipe.wrapStar:
            Object u = universe(parser);
            push(
                stack,
                _Universe._lookupStarRti(
                    u, toType(u, environment(parser), pop(stack))));
            break;

          case Recipe.wrapQuestion:
            Object u = universe(parser);
            push(
                stack,
                _Universe._lookupQuestionRti(
                    u, toType(u, environment(parser), pop(stack))));
            break;

          case Recipe.wrapFutureOr:
            Object u = universe(parser);
            push(
                stack,
                _Universe._lookupFutureOrRti(
                    u, toType(u, environment(parser), pop(stack))));
            break;

          case Recipe.startFunctionArguments:
            pushStackFrame(parser, stack);
            break;

          case Recipe.endFunctionArguments:
            handleFunctionArguments(parser, stack);
            break;

          case Recipe.startOptionalGroup:
            pushStackFrame(parser, stack);
            break;

          case Recipe.endOptionalGroup:
            handleOptionalGroup(parser, stack);
            break;

          case Recipe.startNamedGroup:
            pushStackFrame(parser, stack);
            break;

          case Recipe.endNamedGroup:
            handleNamedGroup(parser, stack);
            break;

          default:
            JS('', 'throw "Bad character " + #', ch);
        }
      }
    }
    Object item = pop(stack);
    return toType(universe(parser), environment(parser), item);
  }

  static void pushStackFrame(Object parser, Object stack) {
    push(stack, position(parser));
    setPosition(parser, _Utils.arrayLength(stack));
  }

  static int handleDigit(int i, int digit, String source, Object stack) {
    int value = Recipe.digitValue(digit);
    for (; i < source.length; i++) {
      int ch = charCodeAt(source, i);
      if (!Recipe.isDigit(ch)) break;
      value = value * 10 + Recipe.digitValue(ch);
    }
    push(stack, value);
    return i;
  }

  static int handleIdentifer(
      Object parser, int start, String source, Object stack, bool hasPeriod) {
    int i = start + 1;
    for (; i < source.length; i++) {
      int ch = charCodeAt(source, i);
      if (ch == Recipe.period) {
        if (hasPeriod) break;
        hasPeriod = true;
      } else if (Recipe.isIdentifierStart(ch) || Recipe.isDigit(ch)) {
        // Accept.
      } else {
        break;
      }
    }
    String string = _Utils.substring(source, start, i);
    if (hasPeriod) {
      push(
          stack,
          _Universe.evalTypeVariable(
              universe(parser), environment(parser), string));
    } else {
      push(stack, string);
    }
    return i;
  }

  static void handleTypeArguments(Object parser, Object stack) {
    Object universe = _Parser.universe(parser);
    Object arguments = collectArray(parser, stack);
    Object head = pop(stack);
    if (_Utils.isString(head)) {
      String name = _Utils.asString(head);
      push(stack, _Universe._lookupInterfaceRti(universe, name, arguments));
    } else {
      Rti base = toType(universe, environment(parser), head);
      switch (Rti._getKind(base)) {
        case Rti.kindFunction:
          push(stack,
              _Universe._lookupGenericFunctionRti(universe, base, arguments));
          break;

        default:
          push(stack, _Universe._lookupBindingRti(universe, base, arguments));
          break;
      }
    }
  }

  static const int optionalPositionalSentinel = -1;
  static const int optionalNamedSentinel = -2;

  static void handleFunctionArguments(Object parser, Object stack) {
    Object universe = _Parser.universe(parser);
    _FunctionParameters parameters = _FunctionParameters.allocate();
    var optionalPositional = _Universe.sharedEmptyArray(universe);
    var optionalNamed = _Universe.sharedEmptyArray(universe);

    Object head = pop(stack);
    if (_Utils.isNum(head)) {
      int sentinel = _Utils.asInt(head);
      switch (sentinel) {
        case optionalPositionalSentinel:
          optionalPositional = pop(stack);
          break;

        case optionalNamedSentinel:
          optionalNamed = pop(stack);
          break;

        default:
          push(stack, head);
          break;
      }
    } else {
      push(stack, head);
    }

    _FunctionParameters._setRequiredPositional(
        parameters, collectArray(parser, stack));
    _FunctionParameters._setOptionalPositional(parameters, optionalPositional);
    _FunctionParameters._setOptionalNamed(parameters, optionalNamed);
    Rti returnType = toType(universe, environment(parser), pop(stack));
    push(stack, _Universe._lookupFunctionRti(universe, returnType, parameters));
  }

  static void handleOptionalGroup(Object parser, Object stack) {
    Object parameters = collectArray(parser, stack);
    push(stack, parameters);
    push(stack, optionalPositionalSentinel);
  }

  static void handleNamedGroup(Object parser, Object stack) {
    Object parameters = collectNamed(parser, stack);
    push(stack, parameters);
    push(stack, optionalNamedSentinel);
  }

  static void handleExtendedOperations(Object parser, Object stack) {
    Object top = pop(stack);
    if (0 == top) {
      push(stack, _Universe._lookupNeverRti(universe(parser)));
      return;
    }
    if (1 == top) {
      push(stack, _Universe._lookupAnyRti(universe(parser)));
      return;
    }
    throw AssertionError('Unexpected extended operation $top');
  }

  static Object collectArray(Object parser, Object stack) {
    var array = _Utils.arraySplice(stack, position(parser));
    toTypes(_Parser.universe(parser), environment(parser), array);
    setPosition(parser, _Utils.asInt(pop(stack)));
    return array;
  }

  static Object collectNamed(Object parser, Object stack) {
    var array = _Utils.arraySplice(stack, position(parser));
    toTypesNamed(_Parser.universe(parser), environment(parser), array);
    setPosition(parser, _Utils.asInt(pop(stack)));
    return array;
  }

  /// Coerce a stack item into an Rti object. Strings are converted to interface
  /// types, integers are looked up in the type environment.
  static Rti toType(Object universe, Rti environment, Object item) {
    if (_Utils.isString(item)) {
      String name = _Utils.asString(item);
      // TODO(sra): Compile this out for minified code.
      if ('dynamic' == name) {
        return _Universe._lookupDynamicRti(universe);
      }
      return _Universe._lookupInterfaceRti(
          universe, name, _Universe.sharedEmptyArray(universe));
    } else if (_Utils.isNum(item)) {
      return _Parser.indexToType(universe, environment, _Utils.asInt(item));
    } else {
      return _castToRti(item);
    }
  }

  static void toTypes(Object universe, Rti environment, Object items) {
    int length = _Utils.arrayLength(items);
    for (int i = 0; i < length; i++) {
      var item = _Utils.arrayAt(items, i);
      Rti type = toType(universe, environment, item);
      _Utils.arraySetAt(items, i, type);
    }
  }

  static void toTypesNamed(Object universe, Rti environment, Object items) {
    int length = _Utils.arrayLength(items);
    assert(length.isEven);
    for (int i = 1; i < length; i += 2) {
      var item = _Utils.arrayAt(items, i);
      Rti type = toType(universe, environment, item);
      _Utils.arraySetAt(items, i, type);
    }
  }

  static Rti indexToType(Object universe, Rti environment, int index) {
    int kind = Rti._getKind(environment);
    if (kind == Rti.kindBinding) {
      if (index == 0) return Rti._getBindingBase(environment);
      var typeArguments = Rti._getBindingArguments(environment);
      int len = _Utils.arrayLength(typeArguments);
      if (index <= len) {
        return _castToRti(_Utils.arrayAt(typeArguments, index - 1));
      }
      // Is index into interface Rti in base.
      index -= len;
      environment = Rti._getBindingBase(environment);
      kind = Rti._getKind(environment);
    } else {
      if (index == 0) return environment;
    }
    if (kind != Rti.kindInterface) {
      throw AssertionError('Indexed base must be an interface type');
    }
    var typeArguments = Rti._getInterfaceTypeArguments(environment);
    int len = _Utils.arrayLength(typeArguments);
    if (index <= len) {
      return _castToRti(_Utils.arrayAt(typeArguments, index - 1));
    }
    throw AssertionError('Bad index $index for $environment');
  }

  static Rti toGenericFunctionParameter(Object universe, Object item) {
    assert(_Utils.isNum(item));
    return _Universe._lookupGenericFunctionParameterRti(
        universe, _Utils.asInt(item));
  }
}

/// Represents the set of supertypes and type variable bindings for a given
/// target type. The target type itself is not stored on the [TypeRule].
class TypeRule {
  TypeRule._() {
    throw UnimplementedError("TypeRule is static methods only.");
  }

  static String lookupTypeVariable(rule, String typeVariable) =>
      JS('', '#.#', rule, typeVariable);

  static JSArray lookupSupertype(rule, String supertype) =>
      JS('', '#.#', rule, supertype);
}

// -------- Subtype tests ------------------------------------------------------

// Future entry point from compiled code.
bool isSubtype(universe, Rti s, Rti t) {
  return _isSubtype(universe, s, null, t, null);
}

bool _isSubtype(universe, Rti s, sEnv, Rti t, tEnv) {
  // TODO(fishythefish): Update for NNBD. See
  // https://github.com/dart-lang/language/blob/master/resources/type-system/subtyping.md#rules

  // Subtyping is reflexive.
  if (_Utils.isIdentical(s, t)) return true;

  if (isTopType(t)) return true;

  if (isJsInteropType(s)) return true;

  if (isTopType(s)) {
    if (isGenericFunctionTypeParameter(t)) return false;
    if (isFutureOrType(t)) {
      // [t] is FutureOr<T>. Check [s] <: T.
      Rti tTypeArgument = Rti._getFutureOrArgument(t);
      return _isSubtype(universe, s, sEnv, tTypeArgument, tEnv);
    }
    return false;
  }

  // Generic function type parameters must match exactly, which would have
  // exited earlier.
  if (isGenericFunctionTypeParameter(s)) return false;
  if (isGenericFunctionTypeParameter(t)) return false;

  if (isNullType(s)) return true;

  if (isFutureOrType(t)) {
    // [t] is FutureOr<T>.
    Rti tTypeArgument = Rti._getFutureOrArgument(t);
    if (isFutureOrType(s)) {
      // [s] is FutureOr<S>. Check S <: T.
      Rti sTypeArgument = Rti._getFutureOrArgument(s);
      return _isSubtype(universe, sTypeArgument, sEnv, tTypeArgument, tEnv);
    } else if (_isSubtype(universe, s, sEnv, tTypeArgument, tEnv)) {
      // `true` because [s] <: T.
      return true;
    } else {
      // Check [s] <: Future<T>.
      String futureClass = JS_GET_NAME(JsGetName.FUTURE_CLASS_TYPE_NAME);
      var argumentsArray = JS('', '[#]', tTypeArgument);
      return _isSubtypeOfInterface(
          universe, s, sEnv, futureClass, argumentsArray, tEnv);
    }
  }

  if (isGenericFunctionKind(t)) {
    return _isGenericFunctionSubtype(universe, s, sEnv, t, tEnv);
  }

  if (isFunctionKind(t)) {
    return _isFunctionSubtype(universe, s, sEnv, t, tEnv);
  }

  if (isFunctionKind(s) || isGenericFunctionKind(s)) {
    return isFunctionType(t);
  }

  assert(Rti._getKind(t) == Rti.kindInterface);
  String tName = Rti._getInterfaceName(t);
  var tArgs = Rti._getInterfaceTypeArguments(t);

  return _isSubtypeOfInterface(universe, s, sEnv, tName, tArgs, tEnv);
}

bool _isGenericFunctionSubtype(universe, Rti s, sEnv, Rti t, tEnv) {
  assert(isGenericFunctionKind(t));
  if (!isGenericFunctionKind(s)) return false;

  var sBounds = Rti._getGenericFunctionBounds(s);
  var tBounds = Rti._getGenericFunctionBounds(t);
  if (!typesEqual(sBounds, tBounds)) return false;
  // TODO(fishythefish): Extend [sEnv] and [tEnv] with bindings for the [s]
  // and [t] type parameters to enable checking the bound against
  // non-type-parameter terms.

  return _isFunctionSubtype(universe, Rti._getGenericFunctionBase(s), sEnv,
      Rti._getGenericFunctionBase(t), tEnv);
}

// TODO(fishythefish): Support required named parameters.
bool _isFunctionSubtype(universe, Rti s, sEnv, Rti t, tEnv) {
  assert(isFunctionKind(t));
  if (!isFunctionKind(s)) return false;

  Rti sReturnType = Rti._getReturnType(s);
  Rti tReturnType = Rti._getReturnType(t);
  if (!_isSubtype(universe, sReturnType, sEnv, tReturnType, tEnv)) return false;

  _FunctionParameters sParameters = Rti._getFunctionParameters(s);
  _FunctionParameters tParameters = Rti._getFunctionParameters(t);

  var sRequiredPositional =
      _FunctionParameters._getRequiredPositional(sParameters);
  var tRequiredPositional =
      _FunctionParameters._getRequiredPositional(tParameters);
  int sRequiredPositionalLength = _Utils.arrayLength(sRequiredPositional);
  int tRequiredPositionalLength = _Utils.arrayLength(tRequiredPositional);
  if (sRequiredPositionalLength > tRequiredPositionalLength) return false;
  int requiredPositionalDelta =
      tRequiredPositionalLength - sRequiredPositionalLength;

  var sOptionalPositional =
      _FunctionParameters._getOptionalPositional(sParameters);
  var tOptionalPositional =
      _FunctionParameters._getOptionalPositional(tParameters);
  int sOptionalPositionalLength = _Utils.arrayLength(sOptionalPositional);
  int tOptionalPositionalLength = _Utils.arrayLength(tOptionalPositional);
  if (sRequiredPositionalLength + sOptionalPositionalLength <
      tRequiredPositionalLength + tOptionalPositionalLength) return false;

  for (int i = 0; i < sRequiredPositionalLength; i++) {
    Rti sParameter = _castToRti(_Utils.arrayAt(sRequiredPositional, i));
    Rti tParameter = _castToRti(_Utils.arrayAt(tRequiredPositional, i));
    if (!_isSubtype(universe, tParameter, tEnv, sParameter, sEnv)) return false;
  }

  for (int i = 0; i < requiredPositionalDelta; i++) {
    Rti sParameter = _castToRti(_Utils.arrayAt(sOptionalPositional, i));
    Rti tParameter = _castToRti(
        _Utils.arrayAt(tRequiredPositional, sRequiredPositionalLength + i));
    if (!_isSubtype(universe, tParameter, tEnv, sParameter, sEnv)) return false;
  }

  for (int i = 0; i < tOptionalPositionalLength; i++) {
    Rti sParameter = _castToRti(
        _Utils.arrayAt(sOptionalPositional, requiredPositionalDelta + i));
    Rti tParameter = _castToRti(_Utils.arrayAt(tOptionalPositional, i));
    if (!_isSubtype(universe, tParameter, tEnv, sParameter, sEnv)) return false;
  }

  var sOptionalNamed = _FunctionParameters._getOptionalNamed(sParameters);
  var tOptionalNamed = _FunctionParameters._getOptionalNamed(tParameters);
  int sOptionalNamedLength = _Utils.arrayLength(sOptionalNamed);
  int tOptionalNamedLength = _Utils.arrayLength(tOptionalNamed);

  for (int i = 0, j = 0; j < tOptionalNamedLength; j += 2) {
    String sName;
    String tName = _Utils.asString(_Utils.arrayAt(tOptionalNamed, j));
    do {
      if (i >= sOptionalNamedLength) return false;
      sName = _Utils.asString(_Utils.arrayAt(sOptionalNamed, i));
      i += 2;
    } while (_Utils.stringLessThan(sName, tName));
    if (_Utils.stringLessThan(tName, sName)) return false;
    Rti sType = _castToRti(_Utils.arrayAt(sOptionalNamed, i - 1));
    Rti tType = _castToRti(_Utils.arrayAt(tOptionalNamed, j + 1));
    if (!_isSubtype(universe, tType, tEnv, sType, sEnv)) return false;
  }

  return true;
}

bool _isSubtypeOfInterface(
    universe, Rti s, sEnv, String tName, Object tArgs, tEnv) {
  assert(Rti._getKind(s) == Rti.kindInterface);
  String sName = Rti._getInterfaceName(s);

  if (sName == tName) {
    var sArgs = Rti._getInterfaceTypeArguments(s);
    int length = _Utils.arrayLength(sArgs);
    assert(length == _Utils.arrayLength(tArgs));
    for (int i = 0; i < length; i++) {
      Rti sArg = _castToRti(_Utils.arrayAt(sArgs, i));
      Rti tArg = _castToRti(_Utils.arrayAt(tArgs, i));
      if (!_isSubtype(universe, sArg, sEnv, tArg, tEnv)) return false;
    }
    return true;
  }

  Object rule = _Universe.findRule(universe, sName);
  if (rule == null) return false;
  var supertypeArgs = TypeRule.lookupSupertype(rule, tName);
  if (supertypeArgs == null) return false;
  int length = _Utils.arrayLength(supertypeArgs);
  assert(length == _Utils.arrayLength(tArgs));
  for (int i = 0; i < length; i++) {
    String recipe = _Utils.asString(_Utils.arrayAt(supertypeArgs, i));
    Rti supertypeArg = _Universe.evalInEnvironment(universe, s, recipe);
    Rti tArg = _castToRti(_Utils.arrayAt(tArgs, i));
    if (!_isSubtype(universe, supertypeArg, sEnv, tArg, tEnv)) return false;
  }

  return true;
}

/// Types are equal if they are structurally equal up to renaming of bound type
/// variables and equating all top types.
///
/// We ignore renaming of bound type variables because we operate on de Bruijn
/// indices, not names.
bool typeEqual(Rti s, Rti t) {
  if (_Utils.isIdentical(s, t)) return true;

  if (isTopType(s)) return isTopType(t);

  int sKind = Rti._getKind(s);
  int tKind = Rti._getKind(t);
  if (sKind != tKind) return false;

  switch (sKind) {
    case Rti.kindStar:
    case Rti.kindQuestion:
    case Rti.kindFutureOr:
      return typeEqual(
          _castToRti(Rti._getPrimary(s)), _castToRti(Rti._getPrimary(t)));

    case Rti.kindInterface:
      if (Rti._getInterfaceName(s) != Rti._getInterfaceName(t)) return false;
      return typesEqual(
          Rti._getInterfaceTypeArguments(s), Rti._getInterfaceTypeArguments(t));

    case Rti.kindBinding:
      return typeEqual(Rti._getBindingBase(s), Rti._getBindingBase(t)) &&
          typesEqual(Rti._getBindingArguments(s), Rti._getBindingArguments(t));

    case Rti.kindFunction:
      return typeEqual(Rti._getReturnType(s), Rti._getReturnType(t)) &&
          functionParametersEqual(
              Rti._getFunctionParameters(s), Rti._getFunctionParameters(t));

    case Rti.kindGenericFunction:
      return typeEqual(
              Rti._getGenericFunctionBase(s), Rti._getGenericFunctionBase(t)) &&
          typesEqual(Rti._getGenericFunctionBounds(s),
              Rti._getGenericFunctionBounds(t));

    default:
      return false;
  }
}

bool typesEqual(Object sArray, Object tArray) {
  int sLength = _Utils.arrayLength(sArray);
  int tLength = _Utils.arrayLength(tArray);
  if (sLength != tLength) return false;
  for (int i = 0; i < sLength; i++) {
    if (!typeEqual(_castToRti(_Utils.arrayAt(sArray, i)),
        _castToRti(_Utils.arrayAt(tArray, i)))) return false;
  }
  return true;
}

bool namedTypesEqual(Object sArray, Object tArray) {
  int sLength = _Utils.arrayLength(sArray);
  int tLength = _Utils.arrayLength(tArray);
  assert(sLength.isEven);
  assert(tLength.isEven);
  if (sLength != tLength) return false;
  for (int i = 0; i < sLength; i += 2) {
    if (_Utils.asString(_Utils.arrayAt(sArray, i)) !=
        _Utils.asString(_Utils.arrayAt(tArray, i))) return false;
    if (!typeEqual(_castToRti(_Utils.arrayAt(sArray, i + 1)),
        _castToRti(_Utils.arrayAt(tArray, i + 1)))) return false;
  }
  return true;
}

// TODO(fishythefish): Support required named parameters.
bool functionParametersEqual(
        _FunctionParameters sParameters, _FunctionParameters tParameters) =>
    typesEqual(_FunctionParameters._getRequiredPositional(sParameters),
        _FunctionParameters._getRequiredPositional(tParameters)) &&
    typesEqual(_FunctionParameters._getOptionalPositional(sParameters),
        _FunctionParameters._getOptionalPositional(tParameters)) &&
    namedTypesEqual(_FunctionParameters._getOptionalNamed(sParameters),
        _FunctionParameters._getOptionalNamed(tParameters));

bool isTopType(Rti t) =>
    isDynamicType(t) || isVoidType(t) || isObjectType(t) || isJsInteropType(t);

bool isDynamicType(Rti t) => Rti._getKind(t) == Rti.kindDynamic;
bool isVoidType(Rti t) => Rti._getKind(t) == Rti.kindVoid;
bool isJsInteropType(Rti t) => Rti._getKind(t) == Rti.kindAny;

bool isFutureOrType(Rti t) => Rti._getKind(t) == Rti.kindFutureOr;

bool isFunctionKind(Rti t) => Rti._getKind(t) == Rti.kindFunction;
bool isGenericFunctionKind(Rti t) => Rti._getKind(t) == Rti.kindGenericFunction;

bool isGenericFunctionTypeParameter(Rti t) =>
    Rti._getKind(t) == Rti.kindGenericFunctionParameter;

bool isObjectType(Rti t) =>
    Rti._getKind(t) == Rti.kindInterface &&
    Rti._getInterfaceName(t) == JS_GET_NAME(JsGetName.OBJECT_CLASS_TYPE_NAME);

// TODO(fishythefish): Which representation should we use for NNBD?
// Do we also need to check for `Never?`, etc.?
bool isNullType(Rti t) =>
    Rti._getKind(t) == Rti.kindInterface &&
    Rti._getInterfaceName(t) == JS_GET_NAME(JsGetName.NULL_CLASS_TYPE_NAME);

bool isFunctionType(Rti t) =>
    Rti._getKind(t) == Rti.kindInterface &&
    Rti._getInterfaceName(t) == JS_GET_NAME(JsGetName.FUNCTION_CLASS_TYPE_NAME);

/// Unchecked cast to Rti.
Rti _castToRti(s) => JS('Rti', '#', s);

///
class _Utils {
  static bool asBool(Object o) => JS('bool', '#', o);
  static double asDouble(Object o) => JS('double', '#', o);
  static int asInt(Object o) => JS('int', '#', o);
  static num asNum(Object o) => JS('num', '#', o);
  static String asString(Object o) => JS('String', '#', o);

  static bool isString(Object o) => JS('bool', 'typeof # == "string"', o);
  static bool isNum(Object o) => JS('bool', 'typeof # == "number"', o);

  static bool instanceOf(Object o, Object constructor) =>
      JS('bool', '# instanceof #', o, constructor);

  static bool isIdentical(s, t) => JS('bool', '# === #', s, t);

  static bool isArray(Object o) => JS('bool', 'Array.isArray(#)', o);

  static int arrayLength(Object array) => JS('int', '#.length', array);

  static Object arrayAt(Object array, int i) => JS('', '#[#]', array, i);

  static void arraySetAt(Object array, int i, Object value) {
    JS('', '#[#] = #', array, i, value);
  }

  static JSArray arrayShallowCopy(Object array) =>
      JS('JSArray', '#.slice()', array);

  static JSArray arraySplice(Object array, int position) =>
      JS('JSArray', '#.splice(#)', array, position);

  static JSArray arrayConcat(Object a1, Object a2) =>
      JS('JSArray', '#.concat(#)', a1, a2);

  static void arrayPush(Object array, Object value) {
    JS('', '#.push(#)', array, value);
  }

  static String substring(String s, int start, int end) =>
      JS('String', '#.substring(#, #)', s, start, end);

  static bool stringLessThan(String s1, String s2) =>
      JS('bool', '# < #', s1, s2);

  static mapGet(cache, key) => JS('', '#.get(#)', cache, key);

  static void mapSet(cache, key, value) {
    JS('', '#.set(#, #)', cache, key, value);
  }
}
// -------- Entry points for testing -------------------------------------------

String testingCanonicalRecipe(rti) {
  return Rti._getCanonicalRecipe(rti);
}

String testingRtiToString(rti) {
  return _rtiToString(_castToRti(rti), null);
}

String testingRtiToDebugString(rti) {
  return _rtiToDebugString(_castToRti(rti));
}

Object testingCreateUniverse() {
  return _Universe.create();
}

void testingAddRules(universe, rules) {
  _Universe.addRules(universe, rules);
}

bool testingIsSubtype(universe, rti1, rti2) {
  return isSubtype(universe, _castToRti(rti1), _castToRti(rti2));
}

Object testingUniverseEval(universe, String recipe) {
  return _Universe.eval(universe, recipe);
}

Object testingEnvironmentEval(universe, environment, String recipe) {
  return _Universe.evalInEnvironment(universe, _castToRti(environment), recipe);
}

Object testingEnvironmentBind(universe, environment, arguments) {
  return _Universe.bind(
      universe, _castToRti(environment), _castToRti(arguments));
}
