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変性 (variance)

TypeScriptでは、型の互換性を判定する際に変性(variance)という概念が使われます。変性とは型同士の関係性を示すもので、TypeScriptにおいてはこの変性を示すためにはジェネリクスの型変数の前にinあるいはoutを付与します。

なお、ここで語られる変性はtsconfig.jsonのstrictFunctionTypesの設定でも変更することができます。
今回は特筆しない限りstrictFunctionTypesはfalseとして説明します。

📄️ strictFunctionTypes

引数型の変性のチェックを厳しくする

共変性 (Covariance)​

共変性はジェネリクスの型変数にoutを付与した場合の変位です。共変性とはサブタイプの関係が保たれることを意味します。

反変性 (Contravariance)​

反変性はジェネリクスの型変数にinを付与した場合の変位です。反変性とはサブタイプの関係が逆転することを意味します。

不変性 (Invariance)​

不変性はジェネリクスの型変数にinとoutを付与した場合の変位です。不変性とは型が共変性でも反変性でもないことを意味します。

双変性 (Bivariance)​

双変性はジェネリクスの型変数にinとoutを付与しない場合の変位です。

ここで例としてひとつの引数Iを受け取り戻り値Oを返す関数の型としてBivariantFunction<I, O>(変位をつけていないのでTypeScriptとしては双変と同じ)を定義します。

ts
type BivariantFunction<I, O> = (arg: I) => O;
ts
type BivariantFunction<I, O> = (arg: I) => O;

ここで引数Iを共変にしたCovariantFunction<in I, O>と戻り値Oを反変にしたContravariantFunction<I, out O>、引数も戻り値も不変にしたInvariantFunction<in out I, in out O>を定義します。するとそれらは次のように定義されます。

ts
type BivariantFunction<I, O> = (arg: I) => O;
type CovariantFunction<I, out O> = BivariantFunction<I, O>;
type ContravariantFunction<in I, O> = BivariantFunction<I, O>;
type InvariantFunction<in out I, in out O> = BivariantFunction<I, O>;
ts
type BivariantFunction<I, O> = (arg: I) => O;
type CovariantFunction<I, out O> = BivariantFunction<I, O>;
type ContravariantFunction<in I, O> = BivariantFunction<I, O>;
type InvariantFunction<in out I, in out O> = BivariantFunction<I, O>;

クラスの継承関係を使った例​

継承関係がわかりやすくなるようにクラスA, B, Cを定義します。AはBを継承し、BはCを継承しており、メソッドを追加しました。

ts
class A {
  public a(): void {
    console.log("a");
  }
}
 
class B extends A {
  public b(): void {
    console.log("b");
  }
}
 
class C extends B {
  public c(): void {
    console.log("c");
  }
}
ts
class A {
  public a(): void {
    console.log("a");
  }
}
 
class B extends A {
  public b(): void {
    console.log("b");
  }
}
 
class C extends B {
  public c(): void {
    console.log("c");
  }
}

各変性の関数のIとOの両方をBにした関数を定義します。

ts
declare const biFunc: BivariantFunction<B, B>;
declare const coFunc: CovariantFunction<B, B>;
declare const contraFunc: ContravariantFunction<B, B>;
declare const inFunc: InvariantFunction<B, B>;
ts
declare const biFunc: BivariantFunction<B, B>;
declare const coFunc: CovariantFunction<B, B>;
declare const contraFunc: ContravariantFunction<B, B>;
declare const inFunc: InvariantFunction<B, B>;

これらの関数のジェネリクスを変更してみます。

ts
const f01: BivariantFunction<A, B> = biFunc;
const f02: BivariantFunction<C, B> = biFunc;
const f03: BivariantFunction<B, A> = biFunc;
const f04: BivariantFunction<B, C> = biFunc;
Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, C>'.
  Property 'c' is missing in type 'B' but required in type 'C'.2322Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, C>'.
  Property 'c' is missing in type 'B' but required in type 'C'.
 
const f05: CovariantFunction<B, A> = coFunc;
const f06: CovariantFunction<B, C> = coFunc;
Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.2322Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.
 
const f07: ContravariantFunction<A, B> = contraFunc;
Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<A, B>'.
  Property 'b' is missing in type 'A' but required in type 'B'.2322Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<A, B>'.
  Property 'b' is missing in type 'A' but required in type 'B'.
const f08: ContravariantFunction<C, B> = contraFunc;
 
const f09: InvariantFunction<A, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<A, B>'.
  Type 'A' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<A, B>'.
  Type 'A' is not assignable to type 'B'.
const f10: InvariantFunction<C, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'B' is not assignable to type 'C'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'B' is not assignable to type 'C'.
const f11: InvariantFunction<B, A> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, A>'.
  Type 'A' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, A>'.
  Type 'A' is not assignable to type 'B'.
const f12: InvariantFunction<B, C> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.
ts
const f01: BivariantFunction<A, B> = biFunc;
const f02: BivariantFunction<C, B> = biFunc;
const f03: BivariantFunction<B, A> = biFunc;
const f04: BivariantFunction<B, C> = biFunc;
Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, C>'.
  Property 'c' is missing in type 'B' but required in type 'C'.2322Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, C>'.
  Property 'c' is missing in type 'B' but required in type 'C'.
 
const f05: CovariantFunction<B, A> = coFunc;
const f06: CovariantFunction<B, C> = coFunc;
Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.2322Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.
 
const f07: ContravariantFunction<A, B> = contraFunc;
Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<A, B>'.
  Property 'b' is missing in type 'A' but required in type 'B'.2322Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<A, B>'.
  Property 'b' is missing in type 'A' but required in type 'B'.
const f08: ContravariantFunction<C, B> = contraFunc;
 
const f09: InvariantFunction<A, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<A, B>'.
  Type 'A' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<A, B>'.
  Type 'A' is not assignable to type 'B'.
const f10: InvariantFunction<C, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'B' is not assignable to type 'C'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'B' is not assignable to type 'C'.
const f11: InvariantFunction<B, A> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, A>'.
  Type 'A' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, A>'.
  Type 'A' is not assignable to type 'B'.
const f12: InvariantFunction<B, C> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'B' is not assignable to type 'C'.

これらの中でエラーになるものをまとめると

  1. f04は引数、戻り値ともに双変でスーパータイプとサブタイプの関係が許容されますが、戻り値のCに対しBはメソッドc()を持っていないためエラーになります
  2. f06は戻り値が共変でスーパータイプの割り当てが許容されますが、戻り値CはBのサブタイプなのでエラーになります
  3. f07は引数が反変でサブタイプの割り当てが許容されますが、引数AはBのスーパータイプなのでエラーになります
  4. f09は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります
  5. f10は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります
  6. f11は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります
  7. f12は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります

また、strictFunctionTypesをtrueにすると上記のエラーに加えて

  1. f01は引数、戻り値ともに双変でスーパータイプとサブタイプの関係が許容されますが、引数のAはメソッドb()を持っていないためエラーになります

ユニオン型を使った例​

ユニオン型を使って継承関係を表してみます。

ts
type A = null;
type B = null | undefined;
type C = null | undefined | string;
ts
type A = null;
type B = null | undefined;
type C = null | undefined | string;

このときAはBの部分型であり、BはCの部分型です。言い換えるとA extends B、B extends Cです。

ts
const f01: BivariantFunction<A, B> = biFunc;
const f02: BivariantFunction<C, B> = biFunc;
const f03: BivariantFunction<B, A> = biFunc;
Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f04: BivariantFunction<B, C> = biFunc;
 
const f05: CovariantFunction<B, A> = coFunc;
Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f06: CovariantFunction<B, C> = coFunc;
 
const f07: ContravariantFunction<A, B> = contraFunc;
const f08: ContravariantFunction<C, B> = contraFunc;
Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.
    Type 'string' is not assignable to type 'B'.2322Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.
    Type 'string' is not assignable to type 'B'.
 
const f09: InvariantFunction<A, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<null, B>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<null, B>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f10: InvariantFunction<C, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.
const f11: InvariantFunction<B, A> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f12: InvariantFunction<B, C> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'C' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'C' is not assignable to type 'B'.
ts
const f01: BivariantFunction<A, B> = biFunc;
const f02: BivariantFunction<C, B> = biFunc;
const f03: BivariantFunction<B, A> = biFunc;
Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'BivariantFunction<B, B>' is not assignable to type 'BivariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f04: BivariantFunction<B, C> = biFunc;
 
const f05: CovariantFunction<B, A> = coFunc;
Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'CovariantFunction<B, B>' is not assignable to type 'CovariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f06: CovariantFunction<B, C> = coFunc;
 
const f07: ContravariantFunction<A, B> = contraFunc;
const f08: ContravariantFunction<C, B> = contraFunc;
Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.
    Type 'string' is not assignable to type 'B'.2322Type 'ContravariantFunction<B, B>' is not assignable to type 'ContravariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.
    Type 'string' is not assignable to type 'B'.
 
const f09: InvariantFunction<A, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<null, B>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<null, B>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f10: InvariantFunction<C, B> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<C, B>'.
  Type 'C' is not assignable to type 'B'.
const f11: InvariantFunction<B, A> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, null>'.
  Type 'B' is not assignable to type 'null'.
    Type 'undefined' is not assignable to type 'null'.
const f12: InvariantFunction<B, C> = inFunc;
Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'C' is not assignable to type 'B'.2322Type 'InvariantFunction<B, B>' is not assignable to type 'InvariantFunction<B, C>'.
  Type 'C' is not assignable to type 'B'.
  1. f03は引数、戻り値ともに双変でスーパータイプとサブタイプの関係が許容されますが、戻り値のAに対しBのundefinedはnullに割り当てることができないためエラーになります
  2. f05は戻り値が共変でスーパータイプの割り当てが許容されますが、戻り値Aに対しBのundefinedはnullに割り当てることができないためエラーになります
  3. f08は引数が反変でサブタイプの割り当てが許容されますが、引数CのstringはBに割り当てることができないためエラーになります
  4. f09は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります
  5. f10は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります
  6. f11は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります
  7. f12は引数、戻り値ともに不変でスーパータイプとサブタイプの関係が許容されないためエラーになります

strictFunctionTypesをtrueにすると上記のエラーに加えて

  1. f02は引数、戻り値ともに双変でスーパータイプとサブタイプの関係が許容されますが、引数CのstringはBに割り当てることができないためエラーになります

継承関係を見る​

継承関係を見るためにConditional Typesを使ってみましょう。ある型TがUのサブタイプかどうかを判定する型IsSubType<T, U>を定義します。

ts
type IsSubType<T, U> = T extends U ? true : false;
ts
type IsSubType<T, U> = T extends U ? true : false;

先ほどのクラスA, B, CにIsSubType<T, U>を適用してみます。

ts
class A {
  public a(): void {
    console.log("a");
  }
}
 
class B extends A {
  public b(): void {
    console.log("b");
  }
}
 
class C extends B {
  public c(): void {
    console.log("c");
  }
}
 
declare const t1: IsSubType<A, A>;
              
const t1: true
declare const t2: IsSubType<B, B>;
              
const t2: true
declare const t3: IsSubType<C, C>;
              
const t3: true
 
declare const t4: IsSubType<A, B>;
              
const t4: false
declare const t5: IsSubType<B, C>;
              
const t5: false
declare const t6: IsSubType<A, C>;
              
const t6: false
 
declare const t7: IsSubType<B, A>;
              
const t7: true
declare const t8: IsSubType<C, B>;
              
const t8: true
declare const t9: IsSubType<C, A>;
              
const t9: true
ts
class A {
  public a(): void {
    console.log("a");
  }
}
 
class B extends A {
  public b(): void {
    console.log("b");
  }
}
 
class C extends B {
  public c(): void {
    console.log("c");
  }
}
 
declare const t1: IsSubType<A, A>;
              
const t1: true
declare const t2: IsSubType<B, B>;
              
const t2: true
declare const t3: IsSubType<C, C>;
              
const t3: true
 
declare const t4: IsSubType<A, B>;
              
const t4: false
declare const t5: IsSubType<B, C>;
              
const t5: false
declare const t6: IsSubType<A, C>;
              
const t6: false
 
declare const t7: IsSubType<B, A>;
              
const t7: true
declare const t8: IsSubType<C, B>;
              
const t8: true
declare const t9: IsSubType<C, A>;
              
const t9: true

自分自身のクラスあるいはサブクラスに限りtrueが返されることがわかります。

ユニオン型も見てみましょう。なお、こちらはユニオン型であるためDistributive Conditional Typeを使用します。

📄️ Distributive Conditional Types

Distributive Conditional Types は日本語では分配された条件型、条件付き型の分配、ユニオン分配、ユニオン型の分配法則などと呼ばれ、 Conditional Types が ジェネリクス型 に適用され、かつ型引数に ユニオン型 が与えられた場合に、そのユニオン型を構成する各メンバーに対して個別に条件判定が適用される（＝分配される）性質を指します。

ts
type IsSubType<T, U> = [T] extends [U] ? true : false;
ts
type IsSubType<T, U> = [T] extends [U] ? true : false;
ts
type A = null;
type B = null | undefined;
type C = null | undefined | string;
 
declare const t1: IsSubType<A, A>;
              
const t1: true
declare const t2: IsSubType<B, B>;
              
const t2: true
declare const t3: IsSubType<C, C>;
              
const t3: true
 
declare const t4: IsSubType<A, B>;
              
const t4: true
declare const t5: IsSubType<B, C>;
              
const t5: true
declare const t6: IsSubType<A, C>;
              
const t6: true
 
declare const t7: IsSubType<B, A>;
              
const t7: false
declare const t8: IsSubType<C, B>;
              
const t8: false
declare const t9: IsSubType<C, A>;
              
const t9: false
ts
type A = null;
type B = null | undefined;
type C = null | undefined | string;
 
declare const t1: IsSubType<A, A>;
              
const t1: true
declare const t2: IsSubType<B, B>;
              
const t2: true
declare const t3: IsSubType<C, C>;
              
const t3: true
 
declare const t4: IsSubType<A, B>;
              
const t4: true
declare const t5: IsSubType<B, C>;
              
const t5: true
declare const t6: IsSubType<A, C>;
              
const t6: true
 
declare const t7: IsSubType<B, A>;
              
const t7: false
declare const t8: IsSubType<C, B>;
              
const t8: false
declare const t9: IsSubType<C, A>;
              
const t9: false

AはBの部分型であり、BはCの部分型であるためt4、t5、t6がtrueになることがわかります。

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