natural-number-within-ts-types

natural-number-within-ts-types.ts

// 配列の先頭以外を抜き取る型
type Tail<T extends any[]> = T extends [any, ...infer U] ? U : []

type Zero = []
type Succ = 'Succ'
type Next<T extends Nat> = [...T, Succ] // どっちかというとNextでやってることがSuccなんだけど,,,簡単のため妥協

// 自然数 Nat
type Nat = Zero | Succ[]

// Nat の値を人間が読めるように変換する型
type NatResolver<T extends Nat> = T['length']

// Nat を数値から生成
type NatGenerator<N extends number, Acc extends Nat = Zero> = Acc['length'] extends N
  ? Acc
  : NatGenerator<N, [Succ, ...Acc]>

// 加算
type Add<T extends Nat, U extends Nat> = [...T, ...U]

// 減算(マイナスになる場合はゼロ)
type Subtract<T extends Nat, U extends Nat> = U extends Zero ? T : Subtract<Tail<T>, Tail<U>>

// 乗算
type Multiply<T extends Nat, U extends Nat, Acc extends Nat = Zero> = U extends Zero
  ? Zero
  : U extends [Succ]
  ? Add<Acc, T>
  : Multiply<T, Tail<U>, Add<Acc, T>>

// 除算(切り捨て)
type Divide<T extends Nat, U extends Nat, Acc extends Nat = Zero> = U extends Zero
  ? never
  : T extends [Succ] | Zero
  ? Acc
  : Divide<Subtract<T, U>, U, Next<Acc>>

// 使用例
type One = Next<Zero>
type Two = Add<One, One>
type Three = Add<Two, One>
type Four = Multiply<Two, Two>
type Five = Add<Two, Three>
type Six = Multiply<Two, Three>
type Ten = NatGenerator<10>
type OneHundred = Multiply<Ten, Ten>

type n1 = NatResolver<One> // 1
type n2 = NatResolver<Two> // 2
type n3 = NatResolver<Three> // 3
type n4 = NatResolver<Four> // 4
type n5 = NatResolver<Five> // 5
type n6 = NatResolver<Six> // 6
type n10 = NatResolver<Ten> // 10
type n100 = NatResolver<OneHundred> // 100

type n24 = NatResolver<Multiply<Six, Four>> // 24
type n20 = NatResolver<Subtract<Multiply<Six, Four>, Four>> // 20

type n0_1 = NatResolver<Multiply<Zero, Six>> // 0
type n0_2 = NatResolver<Subtract<Two, Six>> // 0

type div_1 = NatResolver<Divide<Ten, Two>> // 10/2 => 5
type div_2 = NatResolver<Divide<Multiply<Six, Four>, Four>> // 24/4 => 6