typescriptの型で計算機

type_calculator.ts

export type Down<A> = A extends [null, ...null[]]
  ? ((..._: A) => null) extends (_:null, ...a:infer T) => null
    ? T
    : never
  : never

export type Up<A extends null[],B extends null|null[] = null> = [...A,...(B extends null ? [B] : B)]

export type Num<N extends number,A extends null[] = []> = {
  0:A,
  1:Num<N,[...A,null]>
}[A["length"] extends N ? 0 : 1]

export type Add<A extends null[],N extends number,C extends null[] = []> = {
  0:A,
  1:Add<Up<A>,N,Up<C>>
}[
  C["length"] extends N ? 0 : 1
]

export type Sub<A extends null[],N extends number,C extends null[] = []> = {
  0:A,
  1:Sub<Down<A>,N,Up<C>>
}[
  C["length"] extends N ? 0 : 1
]

export type Mul<A extends null[],N extends number,C extends null[] = [null],FAL extends null[]=A> = {
  0:A,
  1:Mul<Up<A,FAL>,N,Up<C>,FAL>
}[C["length"] extends N ? 0 : 1]

export type Get<A extends null[]> = A["length"]

/*
  // 50*20 = 1000
  type i = Get<
    Mul<Num<50>,20>
  >
*/