typescriptでi=ssk

NISHIO Hirokazu [Translate]

TypeScriptでI=SSK
TypeScriptの型
tslet I: <T>(x: T) => T;
let K: <T1, T2>(x: T1) => ((y: T2) => T1) = (x) => {
  return (y) => x;
};
let S: <Tz, Tyz, Ts>(x: (z: Tz) => ((yz: Tyz) => Ts)) => ((y: (z: Tz) => Tyz) => ((z: Tz) => Ts)
) = (x) => {
  return (y) => {
    return (z) => {
      return x(z)(y(z));
    }
  }
}
let SKK = S(K)(K);
I = SKK;
let x: 0 = SKK(0);

VSCodeの自動インデントで比較的まともな見栄えにならないかなと少し工夫してみた
tslet S: <Tz, Tyz, Ts>
  (x: ((z: Tz) => ((yz: Tyz) => Ts)))
  =>
  (y: (z: Tz) => Tyz)
    =>
    (z: Tz)
      => Ts
  =
  (x) => (
    (y) => (
      (z) => (
        x(z)(y(z))
      )
    )
  )

ts{
  type Tx<Txx> = (x: Tx<Txx>) => Txx
  let M: <Txx>(x: Tx<Txx>) => Txx = (x) => (x(x));
}

次はこれからanyを消すパズルです
tslet iota: (x: any) => any = (x) => x(S)(K);
let I = iota(iota);

うーん、素朴にやったら謎の型ができてしまった
ts  type Ts = typeof S;
  type Tk = typeof K;
  let xs: <Tr>(x: (s: Ts) => Tr) => Tr = (x) => x(S);
  let yk: <Tr>(y: (k: Tk) => Tr) => Tr = (y) => y(K);

  let iota: <Txsk>(x: (s: Ts) => (k: Tk) => Txsk) => Txsk = (x) => x(S)(K);
  //let I = iota(iota);  // エラーメッセージは下記

  let a = S(S);
  let b = S(S)(K);  // let b: (z: (z: {}) => (yz: {}) => {}) => (z: {}) => {}
  let c = S(S)(K)(K)


Argument of type 
'<Txsk>(x: (s: <Tz, Tyz, Ts>(x: (z: Tz) => (yz: Tyz) => Ts) => (y: (z: Tz) => Tyz) => (z: Tz) => Ts) => (k: <T1, T2>(x: T1) => (y: T2) => T1) => Txsk) => Txsk'
is not assignable to parameter of type 
'(s: <Tz, Tyz, Ts>(x: (z: Tz) => (yz: Tyz) => Ts) => (y: (z: Tz) => Tyz) => (z: Tz) => Ts) => (k: <T1, T2>(x: T1) => (y: T2) => T1) => {}'.

Types of parameters 'x' and 's' are incompatible.
Type 
'(y: (z: (z: {}) => (yz: {}) => {}) => (z: {}) => {}) => (z: (z: {}) => (yz: {}) => {}) => (z: {}) => {}' 
is not assignable to type 
'(k: <T1, T2>(x: T1) => (y: T2) => T1) => (z: {}) => {}'.

TypeScript

"Engineer's way of creating knowledge" the English version of my book is now available on [Engineer's way of creating knowledge]

(C)NISHIO Hirokazu / Converted from [Scrapbox] at 11/23/2025, 3:54:39 PM[Edit]

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