TypeScriptの型で順序数を定義して、1+2が3であることをプログラムを動かさずに型定義で示す

ordinalNumber.ts

// http://www.typescriptlang.org/play/#code/PTAEHkCcBMEsDsCGAbUA5ArgWwEYFNJRo8AzBWAF1gHt4AoCgTwAc9QBJeAY0jyz3gUAPABUAfKAC8oANoiAugG4GLNuHhtpMpStagRAd2qgTUjt179BQ9XjHKmekQAtebM5x58Bww9Xu6bABi1BiEJtKelj6irnh2ynQgoADCtF4UbCQY3FS0dNm5NPCgzMgYAM62omIAFABuKABc+gCULVHe1uKgAN50JrwUYSUyjcg6AL50SWBpFniZoPDY+JB0XLQVFKC0eC22ZtrKm-DboBRGLX5mZZW2tXutiafnvBUYyDvSd1UatZdqM8NlsduMAILXIymaTvT4URSgZIAUUgkGo61eYJQACFrnFNKA4V8TqDQOMUi0QmEIkS8B8SUiwKj0esgA

// Ordinal Number definition
type Increment<T> = [T];
type One = [];
type Two    = Increment<One>;
type Three  = Increment<Two>;
type Four   = Increment<Three>;

// Concrete function
function plusOne<T>(val: T): Increment<T> {
  return [val];
}

// Concrete number
const one: One = [];
const two: Two = plusOne(one);

const result = plusOne(two);
const valA: Two   = result; // Error
const valB: Three = result;
const valC: Four  = result; // Error