map-morphism.ts

map-morphism.ts

// List
type List<A> = Nil | Cons<A>;

interface Nil {
  readonly _tag: "Nil";
}

interface Cons<A> {
  readonly _tag: "Cons";
  readonly head: A;
  readonly tail: List<A>;
}

const nil: List<never> = { _tag: "Nil" };
 
// Helpers
const cons = <A>(head: A, tail: List<A>): List<A> => ({
  _tag: "Cons",
  head,
  tail,
});
  
const isNil = <A>(xs: List<A>): xs is Nil => xs._tag === "Nil";
  
// Matcher
type Match = <A, B>(
  onNil: () => B,
  onCons: (head: A, tail: List<A>) => B
) => (xs: List<A>) => B;
  
const match: Match = (onNil, onCons) => (xs) =>
  isNil(xs) ? onNil() : onCons(xs.head, xs.tail);
  
// Example
const list: List<string> = cons("a", cons("bb", cons("ccc", nil)));
  
type StrLength = (x: string) => number;
const strLength: StrLength = (x) => x.length;

type MapList = <A, B>(f: (x: A) => B) => (Fx: List<A>) => List<B>;
const map_list: MapList = (f) =>
  match(
    () => nil,
    (head, tail) => cons(f(head), map_list(f)(tail))
  );

// strLength: string → number
// listStrLength: List<string> → List<number>
const listStrLength = map_list(strLength);
console.log(listStrLength(list)));