javascripthaskellrecursionfunctional-programmingmutual-recursion

How to translate the poly-variadic fix-point combinator to a strict language?


I am attempting to translate the following Haskell code to Javascript:

fix_poly :: [[a] -> a] -> [a]
fix_poly fl = fix (\self -> map ($ self) fl)
  where fix f = f (fix f)

I have trouble understanding ($ self) though. Here is what I've achieved so far:

const structure = type => cons => {
  const f = (f, args) => ({
    ["run" + type]: f,
    [Symbol.toStringTag]: type,
    [Symbol("args")]: args
  });

  return cons(f);
};

const Defer = structure("Defer") (Defer => thunk => Defer(thunk));

const defFix = f => f(Defer(() => defFix(f)));

const defFixPoly = (...fs) =>
  defFix(self => fs.map(f => f(Defer(() => self))));

const pair = defFixPoly(
  f => n => n === 0
    ? true
    : f.runDefer() [1] (n - 1),
  f => n => n === 0
    ? false
    : f.runDefer() [0] (n - 1));

pair[0] (2); // true expected but error is thrown

The error is Uncaught TypeError: f.runDefer(...)[1] is not a function.

Here is the source.


Solution

  • The definition of defFixPoly has an extra layer of Defer than it should. Since self is already a Defer value, you can just pass it directly to f rather than wrapping it again.

    const defFixPoly = (...fs) =>
      defFix(self => fs.map(f => f(self)));
    

    const structure = type => cons => {
      const f = (f, args) => ({
        ["run" + type]: f,
        [Symbol.toStringTag]: type,
        [Symbol("args")]: args
      });
    
      return cons(f);
    };
    
    const Defer = structure("Defer") (Defer => thunk => Defer(thunk));
    
    const defFix = f => f(Defer(() => defFix(f)));
    
    const defFixPoly = (...fs) =>
      defFix(self => fs.map(f => f(self)));
    
    const pair = defFixPoly(
      f => n => n === 0
        ? true
        : f.runDefer() [1] (n - 1),
      f => n => n === 0
        ? false
        : f.runDefer() [0] (n - 1));
    
    console.log(pair[0] (2)); // true expected

    This now defines mutually recursive isEven and isOdd functions.

    const isEven = pair[0];
    const isOdd = pair[1];