gistfile1.ts

// x :: Either (Either a b) c -> Either a (Either b c)
// x = either (either Left (Right . Left)) (Right . Right)

interface Either<A,B> {
  left?   : A;
  right?  : B;
}

class Fns
{
  static Left<A,B>(a : A) : Either<A,B>
  {
    return { left : a };
  }

  static Right<A,B>(b : B) : Either<A,B>
  {
    return { right : b };
  }

  static either<A,B,C>(f : (a : A) => C, g : (b : B) => C) : (v : Either<A,B>) => C
  {
    return function (v : Either<A,B>) : C
    {
      if (v.left  !== undefined) return f(v.left );
      if (v.right !== undefined) return g(v.right);
    }
  }

  static cmp<A,B,C>(f : (b : B) => C, g : (a : A) => B) : (a : A) => C
  {
    return function (a : A) : C
    {
      return f(g(a));
    };
  }

  static f<A,B,C>(v : Either<Either<A,B>,C>) : Either<A,Either<B,C>>
  {
    // Type error, but typechecks:
    // return Fns.either(Fns.either(Fns.Left, Fns.cmp(Fns.Right, Fns.Left)), Fns.cmp(Fns.Right, Fns.Right));

    // Correct, but doesn't type check:
    // > Type 'Either<{}, {}>' is not assignable to type 'Either<A, Either<B, C>>'.
    // > Type '{}' is not assignable to type 'A'.
    // return Fns.either(Fns.either(Fns.Left, Fns.cmp(Fns.Right, Fns.Left)), Fns.cmp(Fns.Right, Fns.Right))(v);

    // Works, too much typing needed to get it to actually type check.
    return <Either<A,Either<B,C>>> Fns.either(Fns.either(Fns.Left, Fns.cmp(Fns.Right, Fns.Left)), Fns.cmp(Fns.Right, Fns.Right))(v);

    // Should be something like this... type params for the cmp calls are wrong!
    // return <Either<A,Either<B,C>>> Fns.either<Either<A,B>,C,Either<A,Either<B,C>>>(Fns.either<A,B,Either<A,Either<B,C>>>(Fns.Left, Fns.cmp<(x : Either<B,C>) => Either<A,Either<B,C>>, (x : C) => Either<B,C>, Either<A, Either<B,C>>>(Fns.Right, Fns.Left)), Fns.cmp<(x : Either<B,C>) => Either<A,Either<B,C>>, (x : C) => Either<B,C>, Either<A, Either<B,C>>>(Fns.Right, Fns.Right))(v);
  }

};

console.log(Fns.f(Fns.Left(Fns.Left(1))));
console.log(Fns.f(Fns.Left(Fns.Right(2))));
console.log(Fns.f(Fns.Right(3)));