I recently implemented delimited continuations in CPS with reset
/shift
:
// reset :: ((a -> a) -> a) -> (a -> r) -> r
reset = k => f => f(k(id));
// shift :: ((a -> r) -> (r -> r) -> r) -> (a -> r) -> r
shift = f => k => f(k) (id);
Studying the theory I realized the following connections:
reset ~ function* // scope of the generator function
shift ~ yield
reset ~ async // scope of the asyn function
shift ~ await
As far as I understand the theory, Javascript's generators are a asymmetric, stackless, one-shot and first class coroutines.
- asymmetric means that the called generator can only yield to its caller
- stackless means a generator cannot yield from within nested functions
- one-shot means that a generator can only resume from a specific position once
- first class means a generator object can be passed around like normal data
Now I want to implement a coroutine based on reset
/shift
with the following traits:
- asymmetric
- stackful
- multi-shot
- first class
When looking at the following contrived example
const id = x => x;
const mul = x => y => x * y;
const add = x => y => x + y;
const sub = x => y => x - y;
const reset = k => f => f(k(id));
const shift = f => k => f(k) (id);
const of = x => k => k(x);
const lift2 = f => tx => ty => k => tx(x => ty(y => k(f(x) (y))));
const k0 = lift2(sub)
(reset
(lift2(add) (of(3))
(shift
(k => of(mul(5) (2))))))
(of(1)); // 9
const k1 = lift2(sub)
(reset
(lift2(add) (of(3))
(shift
(k => of(k(mul(5) (2)))))))
(of(1)); // 12
const k2 = lift2(sub)
(reset
(lift2(add) (of(3))
(shift
(k => of(k(k(mul(5) (2))))))))
(of(1)); // 15
console.log(k0(id));
console.log(k1(id));
console.log(k2(id));
it seems that reset
/shift
already meet the last two criteria, because delimited continuations are just first class, composable functions and I can invoke the continuation k
as often as required.
To answer the why, I want to bypass the following limitation in connection with the list monad.
Are these assumptions correct?
Even if I haven't make any mistakes so far I am overwhelmed by the complexity of the task at this point. I have no clue how to implement the desired coroutine or even where to begin. I didn't found an example implementation either. I don't expect a complete implementation but maybe some guidance to achieve my goal.
Goal
I want to bypass the following limitation of coroutines implemented by Javascript's generators:
const arrMap = f => xs =>
xs.map(x => f(x));
const arrAp = fs => xs =>
fs.reduce((acc, f) =>
acc.concat(xs.map(x => f(x))), []);
const arrChain = xs => fm =>
xs.reduce((acc, x) => acc.concat(fm(x)), []);
const arrOf = x => [x];
const do_ = (of, chain) => it => {
const loop = ({done, value}) =>
done
? value
: chain(value) (x => loop(it.next(x)));
return loop(it.next());
};
const z = function*() {
const x = yield [1,2,3]
return [x, x];
}
console.log(
arrChain([1,2,3]) (x => [x, x]));
console.log(
do_(arrOf, arrChain) (z()));