I’ve been trying to implement an Apply/Applicative type based on Javascript Functor, Applicative, Monads in pictures and the blog series Fantas, Eel, and Specification.
I think I’m making good progress, but I ran in to a case I couldn’t really find in any of the articles.
TL;DR Question
If lift2 is
f -> A.of(x) -> A.of(y) -> A.of(f (x) (y)) -or- A(y).ap(A(x).map(f))
what is the theory/name/type behind
A.of(f) -> A.of(x) -> A.of(y) -> A(f (x) (y)) -or- A(y).ap(A(x).ap(A(f)))
Introduction
I’m working with knockout.js, which gives me observable values. I’m trying to use them in a kind of functional fashion, extending them when needed.
First, I implemented map to make myself a functor:
ko.subscribable.fn.map = function(f) {
// note: calling without arguments is knockout's
// way of "unwrapping"
return ko.pureComputed(
() => f(this())
);
}
This allows me to do things like:
// "Pure" part describing my app
const myValue = ko.observable(2);
const doubleThat = myValue.map(x => x * 2);
// In- and output (IO?)
doubleThat.subscribe(console.log);
myValue(3); // Logs 6
Then, I ran in to the problem of working with functions that take multiple arguments. For example:
const filter = (pred, xs) => xs.filter(pred);
I solved my issues by implementing ap and currying my functions:
ko.subscribable.fn.ap = function(sf) {
return ko.pureComputed(
() => sf () (this())
);
};
const filter = pred => xs => xs.filter(pred);
With these changes in place, I can do:
const odd = x => x % 2 === 1;
const myPred = ko.observable(odd);
const myValues = ko.observable([ 1, 2, 3 ]);
const myFilter = myPred.map(filter);
const myResult = myValues.ap(filter); // S([ 1, 3 ])
The definition of lift2 gives me another way of writing the same thing.
const myResult = lift2 (filter) (myPred) (myResult)
So far, so good. I can use the dot-calls if the interim result is reusable, and a liftN call if I only care about the final outcome.
The problem
The liftN way of chaining one map with N - 1 calls to ap only works if I use plain functions. In my app however, I often deal with functions that are themselves wrapped in subscribables! For example:
const sum = x => y => x + y;
const mathStrategy = ko.observable(sum);
const v1 = ko.observable(2);
const v2 = ko.observable(3);
My attempts
Chaining works, but quickly gets very hard to understand.
// Ugly...
const myResult = v2.ap(v1.ap(mathStrategy)); // S(5)
I can use liftN, but only if I make sure my first function is id.
// Also ugly...
const id = x => x;
const myResultL = lift3 (id) (mathStrategy) (v1) (v2); // S(5)
My questions
- If
lift2handlesf -> A.of(x) -> A.of(y) -> A.of(f (x) (y)), what is the theory/name/type behindA.of(f) -> A.of(x) -> A.of(y) -> A(f (x) (y)) - If such a thing does not really “exist”, would it be okay to write an implementation of
apthat unwrapsA(f)on the go? (i.e.f => ko.unwrap (f) (x))
Code example
Object.assign(ko.subscribable, {
of: function(x) {
return ko.pureComputed(() => x)
}
});
Object.assign(ko.subscribable.fn, {
map: function(f) {
return ko.pureComputed(() => f(this()));
},
ap: function(sf) {
return ko.pureComputed(() => sf () (this()));
},
toString: function() {
return `S(${JSON.stringify(this())})`;
}
});
// Example code:
const sum = x => y => x + y;
const mult = x => y => x * y;
const mathStrategy = ko.observable(sum);
const v1 = ko.observable(1);
const v2 = ko.observable(3);
const result = v2.ap(v1.ap(mathStrategy));
console.log(result); // S(4)
v1(2);
mathStrategy(mult);
console.log(result); // S(6).as-console-wrapper { min-height: 100% !important; }<script src="https://cdnjs.cloudflare.com/ajax/libs/knockout/3.4.2/knockout-min.js"></script>
Note: This is kind of related to a question I asked earlier. Back then, I was focusing on lazily unwrapping A(x) and A(y), which I have given up on by now .
