Can`t realize ap composition

[Ne4to777]

Fantasy Land spec:
v.ap(u.ap(a.map(f => g => x => f(g(x))))) is equivalent to v.ap(u).ap(a) (composition)

Implementation:

const v = Task.of(f => g => x => f(g(x)))
const u = Task.of(x => x * 3)
const a = Task.of(x => x + 3)

v
.ap(u
.ap(a
.map(f => g => x => f(g(x)))))
.fork(console.error, console.log)

Log: g => x => f(g(x))

v
.ap(u)
.ap(a)
.fork(console.error, console.log)

Log: x => f(g(x))

[robotlolita]

The composition rule states:

v ap (u ap (a map \f. \g. \x. f (g x)))  <==>  (v ap u) ap a

But this was changed at some point. The old specification (which is what this library implements) instead stated:

((a map \f. \g. \x. f (g x)) ap u) ap v  <==>  a ap (u ap v)

So v is the value you want to apply (what goes into x), u and a are respectively g and f. Thus, you need:

const v = Task.of(3);
const u = Task.of(x => x * 3)
const a = Task.of(x => x + 3)

With that, you should have the equivalence:

a.ap(u.ap(v))  <==>  a.map(f => g => x => f(g(x))).ap(u).ap(v)

Here's the relevant discussion about the change: fantasyland/fantasy-land#50

Note that this library is not maintained anymore. The new version implements Fantasy Land 2.x specification (https://folktale.origamitower.com/api/v2.3.0/en/-unknown-module-.folktale.concurrency.future._future.fantasy-land-ap.html)

[Ne4to777]

Hmm. Actual specification: https://github.com/fantasyland/fantasy-land#apply

[robotlolita]

Yes, that's the version 4 of the Fantasy Land specification.

This library does not implement version 4. It implements version 1. In version 1, the arguments to ap were flipped.