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Q&A How to implement `map` using the fish (>=>, Kleisli composition) operator in F#?

Is there a "cleaner" implementation similar to map's? Yes: let map f = id >=> switch f This follows from two of your other equations: map f = bind (switch f) g >=> h = g >...

posted 9mo ago by r~~‭  ·  edited 9mo ago by r~~‭

Answer
#4: Post edited by user avatar r~~‭ · 2024-04-04T04:02:38Z (9 months ago)
  • > Is there a "cleaner" implementation similar to `map`'s?
  • Yes:
  • ```
  • let map f = id >=> switch f
  • ```
  • This follows from two of your other equations:
  • ```
  • map f = bind (switch f)
  • g >=> h = g >> bind h
  • ```
  • So if you want to get `bind (switch f)` out of `(>=>)`, you can start by making `h = switch f`, then get rid of the superfluous composition by letting `g` be `id` and you're done.
  • ```
  • g >=> h = g >> bind h <------ (h = switch f)
  • = g >=> switch f = g >> bind (switch f)
  • = g >=> switch f = g >> map f <------ (g = id)
  • = id >=> switch f = id >> bind (switch f)
  • ```
  • > Is there a "cleaner" implementation similar to `map`'s?
  • Yes:
  • ```
  • let map f = id >=> switch f
  • ```
  • This follows from two of your other equations:
  • ```
  • map f = bind (switch f)
  • g >=> h = g >> bind h
  • ```
  • So if you want to get `bind (switch f)` out of `(>=>)`, you can start by making `h = switch f`, then get rid of the superfluous composition by letting `g` be `id` and you're done.
  • ```
  • g >=> h = g >> bind h <------ (h = switch f)
  • g >=> switch f = g >> bind (switch f)
  • g >=> switch f = g >> map f <------ (g = id)
  • id >=> switch f = id >> map f
  • id >=> switch f = map f
  • ```
#3: Post edited by user avatar toraritte‭ · 2024-04-03T16:21:24Z (9 months ago)
  • > Is there a "cleaner" implementation similar to `map`'s?
  • Yes:
  • ```
  • let map f = id >=> switch f
  • ```
  • This follows from two of your other equations:
  • ```
  • map f = bind (switch f)
  • g >=> h = g >> bind h
  • ```
  • So if you want to get `bind (switch f)` out of `(>=>)`, you can start by making `h = switch f`, and then you have `g >=> switch f = g >> bind (switch f) = g >> map f`. Get rid of the superfluous composition by letting `g` be `id` and you're done.
  • > Is there a "cleaner" implementation similar to `map`'s?
  • Yes:
  • ```
  • let map f = id >=> switch f
  • ```
  • This follows from two of your other equations:
  • ```
  • map f = bind (switch f)
  • g >=> h = g >> bind h
  • ```
  • So if you want to get `bind (switch f)` out of `(>=>)`, you can start by making `h = switch f`, then get rid of the superfluous composition by letting `g` be `id` and you're done.
  • ```
  • g >=> h = g >> bind h <------ (h = switch f)
  • = g >=> switch f = g >> bind (switch f)
  • = g >=> switch f = g >> map f <------ (g = id)
  • = id >=> switch f = id >> bind (switch f)
  • ```
#2: Post edited by user avatar r~~‭ · 2024-04-02T23:14:54Z (9 months ago)
  • > Is there a "cleaner" implementation similar to `map`'s?
  • Yes:
  • ```
  • let map f = id >=> switch f
  • ```
  • > Is there a "cleaner" implementation similar to `map`'s?
  • Yes:
  • ```
  • let map f = id >=> switch f
  • ```
  • This follows from two of your other equations:
  • ```
  • map f = bind (switch f)
  • g >=> h = g >> bind h
  • ```
  • So if you want to get `bind (switch f)` out of `(>=>)`, you can start by making `h = switch f`, and then you have `g >=> switch f = g >> bind (switch f) = g >> map f`. Get rid of the superfluous composition by letting `g` be `id` and you're done.
#1: Initial revision by user avatar r~~‭ · 2024-04-02T21:02:56Z (9 months ago)
> Is there a "cleaner" implementation similar to `map`'s?

Yes:

```
let map f = id >=> switch f
```