## Stream: Coq users

### Topic: Composition of 2 functions

#### Julin S (Dec 07 2021 at 03:45):

How can we obtain the composition of two functions for use with `List.map`? Do we always have to use `compose` or can we use function application with parenthesis?

I was trying to apply the `List.map` function to a list of tuples (2 nats each) like

``````Definition lst := [(1,10); (2,20); (3,30)].

Definition bar (n : nat) := n + 100.
``````

I wanted to take the second element of each tuple and apply the `bar` function on it to produce a new list.

I tried

``````Compute List.map (bar snd) lst.
(*
The term "snd" has type "?A0 * ?B0 -> ?B0" while it is expected to have type
"nat".
*)
``````

Type of `snd` is `(?A * ?B) -> ?B` which in the case of `lst` would become `(nat * nat) -> nat`.
And type of `bar` is `nat -> nat`.

It worked when I tried using `compose` from `Coq.Program.Basics`.

``````Compute List.map (compose bar snd) lst.
(*
= [110; 120; 130]
: list nat
*)
``````

Is function composition not possible by simply writing them together? Do we always need `compose`?

#### Paolo Giarrusso (Dec 07 2021 at 06:08):

Indeed, function composition is compose and not application; the type signature of compose describes exactly the job of composition.

#### Ali Caglayan (Dec 08 2021 at 10:35):

`compose` exists for proof search. i.e. for typeclass search to be able to recognise a specific composition and find instances that way. You can also write `fun x => bar (snd x))` for that function.

Last updated: Sep 30 2023 at 05:01 UTC