Juxt

Hello and thank you for creating F#+! I'd like to propose adding juxtapose functions to the Operators module. These functions are defined as follows:

let juxt2 f g x = f x, g x
let juxt3 f g h x = f x, g x, h x
let juxt4 f g h i x = f x, g x, h x, i x
// etc

This function is called juxt in Clojure and the Python toolz library. I believe this function was first introduced by John Backus in his paper called Can programming be liberated from the von Neumann style? where it was called construction.

In Haskell and F#+ there's a similar function called sequence. Unfortunately, it returns a list and not a tuple, forcing all the result types to be the same.

juxt in combination with item and uncurry/uncurryN make point-free programming with tuples easier. Here are some examples:

open FSharpPlus

// Basic examples
let square: float -> float =
    juxt2 id id >> uncurry ( * )

let avg: list<float> -> float =
    juxt2 List.sum (List.length >> float) >> uncurry (/)

// Grouping and ungrouping tuples
let ``(a,b),c``   (a,b,c)   = (a,b),c
let ``~(a,b),c~`` ((a,b),c) = a,b,c

``(a,b),c``(1,2,3)     = (juxt2 (juxt2 item1 item2) item3)(1,2,3) // ((1, 2), 3)
``~(a,b),c~``((1,2),3) = (juxt3 (item1 >> item1) (item1 >> item2) item2)((1,2),3) // (1, 2, 3)

Please let me know if this function already exists in F#+ (or F# for that matter) and I missed it. Thank you!

Start in the Operators module and inspect the existing sequence, item, uncurry, and uncurryN functions to match their naming and organization. Implement the proposed juxt2, juxt3, and juxt4 variants, then add coverage for the tuple-producing examples and confirm the project tests pass.