javascript - How to compose functions of varying arity using Lodash flow?

Question

I want to do some function composition. I know already this:

If f3(x) shall be the same as f1(f2(x)) then f3 = _.flowRight(f1,f2);

If f3(x,y) shall be the same as f1(x, f2(y)) then …?

(The use case is the composition of node.js/express middleware functions.)

Answer 1

In the following images, I use {_} as a placeholder for a value. Think of it as a hole in the code where we pass something in.

Ok let's imagine what your function would have to do...

• Does this seems like a generic transformation? ie, do you think we can use this in many places? – functional programming promotes building functions which are highly reusable and can be combined in various ways.
• What is the difference between f1 and f2? f1 is a unary function which will only get one arg, f2 is a binary function which will get two. Are you going to remember which one goes in which place?
• What governs the position that f1(x) gets placed in f2?
  • Compare f2(y,f1(x)) ...
  • to f2(f1(x),y)
  • is one of those more useful than the other?
  • are you going to remember which position f1 gets?

---

Recall that function composition should be able to chain as many functions together as you want. To help you understand the futility of someFunc, let's imagine it accepting up to 3 functions and 3 arguments.

• Is there even a pattern here? Maybe, but you still have the awkward unary function f1 that only gets one arg, while f2 and f3 each get 2
• Is it true that f2 and f3 are going need the value of the previous function calls on the right side always ?
  • Compare f3(z,f2(y,f1(x)))
  • to f3(f2(y,f1(x)),z)
  • Maybe f3 needs to chain left, but f2 chains from the right?
  • I can't imagine your entire API of binary functions would magically need chained arguments in the same place
• You've already mixed unary with binary functions in your composition; why arbitrarily limit it to just functions of those type then? What about a function of 3 or more arguments?

---

The answer is self-realizing

Function composition is being misused here. Function composition pretty much only works when you're composing unary functions exclusive (functions accepting 1 argument each). It immediately breaks down and cannot be generalised when mixing in functions of higher arity.

Going back to your code now, if f3 needs a name and it is the combination of f1, f2, and two parameters, it should be plainly expressed as …

const f3 = (x,y) => f1(x, f2(y))

Because it makes so many arbitrary choices, it cannot be generalized in any useful way. Just let it be as it is.

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"So is there any way to compose functions of varying arity?"

Sure, there are a couple techniques of varied practicality. I'll demonstrate use of the highly practical partial function here

const partial = (f,...xs) => (...ys) => f(...xs, ...ys)

const add = (x,y) => x + y

const mult = (x,y) => x * y

const sq = x => mult (x,x)

// R.I.P. lodash.flowRight
const compose = ([f,...fs]) => x =>
  f === undefined ? x : f (compose (fs) (x))
                  
let f = compose([partial(add, 1), sq, partial(mult, 3)])

console.log(f(2))
// add(1, square(mult(3, 2)))
// add(1, square(6))
// add(1, 36)
// => 37