[Functional Programming] From simple implementation to Currying to Partial Application

Let's say we want to write a most simple implementation 'avg' function:

const avg = list => {
    let sum = 0;
    for(let i = 0; i < list.length; i++) {
        sum += list[i]
    }
    return sum / list.length
}

Basiclly, the 'avg' function doing two things:

• Calculate sum
• Divide sum / length

It works fine for tiny / small application, but for the large application, we need to think about reuseablitiy. We want to breakdown one function and think about any reuseable partten, which later can be reused.

In the following examples, We want to bring in two libarays which are commonly used in FP. One is Ramda, another one is Crocks.

Currying:

First, we want to write 'sum' and 'devide' functions by ourselves:

const { curry, reduce, compose } = require("crocks");
const R = require("ramda");

const sum = reduce(R.add, 0);
// divideByLen :: [Number] -> Number -> Number
const divideByLen = curry(
  compose(
    R.flip(R.divide),
    R.length
  )
);

'sum' is simple, using 'reduce' from Crocks, you can also write JS reduce, doesn't matter.

What we need to explain is 'divideByLen' function. 

• Why 'curry'?

Basic we want to call divideByLen in two ways:

divideByLen([1,2,3], sum([1,2,3]))
divideByLen([1,2,3])(sum([1,2,3]))

[Notice] You need to bring in 'curry' from Crocks, it is more flexable. 

• Why 'flip'?

Because R.divide(sum, length), we need to feed the divide function with sum as first argement, then length as second arguement. But when we write code, length will be feeded frist, sum will be partially applied, it will come second, therefore we need to call 'flip'.

Bring all together:

const avg = list =>
  compose(
    divideByLen(list),
    sum
  )(list);

We notice that, we have to pass 'list' to both Sum(list) and divideByLen(list). The code looks not so good. Whenever you are facing the situation, you need to pass the same arguement to two functions in parallel. You can consider to using 'Partial Application'.

Partial Application:

// Ramda

const avg = R.converge(R.divide, [R.sum, R.length]);

We are using 'Ramda's converge' function, bascilly you have pass in a data, the data will be passed to R.sum(data) & R.length(data), the return results of those two functions, will be passed to R.divide(resOfSum, resOfLength). 

//Crocks:

const { curry, fanout, merge, compose } = require("crocks");

const avg = compose(
  merge(R.divide),
  fanout(R.sum, R.length)
);

We are using the Pair ADT, the data will be passed to R.sum(data) & R.length(data) thought 'fanout' function, it returns Pair(resOfSum, resOfLength).

Then we use 'merge', it works with Pair ADT, we merge two results by R.divide(resOfSum, resOfLength).