monoids is a semi-group with a neutral element. A semigroup, it does not have an element to return so it‘s not a safe operation, whereas with the monoids we could take as many as we possibly want, even none, and still return us back something. It‘s a perfectly safe operation here that we can reduce as many of them as we‘d like.

For example to Sum():

const Sum = x => ({   concat: o => Sum(x + o.x) })

‘Zero‘ neutral element for Sum semi-group, so Sum is monoids.

2 + 0 //21 + 0 //1x + 0 //x

So we can define an interface for Sum:

Sum.empty = () => Sum(0)

And if we concat Sum.empty to anything, it won‘t affect the result:

Sum.empty().concat(Sum(1)) // Sum(1)

The same as All():

All.empty = () => All(true)// true && true -->  true// false && true -->  false 

But for the First(), we can not find a neutal element for it, because it just throw away the rest value only keep the first value and first value can be undefined.

[1,2,3] && undefined --> 1undefined && [1,2,3]  --> error

Monodis also looks like reduce:

const sum = xs =>  xs.reduce((acc, x) => acc + x, 0)console.log(sum([1,2,3])) //6const all = xs =>  xs.reduce((acc, x) => acc && x, true)console.log(all([true, false])) //falseconst first = xs =>  xs.reduce((acc, x) => acc)console.log(first([1,2,3]))console.log(first([])) //Error

[JS Compose] 7. Ensure failsafe combination using monoids