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