Semigroup

Graphic

graph LR; A[Semigroup]

Semigroup must have a concat method. The concat method takes one argument: s.concat(b)

A Semigroup’s concat method must take another value of the same type, and return a third value of the same type.

Examples

JavaScript’s “String” type is already semigroup:

// 'hello, world!'
'hello'.concat(', world!')

// This operation is associative, too!
'hello'.concat(', ').concat('world!')
'hello'.concat(', '.concat('world!'))

JavaScript’s “Arrays” are already valid semigroups, too:

[1, 2].concat([3, 4]) // [1, 2, 3, 4]

// Aaand it's associative!
[1].concat([2, 3]).concat([4])
[1].concat([2, 3].concat([4]))

Concat with custom type:

const Sum = (value) => ({
  value,
  concat: (y) => Sum(value + y.value),
  empty: () => Sum.empty()
})

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

Sum.prototype.concat = function (that) {
  return Sum(this.val + that.val)
}

Sum(2).concat(Sum(3)).value // 5

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