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@ -539,7 +539,7 @@ randIter.next() // Each execution gives a random value, expression is evaluated
## Monoid ## Monoid
An object with a function that "combines" that object with another of the same type. An object with a function that "combines" that object with another of the same type (semigroup) which has an "identity" value.
One simple monoid is the addition of numbers: One simple monoid is the addition of numbers:
@ -548,11 +548,13 @@ One simple monoid is the addition of numbers:
``` ```
In this case number is the object and `+` is the function. In this case number is the object and `+` is the function.
An "identity" value must also exist that when combined with a value doesn't change it. When any value is combined with the "identity" value the result must be the original value. The identity must also be commutative.
The identity value for addition is `0`. The identity value for addition is `0`.
```js ```js
1 + 0 // 1 1 + 0 // 1
0 + 1 // 1
1 + 0 === 0 + 1
``` ```
It's also required that the grouping of operations will not affect the result (associativity): It's also required that the grouping of operations will not affect the result (associativity):
@ -573,15 +575,10 @@ The identity value is empty array `[]`
;[1, 2].concat([]) // [1, 2] ;[1, 2].concat([]) // [1, 2]
``` ```
If identity and compose functions are provided, functions themselves form a monoid: As a counterexample, subtraction does not form a monoid because there is no commutative identity value:
```js ```js
const identity = (a) => a 0 - 4 === 4 - 0 // false
const compose = (f, g) => (x) => f(g(x))
```
`foo` is any function that takes one argument.
```
compose(foo, identity) ≍ compose(identity, foo) ≍ foo
``` ```
## Monad ## Monad