@@ -35,9 +35,8 @@ __Table of Contents__
3535* [ Lambda Calculus (TODO)] ( #lambda-calculus-todo )
3636* [ Lazy evaluation (TODO)] ( #lazy-evaluation-todo )
3737* [ Functor (TODO)] ( #functor-todo )
38- * [ Applicative (TODO)] ( #applicative-todo )
3938* [ Applicative Functor (TODO)] ( #applicative-functor-todo )
40- * [ Monoid (TODO) ] ( #monoid-todo )
39+ * [ Monoid] ( #monoid )
4140* [ Monad (TODO)] ( #monad-todo )
4241* [ Comonad (TODO)] ( #comonad-todo )
4342* [ Morphism (TODO)] ( #morphism-todo )
@@ -588,20 +587,31 @@ object.map(compose(f, g)) ≍ object.map(g).map(f)
588587
589588## Pointed Functor (TODO)
590589
591- ## Applicative (TODO)
590+ ## Applicative Functor (TODO)
591+ 592592
593- ## Applicative Functore (TODO)
593+ ## Monoid
594594
595- ## Monoid (TODO)
595+ An object with a function that "combines" that object with another of the same type
596+ and an "empty" value, which can be added with no effect.
596597
597- An object with a function that "combines" that object with another of the same type.
598+ One simple monoid is the addition of numbers
599+ (with ` __add__ ` as an addition function and ` 0 ` as an empty element):
600+ 601+ ``` python
602+ >> > assert 1 + 1 + 0 == 2
603+ >> >
604+ ```
598605
599- One simple monoid is the addition of numbers :
606+ Tuples, lists, and strings are also monoids :
600607
601608``` python
602- 1 + 1 # 2
609+ >> > assert (1 ,) + (2 ,) + () == (1 , 2 )
610+ >> > assert [1 ] + [2 ] + [] == [1 , 2 ]
611+ >> > assert ' a' + ' b' + ' ' == ' ab'
612+ >> >
603613```
604- In this case number is the object and ` + ` is the function.
614+ 605615
606616## Monad (TODO)
607617
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