Functional programming terms in my own words

This article is a reference (mostly for myself) that gives simple explanations for functional programming terms. It also shows relations between terms.

Much of the information here has been learned from the excellent book, PureScript by Example.

Terms

Type Class

A thing.

Semigroup

A type class that supports concatenation.

The concatentation operatior is <>

class Semigroup a where
  (<>) :: a -> a -> a

Examples

• Arrays: [1,2] <> [3,4] = [1,2,3,4]
• Strings: "hi " <> "everyone" = "hi everyone"

Monoid

A type class that has an empty value.

class (Semigroup m) <= Monoid m where
  mempty :: m

A Monoid is also a:

• Semigroup

Examples

• Arrays: [] in: [1,2] <> [] = [1,2]
• Strings: "" in: "" <> "hey"= "hey"

Foldable

A type class. Still working on the mental model for this one.

Here are the laws:

class Foldable f where
  foldr :: forall a b. (a -> b -> b) -> b -> f a -> b
  foldl :: forall a b. (b -> a -> b) -> b -> f a -> b
  foldMap :: forall a m. (Monoid m) => (a -> m) -> f a -> m

Functor

A type class that uses the lifting operator (think map).

class Functor f where
  (<$>) :: forall a b. (a -> b) -> f a -> f b

It also follows the following laws:

• Identity law: id <$> x = x
• Composition law: g <$> (f <$> x) = (g <<< f) <$> x

Applicative

Defines pure and <*>

An applicative is a:

• Functor