Under

The best way to understand any given typeclass is to find its documentation online. This is usually easy with Google, or failing that, Hoogle.

Show

A class for converting a type into a String, which can be displayed. String is a legacy type, but Show is widely used, and can be derived by Haskell:

repl example

> data Piece = Bishop | Knight deriving Show
> show Bishop
"Bishop"

Gotcha

repl example

> show (+)
"No instance for (Show (Integer -> Integer -> Integer))..."

Haskell won't show arbitrary functions, because they don't have a Show instance. This makes sense, since it is impossible to show all the (infinite) input-output pairs of a function.

Eq

Ord

Num

Semigroup

Provides a method to combine two values: (<>) :: a -> a -> a

Any instance should define <> such that it is associative (i.e. a <> (b <> c) = (a <> b) <> c)

Text

repl example

> :set -XOverloadedStrings
> import Data.Text
> text = "hello"
> text2 = "world"
> text <> text2
"helloworld"

Monoid

Any

All

Sum

Product

Foldable

Functor

class Functor (f :: * -> *) where -- (1)!
    fmap :: (a -> b) -> f a -> f b

1. The kind signature f :: * -> * requires the GHC2021 standard extensions.

Hint

Types which are instances of Functor must have kind * -> *.

So Int or Bool or Either Int Bool or [Int] **cannot be instances of Functor, but Either Int, or [] can. (See section on partial application of types.)

List

The definition of fmap for [] is just map

repl example

> ls = [1 :: Int, 2, 3]
> :t ls 
ls :: [Int]
> fmap even ls
[False,True,False]
> :t fmap even ls
fmap even ls :: [Bool]

Maybe

repl example

> maybeChar = Just 'a'
> :t maybeChar
maybeChar :: Maybe Char
> fmap (=='a') maybeChar
Just True
> :t fmap (=='a') maybeChar
fmap (=='a') maybeChar :: Maybe Bool

Reader r

State s

Fix f

Free f

Cont r

Applicative

Monad

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Last update: January 13, 2023
Created: January 11, 2023

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