Type classes are an indefensible part of how we write Haskell. A lot of the rest of this material won't make a lot of sense without them🤪

Calling them "type classes" is both a stroke of genius and a terrible mistake. There are absolutely strong parallels with classes from object-oriented programming. They also mostly work the exact opposite way that you'd expect coming from OOP.

Type classes let you define a common interface across many types. The concrete function that gets called gets determined by how you define an `instance`

of that `class`

.

For example, let's say that you have these functions:

add :: Int -> Int -> Intadd a b = a + b(++) :: [a] -> [a] -> [a][] ++ bs = bs(a : as) ++ bs = a : as ++ bsappend :: Text -> Text -> Textappend a b = -- Long complex function-- Function composition(.) :: (b -> c) -> (a -> b) -> (a -> c)f . g = \x -> f (g x)

In a sense, all of these do the same thing: they combine values of a common type together (i.e. they all have the form `a -> a -> a`

) While we may expect them to behave in some common ways, the exact meaning of that depends on the specific type. Why not write functions that could work on any of these types with respect to this combining behaviour?

We can define a common interface for this "combinable" behaviour!

class Combinable a wherecombine :: a -> a -> a

This is called a semigroup in maths, so the version in the library is actually called `Semigroup`

. Don't let the math-y name scare you! It's actually very straightforward for a "combinable" thing.

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

Let's write some instances!

instance Semigroup Int wherea <> b = a + binstance Semigroup [a] whereas <> bs = as ++ bsinstance Semigroup Text wherea <> b = append a b

Finally, let's use it in a function. We place "class constraints" before the arguments in the type signature, separated by a `=>`

.

triple :: Semigroup a => a -> atriple x = x <> x <> xtriple 10-- 30triple [1, 2, 3]-- [1, 2, 3, 1, 2, 3, 1, 2, 3]triple "hi"-- "hihihi"(triple (*2)) 5-- 40

Libraries tend to give you a lot of "functions for free" to go with your instance. It's typically worth it to define an instance for a new data type.

Unlike OO where inheritance happens on concrete data, Haskell's "inheritance" on interfaces is more like saying "assuming that you have an `x`

, then you can also do `y`

!" It lets you extend abstract interfaces with more functions. This usually makes for a smaller number of types that have the new interface, because they need the old type class, plus an instance for the new one, which is not always even possible!

Let's extend that Semigroup to have an element that when used with `<>`

is a no op. We'll call this `mempty`

, because of how it works on lists ([] ++ xs = xs) and because the name `id`

was already taken.

class Semigroup a => Monoid a wheremempty :: a

By definition, a Monoid is assumed to have a Semigroup instance kicking around. It has both `mempty`

and `<>`

automatically available. Let's look at a few of these:

intance Monoid Int wheremempty = 0instance Monoid [a] wheremempty = []instance Monoid Text wheremempty = ""instance Monoid (-> a) wheremempty = id

The most widely-used type class heirarchy is the `Functor`

tree, which includes the infamour `Monad`

class. These also have special rules that you need to obey when writing instances for, but you'll mostly be using someone else's so don't worry about them too much for now.

There's also highly-recommended visual guide for the following material at Functors, Applicatives, And Monads In Pictures.

You may not know it, but you're already familair with functors!

class Functor wherefmap :: (a -> b) -> f a -> f b

You'll see a lot of `fmap`

's operator variants `<$>`

and `<&>`

floating around

fmap show [1,2,3] -- ["1", "2", "3"]show <$> [1,2,3] -- ["1", "2", "3"]

The pun here is that it's the same as `$`

(application) but working on something that's been put into a container (practically any sum or product type), hence the visual pun of `<$>`

. Same goes for `&`

(pipe) and `<&>`

.

show $ 1 -- "1"show <$> [1, 2, 3] -- ["1", "2", "3"]1 & show -- "1"[1, 2, 3] <&> show -- ["1", "2", "3"]

`Applicative`

s add a lot of power to `Functors`

by defining two functions:

`pure`

(also known as the somewhat confusingly named`return`

) takes a plain value and wraps it in a container.`<*>`

does function application when both functions and arguments are wrapped

class Functor f => Applicative f wherepure :: a -> f a(<*>) :: f (a -> b) -> f a -> f b

The `<*>`

is often referred to as the Tie Fighter operator 🤣 It's also called `ap`

, short for "applicative apply".

For example, on `Maybe`

:

instance Applicative (Maybe a) wherepure x = Just xJust f <*> Just x = Just $ f x_ <*> _ = Nothingpure 4 :: Just Int -- Just 4pure "hi" :: Just Text -- Just "hi"Just (*10) <*> Just 6 -- Just 60Nothing <*> Just 6 -- NothingJust (*10) <*> Nothing -- Nothing

class Applicative m => Monad m where(>>=) :: m a -> (a -> m b) -> m bjoin :: m (m a) -> m a

`>>=`

is pronounced "bind". This is because when you use it to link into the next function, it "binds" to the first argument, like a supercharged pipe. Further, because of how scoping rules work, argument name bindings last until the end of the chain:

[1,2,3] >>= \a ->[a + 1] >>= \b ->[(show b, a * 10)]-- [("2", 10), ("3", 20), ("4", 30)]

There's also an inverted bind operator, =<< with arguments reversed

Let's look at a couple instances:

instance Monad [a] wherejoin xs = foldr (++) [] xsxs >>= f = join (f <$> xs)instance Monad (Maybe a) wherejoin Nothing = Nothingjoin (Just inner) = innerNothing >>= f = NothingJust x >>= f = Just (f x)

`>>=`

is special compared to `<$>`

and `<*>`

. It doesn't run out of arguments, and can be chained forever.

[1,2,3] >>= \a ->pure (a + 1) >>= \b ->pure (b * 10) >>= \c ->pure (c - 5)-- [15, 25, 35]

It can also be used to change behaviour, changing its structure based on arguments:

[1,2,3] >>= \a ->if rem a 2 == 0 then [a + 1] else [a, a * 2, a * 3] >>= \b ->if b > 10 then [a] else [b]-- [1, 2, 3, 3, 3, 6, 9]Just 42 >>= \a ->if a > 10 then Nothing else Just a >>= \b ->Just (b * 10) >>= \c ->Just (show c)-- Nothing

Above there's a lot of `>>=`

and nesting to keep it straight. Haskell has "do notation" to clean this up, make it feel like an linear set of instructions, and also pun on a lot of imperative programming.

When using do notion, we often replace `pure`

with `return`

, which is the same function but renamed for extra imperative punning.

`return`

does not exit out of the function chain. It is the same function as `pure`

and only wraps values in the correct container.

Bind

Do Notation

Bind

[1,2,3] >>= \a ->pure (a + 1) >>= \b ->pure (b * 10) >>= \c ->pure (c - 5)

Do Notation

doa <- [1, 2, 3]b <- return $ a + 1c <- return $ b * 10return $ c - 5

There's also a special variant of `let`

that lets you skip the `<-`

for simple values.

Without Let

With Let

Without Let

doa <- [1, 2, 3]b <- return (a * 10)return (b + 1)

With Let

dolet as = [1, 2, 3]let b = fmap (*10) asreturn (b + 1)

How these all relate to each other can be hard to keep straight at first. Here's a handy guide in pseudocode:

-- WARNING: Abuse of notation!(a -> b) $ a == b -- Plain function(a -> b) <$> m a == m b -- Functorm (a -> b) <*> m a == m b -- Applicative(a -> m b) =<< m a == m b -- Monad{-| Legenda is a valueb is a valuem is a data wrapper / container-}

For the compiler to know that there are not duplicate, conflicting instances for type classes, instances need to be written in the same module as the `class`

declaration, or in the same module as a datatype definition. But what happens when you need to add an instance from a library to a datatype that's also from a library?

These are called type class "orphans," and we ~~shove ~~ isolate them in a module (or submodules) called `Fission.Internal.Orphanage`

. Importing this module doesn't have any actual exports, but you do need to signal to the compiler that it's a dependency for the module that you're writing. Importing it normally will lead to the linter complaining about an unused import. You can get around this warning by explicitely showiung that are no imports:

import Fission.Internal.Orphanage ()

The downside to having all of your orphan instances in a single module is that it progressivbley slows your compile times down after touching the orphanage because it need to check every module that imports it for new instances. As this file grows, it is typically a good idea to break it into submodules, and only import the orphan modules that you actually need in each scenario.