# Typeclasses and higher-kinded types in Wipple

January 10, 2022

Typeclasses are a powerful construct used in functional programming languages like Haskell. Essentially, they allow you to overload functions so that they can operate on different types. Let's take a look at Wipple's `show`

function:

`show :: Show A => A -> ()`

This means that `show`

accepts any value where `Show`

is defined for the value's type. Well what is `Show`

? It's a **trait**, Wipple's name for typeclasses. To create a trait, just provide a type definition:

`A => Show A :: A -> Text`

Note: This syntax is lightweight but ambiguous in some edge cases. If you want to add a type annotation on a value like

`f x :: A`

, you should wrap the value in parentheses:`(f x) :: A`

.

In Wipple, a trait is a construct whose value depends on its type. We can provide multiple definitions for `Show`

to define it for various types!

`Show Text : it Show Number : n -> ... Show Boolean : b -> if b "True" "False"`

Another good example of traits in action is the `Equal`

trait, which can be defined to support equality on types:

`A => Equal A :: A -> A -> Boolean [operator 5] = : Equal -- = :: Equal A => A -> A -> Boolean`

Now let's take a look at the `|`

(map) operator. What do you think its type is?

`[operator 7] | : functor -> f -> Functor f functor`

First, what's a functor??? Without getting too technical, a functor is basically a container that supports the map operation on its contents. For example, we can use `|`

with `List`

s, `Maybe`

s, and `Result`

s:

`'(1 2 3) | increment = '(2 3 4) Some 1 | increment = Some 2 None | increment = None Success 1 | increment = Success 2 Error "oh no" | increment = Error "oh no"`

So, the job of the `|`

operator is to take a container holding some value(s) `A`

, and apply a function `A -> B`

to the value(s) so that we end up with the same container holding the new value(s) `B`

. To express this in the type system, we need a new feature — higher-kinded types! It looks like this:

`(F _) => Functor F :: A => B => (A -> B) -> F A -> F B`

Notice that instead of providing a type variable like `A`

, we provide a "type function" `F`

that takes an input `_`

. We can then provide the input `A`

to build a container `F A`

, and so on. For example, we can define `Functor`

for `Maybe A`

, for any `A`

:

`A => Functor (Maybe A) : f -> x? -> when x? { Some x -> Some (f x) None -> None }`

Thus, the type of `|`

is:

`| :: Functor (F _) => A => B => F A -> (A -> B) -> F B`

For now, only traits with a single parameter are supported. (This restriction is also present in vanilla Haskell because it causes ambiguity.) But that shouldn't prevent very many use cases!

### The new type function syntax

You may have noticed that I reworked the syntax for what used to be `for`

functions. In the new syntax, you declare a single type variable with an optional set of traits for which the type is defined. This syntax is a little more concise while still making clear the difference between implicit and explicit type checking.

`A => ... -- introduce type variable A Show A => ... -- introduce type variable A where Show A is defined (Show Equal) A => ... -- introduce type variable A where Show A and Equal A are defined (F _) => ... -- introduce higher-kinded type F Functor (F _) => ... -- introduce higher-kinded type F where Functor (F _) is defined`

### Conclusion

All in all, I'm really excited to start working on implementing this in the Wipple compiler. Once I have a working, type safe `|`

operator, I can start work on pattern matching and then the standard library!