A short intro to type classes in Haskell

19 June 2016
#haskell#functional programming#type theory#lambda calculus

Haskell as a language always fascinates me with its unique typesystem and constructs that offers expressiveness unlike other languages.

In this article, I want to share something I learned about type classes in Haskell. To do that, we need an example!

Let's create a simple function in haskell that does some arithmetic to understand typeclasses.

So here's our magical function:

-- simple_haskell.hs
magical x y = (x + y) * (x - y)

Let's load this up in ghci real quick.

ghci> :l simple_haskell.hs

Let's see the type of function magical by running:

:t magical

We get something like:

Num a => a -> a -> a

That's a lot of a's and I could hardly figure out what all that meant.

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Y u no simple to read haskell. :|

After endless sessions of skimming the interwebs here and there, I think I have a decent understanding from which to reason further about typeclasses.

So, let's visit our signature again and break it down, shall we!

In the signature above, the a -> a -> a denotes that our function magical takes two types a (the first two a's) and returns a type a.

Take a note that the last one always is the return type. Actually, there is more going on here, which is called currying in functional lingo, but that will be part of another post.

Side note: Functions in haskell always have an arity of 1, which means they always have one arguement.

It's an unfamiliar syntax to many but not until you learn about lambda calculus or if you have some functional programming background.

Anyways, what's with the first Num a. This is what what we are interested in. The Num in Num a, is a typeclass in haskell, and the a, is what we call a type variable, (just a placeholder if you will).

Typeclasses in haskell are a construct which encapsulates different functions or behaviors for any type, that falls under that typeclass. They allow you to generalize over a multitude of types confirming to a set of protocol.

As an analogy, the Num typeclass in Haskell is a holder of a family of concrete Numish types, which can be int, long, float, double etc. Similary Eq is another typeclass in haskell used to provide total ordering semantics for two comparable types.

That's all folks. I intend to update this article in future with more details.

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