Understanding the Haskell Type System: From Typeclasses to Data Structures

In this tutorial — inspired by my video “Structure de données et système de types en Haskell” — we dive into the heart of what makes Haskell so expressive: its type system.

This article targets an intermediate audience: you already know what a function or a list is, but now you want to understand why types in Haskell feel so different — and powerful — compared to other languages.

1. Why types matter in Haskell

In Haskell, types are not just annotations — they are first-class citizens that define how values behave and interact. The compiler (GHC) uses types to enforce correctness, optimize performance, and even help you reason about your program.

Every value in Haskell has a type, and Haskell’s compiler infers those types automatically. But you can (and should) write them explicitly to make your intent clear. 

add :: Int -> Int -> Int
add x y = x + y

This tells the compiler that add takes two integers and returns another integer.

2. Type inference and polymorphism

Haskell’s compiler can infer types thanks to a mechanism called Hindley–Milner type inference. For example, if you omit the type signature: 

identity x = x

The compiler infers the most general type possible: 

identity :: a -> a

Here, a is a type variable, meaning identity can work on any type — integers, strings, lists, you name it. This is what we call parametric polymorphism.

3. Typeclasses — defining shared behavior

A typeclass in Haskell defines a set of behaviors that different types can implement. Think of it as an interface, but purely functional and extensible. 

class Eq a where
  (==) :: a -> a -> Bool
  (/=) :: a -> a -> Bool

The Eq typeclass defines equality. Any type that implements Eq must provide definitions for (==) and (/=).

To make your own type an instance of Eq: 

data Color = Red | Green | Blue

instance Eq Color where
  Red   == Red   = True
  Green == Green = True
  Blue  == Blue  = True
  _     == _     = False

Now, you can compare Color values directly: 

Red == Blue   -- False
Green == Green -- True

4. Custom data types and pattern matching

One of Haskell’s most elegant features is the ability to define your own data structures. Let’s define a simple Shape type: 

data Shape
  = Circle Float
  | Rectangle Float Float

You can now create shapes like Circle 5 or Rectangle 4 6. Pattern matching makes it trivial to extract values from these structures: 

area :: Shape -> Float
area (Circle r) = pi * r ^ 2
area (Rectangle w h) = w * h

Each constructor of the type is handled as a different pattern. This is one of Haskell’s most powerful ways of structuring logic — the compiler ensures you’ve covered all possible cases.

Very usefull when working on graphs and trees ;)

5. Type synonyms and newtype

Sometimes you want to make your code more readable without introducing a new data constructor. That’s where type and newtype come in. 

type Name = String
type Age = Int

data Person = Person Name Age

The type keyword doesn’t create a new type — it’s just an alias. If you need a distinct type with a single underlying representation, use newtype: 

newtype UserId = UserId Int

Unlike type, newtype creates a truly distinct type that can have its own instances and behaviors, even though it’s represented by the same underlying value at runtime.

6. Deriving standard behaviors

Instead of manually writing instances for basic behaviors like equality or printing, Haskell lets you automatically derive them. 

data Point = Point Float Float
  deriving (Show, Eq)

Now you can print and compare points directly: 

Point 2 3 == Point 2 3  -- True
print (Point 1 5)       -- "Point 1.0 5.0"

7. Bringing it all together

The Haskell type system is not just about safety — it’s about expressing ideas clearly. By using typeclasses, data definitions, and polymorphism, you can make illegal states unrepresentable and describe the logic of your program at the type level.

  • Types describe what’s possible.
  • Typeclasses describe what’s allowed.
  • Pattern matching reveals what’s inside.

Once you start thinking in types, your Haskell code becomes not only correct — but self-documenting.

8. Wrap-up

In this intermediate overview, we explored:

  • How type inference and polymorphism make functions generic
  • What typeclasses are and how they model shared behavior
  • How to define your own data types and pattern match on them
  • When to use type vs newtype
  • How deriving simplifies standard operations

In short, the Haskell type system isn’t just a safety net — it’s a design language. Mastering it is the first real step toward writing expressive, composable, and reliable Haskell code.