data, type, newtype, instance, class

One of the first things to confuse me about Haskell was the number of keywords related to types. The five (I know, 5 isn’t that many) I’ve counted in Haskell 98 are data, type, newtype, instance, and class. I was unable to find a comprehensive discussion of what each of them means and how they are related to each other. I’ll break these keywords up linto 2 related sets. data, type, and newtype are all ways to declare a new type. instance and class are slightly different. Let’s take a closer look at them.

data, type, newtype

data is used to declare a new algebraic data type. We can use it to create a boolean or, in this case, the maybe monad:

data Bool = True | False
data Maybe a = Nothing | Just a

type is used to create an alias for an algebraic data type. A good example of this is included in the Prelude:

type String = [Char]

newtype acts similarly to type with a syntax akin to data. Thus we can write the following:

newtype Radius = Radius Double
data Diameter = Diameter Double

Okay, so what’s the difference between newtype and data? Three things (that I’m aware of):

newtype can only have a single constructor taking a single argument.
newtype creates a strict value constructor and type creates a lazy one (see [1]).
newtype introduces no runtime overhead.

class, instance

A typeclass is a way to guarantee that a type implements certain functions (or data). A type is declared to implement the functions using the keyword instance. An example will be helpful:

--Normally I would use Double, but Int's will be easier to read
type Point = (Int, Int)
data Triangle = Triangle Point Point Point deriving (Show)
data Square = Square Point Point Point Point deriving (Show)

class Shape a where
  rotate :: a -> a
  simple :: a

instance Shape Triangle where
  rotate (Triangle x y z) = Triangle z x y
  simple = Triangle (0, 0) (1, 0) (0, 1)

instance Shape Square where
  rotate (Square w x y z) = Square z w x y
  simple = Square (0, 0) (1, 0) (1, 1) (0, 1)

As you can see, we first define 3 simple types. Next, the ”class Shape ...” bit, that’s the typeclass definition. All we’re doing is telling the compiler what must be defined for an instance of Shape. With the instance keyword, we make our classes instances of Shape by defining the necessary stuff (i.e. rotate and simple). Let’s try it in GHCi:

Prelude> :l shape.hs
[1 of 1] Compiling Main.             ( shape.hs, interpreted )
*Main> simple :: Square
Square (0,0) (1,0) (1,1) (0,1)
*Main> rotate it
Square (0,1) (0,0) (1,0) (1,1)
*Main> simple :: Triangle
Triangle (0,0) (1,0) (0,1)
*Main> rotate it
Triangle (0,1) (0,0) (1,0)
*Main> rotate it
Triangle (1,0) (0,1) (0,0)

Cool! Because Square and Triangle instantiate Shape, we know that we can call rotate on them. That’s all a typeclass does. I tend to think of them as an interface or a contract.

Summary

Remember, data, type and newtype are about making types. instance and class are about making typeclasses.

PS, there’s another keyword, deriving, that could fit in this discussion. It seems less confusing to me, so I won’t cover it.

data, type, newtype, instance, class