Data Types

Data Type Definition

data Bool = False | True
data Module = CS141 | CS256 | CS118 | CS132 ...
data Unit = Unit
not :: Bool -> Bool
not True  = False -- Pattern matching on constructors
not False = True  -- Constructors as values

This is the definition of the data type for Bool. “Bool” is the name of the type, and “False” and “True” are data constructors.

• We can pattern-match on data constructors
• We can use data constructors as values
• We can have as many number of data constructors as we want
• Name of the type is not the same as the data constructor (although we can name them the same)
• Data constructors can have parameters.

Parametrised Data Constructors

We can add parameters to a data constructor by adding their types after the constructor’s name.

data Shape = Rect Double Double
           | Circle Double

We can treat data constructors like a function.

Rect   :: Double -> Double -> Shape
Circle :: Double -> Shape

Recursive Data Types

data Nat = Zero | Succ Nat

data BinTree a = Leaf a | Node (BinTree a) (BinTree a)

Type Aliases

We can define aliases for a certain type.

type String = [Char]
type Memory = [(String, Int)] -- Recall coursework 2
type Predicate a = a -> Bool

Derivable Type Classes