Type Classes & Custom Types

Algebraic Data Types

ADTs model domain concepts precisely. 'data Shape = Circle Double | Rectangle Double Double | Triangle Double Double Double' is a sum type — a Shape is one of three variants. 'data Person = Person { name :: String, age :: Int }' is a product type with named fields (record syntax). Pattern match on constructors to handle each case. The compiler warns if you miss a case.

Deriving Type Classes

Add 'deriving (Eq, Ord, Show, Read, Enum, Bounded)' to automatically generate standard instances. Eq: (==) and (/=). Ord: (<), compare. Show: show turns a value to a String. Read: read parses a String. Deriving handles nested types automatically. For custom behavior, write a manual instance: 'instance Show Shape where show (Circle r) = ...'

Type Classes in Depth

A type class defines an interface. 'class Container f where empty :: f a; insert :: a -> f a -> f a; toList :: f a -> [a]'. Types implement it: 'instance Container [] where ...'. Functor, Foldable, and Traversable are the standard type classes for container types. A type that is a Functor can use fmap; a Foldable can use foldr/sum/length; a Traversable can sequence effects through a structure.

data Shape
  = Circle    Double
  | Rectangle Double Double
  | Triangle  Double Double Double
  deriving (Show, Eq)

area :: Shape -> Double
area (Circle r)        = pi * r * r
area (Rectangle w h)   = w * h
area (Triangle a b c)  =
  let s = (a + b + c) / 2
  in  sqrt (s * (s-a) * (s-b) * (s-c))  -- Heron's formula

perimeter :: Shape -> Double
perimeter (Circle r)       = 2 * pi * r
perimeter (Rectangle w h)  = 2 * (w + h)
perimeter (Triangle a b c) = a + b + c

-- Type class instance for ordering by area
instance Ord Shape where
  compare s1 s2 = compare (area s1) (area s2)

-- Usage
shapes :: [Shape]
shapes = [Circle 5, Rectangle 3 4, Triangle 3 4 5]

largest :: Shape
largest = maximum shapes  -- uses Ord instance