Type Classes in more Detail

Type class and instance declarations

Defining type classes

• A type class is a set of types for which some operations are defined.

• Haskell has some standard type classes that are defined in the Standard Prelude.

• You can also define your own.

A type for bright colors

Suppose we’re computing with colors. Here’s a type, and a couple of functions.

 data Bright
 = Blue
 | Red
 deriving (Read, Show)

 darkBright :: Bright -> Bool
 darkBright Blue = True
 darkBright Red = False

 lightenBright :: Bright -> Bright
 lightenBright Blue = Red
 lightenBright Red = Red

A type for milder colors

Now, suppose we have a different type that needs similar functions.

 data Pastel
 = Turquoise
 | Tan
 deriving (Read, Show)

 darkPastel :: Pastel -> Bool
 darkPastel Turquoise = True
 darkPastel Tan = False

 lightenPastel :: Pastel -> Pastel
 lightenPastel Turquoise = Tan
 lightenPastel Tan = Tan

Defining a type class

• Both of our color types have functions to decide whether it’s dark,
  or to lighten it.

• We can define a class (Color) and its corresponding functions.

 class Color a where
 dark :: a -> Bool
 lighten :: a -> a

This says

• (Color) is a type class

• The type variable (a) stands for a particular type that is in the
  class (Color)

• For any type (a) in (Color), there are two functions you can use:
  (dark) and (lighten), with the specified types.

Defining instances for the type class

• An (instance) declaration says that a type is a member of a type
  class.

• When you declare an instance, you need to define the class
  functions.

• The following says that the type (Bright) is in the class (Color),
  and for that instance, the (dark) function is actually (darkBright).

 instance Color Bright where
 dark = darkBright
 lighten = lightenBright

• Similarly, we can declare that (Pastel) is in (Color), but it has
  different functions to implement the class operations.

 instance Color Pastel where
 dark = darkPastel
 lighten = lightenPastel

Predefined type classes

Haskell provides several standard type classes. We have a look at two of them: (Num) and (Show).

The Num class

• (Num) is the class of numeric types.
• Here is (part of) its class declaration:

 class Num a where
 (+), (-), (*) :: a -> a -> a

Num instances

• There are many numeric types; two of them are (Int) and (Double).

• There are primitive monomorphic functions that perform arithmetic on
  these types (these aren’t the real names):

addInt, subInt, mulInt :: Int -> Int -> Int
addDbl, subDbl, mulDbl :: Double -> Double -> Double

 instance Num Int where
 (+) = addInt
 (-) = subInt
 (*) = mulInt

 instance Num Double where
 (+) = addDbl
 (-) = subDbl
 (*) = mulDbl

Hierarchy of numeric classes

• There are some operations (addition) that are valid for all numeric
  types.

• There are some others (e.g. trigonometric functions) that are valid
  only for some numeric types.

• Therefore there is a rich hierarchy of subclasses, including

  • (Integral) — class of numeric types that represent integer
    values, including (Int), (Integer), and more.

  • (Fractional) — class of types that can represent fractions.

  • (Floating) — class containing (Float), (Double), etc.

  • (Bounded) — class of numeric types that have a minimal and
    maximal element.

  • (Bits) — class of types where you can access the representation
    as a sequence of bits, useful for systems programming and
    digital circuit design.

• If you want to get deeply into numeric classes and types, refer to
  the Haskell documentation.

The Show class

• We have been using (show) to convert a data value to a string, which
  can then be written to output.

• Some values can be “shown”, but not all.

• For example, it is impossible in general to show a function.

• Therefore (show) needs a type class!

• [show :: Show, a Rightarrow a rightarrow ,String]

Defining your own Show instance

 data Foo = Bar | Baz

We might want our own peculiar string representation:

 instance Show Foo where
 show Bar = "it is a bar"
 show Baz = "this is a baz"

Recall that when you enter an expression (exp) into ghci, it prints
(show exp). So we can try out our strange instance declaration:

 *Main> Bar
 it is a bar
 *Main> Baz
 this is a baz

Deriving Show

This is a similar type, but it has a (deriving) clause.

 data Foo2 = Bar2 | Baz2
 deriving (Read, Show)

Haskell will automatically define an instance of (show) for (Foo2),
using the obvious definition:

 *Main> Bar2
 Bar2
 *Main> Baz2
 Baz2

More standard typeclasses

Here is a summary of some of the type classes defined in the standard
libraries.

• (Num) — numbers, with many subclasses for specific kinds of number.

• (Read) — types that can be “read in from” a string.

• (Show) — types that can be “shown to” a string.

• (Eq) — types for which the equality operator (==) is defined.

• (Ord) — types for which you can do comparisons like (<), (>), etc.

• (Enum) — types where the values can be enumerated in sequence; this
  is used for example in the notation ([1..n]) and (‘a’..’z’).

 *Main> [1..10]
 [1,2,3,4,5,6,7,8,9,10]
 *Main> ['a'..'z']
 "abcdefghijklmnopqrstuvwxyz"