Types and Typeclasses
Resources
Checking types on ghci
Use the :t command followed by a valid expression.
ghci> :t 'a' 'a' :: Char ghci> :t True True :: Bool ghci> :t "HELLO!" "HELLO!" :: [Char] ghci> :t (True, 'a') (True, 'a') :: (Bool, Char) ghci> :t 4 == 5 4 == 5 :: Bool
Function Types
We can choose to give functions an explicit type definition. This is considered good practice except for short functions.
removeNonUppercase :: [Char] -> [Char] removeNonUppercase st = [ c | c <- st, c `elem` ['A'..'Z']]
Here is an example for a function that takes three Int args and adds them together.
addThree :: Int -> Int -> Int -> Int addThree x y z = x + y + z
Typeclasses
A typeclass is a sort of interface that defines some behavior. If a type is a part of a typeclass, that means that is supports and implements the behaviour the typeclass describes.
ghci> :t (==) (==) :: Eq a => a -> a -> Bool ghci> 5 /= 5 False ghci> :t 5 /= 5 5 /= 5 :: Bool ghci> :t (>) (>) :: Ord a => a -> a -> Bool
Typeclass Ord covers all comparing functions.
ghci> "Abrakadabra" < "Zebra" True ghci> "Abrakadabra" `compare` "Zebra" LT ghci> 5 >= 2 True ghci> 5 `compare` 3 GT
Members of Show can be presented as strings. All types covered so far except for functions are a part of Show. The most used function that deals with the Show typeclass is show. It takes a value whose type is a member of Show and presents it to us as a string.
ghci> show 3 "3" ghci> show 5.334 "5.334" ghci> show True "True"
Read is sort of the opposite typeclass of Show. The read function takes a string and returns a type which is a member of Read.
ghci> read "True" || False True ghci> read "8.2" + 3.8 12.0 ghci> read "5" - 2 3 ghci> read "[1,2,3,4]" ++ [3] [1,2,3,4,3]
Type Annotations
Type annotations are a way of explicitly saying what the type of an expression should be. We do that by adding :: at the end of the expression and then specifying a type. Observe:
ghci> read "5" :: Int 5 ghci> read "5" :: Float 5.0 ghci> (read "5" :: Float) * 4 20.0 ghci> read "[1,2,3,4]" :: [Int][1,2,3,4] ghci> read "(3, 'a')" :: (Int, Char) (3, 'a')
Enum Members
Enum members are sequentially ordered types — they can be enumerated. The main advantage of the Enum typeclass is that we can use its types in list ranges. They also have defined successors and predecesors, which you can get with the succ and pred functions. Types in this class: (), Bool, Char, Ordering, Int, Integer, Float and Double.
ghci> ['a'..'e'] "abcde" ghci> [LT .. GT] [LT,EQ,GT] ghci> [3 .. 5] [3,4,5] ghci> succ 'B' 'C'
Bounded
Bounded members have an upper and a lower bound.
ghci> minBound :: Int -2147483648 ghci> maxBound :: Char '\1114111' ghci> maxBound :: Bool True ghci> minBound :: Bool False
minBound and maxBound are interesting because they have a type of (Bounded a) => a. In a sense they are polymorphic constants.
All tuples are also part of Bounded if the components are also in it.
ghci> maxBound :: (Bool, Int, Char) (True,2147483647,'\1114111')
Num
Num is a numeric typeclass. Its members have the property of being able to act like numbers. Let's examine the type of a number.
ghci> :t 20 20 :: (Num t) => t
It appears that whole numbers are also polymorphic constants. They can act like any type that's a member of the Num typeclass.
ghci> 20 :: Int 20 ghci> 20 :: Integer 20 ghci> 20 :: Float 20.0 ghci> 20 :: Double 20.0
Those are types that are in the Num typeclass. If we examine the type of *, we'll see that it accepts all numbers.
ghci> :t (*) (*) :: (Num a) => a -> a -> a
It takes two numbers of the same type and returns a number of that type. That's why (5 :: Int) * (6 :: Integer) will result in a type error whereas 5 * (6 :: Integer) will work just fine and produce an Integer because 5 can act like an Integer or an Int.
To join Num, a type must already be friends with Show and Eq.
Integral includes only integral (whole) numbers. In this typeclass are Int and Integer.
Floating includes only floating point numbers, so Float and Double.