Learn you a Haskell for Great Good:chapter - Types and Typeclasses

Types and Typeclasses

Believe the type

Previously we mentioned that Haskell has a static type system. The type of every expression is known at compile time, which leads to safer code. If you write a program where you try to divide a boolean type with some number, it won't even compile.

That's good because it's better to catch such errors at compile time instead of having your program crash. Everything in Haskell has a type, so the compiler can reason quite a lot about your program before compiling it.

Unlike Java or Pascal, Haskell has type inference. If we write a number, we don't have to tell Haskell it's a number. It can infer that on its own, so we don't have to explicitly write out the types of our functions and expressions to get things done.

We covered some of the basics of Haskell with only a very superficial glance at types. However, understanding the type system is a very important part of learning Haskell.

A type is a kind of label that every expression has. It tells us in which category of things that expression fits. The expression True is a boolean, "hello" is a string, etc.

Now we'll use GHCI to examine the types of some expressions. We'll do that by using the :t command which, followed by any valid expression, tells us its type. Let's give it a whirl.

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

Here we see that doing :t on an expression prints out the expression followed by :: and its type. :: is read as "has type of". Explicit types are always denoted with the first letter in capital case. 'a', as it would seem, has a type of Char. It's not hard to conclude that it stands for character. True is of a Bool type. That makes sense. But what's this?

Examining the type of "HELLO!" yields a [Char]. The square brackets denote a list. So we read that as it being a list of characters. Unlike lists, each tuple length has its own type. So the expression of (True, 'a') has a type of (Bool, Char), whereas an expression such as ('a','b','c') would have the type of (Char, Char, Char). 4 == 5 will always return False, so its type is Bool.

Functions also have types. When writing our own functions, we can choose to give them an explicit type declaration. This is generally considered to be good practice except when writing very short functions. From here on, we'll give all the functions that we make type declarations.

Remember the list comprehension we made previously that filters a string so that only caps remain? Here's how it looks like with a type declaration.

removeNonUppercase :: [Char] -> [Char]

removeNonUppercase st = [ c | c <- st, c `elem` ['A'..'Z']]

removeNonUppercase has a type of [Char] -> [Char], meaning that it maps from a string to a string. That's because it takes one string as a parameter and returns another as a result. The [Char] type is synonymous with String so it's clearer if we write removeNonUppercase :: String -> String.

We didn't have to give this function a type declaration because the compiler can infer by itself that it's a function from a string to a string but we did anyway. But how do we write out the type of a function that takes several parameters? Here's a simple function that takes three integers and adds them together:

addThree :: Int -> Int -> Int -> Int

addThree x y z = x + y + z

The parameters are separated with -> and there's no special distinction between the parameters and the return type. The return type is the last item in the declaration and the parameters are the first three.

Later on we'll see why they're all just separated with -> instead of having some more explicit distinction between the return types and the parameters like Int, Int, Int -> Int or something.

If you want to give your function a type declaration but are unsure as to what it should be, you can always just write the function without it and then check it with :t. Functions are expressions too, so :t works on them without a problem.

Here's an overview of some common types.

Int stands for integer. It's used for whole numbers. 7 can be an Int but 7.2 cannot. Int is bounded, which means that it has a minimum and a maximum value. Usually on 32-bit machines the maximum possible Int is 2147483647 and the minimum is -2147483648.

Integer stands for, er … also integer. The main difference is that it's not bounded so it can be used to represent really really big numbers. I mean like really big. Int, however, is more efficient.

factorial :: Integer -> Integer

factorial n = product [1..n]

ghci> factorial 50

30414093201713378043612608166064768844377641568960512000000000000

Float is a real floating point with single precision.

circumference :: Float -> Float

circumference r = 2 * pi * r

ghci> circumference 4.0

25.132742

Double is a real floating point with double the precision!

circumference' :: Double -> Double

circumference' r = 2 * pi * r

ghci> circumference' 4.0

25.132741228718345

Bool is a boolean type. It can have only two values: True and False.

Char represents a character. It's denoted by single quotes. A list of characters is a string.

Tuples are types but they are dependent on their length as well as the types of their components, so there is theoretically an infinite number of tuple types, which is too many to cover in this tutorial. Note that the empty tuple () is also a type which can only have a single value: ()

Type variables

What do you think is the type of the head function? Because head takes a list of any type and returns the first element, so what could it be? Let's check!

ghci> :t head

head :: [a] -> a

Hmmm! What is this a? Is it a type? Remember that we previously stated that types are written in capital case, so it can't exactly be a type. Because it's not in capital case it's actually a type variable. That means that a can be of any type.

This is much like generics in other languages, only in Haskell it's much more powerful because it allows us to easily write very general functions if they don't use any specific behavior of the types in them. Functions that have type variables are called polymorphic functions. The type declaration of head states that it takes a list of any type and returns one element of that type.

Although type variables can have names longer than one character, we usually give them names of a, b, c, d …

Remember fst? It returns the first component of a pair. Let's examine its type.

ghci> :t fst

fst :: (a, b) -> a

We see that fst takes a tuple which contains two types and returns an element which is of the same type as the pair's first component. That's why we can use fst on a pair that contains any two types.

Note that just because a and b are different type variables, they don't have to be different types. It just states that the first component's type and the return value's type are the same.

Typeclasses 101

A typeclass is a sort of interface that defines some behavior. If a type is a part of a typeclass, that means that it supports and implements the behavior the typeclass describes.

A lot of people coming from OOP get confused by typeclasses because they think they are like classes in object oriented languages. Well, they're not. You can think of them kind of as Java interfaces, only better.

What's the type signature of the == function?

ghci> :t (==)

(==) :: (Eq a) => a -> a -> Bool

Note: the equality operator, == is a function. So are +, *, -, / and pretty much all operators. If a function is comprised only of special characters, it's considered an infix function by default. If we want to examine its type, pass it to another function or call it as a prefix function, we have to surround it in parentheses.

Interesting. We see a new thing here, the => symbol. Everything before the => symbol is called a class constraint. We can read the previous type declaration like this: the equality function takes any two values that are of the same type and returns a Bool. The type of those two values must be a member of the Eq class (this was the class constraint).

The Eq typeclass provides an interface for testing for equality. Any type where it makes sense to test for equality between two values of that type should be a member of the Eq class. All standard Haskell types except for IO (the type for dealing with input and output) and functions are a part of the Eq typeclass.

The elem function has a type of (Eq a) => a -> [a] -> Bool because it uses == over a list to check whether some value we're looking for is in it.

Some basic typeclasses:

Eq is used for types that support equality testing. The functions its members implement are == and /=. So if there's an Eq class constraint for a type variable in a function, it uses == or /= somewhere inside its definition. All the types we mentioned previously except for functions are part of Eq, so they can be tested for equality.

ghci> 5 == 5

True

ghci> 5 /= 5

False

ghci> 'a' == 'a'

True

ghci> "Ho Ho" == "Ho Ho"

True

ghci> 3.432 == 3.432

True

Ord is for types that have an ordering.

ghci> :t (>)

(>) :: (Ord a) => a -> a -> Bool

All the types we covered so far except for functions are part of Ord. Ord covers all the standard comparing functions such as >, <, >= and <=. The compare function takes two Ord members of the same type and returns an ordering. Ordering is a type that can be GT, LT or EQ, meaning greater than, lesser than and equal, respectively.

To be a member of Ord, a type must first have membership in the prestigious and exclusive Eq club.

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