Functions
Function application¶
Given a function, such as:
we can call it on input as follows:
One can also write add1(2)
, but Haskell convention is to avoid brackets where possible.
Note
One can choose any name for an argument (provided it is alphanumeric and starts with a lowercase letter).
If you have named something else by the same name elsewhere, that is fine:
The occurrence of x
on the right of line 2 refers to the occurrence on the left of line 2, not the occurrence on line 1.
Arguments¶
In Haskell, a function has a single argument, but that argument can be a tuple of multiple values:
Currying¶
Another approach to taking multiple arguments, more commonly used, is shown here:
 By convention in Haskell,
Int > Int > Int
meansInt > (Int > Int)
, not(Int > Int) > Int
.
As the type signature indicates, the first argument is an integer, but the output is a function which takes a second integer and returns an integer.
Accordingly, we can apply exampleFunc
to an integer, say 5
, and obtain an "add 5" function:
> :t exampleFunc 4
(Int > Int)
> add4 = exampleFunc 4
> add4 5
9
 or directly
> (exampleFunc 4) 5  (1)!
9
 By convention in Haskell,
exampleFunc 4 5
means(exampleFunc 4) 5
.
This is often referred to as partial application. exampleFunc
would be described as a curried function.
Hint
When you see a function with a type like Type1 > Type2 > Type3 > Type4
(which brackets as: Type1 > (Type2 > (Type3 > Type4))
), you can think of it as taking Type1
, Type2
and Type3
as inputs, and outputting Type4
.
Partial application for types¶
The same holds for types and their kinds:
> :kind Either
Either :: * > (* > *)
> :kind Either Bool
Either Bool :: * > *
> :kind Either Bool Int
Either Bool Int :: *
Pattern matching on sum types¶
When defining a function, you can pattern match:
exampleFunc :: Either Int Bool > Int
exampleFunc (Left i) = i  (1)!
exampleFunc (Right True) = 1
exampleFunc (Right _) = 0  (2)!

i
matches anyInt
. It has to be anInt
because the input has typeEither Int Bool
(Int
is on the left). 
The underscore
_
matchesBool
. It has to be aBool
because the input has typeEither Int Bool
(Bool
is on the right).
Here is how the function behaves:
Here, (Left i)
, (Right True)
and (Right _)
are all patterns.
The patterns are matched topdown. For example, if the function were:
Then:
because line 3 would be matched before line 4 was reached.
Pattern matching on product types¶
The above example concerns a type that is either a Right True
or a Right False
or a Left 0
, or a Left 1
...In other words, it is a sum type.
Pattern matching also works with products (and products of sums, sums of products, and so on):
> ex = (True, False)
> (b1, b2) = ex
> b1
True
> b2
False
 with a custom type
> data Entity = Sq Int Bool
> entity = Sq 4 False
> Sq i b = entity
> i
4
> b
False
This works also in functions:
> data Color = White  Black deriving Show
> data PieceType = Bishop  Knight deriving Show
> data Piece = P PieceType Color deriving Show
> getColor (P _ c) = c
> getColor (P Bishop White)
White
Note
Patterns can be arbitrarily deeply nested, as in:
data Color = Black  White
data Piece = Bishop Color  Knight Color
getColor :: Either Bool Piece > Maybe Color
getColor (Right (Bishop c)) = Just c
getColor (Right (Knight c)) = Just c
getColor (Left _) = Nothing
And also used with recursive types
Pattern matching lists¶
Pattern matching also applies to lists, since they are recursive types:
Tip
A classic example of returning an error when getting the first element of an empty list:
Using @ in patterns¶
 first example
> let whole@(a,b) = ('a', True)
> a
'a'
> b
True
> whole
('a',True)
 second example
> let whole@(a, left@(b, c)) = ('a', (True, ()))
> a
'a'
> b
True
> c
()
> whole
('a',(True,()))
> left
(True,())
And in a function:
exampleFunc :: (Int, Bool) > (Int, Bool)
exampleFunc whole@(int,bool)
 even int = whole
 otherwise = (int  1, not bool)
Created: January 7, 2023