Infix Functions In Haskell

Infix functions

Functions in Haskell default to prefix syntax, meaning that the function being applied is at the beginning of the expression rather than the middle.

Operators are functions which can be used in infix style. All operators are functions.

The syntax between prefix functions and infix functions is interchangeable, with a small change:

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prefixFunc a b

a `prefixFunc` b

a infixFunc b

(infixFunc) a b

Associativity and Precedence

We can ask GHCi for information such as associativity and precedence of operators and functions by using :info command.

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:info (*)

class Num a where
  ...
  (*) :: a -> a -> a
  ...

infixl 7 *

The infixl means (*) is an infix function, and it is left associative. 7 is the precedence, higher is applied first, on a scale of 0 - 9.

Parenthesizing

When you want to refer to an infix function without applying any arguments, or use them as prefix functions instead of infix, you need warp the infix function in parentheses.

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(+) 1 2

In order to partially apply functions, you can use sectioning.

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(+ 1) 2

With commutative functions, such as addition, it makes no difference between (+1) and (1+). If you use sectioning with a function that is not commutative, the order matters.

($) operator

The ($) operator is a convenience for expressing something with fewer pairs of parentheses. The information of ($) operator is

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($) ::
  forall (r :: GHC.Types.RuntimeRep) a (b :: TYPE r).
  (a -> b) -> a -> b
infixr 0 $

Composition operator

Function composition is a type of higher-order function that allows us to combine functions such that the result of applying one function gets passed to the next function as an argument.

The composition operator is defined as:

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(.) :: (b -> c) -> (a -> b) -> a -> c
infixr 9 .

For example:

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f :: Bool -> String
f x = 
  case x of
    True -> "it is true."
    False -> "it is false."

g :: Int -> Bool
g x = x == 1

(f.g) 5 -- it is false.

We can think of the (.) or composition operator as being a way of pipelining data through multiple functions.

Pointfree

In Haskell the precedence of an ordinary function call (white space, usually) is of 10. While the composition operator has a precedence of 9. It results in the case where we want to compose functions then apply it to some parameter, we have to parenthesize the composition so as to keep the application in right order.

With the help of ($) operator, the syntax can be much neater:

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(f.g) 5 -- it is false.
f.g $ 1 -- it is true.

Further more, we can focus on composing functions, rather than applying functions, which is thus pretty elegant:

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print :: Show a => a -> IO()
print a = (putStrLn . show) a

-- pointfree version
print :: Show a => a -> IO()
print = putStrLn . show

Pointfree refers to a style of composing functions without specifying their arguments. The “point” in “pointfree” refers to the arguments, not to the function composition operator.

(->) operator

The type constructor for functions, (->), is also a function, whose information is like:

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data (->) t1 t2
infixr 0 `(->)`

Since (->) is an infix operator and right associative, it makes currying the default in Haskell.

Infix type constructor and data constructor

Any operator that starts with a colon (:) must be an infix type or data constructor. All infix data constructors must start with a colon. The type constructor of functions, (->), is the only infix type constructor that doesn’t start with a colon. Another exception is that they cannot be (::) as this syntax is reserved for type assertions.

Data constructors with only non-alphanumeric symbols and that begin with a colon are infix by default; those with alphanumeric names are prefix by default.

The above two are inconsistent with each other?