[Haskell-cafe] Unary functions and infix notation

Johannes Emerich johannes at emerich.de
Fri Sep 6 17:04:12 CEST 2013

As is well known, any binary function f can be turned into an infix operator by surrounding it with backticks:

    f a b   -- prefix application
    a `f` b -- infix application

It is then possible to take left and right sections, i.e. partially applying f:

    (a `f`) -- equivalent to \b -> a `f` b
    (`f` b) -- equivalent to \a -> a `f` b

This extends relatively naturally to functions of arity greater than two, where usage of a function in infix notation produces a binary operator that returns a function of arity n-2.

Weirdly, however, infix notation can also be used for unary functions with polymorphic types, as the following ghci session shows:

   Prelude> :t (`id` 1)
   (`id` 1) :: Num a => (a -> t) -> t
   Prelude> (`id` 1) (\y -> show y ++ ".what")

Desugaring of an equivalent source file shows that id is applied to the anonymous function, which is then applied to 1.

The following example of a function that is not polymorphic in its return type behaves closer to what I would have expected: It does not work.

   Prelude> let z = (\y -> True) :: a -> Bool
   Prelude> :t (`z` True)

       The operator `z' takes two arguments,
       but its type `a0 -> Bool' has only one
       In the expression: (`z` True)

What is the purpose/reason for this behaviour?

Thank you,

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