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Partial Application and Currying

Currying

Consider a type signature of a function with three arguments:

 f :: X -> Y -> Z -> A

The arrow “->” is right-associative, so this is the same as:

 f :: X -> (Y -> (Z -> A))

What this means is that we can consider f as a function with a single argument of type X which returns a function of type Y->Z->A.

The technique of rewriting a function of multiple arguments into a sequence of functions with a single argument is called currying. We can illustrate this best using a lambda function:

 x y z -> ...
 x -> (y z -> ...)
 x -> (y -> (z -> ... )) 

The name “currying”, is a reference to logician Haskell Curry. The concept was actually proposed originally by another logician, Moses Schönfinkel, but his name was not so catchy.

Partial application

Partial application means that we don’t need to provide all arguments to a function. For example, given

 sq x y = x*x+y*y

We note that function application associates to the left, so the following equivalence holds

 sq x y = (sq x) y

We can therefore create a specialised function by partial application of x:

 sq4 = sq 4 -- = y -> 16+y*y
 sq4 3 -- = (sq 4) 3 = sq 4 3 = 25

This is why you can write things like:

 doubles = map (*2) [1 .. ]