Partial application and closures

Question

I was asked what\'s the relationship between partial function application and closures. I would say there isn\'t any, unless I\'m missing the point. Let\'s say I\'m writing in p

Answer 1

Partial application is a technique whereby you take an existing function and a subset of it's arguments, and produce a new function that accepts the remaining arguments.

In other words, if you have function F(a, b), a function that applies partial application of a would look like B(fn, a) where F(a, b) = B(F, a)(b).

In your example you're simply creating new functions, rather than applying partial application to the existing one.

Here's an example in python:

def curry_first(fn, arg):
    def foo(*args):
       return fn(arg, *args)
    return foo

This creates a closure over the supplied function and argument. A new function is returned that calls the first function with new argument signature. The closure is important - it allows fn access to arg. Now you can do this sort of thing:

add = lambda x, y : x + y;
add2 = curry_first(add, 2)
add2(4) # returns 6

I've usually heard this referred to as currying.