What is the differences and possible similarities of closures and currying?

Question

I've read through some of the post on here about closures and currying but I feel like I didn't find the answer. So what's the differences and possibly the similarities of closures and currying? Thanks for the help :)

Answer 1

Currying is really a mathematical concept first and foremost. It's the just observation that for any n-ary function f: S₀×...S_n → R, you can define a new function fprime (just found a markdown bug!) with n-1 parameters where that first parameter is replaced by a constant. So, if you have a function add(a,b), you can define a new function add1(b) as

add1(b) ::= add(1, b)

...reading "::=" as "is defined to be."

A closure is more of a programming concept. (Of course, everything in programming is a mathematical concept as well, but closures became interesting because of programming.) When you construct a closure, you bind one or more variables; you're creating a chunk of code that has some variables tied to it.

The relationship is that you can use a closure in order to implement currying: you could build your add1 function above by making a closure in which that first parameter is bound to 1.