Under: A new Idiom from the J language

Thanks to this post I've started the year discovering a language I never knew existed - and a cool little feature in it.

Imagine you have a function called g

g(5) #returns 10

Now imagine you have another function which undoes whatever happened in g.

undo-g(10) #returns 5

Not too impressive on the face of it. You could guess that g just multiplies by 2 and undo-g divides by 2. The J language comes with some of these built in. Which it calls obverse functions.

   4 + 4
8
   4 +^:_1 (4)
0

In this function +^:_1 effectively means apply the + function -1 times. You could do it twice:

   4 +^:_2 (4)
_4 (In J _4 means -4)

Seem crazy? Stay with it...

How many times do you see this sort of pattern in your code?

OpenFile
    ReadData
CloseFile

OpenSocket
    SendData
CloseSocket

Look familiar? Well, because J has the idea of obverse functions you get a lovely little syntax that J calls Under which covers this pattern. In J it looks like this

f&.g x

Which means apply g to x. Then apply f. Then apply the inverse of g.

    obverse(func(verb(x))) #J calls functions verbs

The J documentation lists loads of cool definitions you can build using under.
Here's the idea in clojure using the under pattern to construct a new definition of multiplication and addition. It's a cool idea to start the year with. I wonder how many places I'll start seeing this pattern? For more information about J check out the excellent J for C Programmers (Rich 2007)