Wednesday, January 17, 2007

Mapping and reducing is like popping and locking for programmers

If you don't read Lambda the Ultimate, that's quite alright. But fairly often over there, you find a link to Why Functional Programming Matters, by John Hughes. Recently, I decided to sit down and actually read it. It's mind-expanding!

Previously, I'd thought about mapping functions onto lists as an operational thing, a set of steps to complete, but that's not the cleanest way to think about it. Mapping is actually a special case of "reduce", an operation where you just go through and replace the all the "cons" functions in a list expression with something else, then evaluate the expression again. "map" functions have a cons in the function they're reducing with, so the end result is another list.

For example: you might write, in lisp: "(mapcar #'(lambda(x) (* x 2)) '(1 2 3 4))", yielding (2 4 6 8).. and you might think of that procedurally... but a map is just a reduce where "cons composed with the mapped function" replaces every "cons". Append can be written similarly; it's all essentially just replacement, function composition and evaluation. The paper also goes into beautiful issues like lazy evaluation (the author says that if he wrote the paper now, the examples would be in Haskell!) and continues to do some lovely examples, some numerical and one very close to our heart: a bot that plays tic-tac-toe, optimally, with pruned game trees.

Years ago, Kurt Eiselt told me that the future of computing was going to be functional languages on very-parallel hardware; functional languages, at least in principle, make synchronization easier by limiting or removing-altogether side effects. (although reconciling this idea with stateful, event-driven end-user applications is another issue!) To an extent, it looks like he was right, and the future is here! MapReduce is the method Google is using to crunch super-giant datasets with enormously parallel clusters. It's not just for functional languages, of course, but the idea is there.

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