Yes, good point. I suppose replaceEach() would be a more descriptive name, so the interface might be HasReplaceEach. It's not as easy to talk about, though. Still better than "functor".

(The function being passed in to map() is an alternate way to represent a very large map, in a mathematical sense.)

Exactly. We'd only call the interface 'Mappable' if the method was called 'map', and that's something that's come from mathematical terminology.

(I'd probably have called the 'Map' class 'Dictionary', if that hadn't already been taken!)

I'd avoid 'replaceEach', because it sounds like it mutates the receiver. Maybe 'withEachReplaced'? Way clunky. In Smalltalk, this method is called 'collect', which is better than 'map', to my eyes, but still not all that obvious [1].

[1] Smalltalk has the names collect, inject, select, and reject for its map, foreach, filter, and complementary filter methods, because of a song: http://smalltalkzen.wordpress.com/2011/02/02/arlo-guthrie-an...

The Smalltalk version of foreach() is called #do:. #inject: is like reduce().

That blog post inspired a fun discussion in the Smalltalk community on what the semantics of #infect: and #neglect: should be!

Mathematicians prefer obscure technical terms to misleading and restrictive metaphors, because obscure terms force you to refer solely to (and eventually internalise) a precise and abstract definition.

I think this is the case for functors, because I've yet to see a metaphor for them which isn't misleading or restrictive. "replaceEach", for instance, would confuse me. I like working with parser combinators, where parsers are functors. If I replaceEach a parser, what have I replaced? The results of the parse? The parser hasn't been run on an input yet. Maybe it never will.

If I replaceEach a promise, what am I replacing? The result of the promise? Maybe the promise will be forever blocked, or maybe I'll cancel it.

If I replaceEach a continuation, what am I replacing?

> because obscure terms force you to refer solely to (and eventually internalise) a precise and abstract definition.

Unless some C++ people decide that “functor” is a wonderful name for a stateful function-like thing which somewhat resembles closures/lambdas but has nothing whatsoever to do with the functors from functional programming.

Well, yes, mathematicians like to be very precise about exactly what a very general abstraction entails, to the point where you are being very precise about how two almost entirely different concepts have almost but not quite nothing in common.

These fine distinctions don't belong in code meant for a general audience. Instead, don't try to generalize so much. It's not important (and in fact it's confusing) that replaceEach can be generalized to work with a parser. Parsers can have a different function with its own name and nobody needs to know that it's sort of the same concept.