Steven D'Aprano <ste...@remove.this.cybersource.com.au> writes: > As near as I can tell, a functor is just an object which is > callable like a function without actually being implemented as a > function, e.g.:
No it's not anything like that either, at least as I'm used to the term in programming or in mathematics. Maybe it's used other ways though. As I'm used to it, it's a feature of certain static type systems. The notion isn't that useful in Python but you could translate it something like this: imagine that the "list" datatype has a couple extra operations: # lift_value turns a normal value from a base type to a 1-element list list.lift_value(x) = [x] # lift_function turns a function on a base type to a higher order # function that operates on a whole list list.lift_function(f) = partial(map, f) Then given a function like def square(x): return x*x you could say lifted_square = list.lifted_function(square) print lifted_square([1,2,3,4,5]) and get [1,4,9,16,25]. Similarly if you had some other type (like a tree data structure), that type could also support a map-like operation so you could lift functions to it (lifting a function and applying it to a tree like [1,[2,3],4] would result in [1,[4,9],16] or whatever). If I remember properly, for type t to be a functor it needs the above two lifting operations, with the property that for a given function f, t.lifted_value(f(x)) = (t.lifted_function(f))(t.lifted_value(x)) I guess this explanation isn't going that well but basically in a statically typed language you'd use functors to convert the signatures of functions to versions that operate on higher types. The idea comes from ML and is used explicitly in Haskell, and I think some of the C++ standard template library can be explained in terms of functors. For the mathematical concept of functors and how they relate to programming (at least Haskell's version), see: http://en.wikibooks.org/Haskell/Category_theory -- http://mail.python.org/mailman/listinfo/python-list
