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copied!<p>There are three different meanings, not much related!</p> <ul> <li><p>In Ocaml it is a parametrized module. See <a href="http://caml.inria.fr/pub/docs/manual-ocaml/manual004.html" rel="noreferrer">manual</a>. I think the best way to grok them is by example: (written quickly, might be buggy)</p> <pre><code>module type Order = sig type t val compare: t -> t -> bool end;; module Integers = struct type t = int let compare x y = x > y end;; module ReverseOrder = functor (X: Order) -> struct type t = X.t let compare x y = X.compare y x end;; (* We can order reversely *) module K = ReverseOrder (Integers);; Integers.compare 3 4;; (* this is false *) K.compare 3 4;; (* this is true *) module LexicographicOrder = functor (X: Order) -> functor (Y: Order) -> struct type t = X.t * Y.t let compare (a,b) (c,d) = if X.compare a c then true else if X.compare c a then false else Y.compare b d end;; (* compare lexicographically *) module X = LexicographicOrder (Integers) (Integers);; X.compare (2,3) (4,5);; module LinearSearch = functor (X: Order) -> struct type t = X.t array let find x k = 0 (* some boring code *) end;; module BinarySearch = functor (X: Order) -> struct type t = X.t array let find x k = 0 (* some boring code *) end;; (* linear search over arrays of integers *) module LS = LinearSearch (Integers);; LS.find [|1;2;3] 2;; (* binary search over arrays of pairs of integers, sorted lexicographically *) module BS = BinarySearch (LexicographicOrder (Integers) (Integers));; BS.find [|(2,3);(4,5)|] (2,3);; </code></pre></li> </ul> <p>You can now add quickly many possible orders, ways to form new orders, do a binary or linear search easily over them. Generic programming FTW.</p> <ul> <li><p>In functional programming languages like Haskell, it means some type constructors (parametrized types like lists, sets) that can be "mapped". To be precise, a functor <code>f</code> is equipped with <code>(a -> b) -> (f a -> f b)</code>. This has origins in category theory. The Wikipedia article you linked to is this usage.</p> <pre><code>class Functor f where fmap :: (a -> b) -> (f a -> f b) instance Functor [] where -- lists are a functor fmap = map instance Functor Maybe where -- Maybe is option in Haskell fmap f (Just x) = Just (f x) fmap f Nothing = Nothing fmap (+1) [2,3,4] -- this is [3,4,5] fmap (+1) (Just 5) -- this is Just 6 fmap (+1) Nothing -- this is Nothing </code></pre></li> </ul> <p>So, this is a special kind of a type constructors, and has little to do with functors in Ocaml!</p> <ul> <li>In imperative languages, it is a pointer to function.</li> </ul>

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