# Using Functors

Since functors are really just parameterized modules, we can use them to produce functions that are parameterized on any structure that matches a signature. That can help to eliminate code duplication. Here are two examples of doing that.

## Example 1: Producing a Test Suite for Multiple Structures

Recall our data structures for stacks:

module type StackSig = sig
type 'a t
val empty : 'a t
val push  : 'a -> 'a t -> 'a t
val peek  : 'a t -> 'a
end

module ListStack = struct
type 'a t = 'a list
let empty = []
let push x s = x::s
let peek = function [] -> failwith "empty" | x::_ -> x
end

(* called MyStack because the standard library already has a Stack *)
module MyStack = struct
type 'a t = Empty | Entry of 'a * 'a t
let empty = Empty
let push x s = Entry (x, s)
let peek = function Empty -> failwith "empty" | Entry(x,_) -> x
end


Suppose we wanted to write code that would test a ListStack:

assert (ListStack.(empty |> push 1 |> peek) = 1)


Unfortunately, to test a MyStack, we'd have to duplicate that code:

assert (MyStack.(empty |> push 1 |> peek) = 1)


And if we had other stack implementations, we'd have to duplicate the test for them, too. That's not so horrible to contemplate if it's just one test case for a couple implementations, but if it's hundreds of tests for even a couple implementations, that's just too much duplication to be good software engineering.

Functors offer a better solution. We can write a functor that is parameterized on the stack implementation, and produces the test for that implementation:

module StackTester (S:StackSig) = struct
assert (S.(empty |> push 1 |> peek) = 1)
end

module MyStackTester = StackTester(MyStack)
module ListStackTester = StackTester(ListStack)


Now we can factor out all our tests into the functor StackTester, and when we apply that functor to a stack implementation, we get a set of tests for that implementation. Of course, this would work with OUnit as well as assertions.

## Example 2: Adding a Function to Multiple Structures

Earlier, we tried to add a function add_all to both ListSetNoDups and ListSetDups without having any duplicated code, but we didn't totally succeed. Now let's really do it right.

The problem we had earlier was that we needed to parameterize the implementation of add_all on the add function in the set data structure. We can accomplish that parameterization with a functor.

Here is a functor that takes in a structure named S that matches the Set signature, then produces a new structure having a single function named add_all in it:

module AddAll(S:Set) = struct
end


Notice how the functor, in its body, uses S.add. It takes the implementation of add from S and uses it to implement add_all, thus solving the exact problem we had before when we tried to use includes.

When we apply AddAll to our set implementations, we get structures containing an add_all function for each implementation:

# module AddAllListSetDups = AddAll(ListSetDups);;
sig
val add_all : 'a list -> 'a ListSetDups.t -> 'a ListSetDups.t
end

sig
val add_all : 'a list -> 'a ListSetNoDups.t -> 'a ListSetNoDups.t
end


So the functor has enabled the code reuse we couldn't get before: we now can implement a single add_all function and from it derive implementations for two different set structures.

But that's the only function those two structures contain. Really what we want is a full set implementation that also contains the add_all function. We can get that by combining includes with functors:

module ExtendSet(S:Set) = struct
include S

end


That functor takes a set structure as input, and produces a structure that contains everything from that set structure (because of the include) as well as a new function add_all that is implemented using the add function from the set.

When we apply the functor, we get a very nice set data structure as a result:

# module ListSetNoDupsExtended = ExtendSet(ListSetNoDups);;
module ListSetNoDupsExtended :
sig
type 'a t = 'a ListSetNoDups.t
val empty : 'a t
val mem : 'a -> 'a t -> bool
val add : 'a -> 'a t -> 'a t
val elts : 'a t -> 'a list
val add_all : 'a list -> 'a t -> 'a t
end


Notice how the output structure records the fact that its type t is the same type as the type t in its input structure. They share it because of the include.

Stepping back, what we just did bears more than a passing resemblance to what you're used to doing in CS 2110 with class extension in Java. We created a base module and extended its functionality with new code while preserving its old functionality. But whereas class extension necessitates that the newly extended class is a subtype of the old, and that it still has all the old functionality, OCaml functors are more fine-grained in what they can accomplish. We can choose whether they include the old functionality. And no subtyping relationships are necessarily involved. Moreover, the functor we wrote can be used to extend any set implementation with add_all, whereas class extension applies to just a single base class. There are ways of achieving something similar in Java with mixins, which weren't supported before Java 1.5.