Being on the curious side of things I have been interested lately in the dualities between programming languages. Like how one feature say Type Classes in Haskell compares to what is available in Scala or OCaml. This has lead to me reading a substantial amount of academic papers about the subject.

So with that in mind I would like to give a brief introduction to OCaml style modules. Perhaps in another post going into how can you encode something like rank n types from Haskell in OCaml which natively doesn’t support them.

Preface, the use of the word module can be confusing, and it sometimes seems that module is used to refer to structures interchangeably. I’ve tried to avoid that but it’s helpful to keep in mind for further reading. Look at what’s on the right hand side of the equals in the code. Let start.

Terminology

OCaml is a member of the ML family of languages, sharing common features like modules, Hindley-Milner type sytem and strict evaluation. OCaml as a language can be though of 2 distinct part; one a core language that’s values and types and a second module language that revolves around modules and signatures. While OCaml does provide some support for bridging these parts in the form of First Class Modules, I won’t cover them here.

The key parts of the module system in OCaml are:

Structures

Signatures

Functors

Structures

Structures provide a way for grouping together related declarations like data types and functions the operate on them; they also provide the values in the module langauge. Below is a module for integer Sets:

1 2 3 4 5 6 7 module IntSet = struct type t = int type set = t list let empty = [] let member i s = List . exists ( fun x -> x = i ) s let insert i s = if member i s then s else ( i :: s ) end

This code defines a new structure using the struct keyword and binds it to a name using module. It’s useful to note that OCaml types are written in lowercase ( t , list and set ) and type variables are written with a single quote 'a . Also type constructors are written differently to Haskell, in Haskell you’d have List a while in OCaml the order is reveresed t list .

Basically a struct is an opening struct followed by a bunch of type and let bindings, and closed with an end .

At the call site exposed declarations are referred to by dot notation:

1 2 IntSet . t IntSet . empty

If no module name is defined within a file, say you have a file called set.ml with:

1 2 3 4 5 type t = int type set = t list let empty = [] let member i s = List . exists ( fun x -> x = i ) s let insert i s = if member i s then s else ( i :: s )

It will implicitly be given a structure name derived from the file name Set but as you may have worked out module names are not bound to file names. Further structures can be nested within other structures, leading to more freedom than just having 1 file becoming 1 module.

1 2 3 4 5 6 module IntSet = struct module Compare = struct type t = int let eql x y = x = y end end ;;

The values within the nested module are referred to like so:

1 IntSet . Compare . eql 1 1 ;;

While it is great to have functions namespaced like so, it would become tedious if you needed to use the longer name to refer to a nested module. OCaml provides a couple of solutions, first local opens.

Rather than having an open statement at the top of the file and bringing every thing into scope for that file we can do a local open and restrict the scope to between the two brackets.

1 IntSet . Compare . ( eql 1 1 );;

The other option available is aliasing the module name to something shorter

1 2 module X = IntSet . Compare ;; X . eql 1 1 ;;

I mentioned open before without saying what it does. Simply open brings the contents of a module within another module, so they can be referred to without the module name prefix.

Signatures

Signatures are the interfaces for structures, a signature defines what parts of a structure is visable from the outside. A signature can be used to hide components of a structure or export some definitions with more general types.

A signature is introduced with the sig keyword

1 2 3 4 5 6 7 8 9 module type Set = sig type elt type t val empty : t val member : elt -> t -> bool val insert : elt -> t -> t end

As you can see looking at our definition of Set, it lists a type and function signatures without specifying a concrete implementation. It’s also bound to a name Set using module type .

As I metnioned before signatures are typically used to hide or change the interface a module exposes. By default all types and functions are exported from a module. Useful for doing things like hiding implementation details or only construct the data type via the invariant-preserving operations that the module provides.

Typically in OCaml you’ll define your struct in one file set.ml and then create a second file set.mli which contains the signature for the module set. Only occasionally will you see the signature and structure defined together.

Functors

Now to the functors, they’re not exactly like Haskell’s though they do perform a kind of mapping.

Functors are for lifting functions into the module language, or another way they are functions from structures to structures. Which brings the abstract idea of functors from category theory back to 2 concrete examples, where Haskell functors are functions from types to types, OCaml’s functors are functions from structures to structures.

Following out set example we can make set operations abstract across both the type inside the set and the equality comparison.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 module type ORDERING = sig type t val compare : t -> t -> int end ;; module type Set = sig type elt type t val empty : t val member : elt -> t -> bool val insert : elt -> t -> t end ;; module MkSet ( Ord : ORDERING ) : ( Set with type elt := Ord . t ) = struct type elt = Ord . t type t = Empty | Node of t * elt * t let empty = Empty let rec insert x = function | Empty -> Node ( Empty , x , Empty ) | Node ( a , y , b ) when Ord . compare x y < 0 -> Node ( insert x a , y , b ) | Node ( a , y , b ) when Ord . compare x y > 0 -> Node ( a , y , insert x b ) | Node ( a , y , b ) as s -> s let rec member x = function | Empty -> false | Node ( l , v , r ) -> let c = Ord . compare x v in c = 0 || member x ( if c < 0 then l else r ) end ;; module IntOrdering = struct type t = int let compare x y = Pervasives . compare x y end ;; module IntSet' = MkSet ( IntOrdering );;

Here we define ORDERING and Set as signatures, similar to our previous definitons. Then a functor is defined MkSet that takes the ORDERING signature and defines the types and functions for set based off that interface. So the definition of MkSet is completely abstracted away from the type used in the set and the functions used on those types. As long as it implements ORDERING .

The last part defines a particular ordering for int using, binding t to int and compare to Int.compare .

Using Modules

After covering what is in the OCaml module system, what exactly do we use it for. At the very basic level we collect together types and functions, which is pretty much what all modules do. Outside of that we can:

Hide implementation details, like the types exported by the module. If we wanted to hide how our Set was implemented we could redefine the functor as:

1 2 3 4 5 6 7 8 9 module type SETFUNCTOR = functor ( O : ORDERING ) -> sig type t = O . t (* concrete *) type set (* abstract *) val empty : set val add : t -> set -> set val member : t -> set -> bool end ;;

Here we expose the elements within the set via type t = O.t so they’re a concrete type, while set isn’t given a definition so the consumers of this module can’t look into that type without using the functions provided in the Set module. This hiding using abstract types lets us swap out different implementations for testing purposes or if requirements change.

Namespace functions and type, all types and functions live within some module. Extending existing modules in a type safe way. You may want to extend a module from a library with extra derived functions. For example the Core library from Jane Street extends the built in OCaml library with a number of new and different functions. eg Say Lists didn’t provide a transpose function. Instantiating modules with State, OCaml allows modules to include mutable state (while we may not particularly like mutable things) sometimes it’s necessary and you may want multiple instances of a particular module with their own state. Functors make doing this more succinct. Collecting definitions and exporting as a single module, e.g. Core.Std inside Jane Street Core library.

Further Reading

The best reference is really Real World OCaml. If you’ve got some Haskell experience and don’t mind reading a paper then “ML Modules and Haskell Type Classes: A Constructive Comparison” by Stefan Wehr and Manuel Chakravarty gives a thorough coverage of how ML modules stack up to Type Classes.