# Real World OCaml (2013)

### Part I. Language Concepts

### Chapter 9. Functors

Up until now, we’ve seen OCaml’s modules play an important but limited role. In particular, we’ve seen them as a mechanism for organizing code into units with specified interfaces. But OCaml’s module system can do much more than that, serving as a powerful tool for building generic code and structuring large-scale systems. Much of that power comes from functors.

Functors are, roughly speaking, functions from modules to modules, and they can be used to solve a variety of code-structuring problems, including:

Dependency injection

Makes the implementations of some components of a system swappable. This is particularly useful when you want to mock up parts of your system for testing and simulation purposes.

Autoextension of modules

Functors give you a way of extending existing modules with new functionality in a standardized way. For example, you might want to add a slew of comparison operators derived from a base comparison function. To do this by hand would require a lot of repetitive code for each type, but functors let you write this logic just once and apply it to many different types.

Instantiating modules with state

Modules can contain mutable states, and that means that you’ll occasionally want to have multiple instantiations of a particular module, each with its own separate and independent mutable state. Functors let you automate the construction of such modules.

These are really just some of the uses that you can put functors to. We’ll make no attempt to provide examples of all of the uses of functors here. Instead, this chapter will try to provide examples that illuminate the language features and design patterns that you need to master in order to use functors effectively.

**A Trivial Example**

Let’s create a functor that takes a module containing a single integer variable x and returns a new module with x incremented by one. This is intended to serve as a way to walk through the basic mechanics of functors, even though it’s not something you’d want to do in practice.

First, let’s define a signature for a module that contains a single value of type int:

*OCaml utop*

# **moduletypeX_int = sigvalx : intend;;**

module type X_int = sig val x : int end

Now we can define our functor. We’ll use X_int both to constrain the argument to the functor and to constrain the module returned by the functor:

*OCaml utop* (part 1)

# **moduleIncrement (M : X_int) : X_int = struct**

** letx = M.x + 1**

** end;;**

module Increment : functor (M : X_int) -> X_int

One thing that immediately jumps out is that functors are more syntactically heavyweight than ordinary functions. For one thing, functors require explicit (module) type annotations, which ordinary functions do not. Technically, only the type on the input is mandatory, although in practice, you should usually constrain the module returned by the functor, just as you should use an mli, even though it’s not mandatory.

The following shows what happens when we omit the module type for the output of the functor:

*OCaml utop* (part 2)

# **moduleIncrement (M : X_int) = struct**

** letx = M.x + 1**

** end;;**

module Increment : functor (M : X_int) -> sig val x : int end

We can see that the inferred module type of the output is now written out explicitly, rather than being a reference to the named signature X_int.

We can use Increment to define new modules:

*OCaml utop* (part 3)

# **moduleThree = structletx = 3end;;**

module Three : sig val x : int end

# **moduleFour = Increment(Three);;**

module Four : sig val x : int end

# **Four.x - Three.x;;**

- : int = 1

In this case, we applied Increment to a module whose signature is exactly equal to X_int. But we can apply Increment to any module that *satisfies* the interface X_int, in the same way that the contents of an ml file must satisfy the mli. That means that the module type can omit some information available in the module, either by dropping fields or by leaving some fields abstract. Here’s an example:

*OCaml utop* (part 4)

# **moduleThree_and_more = struct**

** letx = 3**

** lety = "three"**

** end;;**

module Three_and_more : sig val x : int val y : string end

# **moduleFour = Increment(Three_and_more);;**

module Four : sig val x : int end

The rules for determining whether a module matches a given signature are similar in spirit to the rules in an object-oriented language that determine whether an object satisfies a given interface. As in an object-oriented context, the extra information that doesn’t match the signature you’re looking for (in this case, the variable y) is simply ignored.

**A Bigger Example: Computing with Intervals**

Let’s consider a more realistic example of how to use functors: a library for computing with intervals. Intervals are a common computational object, and they come up in different contexts and for different types. You might need to work with intervals of floating-point values or strings or times, and in each of these cases, you want similar operations: testing for emptiness, checking for containment, intersecting intervals, and so on.

Let’s see how to use functors to build a generic interval library that can be used with any type that supports a total ordering on the underlying set over which you want to build intervals.

First we’ll define a module type that captures the information we’ll need about the endpoints of the intervals. This interface, which we’ll call Comparable, contains just two things: a comparison function and the type of the values to be compared:

*OCaml utop* (part 5)

# **moduletypeComparable = sig**

** typet**

** valcompare : t -> t -> int**

** end ;;**

module type Comparable = sig type t val compare : t -> t -> int end

The comparison function follows the standard OCaml idiom for such functions, returning 0 if the two elements are equal, a positive number if the first element is larger than the second, and a negative number if the first element is smaller than the second. Thus, we could rewrite the standard comparison functions on top of compare.

*OCaml*

compare x y < 0 *(* x < y *)*

compare x y = 0 *(* x = y *)*

compare x y > 0 *(* x > y *)*

(This idiom is a bit of a historical error. It would be better if compare returned a variant with three cases for less than, greater than, and equal. But it’s a well-established idiom at this point, and unlikely to change.)

The functor for creating the interval module follows. We represent an interval with a variant type, which is either Empty or Interval (x,y), where x and y are the bounds of the interval. In addition to the type, the body of the functor contains implementations of a number of useful primitives for interacting with intervals:

*OCaml utop* (part 6)

# **moduleMake_interval(Endpoint : Comparable) = struct**

** typet = | IntervalofEndpoint.t * Endpoint.t**

** | Empty**

** (** [create low high] creates a new interval from [low] to**

** [high]. If [low > high], thentheintervalisempty *)**

** letcreatelowhigh =**

** ifEndpoint.comparelowhigh > 0thenEmpty**

** elseInterval (low,high)**

** (** Returns true iff the interval is empty *)**

** letis_empty = function**

** | Empty -> true**

** | Interval _ -> false**

** (** [contains t x] returns true iff [x] is contained in the**

** interval [t] *)**

** letcontainstx =**

** matchtwith**

** | Empty -> false**

** | Interval (l,h) ->**

** Endpoint.comparexl >= 0 && Endpoint.comparexh <= 0**

** (** [intersect t1 t2] returns the intersection of the two input**

** intervals *)**

** letintersectt1t2 =**

** letminxy = ifEndpoint.comparexy <= 0thenxelseyin**

** letmaxxy = ifEndpoint.comparexy >= 0thenxelseyin**

** matcht1,t2with**

** | Empty, _ | _, Empty -> Empty**

** | Interval (l1,h1), Interval (l2,h2) ->**

** create (maxl1l2) (minh1h2)**

** end ;;**

module Make_interval :

functor (Endpoint : Comparable) ->

sig

type t = Interval of Endpoint.t * Endpoint.t | Empty

val create : Endpoint.t -> Endpoint.t -> t

val is_empty : t -> bool

val contains : t -> Endpoint.t -> bool

val intersect : t -> t -> t

end

We can instantiate the functor by applying it to a module with the right signature. In the following code, rather than name the module first and then call the functor, we provide the functor input as an anonymous module:

*OCaml utop* (part 7)

# **moduleInt_interval =**

** Make_interval(struct**

** typet = int**

** letcompare = Int.compare**

** end);;**

module Int_interval :

sig

type t = Interval of int * int | Empty

val create : int -> int -> t

val is_empty : t -> bool

val contains : t -> int -> bool

val intersect : t -> t -> t

end

If the input interface for your functor is aligned with the standards of the libraries you use, then you don’t need to construct a custom module to feed to the functor. In this case, we can directly use the Int or String modules provided by Core:

*OCaml utop* (part 8)

# **moduleInt_interval = Make_interval(Int) ;;**

module Int_interval :

sig

type t = Make_interval(Core.Std.Int).t = Interval of int * int | Empty

val create : int -> int -> t

val is_empty : t -> bool

val contains : t -> int -> bool

val intersect : t -> t -> t

end

# **moduleString_interval = Make_interval(String) ;;**

module String_interval :

sig

type t =

Make_interval(Core.Std.String).t =

Interval of string * string

| Empty

val create : string -> string -> t

val is_empty : t -> bool

val contains : t -> string -> bool

val intersect : t -> t -> t

end

This works because many modules in Core, including Int and String, satisfy an extended version of the Comparable signature described previously. Such standardized signatures are good practice, both because they make functors easier to use, and because they encourage standardization that makes your codebase easier to navigate.

We can use the newly defined Int_interval module like any ordinary module:

*OCaml utop* (part 9)

# **leti1 = Int_interval.create38;;**

val i1 : Int_interval.t = Int_interval.Interval (3, 8)

# **leti2 = Int_interval.create410;;**

val i2 : Int_interval.t = Int_interval.Interval (4, 10)

# **Int_interval.intersecti1i2;;**

- : Int_interval.t = Int_interval.Interval (4, 8)

This design gives us the freedom to use any comparison function we want for comparing the endpoints. We could, for example, create a type of integer interval with the order of the comparison reversed, as follows:

*OCaml utop* (part 10)

# **moduleRev_int_interval =**

** Make_interval(struct**

** typet = int**

** letcomparexy = Int.compareyx**

** end);;**

module Rev_int_interval :

sig

type t = Interval of int * int | Empty

val create : int -> int -> t

val is_empty : t -> bool

val contains : t -> int -> bool

val intersect : t -> t -> t

end

The behavior of Rev_int_interval is of course different from Int_interval:

*OCaml utop* (part 11)

# **letinterval = Int_interval.create43;;**

val interval : Int_interval.t = Int_interval.Empty

# **letrev_interval = Rev_int_interval.create43;;**

val rev_interval : Rev_int_interval.t = Rev_int_interval.Interval (4, 3)

Importantly, Rev_int_interval.t is a different type than Int_interval.t, even though its physical representation is the same. Indeed, the type system will prevent us from confusing them.

*OCaml utop* (part 12)

# **Int_interval.containsrev_interval3;;**

Characters 22-34:

Error: This expression has type Rev_int_interval.t

but an expression was expected of type Int_interval.t

This is important, because confusing the two kinds of intervals would be a semantic error, and it’s an easy one to make. The ability of functors to mint new types is a useful trick that comes up a lot.

**Making the Functor Abstract**

There’s a problem with Make_interval. The code we wrote depends on the invariant that the upper bound of an interval is greater than its lower bound, but that invariant can be violated. The invariant is enforced by the create function, but because Interval.t is not abstract, we can bypass thecreate function:

*OCaml utop* (part 13)

# **Int_interval.is_empty (* going through create *)**

** (Int_interval.create43) ;;**

- : bool = true

# **Int_interval.is_empty (* bypassing create *)**

** (Int_interval.Interval (4,3)) ;;**

- : bool = false

To make Int_interval.t abstract, we need to restrict the output of Make_interval with an interface. Here’s an explicit interface that we can use for that purpose:

*OCaml utop* (part 14)

# **moduletypeInterval_intf = sig**

** typet**

** typeendpoint**

** valcreate : endpoint -> endpoint -> t**

** valis_empty : t -> bool**

** valcontains : t -> endpoint -> bool**

** valintersect : t -> t -> t**

** end;;**

module type Interval_intf =

sig

type t

type endpoint

val create : endpoint -> endpoint -> t

val is_empty : t -> bool

val contains : t -> endpoint -> bool

val intersect : t -> t -> t

end

This interface includes the type endpoint to give us a way of referring to the endpoint type. Given this interface, we can redo our definition of Make_interval. Notice that we added the type endpoint to the implementation of the module to match Interval_intf:

*OCaml utop*

**# moduleMake_interval(Endpoint : Comparable) : Interval_intf = struct**

** typeendpoint = Endpoint.t**

** typet = | IntervalofEndpoint.t * Endpoint.t**

** | Empty**

** ...**

** end ;;**

module Make_interval : functor (Endpoint : Comparable) -> Interval_intf

**Sharing Constraints**

The resulting module is abstract, but it’s unfortunately too abstract. In particular, we haven’t exposed the type endpoint, which means that we can’t even construct an interval anymore:

*OCaml utop* (part 16)

# **moduleInt_interval = Make_interval(Int);;**

module Int_interval :

sig

type t = Make_interval(Core.Std.Int).t

type endpoint = Make_interval(Core.Std.Int).endpoint

val create : endpoint -> endpoint -> t

val is_empty : t -> bool

val contains : t -> endpoint -> bool

val intersect : t -> t -> t

end

# **Int_interval.create34;;**

Characters 20-21:

Error: This expression has type int but an expression was expected of type

Int_interval.endpoint

To fix this, we need to expose the fact that endpoint is equal to Int.t (or more generally, Endpoint.t, where Endpoint is the argument to the functor). One way of doing this is through a *sharing constraint*, which allows you to tell the compiler to expose the fact that a given type is equal to some other type. The syntax for a simple sharing constraint is as follows:

*Syntax*

*<**Module_type**>* **withtype** *<**type**>* = *<**type'**>*

The result of this expression is a new signature that’s been modified so that it exposes the fact that *type* defined inside of the module type is equal to *type'* whose definition is outside of it. One can also apply multiple sharing constraints to the same signature:

*Syntax*

*<**Module_type**>* **withtype** *<**type1**>* = *<**type1'**>* **and** *<**type2**>* = *<**type2'**>*

We can use a sharing constraint to create a specialized version of Interval_intf for integer intervals:

*OCaml utop* (part 17)

# **moduletypeInt_interval_intf =**

** Interval_intfwithtypeendpoint = int;;**

module type Int_interval_intf =

sig

type t

type endpoint = int

val create : endpoint -> endpoint -> t

val is_empty : t -> bool

val contains : t -> endpoint -> bool

val intersect : t -> t -> t

end

We can also use sharing constraints in the context of a functor. The most common use case is where you want to expose that some of the types of the module being generated by the functor are related to the types in the module fed to the functor.

In this case, we’d like to expose an equality between the type endpoint in the new module and the type Endpoint.t, from the module Endpoint that is the functor argument. We can do this as follows:

*OCaml utop*

**# moduleMake_interval(Endpoint : Comparable)**

** : (Interval_intfwithtypeendpoint = Endpoint.t)**

** = struct**

** typeendpoint = Endpoint.t**

** typet = | IntervalofEndpoint.t * Endpoint.t**

** | Empty**

** ...**

** end ;;**

module Make_interval :

functor (Endpoint : Comparable) ->

sig

type t

type endpoint = Endpoint.t

val create : endpoint -> endpoint -> t

val is_empty : t -> bool

val contains : t -> endpoint -> bool

val intersect : t -> t -> t

end

So now, the interface is as it was, except that endpoint is known to be equal to Endpoint.t. As a result of that type equality, we can again do things that require that endpoint be exposed, like constructing intervals:

*OCaml utop* (part 19)

# **moduleInt_interval = Make_interval(Int);;**

module Int_interval :

sig

type t = Make_interval(Core.Std.Int).t

type endpoint = int

val create : endpoint -> endpoint -> t

val is_empty : t -> bool

val contains : t -> endpoint -> bool

val intersect : t -> t -> t

end

# **leti = Int_interval.create34;;**

val i : Int_interval.t = <abstr>

# **Int_interval.containsi5;;**

- : bool = false

**Destructive Substitution**

Sharing constraints basically do the job, but they have some downsides. In particular, we’ve now been stuck with the useless type declaration of endpoint that clutters up both the interface and the implementation. A better solution would be to modify the Interval_intf signature by replacingendpoint with Endpoint.t everywhere it shows up, and deleting the definition of endpoint from the signature. We can do just this using what’s called *destructive substitution*. Here’s the basic syntax:

*Syntax*

*<**Module_type**>* **withtype** *<**type**>* := *<**type'**>*

The following shows how we could use this with Make_interval:

*OCaml utop* (part 20)

# **moduletypeInt_interval_intf =**

** Interval_intfwithtypeendpoint := int;;**

module type Int_interval_intf =

sig

type t

val create : int -> int -> t

val is_empty : t -> bool

val contains : t -> int -> bool

val intersect : t -> t -> t

end

There’s now no endpoint type: all of its occurrences of have been replaced by int. As with sharing constraints, we can also use this in the context of a functor:

*OCaml utop*

**# moduleMake_interval(Endpoint : Comparable)**

** : Interval_intfwithtypeendpoint := Endpoint.t =**

** struct**

** typet = | IntervalofEndpoint.t * Endpoint.t**

** | Empty**

** ...**

** end ;;**

module Make_interval :

functor (Endpoint : Comparable) ->

sig

type t

val create : Endpoint.t -> Endpoint.t -> t

val is_empty : t -> bool

val contains : t -> Endpoint.t -> bool

val intersect : t -> t -> t

end

The interface is precisely what we want: the type t is abstract, and the type of the endpoint is exposed; so we can create values of type Int_interval.t using the creation function, but not directly using the constructors and thereby violating the invariants of the module:

*OCaml utop* (part 22)

# **moduleInt_interval = Make_interval(Int);;**

module Int_interval :

sig

type t = Make_interval(Core.Std.Int).t

val create : int -> int -> t

val is_empty : t -> bool

val contains : t -> int -> bool

val intersect : t -> t -> t

end

# **Int_interval.is_empty**

** (Int_interval.create34);;**

- : bool = false

# **Int_interval.is_empty**

** (Int_interval.Interval (4,3));;**

Characters 40-48:

Error: Unbound constructor Int_interval.Interval

In addition, the endpoint type is gone from the interface, meaning we no longer need to define the endpoint type alias in the body of the module.

It’s worth noting that the name is somewhat misleading, in that there’s nothing destructive about destructive substitution; it’s really just a way of creating a new signature by transforming an existing one.

**Using Multiple Interfaces**

Another feature that we might want for our interval module is the ability to *serialize*, i.e., to be able to read and write intervals as a stream of bytes. In this case, we’ll do this by converting to and from s-expressions, which were mentioned already in *Chapter 7*. To recall, an s-expression is essentially a parenthesized expression whose atoms are strings, and it is a serialization format that is used commonly in Core. Here’s an example:

*OCaml utop* (part 23)

# **Sexp.of_string"(This is (an s-expression))";;**

- : Sexp.t = (This is (an s-expression))

Core comes with a syntax extension called Sexplib which can autogenerate s-expression conversion functions from a type declaration. Attaching with sexp to a type definition signals to the extension to generate the converters. Thus, we can write:

*OCaml utop* (part 24)

# **typesome_type = int * stringlistwithsexp;;**

type some_type = int * string list

val some_type_of_sexp : Sexp.t -> int * string list = <fun>

val sexp_of_some_type : int * string list -> Sexp.t = <fun>

# **sexp_of_some_type (33, ["one"; "two"]);;**

- : Sexp.t = (33 (one two))

# **Sexp.of_string"(44 (five six))" |> some_type_of_sexp;;**

- : int * string list = (44, ["five"; "six"])

We’ll discuss s-expressions and Sexplib in more detail in *Chapter 17*, but for now, let’s see what happens if we attach the with sexp declaration to the definition of t within the functor:

*OCaml utop*

**# moduleMake_interval(Endpoint : Comparable)**

** : (Interval_intfwithtypeendpoint := Endpoint.t) = struct**

** typet = | IntervalofEndpoint.t * Endpoint.t**

** | Empty**

** withsexp**

** ...**

** end ;;**

Characters 136-146:

Error: Unbound value Endpoint.t_of_sexp

The problem is that with sexp adds code for defining the s-expression converters, and that code assumes that Endpoint has the appropriate sexp-conversion functions for Endpoint.t. But all we know about Endpoint is that it satisfies the Comparable interface, which doesn’t say anything about s-expressions.

Happily, Core comes with a built-in interface for just this purpose called Sexpable, which is defined as follows:

*OCaml*

**moduletypeSexpable** = **sig**

**type** t

**val** sexp_of_t : t -> **Sexp**.t

**val** t_of_sexp : **Sexp**.t -> t

**end**

We can modify Make_interval to use the Sexpable interface, for both its input and its output. First, let’s create an extended version of the Interval_intf interface that includes the functions from the Sexpable interface. We can do this using destructive substitution on the Sexpable interface, to avoid having multiple distinct type t’s clashing with each other:

*OCaml utop* (part 26)

# **moduletypeInterval_intf_with_sexp = sig**

** includeInterval_intf**

** includeSexpablewithtypet := t**

** end;;**

module type Interval_intf_with_sexp =

sig

type t

type endpoint

val create : endpoint -> endpoint -> t

val is_empty : t -> bool

val contains : t -> endpoint -> bool

val intersect : t -> t -> t

val t_of_sexp : Sexp.t -> t

val sexp_of_t : t -> Sexp.t

end

Equivalently, we can define a type t within our new module, and apply destructive substitutions to all of the included interfaces, Interval_intf included, as shown in the following example. This is somewhat cleaner when combining multiple interfaces, since it correctly reflects that all of the signatures are being handled equivalently:

*OCaml utop* (part 27)

# **moduletypeInterval_intf_with_sexp = sig**

** typet**

** includeInterval_intfwithtypet := t**

** includeSexpable withtypet := t**

** end;;**

module type Interval_intf_with_sexp =

sig

type t

type endpoint

val create : endpoint -> endpoint -> t

val is_empty : t -> bool

val contains : t -> endpoint -> bool

val intersect : t -> t -> t

val t_of_sexp : Sexp.t -> t

val sexp_of_t : t -> Sexp.t

end

Now we can write the functor itself. We have been careful to override the sexp converter here to ensure that the data structure’s invariants are still maintained when reading in from an s-expression:

*OCaml utop* (part 28)

# **moduleMake_interval(Endpoint : sig**

** typet**

** includeComparablewithtypet := t**

** includeSexpable withtypet := t**

** end)**

** : (Interval_intf_with_sexpwithtypeendpoint := Endpoint.t)**

** = struct**

** typet = | IntervalofEndpoint.t * Endpoint.t**

** | Empty**

** withsexp**

** (** [create low high] creates a new interval from [low] to**

** [high]. If [low > high], thentheintervalisempty *)**

** letcreatelowhigh =**

** ifEndpoint.comparelowhigh > 0thenEmpty**

** elseInterval (low,high)**

** (* put a wrapper around the autogenerated [t_of_sexp] to enforce**

** theinvariantsofthedatastructure *)**

** lett_of_sexpsexp =**

** matcht_of_sexpsexpwith**

** | Empty -> Empty**

** | Interval (x,y) -> createxy**

** (** Returns true iff the interval is empty *)**

** letis_empty = function**

** | Empty -> true**

** | Interval _ -> false**

** (** [contains t x] returns true iff [x] is contained in the**

** interval [t] *)**

** letcontainstx =**

** matchtwith**

** | Empty -> false**

** | Interval (l,h) ->**

** Endpoint.comparexl >= 0 && Endpoint.comparexh <= 0**

** (** [intersect t1 t2] returns the intersection of the two input**

** intervals *)**

** letintersectt1t2 =**

** letminxy = ifEndpoint.comparexy <= 0thenxelseyin**

** letmaxxy = ifEndpoint.comparexy >= 0thenxelseyin**

** matcht1,t2with**

** | Empty, _ | _, Empty -> Empty**

** | Interval (l1,h1), Interval (l2,h2) ->**

** create (maxl1l2) (minh1h2)**

** end;;**

module Make_interval :

functor

(Endpoint : sig

type t

val compare : t -> t -> int

val t_of_sexp : Sexp.t -> t

val sexp_of_t : t -> Sexp.t

end) ->

sig

type t

val create : Endpoint.t -> Endpoint.t -> t

val is_empty : t -> bool

val contains : t -> Endpoint.t -> bool

val intersect : t -> t -> t

val t_of_sexp : Sexp.t -> t

val sexp_of_t : t -> Sexp.t

end

And now, we can use that sexp converter in the ordinary way:

*OCaml utop* (part 29)

# **moduleInt_interval = Make_interval(Int) ;;**

module Int_interval :

sig

type t = Make_interval(Core.Std.Int).t

val create : int -> int -> t

val is_empty : t -> bool

val contains : t -> int -> bool

val intersect : t -> t -> t

val t_of_sexp : Sexp.t -> t

val sexp_of_t : t -> Sexp.t

end

# **Int_interval.sexp_of_t (Int_interval.create34);;**

- : Sexp.t = (Interval 3 4)

# **Int_interval.sexp_of_t (Int_interval.create43);;**

- : Sexp.t = Empty

**Extending Modules**

Another common use of functors is to generate type-specific functionality for a given module in a standardized way. Let’s see how this works in the context of a functional queue, which is just a functional version of a FIFO (first-in, first-out) queue. Being functional, operations on the queue return new queues, rather than modifying the queues that were passed in.

Here’s a reasonable mli for such a module:

*OCaml*

**type'**a t

**val** empty : **'**a t

*(** [enqueue q el] adds [el] to the back of [q] *)*

**val** enqueue : **'**a t -> **'**a -> **'**a t

*(** [dequeue q] returns None if the [q] is empty, otherwise returns*

* the first element of the queue and the remainder of the queue *)*

**val** dequeue : **'**a t -> (**'**a * **'**a t) option

*(** Folds over the queue, from front to back *)*

**val** fold : **'**a t -> init:**'**acc -> f:(**'**acc -> **'**a -> **'**acc) -> **'**acc

The preceding Fqueue.fold function requires some explanation. It follows the same pattern as the List.fold function we described in *Using the List Module Effectively*. Essentially, Fqueue.fold q ~init ~f walks over the elements of q from front to back, starting with an accumulator of initand using f to update the accumulator value as it walks over the queue, returning the final value of the accumulator at the end of the computation. fold is a quite powerful operation, as we’ll see.

We’ll implement Fqueue the well known trick of maintaining an input and an output list so that one can efficiently enqueue on the input list and efficiently dequeue from the output list. If you attempt to dequeue when the output list is empty, the input list is reversed and becomes the new output list. Here’s the implementation:

*OCaml*

**openCore**.**Std**

**type'**a t = **'**a **list** * **'**a **list**

**let** empty = ([],[])

**let** enqueue (in_list, out_list) x =

(x :: in_list,out_list)

**let** dequeue (in_list, out_list) =

**match** out_list **with**

| hd :: tl -> **Some** (hd, (in_list, tl))

| [] ->

**matchList**.rev in_list **with**

| [] -> **None**

| hd :: tl -> **Some** (hd, ([], tl))

**let** fold (in_list, out_list) ~init ~f =

**let** after_out = **List**.fold ~init ~f out_list **in**

**List**.fold_right ~init:after_out ~f:(**fun** x acc -> f acc x) in_list

One problem with Fqueue is that the interface is quite skeletal. There are lots of useful helper functions that one might want that aren’t there. The List module, by way of contrast, has functions like List.iter, which runs a function on each element; and List.for_all, which returns true if and only if the given predicate evaluates to true on every element of the list. Such helper functions come up for pretty much every container type, and implementing them over and over is a dull and repetitive affair.

As it happens, many of these helper functions can be derived mechanically from the fold function we already implemented. Rather than write all of these helper functions by hand for every new container type, we can instead use a functor to add this functionality to any container that has afold function.

We’ll create a new module, Foldable, that automates the process of adding helper functions to a fold-supporting container. As you can see, Foldable contains a module signature S which defines the signature that is required to support folding; and a functor Extend that allows one to extend any module that matches Foldable.S:

*OCaml*

**openCore**.**Std**

**moduletypeS** = **sig**

**type'**a t

**val** fold : **'**a t -> init:**'**acc -> f:(**'**acc -> **'**a -> **'**acc) -> **'**acc

**end**

**moduletypeExtension** = **sig**

**type'**a t

**val** iter : **'**a t -> f:(**'**a -> **unit**) -> **unit**

**val** length : **'**a t -> **int**

**val** count : **'**a t -> f:(**'**a -> **bool**) -> **int**

**val** for_all : **'**a t -> f:(**'**a -> **bool**) -> **bool**

**val** exists : **'**a t -> f:(**'**a -> **bool**) -> **bool**

**end**

*(* For extending a Foldable module *)*

**moduleExtend**(**Arg** : **S**)

: (**Extensionwithtype'**a t := **'**a **Arg**.t) =

**struct**

**openArg**

**let** iter t ~f =

fold t ~init:() ~f:(**fun** () a -> f a)

**let** length t =

fold t ~init:0 ~f:(**fun** acc _ -> acc + 1)

**let** count t ~f =

fold t ~init:0 ~f:(**fun** count x -> count + **if** f x **then** 1 **else** 0)

**exceptionShort_circuit**

**let** for_all c ~f =

**try** iter c ~f:(**fun** x -> **if** not (f x) **thenraiseShort_circuit**); true

**withShort_circuit** -> false

**let** exists c ~f =

**try** iter c ~f:(**fun** x -> **if** f x **thenraiseShort_circuit**); false

**withShort_circuit** -> true

**end**

Now we can apply this to Fqueue. We can create an interface for an extended version of Fqueue as follows:

*OCaml*

**type'**a t

**include** (**moduletypeofFqueue**) **withtype'**a t := **'**a t

**includeFoldable**.**Extensionwithtype'**a t := **'**a t

In order to apply the functor, we’ll put the definition of Fqueue in a submodule called T, and then call Foldable.Extend on T:

*OCaml*

**includeFqueue**

**includeFoldable**.**Extend**(**Fqueue**)

Core comes with a number of functors for extending modules that follow this same basic pattern, including:

Container.Make

Very similar to Foldable.Extend.

Comparable.Make

Adds support for functionality that depends on the presence of a comparison function, including support for containers like maps and sets.

Hashable.Make

Adds support for hashing-based data structures including hash tables, hash sets, and hash heaps.

Monad.Make

For so-called monadic libraries, like those discussed in Chapters *7* and *18*. Here, the functor is used to provide a collection of standard helper functions based on the bind and return operators.

These functors come in handy when you want to add the same kind of functionality that is commonly available in Core to your own types.

We’ve really only covered some of the possible uses of functors. Functors are really a quite powerful tool for modularizing your code. The cost is that functors are syntactically heavyweight compared to the rest of the language, and that there are some tricky issues you need to understand to use them effectively, with sharing constraints and destructive substitution being high on that list.

All of this means that for small and simple programs, heavy use of functors is probably a mistake. But as your programs get more complicated and you need more effective modular architectures, functors become a highly valuable tool.