Variables and Functions - Language Concepts - Real World OCaml (2013)

Real World OCaml (2013)

Part I. Language Concepts

Chapter 2. Variables and Functions

Variables and functions are fundamental ideas that show up in virtually all programming languages. OCaml has a different take on these concepts than most languages you’re likely to have encountered, so this chapter will cover OCaml’s approach to variables and functions in some detail, starting with the basics of how to define a variable, and ending with the intricacies of functions with labeled and optional arguments.

Don’t be discouraged if you find yourself overwhelmed by some of the details, especially toward the end of the chapter. The concepts here are important, but if they don’t connect for you on your first read, you should return to this chapter after you’ve gotten a better sense for the rest of the language.


At its simplest, a variable is an identifier whose meaning is bound to a particular value. In OCaml these bindings are often introduced using the let keyword. We can type a so-called top-level let binding with the following syntax. Note that variable names must start with a lowercase letter or an underscore:


let <variable> = <expr>

As we’ll see when we get to the module system in Chapter 4, this same syntax is used for let bindings at the top level of a module.

Every variable binding has a scope, which is the portion of the code that can refer to that binding. When using utop, the scope of a top-level let binding is everything that follows it in the session. When it shows up in a module, the scope is the remainder of that module.

Here’s a simple example:

OCaml utop

# letx = 3;;

val x : int = 3

# lety = 4;;

val y : int = 4

# letz = x + y;;

val z : int = 7

let can also be used to create a variable binding whose scope is limited to a particular expression, using the following syntax:


let <variable> = <expr1> in <expr2>

This first evaluates expr1 and then evaluates expr2 with variable bound to whatever value was produced by the evaluation of expr1. Here’s how it looks in practice:

OCaml utop (part 1)

# letlanguages = "OCaml,Perl,C++,C";;

val languages : string = "OCaml,Perl,C++,C"

# letdashed_languages =

letlanguage_list = String.splitlanguages ~on:','in

String.concat ~sep:"-"language_list


val dashed_languages : string = "OCaml-Perl-C++-C"

Note that the scope of language_list is just the expression String.concat ~sep:"-" language_list and is not available at the toplevel, as we can see if we try to access it now:

OCaml utop (part 2)

# language_list;;

Characters -1-13:

Error: Unbound value language_list

A let binding in an inner scope can shadow, or hide, the definition from an outer scope. So, for example, we could have written the dashed_languages example as follows:

OCaml utop (part 3)

# letlanguages = "OCaml,Perl,C++,C";;

val languages : string = "OCaml,Perl,C++,C"

# letdashed_languages =

letlanguages = String.splitlanguages ~on:','in

String.concat ~sep:"-"languages


val dashed_languages : string = "OCaml-Perl-C++-C"

This time, in the inner scope we called the list of strings languages instead of language_list, thus hiding the original definition of languages. But once the definition of dashed_languages is complete, the inner scope has closed and the original definition of languages reappears:

OCaml utop (part 4)

# languages;;

- : string = "OCaml,Perl,C++,C"

One common idiom is to use a series of nested let/in expressions to build up the components of a larger computation. Thus, we might write:

OCaml utop (part 5)

# letarea_of_ringinner_radiusouter_radius =

letpi = acos (-1.) in

letarea_of_circler = pi *. r *. rin

area_of_circleouter_radius -. area_of_circleinner_radius


val area_of_ring : float -> float -> float = <fun>

# area_of_ring1. 3.;;

- : float = 25.1327412287

It’s important not to confuse a sequence of let bindings with the modification of a mutable variable. For example, consider how area_of_ring would work if we had instead written this purposefully confusing bit of code:

OCaml utop (part 6)

# letarea_of_ringinner_radiusouter_radius =

letpi = acos (-1.) in

letarea_of_circler = pi *. r *. rin

letpi = 0. in

area_of_circleouter_radius -. area_of_circleinner_radius


Characters 126-128:

Warning 26: unused variable pi.

val area_of_ring : float -> float -> float = <fun>

Here, we redefined pi to be zero after the definition of area_of_circle. You might think that this would mean that the result of the computation would now be zero, but in fact, the behavior of the function is unchanged. That’s because the original definition of pi wasn’t changed; it was just shadowed, which means that any subsequent reference to pi would see the new definition of pi as 0, but earlier references would be unchanged. But there is no later use of pi, so the binding of pi to 0. made no difference. This explains the warning produced by the toplevel telling us that there is an unused definition of pi.

In OCaml, let bindings are immutable. There are many kinds of mutable values in OCaml, which we’ll discuss in Chapter 8, but there are no mutable variables.


One source of confusion for people new to OCaml is the fact that variables are immutable. This seems pretty surprising even on linguistic terms. Isn’t the whole point of a variable that it can vary?

The answer to this is that variables in OCaml (and generally in functional languages) are really more like variables in an equation than a variable in an imperative language. If you think about the mathematical identity x(y + z) = xy + xz, there’s no notion of mutating the variables x, y, and z. They vary in the sense that you can instantiate this equation with different numbers for those variables, and it still holds.

The same is true in a functional language. A function can be applied to different inputs, and thus its variables will take on different values, even without mutation.

Pattern Matching and let

Another useful feature of let bindings is that they support the use of patterns on the lefthand side. Consider the following code, which uses List.unzip, a function for converting a list of pairs into a pair of lists:

OCaml utop (part 7)

# let (ints,strings) = List.unzip [(1,"one"); (2,"two"); (3,"three")];;

val ints : int list = [1; 2; 3]

val strings : string list = ["one"; "two"; "three"]

Here, (ints,strings) is a pattern, and the let binding assigns values to both of the identifiers that show up in that pattern. A pattern is essentially a description of the shape of a data structure, where some components are identifiers to be bound. As we saw in Tuples, Lists, Options, and Pattern Matching, OCaml has patterns for a variety of different data types.

Using a pattern in a let binding makes the most sense for a pattern that is irrefutable, i.e., where any value of the type in question is guaranteed to match the pattern. Tuple and record patterns are irrefutable, but list patterns are not. Consider the following code that implements a function for upper casing the first element of a comma-separated list:

OCaml utop (part 8)

# letupcase_first_entryline =

let (first :: rest) = String.split ~on:','linein

String.concat ~sep:"," (String.uppercasefirst :: rest)


Characters 40-53:

Warning 8: this pattern-matching is not exhaustive.

Here is an example of a value that is not matched:


val upcase_first_entry : string -> string = <fun>

This case can’t really come up in practice, because String.split always returns a list with at least one element. But the compiler doesn’t know this, and so it emits the warning. It’s generally better to use a match statement to handle such cases explicitly:

OCaml utop (part 9)

# letupcase_first_entryline =

matchString.split ~on:','linewith

| [] -> assertfalse(* String.split returns at least one element *)

| first :: rest -> String.concat ~sep:"," (String.uppercasefirst :: rest)


val upcase_first_entry : string -> string = <fun>

Note that this is our first use of assert, which is useful for marking cases that should be impossible. We’ll discuss assert in more detail in Chapter 7.


Given that OCaml is a functional language, it’s no surprise that functions are important and pervasive. Indeed, functions have come up in almost every example we’ve done so far. This section will go into more depth, explaining the details of how OCaml’s functions work. As you’ll see, functions in OCaml differ in a variety of ways from what you’ll find in most mainstream languages.

Anonymous Functions

We’ll start by looking at the most basic style of function declaration in OCaml: the anonymous function. An anonymous function is a function that is declared without being named. These can be declared using the fun keyword, as shown here:

OCaml utop (part 10)

# (funx -> x + 1);;

- : int -> int = <fun>

Anonymous functions operate in much the same way as named functions. For example, we can apply an anonymous function to an argument:

OCaml utop (part 11)

# (funx -> x + 1) 7;;

- : int = 8

Or pass it to another function. Passing functions to iteration functions like is probably the most common use case for anonymous functions:

OCaml utop (part 12)

# ~f:(funx -> x + 1) [1;2;3];;

- : int list = [2; 3; 4]

You can even stuff them into a data structure:

OCaml utop (part 13)

# letincrements = [ (funx -> x + 1); (funx -> x + 2) ] ;;

val increments : (int -> int) list = [<fun>; <fun>]

# ~f:(fung -> g5) increments;;

- : int list = [6; 7]

It’s worth stopping for a moment to puzzle this example out, since this kind of higher-order use of functions can be a bit obscure at first. Notice that (fun g -> g 5) is a function that takes a function as an argument, and then applies that function to the number 5. The invocation of List.mapapplies (fun g -> g 5) to the elements of the increments list (which are themselves functions) and returns the list containing the results of these function applications.

The key thing to understand is that functions are ordinary values in OCaml, and you can do everything with them that you’d do with an ordinary value, including passing them to and returning them from other functions and storing them in data structures. We even name functions in the same way that we name other values, by using a let binding:

OCaml utop (part 14)

# letplusone = (funx -> x + 1);;

val plusone : int -> int = <fun>

# plusone3;;

- : int = 4

Defining named functions is so common that there is some syntactic sugar for it. Thus, the following definition of plusone is equivalent to the previous definition:

OCaml utop (part 15)

# letplusonex = x + 1;;

val plusone : int -> int = <fun>

This is the most common and convenient way to declare a function, but syntactic niceties aside, the two styles of function definition are equivalent.


Functions and let bindings have a lot to do with each other. In some sense, you can think of the parameter of a function as a variable being bound to the value passed by the caller. Indeed, the following two expressions are nearly equivalent:

OCaml utop (part 16)

# (funx -> x + 1) 7;;

- : int = 8

# letx = 7inx + 1;;

- : int = 8

This connection is important, and will come up more when programming in a monadic style, as we’ll see in Chapter 18.

Multiargument functions

OCaml of course also supports multiargument functions, such as:

OCaml utop (part 17)

# letabs_diffxy = abs (x - y);;

val abs_diff : int -> int -> int = <fun>

# abs_diff34;;

- : int = 1

You may find the type signature of abs_diff with all of its arrows a little hard to parse. To understand what’s going on, let’s rewrite abs_diff in an equivalent form, using the fun keyword:

OCaml utop (part 18)

# letabs_diff =

(funx -> (funy -> abs (x - y)));;

val abs_diff : int -> int -> int = <fun>

This rewrite makes it explicit that abs_diff is actually a function of one argument that returns another function of one argument, which itself returns the final result. Because the functions are nested, the inner expression abs (x - y) has access to both x, which was bound by the outer function application, and y, which was bound by the inner one.

This style of function is called a curried function. (Currying is named after Haskell Curry, a logician who had a significant impact on the design and theory of programming languages.) The key to interpreting the type signature of a curried function is the observation that -> is right-associative. The type signature of abs_diff can therefore be parenthesized as follows:

OCaml: variables-and-functions/abs_diff.mli

val abs_diff : int -> (int -> int)

The parentheses don’t change the meaning of the signature, but they make it easier to see the currying.

Currying is more than just a theoretical curiosity. You can make use of currying to specialize a function by feeding in some of the arguments. Here’s an example where we create a specialized version of abs_diff that measures the distance of a given number from 3:

OCaml utop (part 19)

# letdist_from_3 = abs_diff3;;

val dist_from_3 : int -> int = <fun>

# dist_from_38;;

- : int = 5

# dist_from_3 (-1);;

- : int = 4

The practice of applying some of the arguments of a curried function to get a new function is called partial application.

Note that the fun keyword supports its own syntax for currying, so the following definition of abs_diff is equivalent to the previous one.

OCaml utop (part 20)

# letabs_diff = (funxy -> abs (x - y));;

val abs_diff : int -> int -> int = <fun>

You might worry that curried functions are terribly expensive, but this is not the case. In OCaml, there is no penalty for calling a curried function with all of its arguments. (Partial application, unsurprisingly, does have a small extra cost.)

Currying is not the only way of writing a multiargument function in OCaml. It’s also possible to use the different parts of a tuple as different arguments. So, we could write:

OCaml utop (part 21)

# letabs_diff (x,y) = abs (x - y);;

val abs_diff : int * int -> int = <fun>

# abs_diff (3,4);;

- : int = 1

OCaml handles this calling convention efficiently as well. In particular it does not generally have to allocate a tuple just for the purpose of sending arguments to a tuple-style function. You can’t, however, use partial application for this style of function.

There are small trade-offs between these two approaches, but most of the time, one should stick to currying, since it’s the default style in the OCaml world.

Recursive Functions

A function is recursive if it refers to itself in its definition. Recursion is important in any programming language, but is particularly important in functional languages, because it is the way that you build looping constructs. (As will be discussed in more detail in Chapter 8, OCaml also supports imperative looping constructs like for and while, but these are only useful when using OCaml’s imperative features.)

In order to define a recursive function, you need to mark the let binding as recursive with the rec keyword, as shown in this function for finding the first sequentially repeated element in a list:

OCaml utop (part 22)

# letrecfind_first_stutterlist =


| [] | [_] ->

(* only zero or one elements, so no repeats *)


| x :: y :: tl ->

ifx = ythenSomexelsefind_first_stutter (y::tl)


val find_first_stutter : 'a list -> 'a option = <fun>

Note that in the code, the pattern | [] | [_] is what’s called an or-pattern, which is a disjunction of two patterns, meaning that it will be considered a match if either pattern matches. In this case, [] matches the empty list, and [_] matches any single element list. The _ is there so we don’t have to put an explicit name on that single element.

We can also define multiple mutually recursive values by using let rec combined with the and keyword. Here’s a (gratuitously inefficient) example:

OCaml utop (part 23)

# letrecis_evenx =

ifx = 0thentrueelseis_odd (x - 1)

and is_oddx =

ifx = 0thenfalseelseis_even (x - 1)


val is_even : int -> bool = <fun>

val is_odd : int -> bool = <fun>

# ~f:is_even [0;1;2;3;4;5];;

- : bool list = [true; false; true; false; true; false]

# ~f:is_odd [0;1;2;3;4;5];;

- : bool list = [false; true; false; true; false; true]

OCaml distinguishes between nonrecursive definitions (using let) and recursive definitions (using let rec) largely for technical reasons: the type-inference algorithm needs to know when a set of function definitions are mutually recursive, and for reasons that don’t apply to a pure language like Haskell, these have to be marked explicitly by the programmer.

But this decision has some good effects. For one thing, recursive (and especially mutually recursive) definitions are harder to reason about than nonrecursive ones. It’s therefore useful that, in the absence of an explicit rec, you can assume that a let binding is nonrecursive, and so can only build upon previous bindings.

In addition, having a nonrecursive form makes it easier to create a new definition that extends and supersedes an existing one by shadowing it.

Prefix and Infix Operators

So far, we’ve seen examples of functions used in both prefix and infix style:

OCaml utop (part 24)

# Int.max34 (* prefix *);;

- : int = 4

# 3 + 4 (* infix *);;

- : int = 7

You might not have thought of the second example as an ordinary function, but it very much is. Infix operators like + really only differ syntactically from other functions. In fact, if we put parentheses around an infix operator, you can use it as an ordinary prefix function:

OCaml utop (part 25)

# (+) 34;;

- : int = 7

# ~f:((+) 3) [4;5;6];;

- : int list = [7; 8; 9]

In the second expression, we’ve partially applied (+) to create a function that increments its single argument by 3.

A function is treated syntactically as an operator if the name of that function is chosen from one of a specialized set of identifiers. This set includes identifiers that are sequences of characters from the following set:


! $ % & * + - . / : < = > ? @ ^ | ~

or is one of a handful of predetermined strings, including mod, the modulus operator, and lsl, for “logical shift left,” a bit-shifting operation.

We can define (or redefine) the meaning of an operator. Here’s an example of a simple vector-addition operator on int pairs:

OCaml utop (part 26)

# let (+!) (x1,y1) (x2,y2) = (x1 + x2, y1 + y2);;

val ( +! ) : int * int -> int * int -> int * int = <fun>

# (3,2) +! (-2,4);;

- : int * int = (1, 6)

Note that you have to be careful when dealing with operators containing *. Consider the following example:

OCaml utop (part 27)

# let(***)xy = (x ** y) ** y;;

Characters 17-18:

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


What’s going on is that (***) isn’t interpreted as an operator at all; it’s read as a comment! To get this to work properly, we need to put spaces around any operator that begins or ends with *:

OCaml utop (part 28)

# let ( *** ) xy = (x ** y) ** y;;

val ( *** ) : float -> float -> float = <fun>

The syntactic role of an operator is typically determined by its first character or two, though there are a few exceptions. Table 2-1 breaks the different operators and other syntactic forms into groups from highest to lowest precedence, explaining how each behaves syntactically. We write !... to indicate the class of operators beginning with !.

Table 2-1. Precedence and associativity

Operator prefix


!..., ?..., ~...


., .(, .[


function application, constructor, assert, lazy

Left associative

-, -.


**..., lsl, lsr, asr

Right associative

*..., /..., %..., mod, land, lor, lxor

Left associative

+..., -...

Left associative


Right associative

@..., ^...

Right associative

=..., <..., >..., |..., &..., $...

Left associative

&, &&

Right associative

or, ||

Right associative



<-, :=

Right associative




Right associative

There’s one important special case: - and -., which are the integer and floating-point subtraction operators, and can act as both prefix operators (for negation) and infix operators (for subtraction). So, both -x and x - y are meaningful expressions. Another thing to remember about negation is that it has lower precedence than function application, which means that if you want to pass a negative value, you need to wrap it in parentheses, as you can see in this code:

OCaml utop (part 29)

# Int.max3 (-4);;

- : int = 3

# Int.max3 -4;;

Characters -1-9:

Error: This expression has type int -> int

but an expression was expected of type int

Here, OCaml is interpreting the second expression as equivalent to:

OCaml utop (part 30)

# (Int.max3) - 4;;

Characters 1-10:

Error: This expression has type int -> int

but an expression was expected of type int

which obviously doesn’t make sense.

Here’s an example of a very useful operator from the standard library whose behavior depends critically on the precedence rules described previously:

OCaml utop (part 31)

# let (|>) xf = fx ;;

val ( |> ) : 'a -> ('a -> 'b) -> 'b = <fun>

It’s not quite obvious at first what the purpose of this operator is: it just takes a value and a function and applies the function to the value. Despite that bland-sounding description, it has the useful role of a sequencing operator, similar in spirit to using the pipe character in the UNIX shell. Consider, for example, the following code for printing out the unique elements of your PATH. Note that List.dedup that follows removes duplicates from a list by sorting the list using the provided comparison function:

OCaml utop (part 32)

# letpath = "/usr/bin:/usr/local/bin:/bin:/sbin";;

val path : string = "/usr/bin:/usr/local/bin:/bin:/sbin"

# String.split ~on:':'path

|> List.dedup

|> List.iter ~f:print_endline






- : unit = ()

Note that we can do this without |>, but the result is a bit more verbose:

OCaml utop (part 33)

# letsplit_path = String.split ~on:':'pathin

letdeduped_path = List.dedup ~compare:String.comparesplit_pathin

List.iter ~f:print_endlinededuped_path






- : unit = ()

An important part of what’s happening here is partial application. For example, List.iter normally takes two arguments: a function to be called on each element of the list, and the list to iterate over. We can call List.iter with all its arguments:

OCaml utop (part 34)

# List.iter ~f:print_endline ["Two"; "lines"];;



- : unit = ()

Or, we can pass it just the function argument, leaving us with a function for printing out a list of strings:

OCaml utop (part 35)

# List.iter ~f:print_endline;;

- : string list -> unit = <fun>

It is this later form that we’re using in the preceding |> pipeline.

But |> only works in the intended way because it is left-associative. Let’s see what happens if we try using a right-associative operator, like (^>):

OCaml utop (part 36)

# let (^>) xf = fx;;

val ( ^> ) : 'a -> ('a -> 'b) -> 'b = <fun>

# Sys.getenv_exn"PATH"

^> String.split ~on:':'path

^> List.dedup

^> List.iter ~f:print_endline


Characters 98-124:

Error: This expression has type string list -> unit

but an expression was expected of type

(string list -> string list) -> 'a

Type string list is not compatible with type

string list -> string list

The type error is a little bewildering at first glance. What’s going on is that, because ^> is right associative, the operator is trying to feed the value List.dedup to the function List.iter ~f:print_endline. But List.iter ~f:print_endline expects a list of strings as its input, not a function.

The type error aside, this example highlights the importance of choosing the operator you use with care, particularly with respect to associativity.

Declaring Functions with Function

Another way to define a function is using the function keyword. Instead of having syntactic support for declaring multiargument (curried) functions, function has built-in pattern matching. Here’s an example:

OCaml utop (part 37)

# letsome_or_zero = function

| Somex -> x

| None -> 0


val some_or_zero : int option -> int = <fun>

# ~f:some_or_zero [Some3; None; Some4];;

- : int list = [3; 0; 4]

This is equivalent to combining an ordinary function definition with a match:

OCaml utop (part 38)

# letsome_or_zeronum_opt =


| Somex -> x

| None -> 0


val some_or_zero : int option -> int = <fun>

We can also combine the different styles of function declaration together, as in the following example, where we declare a two-argument (curried) function with a pattern match on the second argument:

OCaml utop (part 39)

# letsome_or_defaultdefault = function

| Somex -> x

| None -> default


val some_or_default : 'a -> 'a option -> 'a = <fun>

# some_or_default3 (Some5);;

- : int = 5

# ~f:(some_or_default100) [Some3; None; Some4];;

- : int list = [3; 100; 4]

Also, note the use of partial application to generate the function passed to In other words, some_or_default 100 is a function that was created by feeding just the first argument to some_or_default.

Labeled Arguments

Up until now, the functions we’ve defined have specified their arguments positionally, i.e., by the order in which the arguments are passed to the function. OCaml also supports labeled arguments, which let you identify a function argument by name. Indeed, we’ve already encountered functions from Core like that use labeled arguments. Labeled arguments are marked by a leading tilde, and a label (followed by a colon) is put in front of the variable to be labeled. Here’s an example:

OCaml utop (part 40)

# letratio ~num ~denom = floatnum /. floatdenom;;

val ratio : num:int -> denom:int -> float = <fun>

We can then provide a labeled argument using a similar convention. As you can see, the arguments can be provided in any order:

OCaml utop (part 41)

# ratio ~num:3 ~denom:10;;

- : float = 0.3

# ratio ~denom:10 ~num:3;;

- : float = 0.3

OCaml also supports label punning, meaning that you get to drop the text after the : if the name of the label and the name of the variable being used are the same. We were actually already using label punning when defining ratio. The following shows how punning can be used when invoking a function:

OCaml utop (part 42)

# letnum = 3in

letdenom = 4in

ratio ~num ~denom;;

- : float = 0.75

Labeled arguments are useful in a few different cases:

§ When defining a function with lots of arguments. Beyond a certain number, arguments are easier to remember by name than by position.

§ When the meaning of a particular argument is unclear from the type alone. Consider a function for creating a hash table whose first argument is the initial size of the array backing the hash table, and the second is a Boolean flag, which indicates whether that array will ever shrink when elements are removed:

val create_hashtable : int -> bool -> ('a,'b) Hashtable.t

The signature makes it hard to divine the meaning of those two arguments. but with labeled arguments, we can make the intent immediately clear:

val create_hashtable :

init_size:int -> allow_shrinking:bool -> ('a,'b) Hashtable.t

Choosing label names well is especially important for Boolean values, since it’s often easy to get confused about whether a value being true is meant to enable or disable a given feature.

§ When defining functions that have multiple arguments that might get confused with each other. This is most at issue when the arguments are of the same type. For example, consider this signature for a function that extracts a substring:

val substring: string -> int -> int -> string

Here, the two ints are the starting position and length of the substring to extract, respectively. We can make this fact more obvious from the signature by adding labeled:

val substring: string -> pos:int -> len:int -> string

This improves the readability of both the signature and of client code that makes use of substring and makes it harder to accidentally swap the position and the length.

§ When you want flexibility on the order in which arguments are passed. Consider a function like List.iter, which takes two arguments: a function and a list of elements to call that function on. A common pattern is to partially apply List.iter by giving it just the function, as in the following example from earlier in the chapter:
OCaml utop (part 43)

§ # String.split ~on:':'path

§ |> List.dedup

§ |> List.iter ~f:print_endline

§ ;;

§ /bin

§ /sbin

§ /usr/bin

§ /usr/local/bin

- : unit = ()

This requires that we put the function argument first. In other cases, you want to put the function argument second. One common reason is readability. In particular, a multiline function passed as an argument to another function is easiest to read when it is the final argument to that function.

Higher-order functions and labels

One surprising gotcha with labeled arguments is that while order doesn’t matter when calling a function with labeled arguments, it does matter in a higher-order context, e.g., when passing a function with labeled arguments to another function. Here’s an example:

OCaml utop (part 44)

# letapply_to_tuplef (first,second) = f ~first ~second;;

val apply_to_tuple : (first:'a -> second:'b -> 'c) -> 'a * 'b -> 'c = <fun>

Here, the definition of apply_to_tuple sets up the expectation that its first argument is a function with two labeled arguments, first and second, listed in that order. We could have defined apply_to_tuple differently to change the order in which the labeled arguments were listed:

OCaml utop (part 45)

# letapply_to_tuple_2f (first,second) = f ~second ~first;;

val apply_to_tuple_2 : (second:'a -> first:'b -> 'c) -> 'b * 'a -> 'c = <fun>

It turns out this order matters. In particular, if we define a function that has a different order

OCaml utop (part 46)

# letdivide ~first ~second = first / second;;

val divide : first:int -> second:int -> int = <fun>

we’ll find that it can’t be passed in to apply_to_tuple_2.

OCaml utop (part 47)

# apply_to_tuple_2divide (3,4);;

Characters 17-23:

Error: This expression has type first:int -> second:int -> int

but an expression was expected of type second:'a -> first:'b -> 'c

But, it works smoothly with the original apply_to_tuple:

OCaml utop (part 48)

# letapply_to_tuplef (first,second) = f ~first ~second;;

val apply_to_tuple : (first:'a -> second:'b -> 'c) -> 'a * 'b -> 'c = <fun>

# apply_to_tupledivide (3,4);;

- : int = 0

As a result, when passing labeled functions as arguments, you need to take care to be consistent in your ordering of labeled arguments.

Optional Arguments

An optional argument is like a labeled argument that the caller can choose whether or not to provide. Optional arguments are passed in using the same syntax as labeled arguments, and, like labeled arguments, can be provided in any order.

Here’s an example of a string concatenation function with an optional separator. This function uses the ^ operator for pairwise string concatenation:

OCaml utop (part 49)

# letconcat ?sepxy =

letsep = matchsepwithNone -> "" | Somex -> xin

x ^ sep ^ y


val concat : ?sep:string -> string -> string -> string = <fun>

# concat"foo""bar" (* without the optional argument *);;

- : string = "foobar"

# concat ~sep:":""foo""bar" (* with the optional argument *);;

- : string = "foo:bar"

Here, ? is used in the definition of the function to mark sep as optional. And while the caller can pass a value of type string for sep, internally to the function, sep is seen as a string option, with None appearing when sep is not provided by the caller.

The preceding example needed a bit of boilerplate to choose a default separator when none was provided. This is a common enough pattern that there’s an explicit syntax for providing a default value, which allows us to write concat more concisely:

OCaml utop (part 50)

# letconcat ?(sep="") xy = x ^ sep ^ y ;;

val concat : ?sep:string -> string -> string -> string = <fun>

Optional arguments are very useful, but they’re also easy to abuse. The key advantage of optional arguments is that they let you write functions with multiple arguments that users can ignore most of the time, only worrying about them when they specifically want to invoke those options. They also allow you to extend an API with new functionality without changing existing code.

The downside is that the caller may be unaware that there is a choice to be made, and so may unknowingly (and wrongly) pick the default behavior. Optional arguments really only make sense when the extra concision of omitting the argument outweighs the corresponding loss of explicitness.

This means that rarely used functions should not have optional arguments. A good rule of thumb is to avoid optional arguments for functions internal to a module, i.e., functions that are not included in the module’s interface, or mli file. We’ll learn more about mlis in Chapter 4.

Explicit passing of an optional argument

Under the covers, a function with an optional argument receives None when the caller doesn’t provide the argument, and Some when it does. But the Some and None are normally not explicitly passed in by the caller.

But sometimes, passing in Some or None explicitly is exactly what you want. OCaml lets you do this by using ? instead of ~ to mark the argument. Thus, the following two lines are equivalent ways of specifying the sep argument to concat:

OCaml utop (part 51)

# concat ~sep:":""foo""bar"(* provide the optional argument *);;

- : string = "foo:bar"

# concat ?sep:(Some":") "foo""bar"(* pass an explicit [Some] *);;

- : string = "foo:bar"

And the following two lines are equivalent ways of calling concat without specifying sep:

OCaml utop (part 52)

# concat"foo""bar"(* don't provide the optional argument *);;

- : string = "foobar"

# concat ?sep:None"foo""bar"(* explicitly pass `None` *);;

- : string = "foobar"

One use case for this is when you want to define a wrapper function that mimics the optional arguments of the function it’s wrapping. For example, imagine we wanted to create a function called uppercase_concat, which is the same as concat except that it converts the first string that it’s passed to uppercase. We could write the function as follows:

OCaml utop (part 53)

# letuppercase_concat ?(sep="") ab = concat ~sep (String.uppercasea) b ;;

val uppercase_concat : ?sep:string -> string -> string -> string = <fun>

# uppercase_concat"foo""bar";;

- : string = "FOObar"

# uppercase_concat"foo""bar" ~sep:":";;

- : string = "FOO:bar"

In the way we’ve written it, we’ve been forced to separately make the decision as to what the default separator is. Thus, if we later change concat’s default behavior, we’ll need to remember to change uppercase_concat to match it.

Instead, we can have uppercase_concat simply pass through the optional argument to concat using the ? syntax:

OCaml utop (part 54)

# letuppercase_concat ?sepab = concat ?sep (String.uppercasea) b ;;

val uppercase_concat : ?sep:string -> string -> string -> string = <fun>

Now, if someone calls uppercase_concat without an argument, an explicit None will be passed to concat, leaving concat to decide what the default behavior should be.

Inference of labeled and optional arguments

One subtle aspect of labeled and optional arguments is how they are inferred by the type system. Consider the following example for computing numerical derivatives of a function of two real variables. The function takes an argument delta, which determines the scale at which to compute the derivative; values x and y, which determine at which point to compute the derivative; and the function f, whose derivative is being computed. The function f itself takes two labeled arguments, x and y. Note that you can use an apostrophe as part of a variable name, so x' and y' are just ordinary variables:

OCaml utop (part 55)

# letnumeric_deriv ~delta ~x ~y ~f =

letx' = x +. deltain

lety' = y +. deltain

letbase = f ~x ~yin

letdx = (f ~x:x' ~y -. base) /. deltain

letdy = (f ~x ~y:y' -. base) /. deltain



val numeric_deriv :

delta:float ->

x:float -> y:float -> f:(x:float -> y:float -> float) -> float * float =


In principle, it’s not obvious how the order of the arguments to f should be chosen. Since labeled arguments can be passed in arbitrary order, it seems like it could as well be y:float -> x:float -> float as it is x:float -> y:float -> float.

Even worse, it would be perfectly consistent for f to take an optional argument instead of a labeled one, which could lead to this type signature for numeric_deriv:


val numeric_deriv :

delta:float ->

x:float -> y:float -> f:(?x:float -> y:float -> float) -> float * float

Since there are multiple plausible types to choose from, OCaml needs some heuristic for choosing between them. The heuristic the compiler uses is to prefer labels to options and to choose the order of arguments that shows up in the source code.

Note that these heuristics might at different points in the source suggest different types. Here’s a version of numeric_deriv where different invocations of f list the arguments in different orders:

OCaml utop (part 56)

# letnumeric_deriv ~delta ~x ~y ~f =

letx' = x +. deltain

lety' = y +. deltain

letbase = f ~x ~yin

letdx = (f ~y ~x:x' -. base) /. deltain

letdy = (f ~x ~y:y' -. base) /. deltain



Characters 130-131:

Error: This function is applied to arguments

in an order different from other calls.

This is only allowed when the real type is known.

As suggested by the error message, we can get OCaml to accept the fact that f is used with different argument orders if we provide explicit type information. Thus, the following code compiles without error, due to the type annotation on f:

OCaml utop (part 57)

# letnumeric_deriv ~delta ~x ~y ~(f: x:float -> y:float -> float) =

letx' = x +. deltain

lety' = y +. deltain

letbase = f ~x ~yin

letdx = (f ~y ~x:x' -. base) /. deltain

letdy = (f ~x ~y:y' -. base) /. deltain



val numeric_deriv :

delta:float ->

x:float -> y:float -> f:(x:float -> y:float -> float) -> float * float =


Optional arguments and partial application

Optional arguments can be tricky to think about in the presence of partial application. We can of course partially apply the optional argument itself:

OCaml utop (part 58)

# letcolon_concat = concat ~sep:":";;

val colon_concat : string -> string -> string = <fun>

# colon_concat"a""b";;

- : string = "a:b"

But what happens if we partially apply just the first argument?

OCaml utop (part 59)

# letprepend_pound = concat"# ";;

val prepend_pound : string -> string = <fun>

# prepend_pound"a BASH comment";;

- : string = "# a BASH comment"

The optional argument ?sep has now disappeared, or been erased. Indeed, if we try to pass in that optional argument now, it will be rejected:

OCaml utop (part 60)

# prepend_pound"a BASH comment" ~sep:":";;

Characters -1-13:

Error: This function has type string -> string

It is applied to too many arguments; maybe you forgot a `;'.

So when does OCaml decide to erase an optional argument?

The rule is: an optional argument is erased as soon as the first positional (i.e., neither labeled nor optional) argument defined after the optional argument is passed in. That explains the behavior of prepend_pound. But if we had instead defined concat with the optional argument in the second position:

OCaml utop (part 61)

# letconcatx ?(sep="") y = x ^ sep ^ y ;;

val concat : string -> ?sep:string -> string -> string = <fun>

then application of the first argument would not cause the optional argument to be erased.

OCaml utop (part 62)

# letprepend_pound = concat"# ";;

val prepend_pound : ?sep:string -> string -> string = <fun>

# prepend_pound"a BASH comment";;

- : string = "# a BASH comment"

# prepend_pound"a BASH comment" ~sep:"--- ";;

- : string = "# --- a BASH comment"

However, if all arguments to a function are presented at once, then erasure of optional arguments isn’t applied until all of the arguments are passed in. This preserves our ability to pass in optional arguments anywhere on the argument list. Thus, we can write:

OCaml utop (part 63)

# concat"a""b" ~sep:"=";;

- : string = "a=b"

An optional argument that doesn’t have any following positional arguments can’t be erased at all, which leads to a compiler warning:

OCaml utop (part 64)

# letconcatxy ?(sep="") = x ^ sep ^ y ;;

Characters 15-38:

Warning 16: this optional argument cannot be erased.

val concat : string -> string -> ?sep:string -> string = <fun>

And indeed, when we provide the two positional arguments, the sep argument is not erased, instead returning a function that expects the sep argument to be provided:

OCaml utop (part 65)

# concat"a""b";;

- : ?sep:string -> string = <fun>

As you can see, OCaml’s support for labeled and optional arguments is not without its complexities. But don’t let these complexities obscure the usefulness of these features. Labels and optional arguments are very effective tools for making your APIs both more convenient and safer, and it’s worth the effort of learning how to use them effectively.