A Guided Tour - Language Concepts - Real World OCaml (2013)

Real World OCaml (2013)

Part I. Language Concepts

Part I covers the basic language concepts you’ll need to know when building OCaml programs. It opens up with a guided tour to give you a quick overview of the language using an interactive command-line interface. The subsequent chapters cover the material that is touched upon by the tour in much more detail, including detailed coverage of OCaml’s approach to imperative programming.

The last few chapters introduce OCaml’s powerful abstraction facilities. We start by using functors to build a library for programming with intervals, and then use first-class modules to build a type-safe plugin system. OCaml also supports object-oriented programming, and we close Part I with two chapters that cover the object system; the first showing how to use OCaml’s objects directly, and the second showing how to use the class system to add more advanced features like inheritance. This description comes together in the design of a simple object-oriented graphics library.

Chapter 1. A Guided Tour

This chapter gives an overview of OCaml by walking through a series of small examples that cover most of the major features of the language. This should provide a sense of what OCaml can do, without getting too deep into any one topic.

Throughout the book we’re going to use Core, a more full-featured and capable replacement for OCaml’s standard library. We’ll also use utop, a shell that lets you type in expressions and evaluate them interactively. utop is an easier-to-use version of OCaml’s standard toplevel (which you can start by typing ocaml at the command line). These instructions will assume you’re using utop specifically.

Before getting started, make sure you have a working OCaml installation so you can try out the examples as you read through the chapter.

OCaml as a Calculator

The first thing you need to do when using Core is to open Core.Std:

OCaml utop

$ utop

# openCore.Std;;

This makes the definitions in Core available and is required for many of the examples in the tour and in the remainder of the book.

Now let’s try a few simple numerical calculations:

OCaml utop (part 1)

# 3 + 4;;

- : int = 7

# 8 / 3;;

- : int = 2

# 3.5 +. 6.;;

- : float = 9.5

# 30_000_000 / 300_000;;

- : int = 100

# sqrt9.;;

- : float = 3.

By and large, this is pretty similar to what you’d find in any programming language, but a few things jump right out at you:

§ We needed to type ;; in order to tell the toplevel that it should evaluate an expression. This is a peculiarity of the toplevel that is not required in standalone programs (though it is sometimes helpful to include ;; to improve OCaml’s error reporting, by making it more explicit where a given top-level declaration was intended to end).

§ After evaluating an expression, the toplevel first prints the type of the result, and then prints the result itself.

§ Function arguments are separated by spaces instead of by parentheses and commas, which is more like the UNIX shell than it is like traditional programming languages such as C or Java.

§ OCaml allows you to place underscores in the middle of numeric literals to improve readability. Note that underscores can be placed anywhere within a number, not just every three digits.

§ OCaml carefully distinguishes between float, the type for floating-point numbers, and int, the type for integers. The types have different literals (6. instead of 6) and different infix operators (+. instead of +), and OCaml doesn’t automatically cast between these types. This can be a bit of a nuisance, but it has its benefits, since it prevents some kinds of bugs that arise in other languages due to unexpected differences between the behavior of int and float. For example, in many languages, 1 / 3 is zero, but 1 / 3.0 is a third. OCaml requires you to be explicit about which operation you’re doing.

We can also create a variable to name the value of a given expression, using the let keyword. This is known as a let binding:

OCaml utop (part 2)

# letx = 3 + 4;;

val x : int = 7

# lety = x + x;;

val y : int = 14

After a new variable is created, the toplevel tells us the name of the variable (x or y), in addition to its type (int) and value (7 or 14).

Note that there are some constraints on what identifiers can be used for variable names. Punctuation is excluded, except for _ and ', and variables must start with a lowercase letter or an underscore. Thus, these are legal:

OCaml utop (part 3)

# letx7 = 3 + 4;;

val x7 : int = 7

# letx_plus_y = x + y;;

val x_plus_y : int = 21

# letx' = x + 1;;

val x' : int = 8

# let _x' = x' + x';;

# _x';;

- : int = 16

Note that by default, utop doesn’t bother to print out variables starting with an underscore.

The following examples, however, are not legal:

OCaml utop (part 4)

# letSeven = 3 + 4;;

Characters 4-9:

Error: Unbound constructor Seven

# let7x = 7;;

Characters 5-10:

Error: This expression should not be a function, the expected type is


# letx-plus-y = x + y;;

Characters 4-5:

Error: Parse error: [fun_binding] expected after [ipatt] (in [let_binding])

The error messages here are a little confusing, but they’ll make more sense as you learn more about the language.

Functions and Type Inference

The let syntax can also be used to define a function:

OCaml utop (part 5)

# letsquarex = x * x ;;

val square : int -> int = <fun>

# square2;;

- : int = 4

# square (square2);;

- : int = 16

Functions in OCaml are values like any other, which is why we use the let keyword to bind a function to a variable name, just as we use let to bind a simple value like an integer to a variable name. When using let to define a function, the first identifier after the let is the function name, and each subsequent identifier is a different argument to the function. Thus, square is a function with a single argument.

Now that we’re creating more interesting values like functions, the types have gotten more interesting too. int -> int is a function type, in this case indicating a function that takes an int and returns an int. We can also write functions that take multiple arguments. (Note that the following example will not work if you haven’t opened Core.Std as was suggested earlier.)

OCaml utop (part 6)

# letratioxy =

Float.of_intx /. Float.of_inty


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

# ratio47;;

- : float = 0.571428571429

The preceding example also happens to be our first use of modules. Here, Float.of_int refers to the of_int function contained in the Float module. This is different from what you might expect from an object-oriented language, where dot-notation is typically used for accessing a method of an object. Note that module names always start with a capital letter.

The notation for the type-signature of a multiargument function may be a little surprising at first, but we’ll explain where it comes from when we get to function currying in Multiargument functions. For the moment, think of the arrows as separating different arguments of the function, with the type after the final arrow being the return value. Thus, int -> int -> float describes a function that takes two int arguments and returns a float.

We can also write functions that take other functions as arguments. Here’s an example of a function that takes three arguments: a test function and two integer arguments. The function returns the sum of the integers that pass the test:

OCaml utop (part 7)

# letsum_if_truetestfirstsecond =


+ (iftestsecondthensecondelse0)


val sum_if_true : (int -> bool) -> int -> int -> int = <fun>

If we look at the inferred type signature in detail, we see that the first argument is a function that takes an integer and returns a boolean, and that the remaining two arguments are integers. Here’s an example of this function in action:

OCaml utop (part 8)

# letevenx =

x mod 2 = 0 ;;

val even : int -> bool = <fun>

# sum_if_trueeven34;;

- : int = 4

# sum_if_trueeven24;;

- : int = 6

Note that in the definition of even, we used = in two different ways: once as the part of the let binding that separates the thing being defined from its definition; and once as an equality test, when comparing x mod 2 to 0. These are very different operations despite the fact that they share some syntax.

Type Inference

As the types we encounter get more complicated, you might ask yourself how OCaml is able to figure them out, given that we didn’t write down any explicit type information.

OCaml determines the type of an expression using a technique called type inference, by which the type of an expression is inferred from the available type information about the components of that expression.

As an example, let’s walk through the process of inferring the type of sum_if_true:

1. OCaml requires that both branches of an if statement have the same type, so the expression if test first then first else 0 requires that first must be the same type as 0, and so first must be of type int. Similarly, from if test second then second else 0 we can infer that secondhas type int.

2. test is passed first as an argument. Since first has type int, the input type of test must be int.

3. test first is used as the condition in an if statement, so the return type of test must be bool.

4. The fact that + returns int implies that the return value of sum_if_true must be int.

Together, that nails down the types of all the variables, which determines the overall type of sum_if_true.

Over time, you’ll build a rough intuition for how the OCaml inference engine works, which makes it easier to reason through your programs. You can make it easier to understand the types of a given expression by adding explicit type annotations. These annotations don’t change the behavior of an OCaml program, but they can serve as useful documentation, as well as catch unintended type changes. They can also be helpful in figuring out why a given piece of code fails to compile.

Here’s an annotated version of sum_if_true:

OCaml utop (part 9)

# letsum_if_true (test : int -> bool) (x : int) (y : int) : int =


+ (iftestythenyelse0)


val sum_if_true : (int -> bool) -> int -> int -> int = <fun>

In the above, we’ve marked every argument to the function with its type, with the final annotation indicating the type of the return value. Such type annotations can be placed on any expression in an OCaml program:

Inferring Generic Types

Sometimes, there isn’t enough information to fully determine the concrete type of a given value. Consider this function.

OCaml utop (part 10)

# letfirst_if_truetestxy =



val first_if_true : ('a -> bool) -> 'a -> 'a -> 'a = <fun>

first_if_true takes as its arguments a function test, and two values, x and y, where x is to be returned if test x evaluates to true, and y otherwise. So what’s the type of first_if_true? There are no obvious clues such as arithmetic operators or literals to tell you what the type of x and y are. That makes it seem like one could use first_if_true on values of any type.

Indeed, if we look at the type returned by the toplevel, we see that rather than choose a single concrete type, OCaml has introduced a type variable 'a to express that the type is generic. (You can tell it’s a type variable by the leading single quote mark.) In particular, the type of the testargument is ('a -> bool), which means that test is a one-argument function whose return value is bool and whose argument could be of any type 'a. But, whatever type 'a is, it has to be the same as the type of the other two arguments, x and y, and of the return value of first_if_true. This kind of genericity is called parametric polymorphism because it works by parameterizing the type in question with a type variable. It is very similar to generics in C# and Java.

The generic type of first_if_true allows us to write this:

OCaml utop (part 11)

# letlong_strings = String.lengths > 6;;

val long_string : string -> bool = <fun>

# first_if_truelong_string"short""loooooong";;

- : string = "loooooong"

As well as this:

OCaml utop (part 12)

# letbig_numberx = x > 3;;

val big_number : int -> bool = <fun>

# first_if_truebig_number43;;

- : int = 4

Both long_string and big_number are functions, and each is passed to first_if_true with two other arguments of the appropriate type (strings in the first example, and integers in the second). But we can’t mix and match two different concrete types for 'a in the same use of first_if_true:

OCaml utop (part 13)

# first_if_truebig_number"short""loooooong";;

Characters 25-32:

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


In this example, big_number requires that 'a be instantiated as int, whereas "short" and "loooooong" require that 'a be instantiated as string, and they can’t both be right at the same time.


There’s a big difference in OCaml (and really in any compiled language) between errors that are caught at compile time and those that are caught at runtime. It’s better to catch errors as early as possible in the development process, and compilation time is best of all.

Working in the toplevel somewhat obscures the difference between runtime and compile-time errors, but that difference is still there. Generally, type errors like this one:

OCaml utop (part 14)

# letadd_potatox =

x + "potato";;

Characters 28-36:

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


are compile-time errors (because + requires that both its arguments be of type int), whereas errors that can’t be caught by the type system, like division by zero, lead to runtime exceptions:

OCaml utop (part 15)

# letis_a_multiplexy =

x mod y = 0 ;;

val is_a_multiple : int -> int -> bool = <fun>

# is_a_multiple82;;

- : bool = true

# is_a_multiple80;;

Exception: Division_by_zero.

The distinction here is that type errors will stop you whether or not the offending code is ever actually executed. Merely defining add_potato is an error, whereas is_a_multiple only fails when it’s called, and then, only when it’s called with an input that triggers the exception.

Tuples, Lists, Options, and Pattern Matching


So far we’ve encountered a handful of basic types like int, float, and string, as well as function types like string -> int. But we haven’t yet talked about any data structures. We’ll start by looking at a particularly simple data structure, the tuple. A tuple is an ordered collection of values that can each be of a different type. You can create a tuple by joining values together with a comma:

OCaml utop (part 16)

# leta_tuple = (3,"three");;

val a_tuple : int * string = (3, "three")

# letanother_tuple = (3,"four",5.);;

val another_tuple : int * string * float = (3, "four", 5.)

(For the mathematically inclined, the * character is used because the set of all pairs of type t * s corresponds to the Cartesian product of the set of elements of type t and the set of elements of type s.)

You can extract the components of a tuple using OCaml’s pattern-matching syntax, as shown below:

OCaml utop (part 17)

# let (x,y) = a_tuple;;

val x : int = 3

val y : string = "three"

Here, the (x,y) on the lefthand side of the let binding is the pattern. This pattern lets us mint the new variables x and y, each bound to different components of the value being matched. These can now be used in subsequent expressions:

OCaml utop (part 18)

# x + String.lengthy;;

- : int = 8

Note that the same syntax is used both for constructing and for pattern matching on tuples.

Pattern matching can also show up in function arguments. Here’s a function for computing the distance between two points on the plane, where each point is represented as a pair of floats. The pattern-matching syntax lets us get at the values we need with a minimum of fuss:

OCaml utop (part 19)

# letdistance (x1,y1) (x2,y2) =

sqrt ((x1 -. x2) ** 2. +. (y1 -. y2) ** 2.)


val distance : float * float -> float * float -> float = <fun>

The ** operator used above is for raising a floating-point number to a power.

This is just a first taste of pattern matching. Pattern matching is a pervasive tool in OCaml, and as you’ll see, it has surprising power.


Where tuples let you combine a fixed number of items, potentially of different types, lists let you hold any number of items of the same type. Consider the following example:

OCaml utop (part 20)

# letlanguages = ["OCaml";"Perl";"C"];;

val languages : string list = ["OCaml"; "Perl"; "C"]

Note that you can’t mix elements of different types in the same list, unlike tuples:

OCaml utop (part 21)

# letnumbers = [3;"four";5];;

Characters 17-23:

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


The List module

Core comes with a List module that has a rich collection of functions for working with lists. We can access values from within a module by using dot notation. For example, this is how we compute the length of a list:

OCaml utop (part 22)

# List.lengthlanguages;;

- : int = 3

Here’s something a little more complicated. We can compute the list of the lengths of each language as follows:

OCaml utop (part 23)

# List.maplanguages ~f:String.length;;

- : int list = [5; 4; 1]

List.map takes two arguments: a list and a function for transforming the elements of that list. It returns a new list with the transformed elements and does not modify the original list.

Notably, the function passed to List.map is passed under a labeled argument ~f. Labeled arguments are specified by name rather than by position, and thus allow you to change the order in which arguments are presented to a function without changing its behavior, as you can see here:

OCaml utop (part 24)

# List.map ~f:String.lengthlanguages;;

- : int list = [5; 4; 1]

We’ll learn more about labeled arguments and why they’re important in Chapter 2.

Constructing lists with ::

In addition to constructing lists using brackets, we can use the operator :: for adding elements to the front of a list:

OCaml utop (part 25)

# "French" :: "Spanish" :: languages;;

- : string list = ["French"; "Spanish"; "OCaml"; "Perl"; "C"]

Here, we’re creating a new and extended list, not changing the list we started with, as you can see below:

OCaml utop (part 26)

# languages;;

- : string list = ["OCaml"; "Perl"; "C"]


Unlike many other languages, OCaml uses semicolons to separate list elements in lists rather than commas. Commas, instead, are used for separating elements in a tuple. If you try to use commas in a list, you’ll see that your code compiles but doesn’t do quite what you might expect:

OCaml utop (part 27)

# ["OCaml", "Perl", "C"];;

- : (string * string * string) list = [("OCaml", "Perl", "C")]

In particular, rather than a list of three strings, what we have is a singleton list containing a three-tuple of strings.

This example uncovers the fact that commas create a tuple, even if there are no surrounding parens. So, we can write:

OCaml utop (part 28)

# 1,2,3;;

- : int * int * int = (1, 2, 3)

to allocate a tuple of integers. This is generally considered poor style and should be avoided.

The bracket notation for lists is really just syntactic sugar for ::. Thus, the following declarations are all equivalent. Note that [] is used to represent the empty list and that :: is right-associative:

OCaml utop (part 29)

# [1; 2; 3];;

- : int list = [1; 2; 3]

# 1 :: (2 :: (3 :: []));;

- : int list = [1; 2; 3]

# 1 :: 2 :: 3 :: [];;

- : int list = [1; 2; 3]

The :: operator can only be used for adding one element to the front of the list, with the list terminating at [], the empty list. There’s also a list concatenation operator, @, which can concatenate two lists:

OCaml utop (part 30)

# [1;2;3] @ [4;5;6];;

- : int list = [1; 2; 3; 4; 5; 6]

It’s important to remember that, unlike ::, this is not a constant-time operation. Concatenating two lists takes time proportional to the length of the first list.

List patterns using match

The elements of a list can be accessed through pattern matching. List patterns are based on the two list constructors, [] and ::. Here’s a simple example:

OCaml utop (part 31)

# letmy_favorite_language (my_favorite :: the_rest) =



Characters 25-69:

Warning 8: this pattern-matching is not exhaustive.

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


val my_favorite_language : 'a list -> 'a = <fun>

By pattern matching using ::, we’ve isolated and named the first element of the list (my_favorite) and the remainder of the list (the_rest). If you know Lisp or Scheme, what we’ve done is the equivalent of using the functions car and cdr to isolate the first element of a list and the remainder of that list.

As you can see, however, the toplevel did not like this definition and spit out a warning indicating that the pattern is not exhaustive. This means that there are values of the type in question that won’t be captured by the pattern. The warning even gives an example of a value that doesn’t match the provided pattern, in particular, [], the empty list. If we try to run my_favorite_language, we’ll see that it works on nonempty list and fails on empty ones:

OCaml utop (part 32)

# my_favorite_language ["English";"Spanish";"French"];;

- : string = "English"

# my_favorite_language[];;

Exception: (Match_failure //toplevel// 0 25).

You can avoid these warnings, and more importantly make sure that your code actually handles all of the possible cases, by using a match statement instead.

A match statement is a kind of juiced-up version of the switch statement found in C and Java. It essentially lets you list a sequence of patterns, separated by pipe characters (|). (The one before the first case is optional.) The compiler then dispatches to the code following the first matching pattern. As we’ve already seen, the pattern can mint new variables that correspond to substructures of the value being matched.

Here’s a new version of my_favorite_language that uses match and doesn’t trigger a compiler warning:

OCaml utop (part 33)

# letmy_favorite_languagelanguages =


| first :: the_rest -> first

| [] -> "OCaml"(* A good default! *)


val my_favorite_language : string list -> string = <fun>

# my_favorite_language ["English";"Spanish";"French"];;

- : string = "English"

# my_favorite_language[];;

- : string = "OCaml"

The preceding code also includes our first comment. OCaml comments are bounded by (* and *) and can be nested arbitrarily and cover multiple lines. There’s no equivalent of C++-style single-line comments that are prefixed by //.

The first pattern, first :: the_rest, covers the case where languages has at least one element, since every list except for the empty list can be written down with one or more ::’s. The second pattern, [], matches only the empty list. These cases are exhaustive, since every list is either empty or has at least one element, a fact that is verified by the compiler.

Recursive list functions

Recursive functions, or functions that call themselves, are an important technique in OCaml and in any functional language. The typical approach to designing a recursive function is to separate the logic into a set of base cases that can be solved directly and a set of inductive cases, where the function breaks the problem down into smaller pieces and then calls itself to solve those smaller problems.

When writing recursive list functions, this separation between the base cases and the inductive cases is often done using pattern matching. Here’s a simple example of a function that sums the elements of a list:

OCaml utop (part 34)

# letrecsuml =


| [] -> 0 (* base case *)

| hd :: tl -> hd + sumtl (* inductive case *)


val sum : int list -> int = <fun>

# sum [1;2;3];;

- : int = 6

Following the common OCaml idiom, we use hd to refer to the head of the list and tl to refer to the tail. Note that we had to use the rec keyword to allow sum to refer to itself. As you might imagine, the base case and inductive case are different arms of the match.

Logically, you can think of the evaluation of a simple recursive function like sum almost as if it were a mathematical equation whose meaning you were unfolding step by step:

OCaml: guided-tour/recursion.ml

sum [1;2;3]

= 1 + sum [2;3]

= 1 + (2 + sum [3])

= 1 + (2 + (3 + sum []))

= 1 + (2 + (3 + 0))

= 1 + (2 + 3)

= 1 + 5

= 6

This suggests a reasonable mental model for what OCaml is actually doing to evaluate a recursive function.

We can introduce more complicated list patterns as well. Here’s a function for removing sequential duplicates:

OCaml utop (part 35)

# letrecdestutterlist =


| [] -> []

| hd1 :: hd2 :: tl ->

ifhd1 = hd2thendestutter (hd2 :: tl)

elsehd1 :: destutter (hd2 :: tl)


Characters 29-171:

Warning 8: this pattern-matching is not exhaustive.

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


val destutter : 'a list -> 'a list = <fun>

Again, the first arm of the match is the base case, and the second is the inductive. Unfortunately, this code has a problem, as is indicated by the warning message. In particular, we don’t handle one-element lists. We can fix this warning by adding another case to the match:

OCaml utop (part 36)

# letrecdestutterlist =


| [] -> []

| [hd] -> [hd]

| hd1 :: hd2 :: tl ->

ifhd1 = hd2thendestutter (hd2 :: tl)

elsehd1 :: destutter (hd2 :: tl)


val destutter : 'a list -> 'a list = <fun>

# destutter ["hey";"hey";"hey";"man!"];;

- : string list = ["hey"; "man!"]

Note that this code used another variant of the list pattern, [hd], to match a list with a single element. We can do this to match a list with any fixed number of elements; for example, [x;y;z] will match any list with exactly three elements and will bind those elements to the variables x, y, and z.

In the last few examples, our list processing code involved a lot of recursive functions. In practice, this isn’t usually necessary. Most of the time, you’ll find yourself happy to use the iteration functions found in the List module. But it’s good to know how to use recursion when you need to do something new.


Another common data structure in OCaml is the option. An option is used to express that a value might or might not be present. For example:

OCaml utop (part 37)

# letdividexy =

ify = 0thenNoneelseSome (x/y) ;;

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

The function divide either returns None if the divisor is zero, or Some of the result of the division otherwise. Some and None are constructors that let you build optional values, just as :: and [] let you build lists. You can think of an option as a specialized list that can only have zero or one elements.

To examine the contents of an option, we use pattern matching, as we did with tuples and lists. Consider the following function for creating a log entry string given an optional time and a message. If no time is provided (i.e., if the time is None), the current time is computed and used in its place:

OCaml utop (part 38)

# letlog_entrymaybe_timemessage =

lettime =


| Somex -> x

| None -> Time.now()


Time.to_sec_stringtime ^ " -- " ^ message


val log_entry : Time.t option -> string -> string = <fun>

# log_entry (SomeTime.epoch) "A long long time ago";;

- : string = "1970-01-01 01:00:00 -- A long long time ago"

# log_entryNone"Up to the minute";;

- : string = "2013-08-18 14:48:08 -- Up to the minute"

This example uses Core’s Time module for dealing with time, as well as the ^ operator for concatenating strings. The concatenation operator is provided as part of the Pervasives module, which is automatically opened in every OCaml program.


log_entry was our first use of let to define a new variable within the body of a function. A let paired with an in can be used to introduce a new binding within any local scope, including a function body. The in marks the beginning of the scope within which the new variable can be used. Thus, we could write:

OCaml utop

# letx = 7in

x + x


- : int = 14

Note that the scope of the let binding is terminated by the double-semicolon, so the value of x is no longer available:

OCaml utop (part 1)

# x;;

Characters -1-1:

Error: Unbound value x

We can also have multiple let statements in a row, each one adding a new variable binding to what came before:

OCaml utop (part 2)

# letx = 7in

lety = x * xin

x + y


- : int = 56

This kind of nested let binding is a common way of building up a complex expression, with each let naming some component, before combining them in one final expression.

Options are important because they are the standard way in OCaml to encode a value that might not be there; there’s no such thing as a NullPointerException in OCaml. This is different from most other languages, including Java and C#, where most if not all data types are nullable, meaning that, whatever their type is, any given value also contains the possibility of being a null value. In such languages, null is lurking everywhere.

In OCaml, however, missing values are explicit. A value of type string * string always contains two well-defined values of type string. If you want to allow, say, the first of those to be absent, then you need to change the type to string option * string. As we’ll see in Chapter 7, this explicitness allows the compiler to provide a great deal of help in making sure you’re correctly handling the possibility of missing data.

Records and Variants

So far, we’ve only looked at data structures that were predefined in the language, like lists and tuples. But OCaml also allows us to define new data types. Here’s a toy example of a data type representing a point in two-dimensional space:

OCaml utop (part 41)

# typepoint2d = { x : float; y : float };;

type point2d = { x : float; y : float; }

point2d is a record type, which you can think of as a tuple where the individual fields are named, rather than being defined positionally. Record types are easy enough to construct:

OCaml utop (part 42)

# letp = { x = 3.; y = -4. };;

val p : point2d = {x = 3.; y = -4.}

And we can get access to the contents of these types using pattern matching:

OCaml utop (part 43)

# letmagnitude { x = x_pos; y = y_pos } =

sqrt (x_pos ** 2. +. y_pos ** 2.);;

val magnitude : point2d -> float = <fun>

The pattern match here binds the variable x_pos to the value contained in the x field, and the variable y_pos to the value in the y field.

We can write this more tersely using what’s called field punning. In particular, when the name of the field and the name of the variable it is bound to coincide, we don’t have to write them both down. Using this, our magnitude function can be rewritten as follows:

OCaml utop (part 44)

# letmagnitude { x; y } = sqrt (x ** 2. +. y ** 2.);;

val magnitude : point2d -> float = <fun>

Alternatively, we can use dot notation for accessing record fields:

OCaml utop (part 45)

# letdistancev1v2 =

magnitude { x = v1.x -. v2.x; y = v1.y -. v2.y };;

val distance : point2d -> point2d -> float = <fun>

And we can of course include our newly defined types as components in larger types. Here, for example, are some types for modeling different geometric objects that contain values of type point2d:

OCaml utop (part 46)

# typecircle_desc = { center: point2d; radius: float }

typerect_desc = { lower_left: point2d; width: float; height: float }

typesegment_desc = { endpoint1: point2d; endpoint2: point2d } ;;

type circle_desc = { center : point2d; radius : float; }

type rect_desc = { lower_left : point2d; width : float; height : float; }

type segment_desc = { endpoint1 : point2d; endpoint2 : point2d; }

Now, imagine that you want to combine multiple objects of these types together as a description of a multiobject scene. You need some unified way of representing these objects together in a single type. One way of doing this is using a variant type:

OCaml utop (part 47)

# typescene_element =

| Circle ofcircle_desc

| Rect ofrect_desc

| Segmentofsegment_desc


type scene_element =

Circle of circle_desc

| Rect of rect_desc

| Segment of segment_desc

The | character separates the different cases of the variant (the first | is optional), and each case has a capitalized tag, like Circle, Rect or Segment, to distinguish that case from the others.

Here’s how we might write a function for testing whether a point is in the interior of some element of a list of scene_elements:

OCaml utop (part 48)

# letis_inside_scene_elementpointscene_element =


| Circle { center; radius } ->

distancecenterpoint < radius

| Rect { lower_left; width; height } ->

point.x > lower_left.x && point.x < lower_left.x +. width

&& point.y > lower_left.y && point.y < lower_left.y +. height

| Segment { endpoint1; endpoint2 } -> false


val is_inside_scene_element : point2d -> scene_element -> bool = <fun>

# letis_inside_scenepointscene =


~f:(funel -> is_inside_scene_elementpointel)


val is_inside_scene : point2d -> scene_element list -> bool = <fun>

# is_inside_scene {x=3.;y=7.}

[ Circle {center = {x=4.;y= 4.}; radius = 0.5 } ];;

- : bool = false

# is_inside_scene {x=3.;y=7.}

[ Circle {center = {x=4.;y= 4.}; radius = 5.0 } ];;

- : bool = true

You might at this point notice that the use of match here is reminiscent of how we used match with option and list. This is no accident: option and list are really just examples of variant types that happen to be important enough to be defined in the standard library (and in the case of lists, to have some special syntax).

We also made our first use of an anonymous function in the call to List.exists. Anonymous functions are declared using the fun keyword, and don’t need to be explicitly named. Such functions are common in OCaml, particularly when using iteration functions like List.exists.

The purpose of List.exists is to check if there are any elements of the list in question on which the provided function evaluates to true. In this case, we’re using List.exists to check if there is a scene element within which our point resides.

Imperative Programming

The code we’ve written so far has been almost entirely pure or functional, which roughly speaking means that the code in question doesn’t modify variables or values as part of its execution. Indeed, almost all of the data structures we’ve encountered are immutable, meaning there’s no way in the language to modify them at all. This is a quite different style from imperative programming, where computations are structured as sequences of instructions that operate by making modifications to the state of the program.

Functional code is the default in OCaml, with variable bindings and most data structures being immutable. But OCaml also has excellent support for imperative programming, including mutable data structures like arrays and hash tables, and control-flow constructs like for and while loops.


Perhaps the simplest mutable data structure in OCaml is the array. Arrays in OCaml are very similar to arrays in other languages like C: indexing starts at 0, and accessing or modifying an array element is a constant-time operation. Arrays are more compact in terms of memory utilization than most other data structures in OCaml, including lists. Here’s an example:

OCaml utop (part 49)

# letnumbers = [| 1; 2; 3; 4 |];;

val numbers : int array = [|1; 2; 3; 4|]

# numbers.(2) <- 4;;

- : unit = ()

# numbers;;

- : int array = [|1; 2; 4; 4|]

The .(i) syntax is used to refer to an element of an array, and the <- syntax is for modification. Because the elements of the array are counted starting at zero, element .(2) is the third element.

The unit type that we see in the preceding code is interesting in that it has only one possible value, written (). This means that a value of type unit doesn’t convey any information, and so is generally used as a placeholder. Thus, we use unit for the return value of an operation like setting a mutable field that communicates by side effect rather than by returning a value. It’s also used as the argument to functions that don’t require an input value. This is similar to the role that void plays in languages like C and Java.

Mutable Record Fields

The array is an important mutable data structure, but it’s not the only one. Records, which are immutable by default, can have some of their fields explicitly declared as mutable. Here’s a small example of a data structure for storing a running statistical summary of a collection of numbers.

OCaml utop (part 50)

# typerunning_sum =

{ mutablesum: float;

mutablesum_sq: float; (* sum of squares *)

mutablesamples: int;



type running_sum = {

mutable sum : float;

mutable sum_sq : float;

mutable samples : int;


The fields in running_sum are designed to be easy to extend incrementally, and sufficient to compute means and standard deviations, as shown in the following example. Note that there are two let bindings in a row without a double semicolon between them. That’s because the double semicolon is required only to tell utop to process the input, not to separate two declarations:

OCaml utop (part 51)

# letmeanrsum = rsum.sum /. floatrsum.samples

letstdevrsum =

sqrt (rsum.sum_sq /. floatrsum.samples

-. (rsum.sum /. floatrsum.samples) ** 2.) ;;

val mean : running_sum -> float = <fun>

val stdev : running_sum -> float = <fun>

We use the function float above, which is a convenient equivalent of Float.of_int provided by the Pervasives library.

We also need functions to create and update running_sums:

OCaml utop (part 52)

# letcreate() = { sum = 0.; sum_sq = 0.; samples = 0 }

letupdatersumx =

rsum.samples <- rsum.samples + 1;

rsum.sum <- rsum.sum +. x;

rsum.sum_sq <- rsum.sum_sq +. x *. x


val create : unit -> running_sum = <fun>

val update : running_sum -> float -> unit = <fun>

create returns a running_sum corresponding to the empty set, and update rsum x changes rsum to reflect the addition of x to its set of samples by updating the number of samples, the sum, and the sum of squares.

Note the use of single semicolons to sequence operations. When we were working purely functionally, this wasn’t necessary, but you start needing it when you’re writing imperative code.

Here’s an example of create and update in action. Note that this code uses List.iter, which calls the function ~f on each element of the provided list:

OCaml utop (part 53)

# letrsum = create();;

val rsum : running_sum = {sum = 0.; sum_sq = 0.; samples = 0}

# List.iter [1.;3.;2.;-7.;4.;5.] ~f:(funx -> updatersumx);;

- : unit = ()

# meanrsum;;

- : float = 1.33333333333

# stdevrsum;;

- : float = 3.94405318873

It’s worth noting that the preceding algorithm is numerically naive and has poor precision in the presence of cancellation. You can look at this Wikipedia article on algorithms for calculating variance for more details, paying particular attention to the weighted incremental and parallel algorithms.


We can create a single mutable value by using a ref. The ref type comes predefined in the standard library, but there’s nothing really special about it. It’s just a record type with a single mutable field called contents:

OCaml utop (part 54)

# letx = { contents = 0 };;

val x : int ref = {contents = 0}

# x.contents <- x.contents + 1;;

- : unit = ()

# x;;

- : int ref = {contents = 1}

There are a handful of useful functions and operators defined for refs to make them more convenient to work with:

OCaml utop (part 55)

# letx = ref0 (* create a ref, i.e., { contents = 0 } *) ;;

val x : int ref = {contents = 0}

# !x (* get the contents of a ref, i.e., x.contents *) ;;

- : int = 0

# x := !x + 1 (* assignment, i.e., x.contents <- ... *) ;;

- : unit = ()

# !x ;;

- : int = 1

There’s nothing magical with these operators either. You can completely reimplement the ref type and all of these operators in just a few lines of code:

OCaml utop (part 56)

# type'aref = { mutablecontents : 'a }

letrefx = { contents = x }

let (!) r = r.contents

let (:=) rx = r.contents <- x


type 'a ref = { mutable contents : 'a; }

val ref : 'a -> 'a ref = <fun>

val ( ! ) : 'a ref -> 'a = <fun>

val ( := ) : 'a ref -> 'a -> unit = <fun>

The 'a before the ref indicates that the ref type is polymorphic, in the same way that lists are polymorphic, meaning it can contain values of any type. The parentheses around ! and := are needed because these are operators, rather than ordinary functions.

Even though a ref is just another record type, it’s important because it is the standard way of simulating the traditional mutable variables you’ll find in most languages. For example, we can sum over the elements of a list imperatively by calling List.iter to call a simple function on every element of a list, using a ref to accumulate the results:

OCaml utop (part 57)

# letsumlist =

letsum = ref0in

List.iterlist ~f:(funx -> sum := !sum + x);



val sum : int list -> int = <fun>

This isn’t the most idiomatic way to sum up a list, but it shows how you can use a ref in place of a mutable variable.

For and While Loops

OCaml also supports traditional imperative control-flow constructs like for and while loops. Here, for example, is some code for permuting an array that uses a for loop. We use the Random module as our source of randomness. Random starts with a default seed, but you can callRandom.self_init to choose a new seed at random:

OCaml utop (part 58)

# letpermutearray =

letlength = Array.lengtharrayin

fori = 0tolength - 2do

(* pick a j to swap with *)

letj = i + Random.int (length - i) in

(* Swap i and j *)

lettmp = array.(i) in

array.(i) <- array.(j);

array.(j) <- tmp



val permute : 'a array -> unit = <fun>

From a syntactic perspective, you should note the keywords that distinguish a for loop: for, to, do, and done.

Here’s an example run of this code:

OCaml utop (part 59)

# letar = Array.init20 ~f:(funi -> i);;

val ar : int array =

[|0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19|]

# permutear;;

- : unit = ()

# ar;;

- : int array =

[|1; 2; 4; 6; 11; 7; 14; 9; 10; 0; 13; 16; 19; 12; 17; 5; 3; 18; 8; 15|]

OCaml also supports while loops, as shown in the following function for finding the position of the first negative entry in an array. Note that while (like for) is also a keyword:

OCaml utop (part 60)

# letfind_first_negative_entryarray =

letpos = ref0in

while !pos < Array.lengtharray && array.(!pos) >= 0do

pos := !pos + 1


if !pos = Array.lengtharraythenNoneelseSome !pos


val find_first_negative_entry : int array -> int option = <fun>

# find_first_negative_entry [|1;2;0;3|];;

- : int option = None

# find_first_negative_entry [|1;-2;0;3|];;

- : int option = Some 1

As a side note, the preceding code takes advantage of the fact that &&, OCaml’s And operator, short-circuits. In particular, in an expression of the form expr1 && expr2, expr2 will only be evaluated if expr1 evaluated to true. Were it not for that, then the preceding function would result in an out-of-bounds error. Indeed, we can trigger that out-of-bounds error by rewriting the function to avoid the short-circuiting:

OCaml utop (part 61)

# letfind_first_negative_entryarray =

letpos = ref0in


letpos_is_good = !pos < Array.lengtharrayin

letelement_is_non_negative = array.(!pos) >= 0in

pos_is_good && element_is_non_negative


pos := !pos + 1


if !pos = Array.lengtharraythenNoneelseSome !pos


val find_first_negative_entry : int array -> int option = <fun>

# find_first_negative_entry [|1;2;0;3|];;

Exception: (Invalid_argument "index out of bounds").

The Or operator, ||, short-circuits in a similar way to &&.

A Complete Program

So far, we’ve played with the basic features of the language via utop. Now we’ll show how to create a simple standalone program. In particular, we’ll create a program that sums up a list of numbers read in from the standard input.

Here’s the code, which you can save in a file called sum.ml. Note that we don’t terminate expressions with ;; here, since it’s not required outside the toplevel:



letrec read_and_accumulate accum =

let line = In_channel.input_line In_channel.stdin in

match line with

| None -> accum

| Some x -> read_and_accumulate (accum +. Float.of_string x)

let () =

printf "Total: %F\n" (read_and_accumulate 0.)

This is our first use of OCaml’s input and output routines. The function read_and_accumulate is a recursive function that uses In_channel.input_line to read in lines one by one from the standard input, invoking itself at each iteration with its updated accumulated sum. Note that input_linereturns an optional value, with None indicating the end of the input stream.

After read_and_accumulate returns, the total needs to be printed. This is done using the printf command, which provides support for type-safe format strings, similar to what you’ll find in a variety of languages. The format string is parsed by the compiler and used to determine the number and type of the remaining arguments that are required. In this case, there is a single formatting directive, %F, so printf expects one additional argument of type float.

Compiling and Running

We’ll compile our program using corebuild, a small wrapper on top of ocamlbuild, a build tool that ships with the OCaml compiler. The corebuild script is installed along with Core, and its purpose is to pass in the flags required for building a program with Core.


$ corebuild sum.native

The .native suffix indicates that we’re building a native-code executable, which we’ll discuss more in Chapter 4. Once the build completes, we can use the resulting program like any command-line utility. We can feed input to sum.native by typing in a sequence of numbers, one per line, hitting Ctrl-D when we’re done:


$ ./sum.native





Total: 100.5

More work is needed to make a really usable command-line program, including a proper command-line parsing interface and better error handling, all of which is covered in Chapter 14.

Where to Go from Here

That’s it for the guided tour! There are plenty of features left and lots of details to explain, but we hope that you now have a sense of what to expect from OCaml, and that you’ll be more comfortable reading the rest of the book as a result.