Paradigm  Multiparadigm: functional, imperative, modular,^{[1]} objectoriented 

Family  ML 
Designed by  Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez 
Developer  Inria 
First appeared  1996 
Stable release  
Typing discipline  Inferred, static, strong, structural 
Implementation language  OCaml, C 
Platform  IA32, x8664, Power, SPARC, ARM 3264 
OS  Crossplatform: Unix, macOS, Windows 
License  LGPLv2.1 
Filename extensions  .ml, .mli 
Website  ocaml 
Influenced by  
C, Caml, Modula3, Pascal, Standard ML  
Influenced  
ATS, Coq, Elm, F#, F*, Haxe, Opa, Rust, Scala  

OCaml (/oʊˈkæməl/ ohKAMəl, formerly Objective Caml) is a generalpurpose, multiparadigm programming language which extends the Caml dialect of ML with objectoriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez, and others.
The OCaml toolchain includes an interactive toplevel interpreter, a bytecode compiler, an optimizing native code compiler, a reversible debugger, and a package manager (OPAM). OCaml was initially developed in the context of automated theorem proving, and has an outsize presence in static analysis and formal methods software. Beyond these areas, it has found serious use in systems programming, web development, and financial engineering, among other application domains.
The acronym CAML originally stood for Categorical Abstract Machine Language, but OCaml omits this abstract machine.^{[3]} OCaml is a free and opensource software project managed and principally maintained by the French Institute for Research in Computer Science and Automation (Inria). In the early 2000s, elements from OCaml were adopted by many languages, notably F# and Scala.
MLderived languages are best known for their static type systems and typeinferring compilers. OCaml unifies functional, imperative, and objectoriented programming under an MLlike type system. Thus, programmers need not be highly familiar with the pure functional language paradigm to use OCaml.
By requiring the programmer to work within the constraints of its static type system, OCaml eliminates many of the typerelated runtime problems associated with dynamically typed languages. Also, OCaml's typeinferring compiler greatly reduces the need for the manual type annotations that are required in most statically typed languages. For example, the data types of variables and the signatures of functions usually need not be declared explicitly, as they do in languages like Java and C#, because they can be inferred from the operators and other functions that are applied to the variables and other values in the code. Effective use of OCaml's type system can require some sophistication on the part of a programmer, but this discipline is rewarded with reliable, highperformance software.
OCaml is perhaps most distinguished from other languages with origins in academia by its emphasis on performance. Its static type system prevents runtime type mismatches and thus obviates runtime type and safety checks that burden the performance of dynamically typed languages, while still guaranteeing runtime safety, except when array bounds checking is turned off or when some typeunsafe features like serialization are used. These are rare enough that avoiding them is quite possible in practice.
Aside from typechecking overhead, functional programming languages are, in general, challenging to compile to efficient machine language code, due to issues such as the funarg problem. Along with standard loop, register, and instruction optimizations, OCaml's optimizing compiler employs static program analysis methods to optimize value boxing and closure allocation, helping to maximize the performance of the resulting code even if it makes extensive use of functional programming constructs.
Xavier Leroy has stated that "OCaml delivers at least 50% of the performance of a decent C compiler",^{[4]} although a direct comparison is impossible. Some functions in the OCaml standard library are implemented with faster algorithms than equivalent functions in the standard libraries of other languages. For example, the implementation of set union in the OCaml standard library in theory is asymptotically faster than the equivalent function in the standard libraries of imperative languages (e.g., C++, Java) because the OCaml implementation exploits the immutability of sets to reuse parts of input sets in the output (see persistent data structure).
Between the 1970s and 1980s, Robin Milner, a British computer scientist and Turing Award winner, worked at the University of Edinburgh's Laboratory for Foundations of Computer Science.^{[5]}^{[6]} Milner and others were working on theorem provers, which were historically developed in languages such as Lisp. Milner repeatedly ran into the issue that the theorem provers would attempt to claim a proof was valid by putting nonproofs together.^{[6]} As a result, he went on to develop the meta language for his Logic for Computable Functions, a language that would only allow the writer to construct valid proofs with its polymorphic type system.^{[7]} ML was turned into a compiler in order to simplify using LCF on different machines, and, by the 1980s, was turned into a complete system of its own.^{[7]} ML would eventually serve as a basis for the creation of OCaml.
In the early 1980s, there were some developments that prompted INRIA's Formel team to become interested in the ML language. Luca Cardelli, a research professor at University of Oxford, used his Functional Abstract Machine to develop a faster implementation of ML, and Robin Milner proposed a new definition of ML in order to avoid divergence between various implementations. Simultaneously, PierreLouis Curien, a senior researcher at Paris Diderot University, developed a calculus of categorical combinators and linked it to lambda calculus, which led to the definition of the Categorical Abstract Machine (CAM). Guy Cousineau, a researcher at Paris Diderot University, recognized that this could be applied as a compilation technique for ML.^{[8]}
Caml was initially designed and developed by INRIA's Formel team headed by Gérard Huet. The first implementation of Caml was created in 1987 and was further developed until 1992. Though it was spearheaded by Ascánder Suárez, Pierre Weis and Michel Mauny carried on with development after he left in 1988.^{[8]}
Guy Cousineau is quoted recalling that his experience with programming language implementation was initially very limited, and that there were multiple inadequacies for which he is responsible. Despite this, he believes that "Ascander, Pierre and Michel did quite a nice piece of work.”^{[8]}
Between 1990 and 1991, Xavier Leroy designed a new implementation of Caml based on a bytecode interpreter written in C. In addition to this, Damien Doligez wrote a memory management system, also known as a sequential garbage collector, for this implementation.^{[7]} This new implementation, known as Caml Light, replaced the old Caml implementation and ran on small desktop machines.^{[8]} In the following years, libraries such as Michel Mauny's syntax manipulation tools appeared and helped promote the use of Caml in educational and research teams.^{[7]}
In 1995, Xavier Leroy released Caml Special Light, which was an improved version of Caml.^{[8]} An optimizing nativecode compiler was added to the bytecode compiler, which greatly increased performance to comparable levels with mainstream languages such as C++.^{[7]}^{[8]} Additionally, Leroy designed a highlevel module system inspired by the module system of Standard ML which provided powerful facilities for abstraction and parameterization and made largerscale programs easier to construct.^{[7]}
Didier Rémy and Jérôme Vouillon designed an expressive type system for objects and classes, which was integrated within Caml Special Light. This led to the emergence of the Objective Caml language, first released in 1996 and subsequently renamed to OCaml in 2011. This object system notably supported many prevalent objectoriented idioms in a statically typesafe way, while those same idioms caused unsoundness or required runtime checks in languages such as C++ or Java. In 2000, Jacques Garrigue extended Objective Caml with multiple new features such as polymorphic methods, variants, and labeled and optional arguments.^{[7]}^{[8]}
Language improvements have been incrementally added for the last two decades in order to support the growing commercial and academic codebases in OCaml.^{[7]} The OCaml 4.0 release in 2012 added Generalized Algebraic Data Types (GADTs) and firstclass modules in order to increase the flexibility of the language.^{[7]} The OCaml 5.0.0 release in 2022^{[9]} is a complete rewrite of the language runtime, removing the global GC lock and adding effect handlers via delimited continuations. These changes enable support for sharedmemory parallelism and colorblind concurrency respectively.
OCaml's development continued within the Cristal team at INRIA until 2005, when it was succeeded by the Gallium team.^{[10]} Subsequently, Gallium was succeeded by the Cambium team in 2019.^{[11]}^{[12]}
OCaml features a static type system, type inference, parametric polymorphism, tail recursion, pattern matching, first class lexical closures, functors (parametric modules), exception handling, effect handling, and incremental generational automatic garbage collection.
OCaml is notable for extending MLstyle type inference to an object system in a generalpurpose language. This permits structural subtyping, where object types are compatible if their method signatures are compatible, regardless of their declared inheritance (an unusual feature in statically typed languages).
A foreign function interface for linking to C primitives is provided, including language support for efficient numerical arrays in formats compatible with both C and Fortran. OCaml also supports creating libraries of OCaml functions that can be linked to a main program in C, so that an OCaml library can be distributed to C programmers who have no knowledge or installation of OCaml.
The OCaml distribution contains:
The native code compiler is available for many platforms, including Unix, Microsoft Windows, and Apple macOS. Portability is achieved through native code generation support for major architectures: IA32, X8664 (AMD64), Power, RISCV, ARM, and ARM64.^{[13]}
OCaml bytecode and native code programs can be written in a multithreaded style, with preemptive context switching. OCaml threads in the same domain^{[14]} execute by time sharing only. However, an OCaml program can contain several domains. There are several libraries for distributed computing such as Functory and ocamlnet/Plasma.
Since 2011, many new tools and libraries have been contributed to the OCaml development environment:
Snippets of OCaml code are most easily studied by entering them into the toplevel REPL. This is an interactive OCaml session that prints the inferred types of resulting or defined expressions.^{[15]} The OCaml toplevel is started by simply executing the OCaml program:
$ ocaml
Objective Caml version 3.09.0
#
Code can then be entered at the "#" prompt. For example, to calculate 1+2*3:
# 1 + 2 * 3;;
 : int = 7
OCaml infers the type of the expression to be "int" (a machineprecision integer) and gives the result "7".
The following program "hello.ml":
print_endline "Hello World!"
can be compiled into a bytecode executable:
$ ocamlc hello.ml o hello
or compiled into an optimized nativecode executable:
$ ocamlopt hello.ml o hello
and executed:
$ ./hello
Hello World!
$
The first argument to ocamlc, "hello.ml", specifies the source file to compile and the "o hello" flag specifies the output file.^{[16]}
The option type constructor in OCaml, similar to the Maybe monad in Haskell, augments a given data type to either return Some value of the given data type, or to return None.^{[17]} This is used to express that a value might or might not be present.
# Some 42;;
 : int option = Some 42
# None;;
 : 'a option = None
This is an example of a function that either extracts an int from an option, if there is one inside, and converts it into a string, or if not, returns an empty string:
let extract o =
match o with
 Some i > string_of_int i
 None > "";;
# extract (Some 42);;
 : string = "42"
# extract None;;
 : string = ""
Lists are one of the fundamental datatypes in OCaml. The following code example defines a recursive function sum that accepts one argument, integers, which is supposed to be a list of integers. Note the keyword rec
which denotes that the function is recursive. The function recursively iterates over the given list of integers and provides a sum of the elements. The match statement has similarities to C's switch element, though it is far more general.
let rec sum integers = (* Keyword rec means 'recursive'. *)
match integers with
 [] > 0 (* Yield 0 if integers is the empty
list []. *)
 first :: rest > first + sum rest;; (* Recursive call if integers is a non
empty list; first is the first
element of the list, and rest is a
list of the rest of the elements,
possibly []. *)
# sum [1;2;3;4;5];;
 : int = 15
Another way is to use standard fold function that works with lists.
let sum integers =
List.fold_left (fun accumulator x > accumulator + x) 0 integers;;
# sum [1;2;3;4;5];;
 : int = 15
Since the anonymous function is simply the application of the + operator, this can be shortened to:
let sum integers =
List.fold_left (+) 0 integers
Furthermore, one can omit the list argument by making use of a partial application:
let sum =
List.fold_left (+) 0
OCaml lends itself to concisely expressing recursive algorithms. The following code example implements an algorithm similar to quicksort that sorts a list in increasing order.
let rec qsort = function
 [] > []
 pivot :: rest >
let is_less x = x < pivot in
let left, right = List.partition is_less rest in
qsort left @ [pivot] @ qsort right
Or using partial application of the >= operator.
let rec qsort = function
 [] > []
 pivot :: rest >
let is_less = (>=) pivot in
let left, right = List.partition is_less rest in
qsort left @ [pivot] @ qsort right
The following program calculates the smallest number of people in a room for whom the probability of completely unique birthdays is less than 50% (the birthday problem, where for 1 person the probability is 365/365 (or 100%), for 2 it is 364/365, for 3 it is 364/365 × 363/365, etc.) (answer = 23).
let year_size = 365.
let rec birthday_paradox prob people =
let prob = (year_size . float people) /. year_size *. prob in
if prob < 0.5 then
Printf.printf "answer = %d\n" (people+1)
else
birthday_paradox prob (people+1)
;;
birthday_paradox 1.0 1
The following code defines a Church encoding of natural numbers, with successor (succ) and addition (add). A Church numeral n
is a higherorder function that accepts a function f
and a value x
and applies f
to x
exactly n
times. To convert a Church numeral from a functional value to a string, we pass it a function that prepends the string "S"
to its input and the constant string "0"
.
let zero f x = x
let succ n f x = f (n f x)
let one = succ zero
let two = succ (succ zero)
let add n1 n2 f x = n1 f (n2 f x)
let to_string n = n (fun k > "S" ^ k) "0"
let _ = to_string (add (succ two) two)
A variety of libraries are directly accessible from OCaml. For example, OCaml has a builtin library for arbitraryprecision arithmetic. As the factorial function grows very rapidly, it quickly overflows machineprecision numbers (typically 32 or 64bits). Thus, factorial is a suitable candidate for arbitraryprecision arithmetic.
In OCaml, the Num module (now superseded by the ZArith module) provides arbitraryprecision arithmetic and can be loaded into a running toplevel using:
# #use "topfind";;
# #require "num";;
# open Num;;
The factorial function may then be written using the arbitraryprecision numeric operators =/, */ and / :
# let rec fact n =
if n =/ Int 0 then Int 1 else n */ fact(n / Int 1);;
val fact : Num.num > Num.num = <fun>
This function can compute much larger factorials, such as 120!:
# string_of_num (fact (Int 120));;
 : string =
"6689502913449127057588118054090372586752746333138029810295671352301633
55724496298936687416527198498130815763789321409055253440858940812185989
8481114389650005964960521256960000000000000000000000000000"
The following program renders a rotating triangle in 2D using OpenGL:
let () =
ignore (Glut.init Sys.argv);
Glut.initDisplayMode ~double_buffer:true ();
ignore (Glut.createWindow ~title:"OpenGL Demo");
let angle t = 10. *. t *. t in
let render () =
GlClear.clear [ `color ];
GlMat.load_identity ();
GlMat.rotate ~angle: (angle (Sys.time ())) ~z:1. ();
GlDraw.begins `triangles;
List.iter GlDraw.vertex2 [1., 1.; 0., 1.; 1., 1.];
GlDraw.ends ();
Glut.swapBuffers () in
GlMat.mode `modelview;
Glut.displayFunc ~cb:render;
Glut.idleFunc ~cb:(Some Glut.postRedisplay);
Glut.mainLoop ()
The LablGL bindings to OpenGL are required. The program may then be compiled to bytecode with:
$ ocamlc I +lablGL lablglut.cma lablgl.cma simple.ml o simple
or to nativecode with:
$ ocamlopt I +lablGL lablglut.cmxa lablgl.cmxa simple.ml o simple
or, more simply, using the ocamlfind build command
$ ocamlfind opt simple.ml package lablgl.glut linkpkg o simple
and run:
$ ./simple
Far more sophisticated, highperformance 2D and 3D graphical programs can be developed in OCaml. Thanks to the use of OpenGL and OCaml, the resulting programs can be crossplatform, compiling without any changes on many major platforms.
The following code calculates the Fibonacci sequence of a number n inputted. It uses tail recursion and pattern matching.
let fib n =
let rec fib_aux m a b =
match m with
 0 > a
 _ > fib_aux (m  1) b (a + b)
in fib_aux n 0 1
Functions may take functions as input and return functions as result. For example, applying twice to a function f yields a function that applies f two times to its argument.
let twice (f : 'a > 'a) = fun (x : 'a) > f (f x);;
let inc (x : int) : int = x + 1;;
let add2 = twice inc;;
let inc_str (x : string) : string = x ^ " " ^ x;;
let add_str = twice(inc_str);;
# add2 98;;
 : int = 100
# add_str "Test";;
 : string = "Test Test Test Test"
The function twice uses a type variable 'a to indicate that it can be applied to any function f mapping from a type 'a to itself, rather than only to int>int functions. In particular, twice can even be applied to itself.
# let fourtimes f = (twice twice) f;;
val fourtimes : ('a > 'a) > 'a > 'a = <fun>
# let add4 = fourtimes inc;;
val add4 : int > int = <fun>
# add4 98;;
 : int = 102
MetaOCaml^{[18]} is a multistage programming extension of OCaml enabling incremental compiling of new machine code during runtime. Under some circumstances, significant speedups are possible using multistage programming, because more detailed information about the data to process is available at runtime than at the regular compile time, so the incremental compiler can optimize away many cases of condition checking, etc.
As an example: if at compile time it is known that some power function x > x^n
is needed often, but the value of n
is known only at runtime, a twostage power function can be used in MetaOCaml:
let rec power n x =
if n = 0
then .<1>.
else
if even n
then sqr (power (n/2) x)
else .<.~x *. .~(power (n  1) x)>.
As soon as n
is known at runtime, a specialized and very fast power function can be created:
.<fun x > .~(power 5 .<x>.)>.
The result is:
fun x_1 > (x_1 *
let y_3 =
let y_2 = (x_1 * 1)
in (y_2 * y_2)
in (y_3 * y_3))
The new function is automatically compiled.
genfft
.Several dozen companies use OCaml to some degree.^{[25]} Notable examples include: