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Paradigm  Multiparadigm: imperative, functional, objectoriented 

Designed by  Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez 
Developer  INRIA 
First appeared  1996 
Stable release  4.07.0
/ July 10, 2018 ^{[1]} 
Typing discipline  Static, strong, inferred 
Implementation language  OCaml, C 
Platform  IA32, x8664, Power, SPARC, ARM 3264 
OS  Crossplatform: Unix, macOS, Windows 
License  LGPL 
Filename extensions  .ml, .mli 
Website  ocaml 
Dialects  
F#, JoCaml, MetaOCaml, OcamlP3l, Reason ML  
Influenced by  
Caml Light, Cool,^{[]}Standard ML  
Influenced  
ATS, Elm, F#, F*, Haxe, Opa, Rust, Scala  

OCaml ( ohKAM?l), originally named Objective Caml, is the main implementation of the programming language Caml, created by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez and others in 1996. A member of the ML language family, OCaml extends the core Caml language with objectoriented programming constructs.
The OCaml toolchain includes an interactive toplevel interpreter, a bytecode compiler, an optimizing native code compiler, a reversible debugger, and a package manager (OPAM). It has a large standard library, making it useful for many of the same applications as Python or Perl, and has robust modular and objectoriented programming constructs that make it applicable for largescale software engineering. OCaml is the successor to Caml Light. The acronym CAML originally stood for Categorical Abstract Machine Language, although OCaml omits this abstract machine.^{[2]}
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, many new languages adopted elements from OCaml, most 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.
OCaml's static type system can help eliminate problems at runtime. However, it also forces the programmer to conform to the constraints of the type system, which can require careful thought and close attention. A typeinferring compiler greatly reduces the need for manual type annotations. For example, the data type of variables and the signature of functions usually need not be declared explicitly, as they do in languages like Java or C#. Nonetheless, effective use of OCaml's type system can require some sophistication on the part of a programmer.
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",^{[3]} but 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).
OCaml features: a static type system, type inference, parametric polymorphism, tail recursion, pattern matching, first class lexical closures, functors (parametric modules), exception 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, SPARC, ARM, and ARM64.^{[4]}
OCaml bytecode and native code programs can be written in a multithreaded style, with preemptive context switching. However, because the garbage collector of the INRIA OCaml system (which is the only currently available full implementation of the language) is not designed for concurrency, symmetric multiprocessing is unsupported.^{[5]} OCaml threads in the same process execute by time sharing only. There are however 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:
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Snippets of OCaml code are most easily studied by entering them into the toplevel. This is an interactive OCaml session that prints the inferred types of resulting or defined expressions. 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! $
Lists are one of the fundamental datatypes in OCaml. The following code example defines a recursive function sum that accepts one argument xs. (Note the keyword rec). The function recursively iterates over a given list and provides a sum of integer elements. The match statement has similarities to C's switch element, though it is far more general.
let rec sum xs =
match xs with
 [] > 0 (* yield 0 if xs has the form [] *)
 x :: xs' > x + sum xs';; (* recursive call if xs has the form x::xs' for suitable x and xs' *)
# sum [1;2;3;4;5];;  : int = 15
Another way is to use standard fold function that works with lists.
let sum xs =
List.fold_left (fun acc x > acc + x) 0 xs;;
# 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 xs =
List.fold_left (+) 0 xs
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
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 "simple.ml" 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^{[6]} 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.^{[12]} Notable examples include: