View source for Caml

{{Short description|Programming language}}
{{Infobox programming language
| name                   = Caml
| logo                   = [[File:Caml.gif]]
| paradigm               = Multi-paradigm: functional, [[Imperative programming|imperative]]
| family = [[ML (programming language)|ML]]
| year                   = 1985
| typing                 = [[Type inference|Inferred]], static, strong
| designer               = [[Biography:Gérard Huet|Gérard Huet]], Guy Cousineau, Ascánder Suárez, Pierre Weis, Michel Mauny (Heavy Caml), [[Biography:Xavier Leroy|Xavier Leroy]] (Caml Light)
| developer              = 
| latest release version = 0.75<ref>{{cite web|title=Latest Caml Light release|url=http://caml.inria.fr/caml-light/release.en.html|accessdate=22 February 2020}}</ref>
| latest release date    = {{start date and age|2002|01|26}}
| latest test version    = 
| latest test date       = 
| dialects               = 
| influenced by          = [[ML (programming language)|ML]]
| influenced             = [[OCaml]]
| operating system       = Cross-platform
| license                =
| website                = {{URL|caml.inria.fr}}}}

'''Caml''' (originally an acronym for '''Categorical Abstract Machine Language''') is a multi-paradigm, [[General-purpose programming language|general-purpose programming language]] which is a dialect of the [[ML (programming language)|ML programming language]] family.  Caml was developed in France at INRIA and ENS.

Caml is statically [[Type system|typed]], [[Eager evaluation|strictly evaluated]], and uses automatic memory management. [[OCaml]], the main descendant of Caml, adds many features to the language, including an [[Object-oriented programming|object layer]].

==Examples==
In the following, {{OCaml|#}} represents the Caml prompt.

===Hello World===
<source lang="ocaml">
print_endline "Hello, world!";;
</source>

===Factorial function (recursion and purely functional programming)===
Many mathematical functions, such as factorial, are most naturally represented in a purely functional form. The following recursive, purely functional Caml function implements factorial:
<source lang=OCaml>
let rec fact n = if n=0 then 1 else n * fact(n - 1);;
</source>
The function can be written equivalently using [[Pattern matching|pattern matching]]:
<source lang=OCaml>
let rec fact = function
  | 0 -> 1
  | n -> n * fact(n - 1);;
</source>
This latter form is the mathematical definition of factorial as a recurrence relation.

Note that the compiler inferred the type of this function to be {{OCaml|int -> int}}, meaning that this function maps ints onto ints. For example, 12! is:
<source lang=OCaml>
 # fact 12;;
 - : int = 479001600
</source>

===Numerical derivative (higher-order functions)===
Since Caml is a functional programming language, it is easy to create and pass around functions in Caml programs. This capability has an enormous number of applications. Calculating the numerical derivative of a function is one such application. The following Caml function {{OCaml|d}} computes the numerical derivative of a given function {{OCaml|f}} at a given point {{OCaml|x}}:
<source lang=OCaml>
let d delta f x =
  (f (x +. delta) -. f (x -. delta)) /. (2. *. delta);;
</source>
This function requires a small value {{OCaml|delta}}. A good choice for delta is the cube root of the [[Machine epsilon|machine epsilon]]{{Citation needed|date=May 2008}}.

The type of the function {{OCaml|d}} indicates that it maps a {{OCaml|float}} onto another function with the type {{OCaml|(float -> float) -> float -> float}}. This allows us to partially apply arguments. This functional style is known as [[Currying|currying]]. In this case, it is useful to partially apply the first argument {{OCaml|delta}} to {{OCaml|d}}, to obtain a more specialised function:
<source lang=OCaml>
# let d = d (sqrt epsilon_float);;
val d : (float -> float) -> float -> float = <fun>
</source>
Note that the inferred type indicates that the replacement {{OCaml|d}} is expecting a function with the type {{OCaml|float -> float}} as its first argument. We can compute a numerical approximation to the derivative of <math>x^3 - x - 1</math> at <math>x=3</math> with:
<source lang=OCaml>
# d (fun x -> x *. x *. x -. x -. 1.) 3.;;
- : float = 26.
</source>
The correct answer is <math>f'(x) = 3x^2 - 1 \rightarrow f'(3) = 27 - 1 = 26</math>.

The function {{OCaml|d}} is called a "[[Higher-order function|higher-order function]]" because it accepts another function ({{OCaml|f}}) as an argument.
We can go further and create the (approximate) derivative of f, by applying {{OCaml|d}} while omitting the {{OCaml|x}} argument:
<source lang=OCaml>
# let f' = d (fun x -> x *. x *. x -. x -. 1.) ;;
val f' : float -> float = <fun>
</source>

The concepts of curried and higher-order functions are clearly useful in mathematical programs. In fact, these concepts are equally applicable to most other forms of programming and can be used to factor code much more aggressively, resulting in shorter programs and fewer bugs.

===Discrete wavelet transform (pattern matching)===
The 1D [[Haar wavelet]] [[Discrete wavelet transform|transform]] of an [[Integer|integer]]-power-of-two-length list of numbers can be implemented very succinctly in Caml and is an excellent example of the use of pattern matching over lists, taking pairs of elements ({{OCaml|h1}} and {{OCaml|h2}}) off the front and storing their sums and differences on the lists {{OCaml|s}} and {{OCaml|d}}, respectively:
<source lang=OCaml>
# let haar l =
   let rec aux l s d = 
     match l, s, d with
       [s], [], d -> s :: d
     | [], s, d -> aux s [] d
     | h1 :: h2 :: t, s, d -> aux t (h1 + h2 :: s) (h1 - h2 :: d)
     | _ -> invalid_arg "haar" 
     in aux l [] [];;
val haar : int list -> int list = <fun>
</source>
For example:
<source lang=OCaml>
  # haar [1; 2; 3; 4; -4; -3; -2; -1];;
   - : int list = [0; 20; 4; 4; -1; -1; -1; -1]
</source>
Pattern matching allows complicated transformations to be represented clearly and succinctly. Moreover, the Caml compiler turns pattern matches into very efficient code, at times resulting in programs that are shorter and faster than equivalent code written with a case statement (Cardelli 1984, p.&nbsp;210.).

==History==
The first Caml implementation was written in [[Lisp (programming language)|Lisp]] by Ascánder Suárez in 1987 at the French Institute for Research in Computer Science and Automation (INRIA).<ref name=inria>[https://caml.inria.fr/about/history.en.html "A History of Caml"], inria.fr</ref>

Its successor, ''Caml Light'', was implemented in [[C (programming language)|C]] by [[Biography:Xavier Leroy|Xavier Leroy]] and Damien Doligez,<ref name=inria/> and the original was nicknamed "Heavy Caml" because of its higher memory and CPU requirements.<ref name=inria/>

''Caml Special Light'' was a further complete rewrite that added a powerful module system to the core language. It was augmented with an [[Object-oriented programming|object layer]] to become ''Objective Caml'', eventually renamed [[OCaml]].

==See also==
*[[Categorical abstract machine]]
*[[OCaml]]

==References==
{{Reflist}}

==Bibliography==
*[http://pauillac.inria.fr/cousineau-mauny/main.html The Functional Approach to Programming with Caml] {{Webarchive|url=https://web.archive.org/web/20071224205843/http://pauillac.inria.fr/cousineau-mauny/main.html |date=2007-12-24 }} by Guy Cousineau and Michel Mauny.
*Cardelli, Luca (1984). [https://dx.doi.org/10.1145/800055.802037 Compiling a functional language] ''ACM Symposium on LISP and functional programming'', Association of Computer Machinery.

==External links==
* – Caml language family

[[Category:ML programming language family]]
[[Category:Programming languages]]

{{Sourceattribution|Caml}}