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<!DOCTYPE html>
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<title>Chapter 1  The core language</title>
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<hr>
<h1 class="chapter" id="sec7">Chapter 1  The core language</h1>
<ul>
<li><a href="coreexamples.html#sec8">1.1  Basics</a>
</li><li><a href="coreexamples.html#sec9">1.2  Data types</a>
</li><li><a href="coreexamples.html#sec10">1.3  Functions as values</a>
</li><li><a href="coreexamples.html#sec11">1.4  Records and variants</a>
</li><li><a href="coreexamples.html#sec12">1.5  Imperative features</a>
</li><li><a href="coreexamples.html#sec13">1.6  Exceptions</a>
</li><li><a href="coreexamples.html#sec14">1.7  Symbolic processing of expressions</a>
</li><li><a href="coreexamples.html#sec15">1.8  Pretty-printing</a>
</li><li><a href="coreexamples.html#sec16">1.9  Standalone OCaml programs</a>
</li></ul>
<p> <a id="c:core-xamples"></a>
</p><p>This part of the manual is a tutorial introduction to the
OCaml language. A good familiarity with programming in a conventional
languages (say, Pascal or C) is assumed, but no prior exposure to
functional languages is required. The present chapter introduces the
core language. Chapter <a href="moduleexamples.html#c%3Amoduleexamples">2</a> deals with the
module system, chapter <a href="objectexamples.html#c%3Aobjectexamples">3</a> with the
object-oriented features, chapter <a href="lablexamples.html#c%3Alabl-examples">4</a> with
extensions to the core language (labeled arguments and polymorphic
variants), and chapter <a href="advexamples.html#c%3Aadvexamples">5</a> gives some advanced examples.</p>
<h2 class="section" id="sec8">1.1  Basics</h2>
<p>For this overview of OCaml, we use the interactive system, which
is started by running <span class="c003">ocaml</span> from the Unix shell, or by launching the
<span class="c003">OCamlwin.exe</span> application under Windows. This tutorial is presented
as the transcript of a session with the interactive system:
lines starting with <span class="c003">#</span> represent user input; the system responses are
printed below, without a leading <span class="c003">#</span>.</p><p>Under the interactive system, the user types OCaml phrases terminated
by <span class="c003">;;</span> in response to the <span class="c003">#</span> prompt, and the system compiles them
on the fly, executes them, and prints the outcome of evaluation.
Phrases are either simple expressions, or <span class="c003">let</span> definitions of
identifiers (either values or functions).
</p><div class="caml-example">
<pre><div class="caml-input"> 1+2*3;;
</div><div class="caml-output ok">- : int = 7
</div></pre>
<pre><div class="caml-input"> let pi = 4.0 *. atan 1.0;;
</div><div class="caml-output ok">val pi : float = 3.14159265358979312
</div></pre>
<pre><div class="caml-input"> let square x = x *. x;;
</div><div class="caml-output ok">val square : float -> float = <fun>
</div></pre>
<pre><div class="caml-input"> square (sin pi) +. square (cos pi);;
</div><div class="caml-output ok">- : float = 1.
</div></pre>
</div><p>The OCaml system computes both the value and the type for
each phrase. Even function parameters need no explicit type declaration:
the system infers their types from their usage in the
function. Notice also that integers and floating-point numbers are
distinct types, with distinct operators: <span class="c003">+</span> and <span class="c003">*</span> operate on
integers, but <span class="c003">+.</span> and <span class="c003">*.</span> operate on floats.
</p><div class="caml-example">
<pre><div class="caml-input"> <U>1.0</U> * 2;;
</div><div class="caml-output error">Error: This expression has type float but an expression was expected of type
int
</div></pre>
</div><p>Recursive functions are defined with the <span class="c003">let rec</span> binding:
</p><div class="caml-example">
<pre><div class="caml-input"> let rec fib n =
if n < 2 then n else fib (n-1) + fib (n-2);;
</div><div class="caml-output ok">val fib : int -> int = <fun>
</div></pre>
<pre><div class="caml-input"> fib 10;;
</div><div class="caml-output ok">- : int = 55
</div></pre>
</div>
<h2 class="section" id="sec9">1.2  Data types</h2>
<p>In addition to integers and floating-point numbers, OCaml offers the
usual basic data types: booleans, characters, and immutable character strings.
</p><div class="caml-example">
<pre><div class="caml-input"> (1 < 2) = false;;
</div><div class="caml-output ok">- : bool = false
</div></pre>
<pre><div class="caml-input"> 'a';;
</div><div class="caml-output ok">- : char = 'a'
</div></pre>
<pre><div class="caml-input"> "Hello world";;
</div><div class="caml-output ok">- : string = "Hello world"
</div></pre>
</div><p>Predefined data structures include tuples, arrays, and lists. General
mechanisms for defining your own data structures are also provided.
They will be covered in more details later; for now, we concentrate on lists.
Lists are either given in extension as a bracketed list of
semicolon-separated elements, or built from the empty list <span class="c003">[]</span>
(pronounce “nil”) by adding elements in front using the <span class="c003">::</span>
(“cons”) operator.
</p><div class="caml-example">
<pre><div class="caml-input"> let l = ["is"; "a"; "tale"; "told"; "etc."];;
</div><div class="caml-output ok">val l : string list = ["is"; "a"; "tale"; "told"; "etc."]
</div></pre>
<pre><div class="caml-input"> "Life" :: l;;
</div><div class="caml-output ok">- : string list = ["Life"; "is"; "a"; "tale"; "told"; "etc."]
</div></pre>
</div><p>As with all other OCaml data structures, lists do not need to be
explicitly allocated and deallocated from memory: all memory
management is entirely automatic in OCaml. Similarly, there is no
explicit handling of pointers: the OCaml compiler silently introduces
pointers where necessary.</p><p>As with most OCaml data structures, inspecting and destructuring lists
is performed by pattern-matching. List patterns have the exact same
shape as list expressions, with identifier representing unspecified
parts of the list. As an example, here is insertion sort on a list:
</p><div class="caml-example">
<pre><div class="caml-input"> let rec sort lst =
match lst with
[] -> []
| head :: tail -> insert head (sort tail)
and insert elt lst =
match lst with
[] -> [elt]
| head :: tail -> if elt <= head then elt :: lst else head :: insert elt tail
;;
</div><div class="caml-output ok">val sort : 'a list -> 'a list = <fun>
val insert : 'a -> 'a list -> 'a list = <fun>
</div></pre>
<pre><div class="caml-input"> sort l;;
</div><div class="caml-output ok">- : string list = ["a"; "etc."; "is"; "tale"; "told"]
</div></pre>
</div><p>The type inferred for <span class="c003">sort</span>, <span class="c003">'a list -> 'a list</span>, means that <span class="c003">sort</span>
can actually apply to lists of any type, and returns a list of the
same type. The type <span class="c003">'a</span> is a <em>type variable</em>, and stands for any
given type. The reason why <span class="c003">sort</span> can apply to lists of any type is
that the comparisons (<span class="c003">=</span>, <span class="c003"><=</span>, etc.) are <em>polymorphic</em> in OCaml:
they operate between any two values of the same type. This makes
<span class="c003">sort</span> itself polymorphic over all list types.
</p><div class="caml-example">
<pre><div class="caml-input"> sort [6;2;5;3];;
</div><div class="caml-output ok">- : int list = [2; 3; 5; 6]
</div></pre>
<pre><div class="caml-input"> sort [3.14; 2.718];;
</div><div class="caml-output ok">- : float list = [2.718; 3.14]
</div></pre>
</div><p>The <span class="c003">sort</span> function above does not modify its input list: it builds
and returns a new list containing the same elements as the input list,
in ascending order. There is actually no way in OCaml to modify
in-place a list once it is built: we say that lists are <em>immutable</em>
data structures. Most OCaml data structures are immutable, but a few
(most notably arrays) are <em>mutable</em>, meaning that they can be
modified in-place at any time.</p>
<h2 class="section" id="sec10">1.3  Functions as values</h2>
<p>OCaml is a functional language: functions in the full mathematical
sense are supported and can be passed around freely just as any other
piece of data. For instance, here is a <span class="c003">deriv</span> function that takes any
float function as argument and returns an approximation of its
derivative function:
</p><div class="caml-example">
<pre><div class="caml-input"> let deriv f dx = function x -> (f (x +. dx) -. f x) /. dx;;
</div><div class="caml-output ok">val deriv : (float -> float) -> float -> float -> float = <fun>
</div></pre>
<pre><div class="caml-input"> let sin' = deriv sin 1e-6;;
</div><div class="caml-output ok">val sin' : float -> float = <fun>
</div></pre>
<pre><div class="caml-input"> sin' pi;;
</div><div class="caml-output ok">- : float = -1.00000000013961143
</div></pre>
</div><p>Even function composition is definable:
</p><div class="caml-example">
<pre><div class="caml-input"> let compose f g = function x -> f (g x);;
</div><div class="caml-output ok">val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = <fun>
</div></pre>
<pre><div class="caml-input"> let cos2 = compose square cos;;
</div><div class="caml-output ok">val cos2 : float -> float = <fun>
</div></pre>
</div><p>Functions that take other functions as arguments are called
“functionals”, or “higher-order functions”. Functionals are
especially useful to provide iterators or similar generic operations
over a data structure. For instance, the standard OCaml library
provides a <span class="c003">List.map</span> functional that applies a given function to each
element of a list, and returns the list of the results:
</p><div class="caml-example">
<pre><div class="caml-input"> List.map (function n -> n * 2 + 1) [0;1;2;3;4];;
</div><div class="caml-output ok">- : int list = [1; 3; 5; 7; 9]
</div></pre>
</div><p>This functional, along with a number of other list and array
functionals, is predefined because it is often useful, but there is
nothing magic with it: it can easily be defined as follows.
</p><div class="caml-example">
<pre><div class="caml-input"> let rec map f l =
match l with
[] -> []
| hd :: tl -> f hd :: map f tl;;
</div><div class="caml-output ok">val map : ('a -> 'b) -> 'a list -> 'b list = <fun>
</div></pre>
</div>
<h2 class="section" id="sec11">1.4  Records and variants</h2>
<p>
<a id="s:tut-recvariants"></a></p><p>User-defined data structures include records and variants. Both are
defined with the <span class="c003">type</span> declaration. Here, we declare a record type to
represent rational numbers.
</p><div class="caml-example">
<pre><div class="caml-input"> type ratio = {num: int; denom: int};;
</div><div class="caml-output ok">type ratio = { num : int; denom : int; }
</div></pre>
<pre><div class="caml-input"> let add_ratio r1 r2 =
{num = r1.num * r2.denom + r2.num * r1.denom;
denom = r1.denom * r2.denom};;
</div><div class="caml-output ok">val add_ratio : ratio -> ratio -> ratio = <fun>
</div></pre>
<pre><div class="caml-input"> add_ratio {num=1; denom=3} {num=2; denom=5};;
</div><div class="caml-output ok">- : ratio = {num = 11; denom = 15}
</div></pre>
</div><p>The declaration of a variant type lists all possible shapes for values
of that type. Each case is identified by a name, called a constructor,
which serves both for constructing values of the variant type and
inspecting them by pattern-matching. Constructor names are capitalized
to distinguish them from variable names (which must start with a
lowercase letter). For instance, here is a variant
type for doing mixed arithmetic (integers and floats):
</p><div class="caml-example">
<pre><div class="caml-input"> type number = Int of int | Float of float | Error;;
</div><div class="caml-output ok">type number = Int of int | Float of float | Error
</div></pre>
</div><p>This declaration expresses that a value of type <span class="c003">number</span> is either an
integer, a floating-point number, or the constant <span class="c003">Error</span> representing
the result of an invalid operation (e.g. a division by zero).</p><p>Enumerated types are a special case of variant types, where all
alternatives are constants:
</p><div class="caml-example">
<pre><div class="caml-input"> type sign = Positive | Negative;;
</div><div class="caml-output ok">type sign = Positive | Negative
</div></pre>
<pre><div class="caml-input"> let sign_int n = if n >= 0 then Positive else Negative;;
</div><div class="caml-output ok">val sign_int : int -> sign = <fun>
</div></pre>
</div><p>To define arithmetic operations for the <span class="c003">number</span> type, we use
pattern-matching on the two numbers involved:
</p><div class="caml-example">
<pre><div class="caml-input"> let add_num n1 n2 =
match (n1, n2) with
(Int i1, Int i2) ->
(* Check for overflow of integer addition *)
if sign_int i1 = sign_int i2 && sign_int (i1 + i2) <> sign_int i1
then Float(float i1 +. float i2)
else Int(i1 + i2)
| (Int i1, Float f2) -> Float(float i1 +. f2)
| (Float f1, Int i2) -> Float(f1 +. float i2)
| (Float f1, Float f2) -> Float(f1 +. f2)
| (Error, _) -> Error
| (_, Error) -> Error;;
</div><div class="caml-output ok">val add_num : number -> number -> number = <fun>
</div></pre>
<pre><div class="caml-input"> add_num (Int 123) (Float 3.14159);;
</div><div class="caml-output ok">- : number = Float 126.14159
</div></pre>
</div><p>The most common usage of variant types is to describe recursive data
structures. Consider for example the type of binary trees:
</p><div class="caml-example">
<pre><div class="caml-input"> type 'a btree = Empty | Node of 'a * 'a btree * 'a btree;;
</div><div class="caml-output ok">type 'a btree = Empty | Node of 'a * 'a btree * 'a btree
</div></pre>
</div><p>This definition reads as follows: a binary tree containing values of
type <span class="c003">'a</span> (an arbitrary type) is either empty, or is a node containing
one value of type <span class="c003">'a</span> and two subtrees containing also values of type
<span class="c003">'a</span>, that is, two <span class="c003">'a btree</span>.</p><p>Operations on binary trees are naturally expressed as recursive functions
following the same structure as the type definition itself. For
instance, here are functions performing lookup and insertion in
ordered binary trees (elements increase from left to right):
</p><div class="caml-example">
<pre><div class="caml-input"> let rec member x btree =
match btree with
Empty -> false
| Node(y, left, right) ->
if x = y then true else
if x < y then member x left else member x right;;
</div><div class="caml-output ok">val member : 'a -> 'a btree -> bool = <fun>
</div></pre>
<pre><div class="caml-input"> let rec insert x btree =
match btree with
Empty -> Node(x, Empty, Empty)
| Node(y, left, right) ->
if x <= y then Node(y, insert x left, right)
else Node(y, left, insert x right);;
</div><div class="caml-output ok">val insert : 'a -> 'a btree -> 'a btree = <fun>
</div></pre>
</div>
<h2 class="section" id="sec12">1.5  Imperative features</h2>
<p>Though all examples so far were written in purely applicative style,
OCaml is also equipped with full imperative features. This includes the
usual <span class="c003">while</span> and <span class="c003">for</span> loops, as well as mutable data structures such
as arrays. Arrays are either given in extension between <span class="c003">[|</span> and <span class="c003">|]</span>
brackets, or allocated and initialized with the <span class="c003">Array.make</span>
function, then filled up later by assignments. For instance, the
function below sums two vectors (represented as float arrays) componentwise.
</p><div class="caml-example">
<pre><div class="caml-input"> let add_vect v1 v2 =
let len = min (Array.length v1) (Array.length v2) in
let res = Array.make len 0.0 in
for i = 0 to len - 1 do
res.(i) <- v1.(i) +. v2.(i)
done;
res;;
</div><div class="caml-output ok">val add_vect : float array -> float array -> float array = <fun>
</div></pre>
<pre><div class="caml-input"> add_vect [| 1.0; 2.0 |] [| 3.0; 4.0 |];;
</div><div class="caml-output ok">- : float array = [|4.; 6.|]
</div></pre>
</div><p>Record fields can also be modified by assignment, provided they are
declared <span class="c003">mutable</span> in the definition of the record type:
</p><div class="caml-example">
<pre><div class="caml-input"> type mutable_point = { mutable x: float; mutable y: float };;
</div><div class="caml-output ok">type mutable_point = { mutable x : float; mutable y : float; }
</div></pre>
<pre><div class="caml-input"> let translate p dx dy =
p.x <- p.x +. dx; p.y <- p.y +. dy;;
</div><div class="caml-output ok">val translate : mutable_point -> float -> float -> unit = <fun>
</div></pre>
<pre><div class="caml-input"> let mypoint = { x = 0.0; y = 0.0 };;
</div><div class="caml-output ok">val mypoint : mutable_point = {x = 0.; y = 0.}
</div></pre>
<pre><div class="caml-input"> translate mypoint 1.0 2.0;;
</div><div class="caml-output ok">- : unit = ()
</div></pre>
<pre><div class="caml-input"> mypoint;;
</div><div class="caml-output ok">- : mutable_point = {x = 1.; y = 2.}
</div></pre>
</div><p>OCaml has no built-in notion of variable – identifiers whose current
value can be changed by assignment. (The <span class="c003">let</span> binding is not an
assignment, it introduces a new identifier with a new scope.)
However, the standard library provides references, which are mutable
indirection cells (or one-element arrays), with operators <span class="c003">!</span> to fetch
the current contents of the reference and <span class="c003">:=</span> to assign the contents.
Variables can then be emulated by <span class="c003">let</span>-binding a reference. For
instance, here is an in-place insertion sort over arrays:
</p><div class="caml-example">
<pre><div class="caml-input"> let insertion_sort a =
for i = 1 to Array.length a - 1 do
let val_i = a.(i) in
let j = ref i in
while !j > 0 && val_i < a.(!j - 1) do
a.(!j) <- a.(!j - 1);
j := !j - 1
done;
a.(!j) <- val_i
done;;
</div><div class="caml-output ok">val insertion_sort : 'a array -> unit = <fun>
</div></pre>
</div><p>References are also useful to write functions that maintain a current
state between two calls to the function. For instance, the following
pseudo-random number generator keeps the last returned number in a
reference:
</p><div class="caml-example">
<pre><div class="caml-input"> let current_rand = ref 0;;
</div><div class="caml-output ok">val current_rand : int ref = {contents = 0}
</div></pre>
<pre><div class="caml-input"> let random () =
current_rand := !current_rand * 25713 + 1345;
!current_rand;;
</div><div class="caml-output ok">val random : unit -> int = <fun>
</div></pre>
</div><p>Again, there is nothing magical with references: they are implemented as
a single-field mutable record, as follows.
</p><div class="caml-example">
<pre><div class="caml-input"> type 'a ref = { mutable contents: 'a };;
</div><div class="caml-output ok">type 'a ref = { mutable contents : 'a; }
</div></pre>
<pre><div class="caml-input"> let ( ! ) r = r.contents;;
</div><div class="caml-output ok">val ( ! ) : 'a ref -> 'a = <fun>
</div></pre>
<pre><div class="caml-input"> let ( := ) r newval = r.contents <- newval;;
</div><div class="caml-output ok">val ( := ) : 'a ref -> 'a -> unit = <fun>
</div></pre>
</div><p>In some special cases, you may need to store a polymorphic function in
a data structure, keeping its polymorphism. Without user-provided
type annotations, this is not allowed, as polymorphism is only
introduced on a global level. However, you can give explicitly
polymorphic types to record fields.
</p><div class="caml-example">
<pre><div class="caml-input"> type idref = { mutable id: 'a. 'a -> 'a };;
</div><div class="caml-output ok">type idref = { mutable id : 'a. 'a -> 'a; }
</div></pre>
<pre><div class="caml-input"> let r = {id = fun x -> x};;
</div><div class="caml-output ok">val r : idref = {id = <fun>}
</div></pre>
<pre><div class="caml-input"> let g s = (s.id 1, s.id true);;
</div><div class="caml-output ok">val g : idref -> int * bool = <fun>
</div></pre>
<pre><div class="caml-input"> r.id <- (fun x -> print_string "called id\n"; x);;
</div><div class="caml-output ok">- : unit = ()
</div></pre>
<pre><div class="caml-input"> g r;;
</div><div class="caml-output ok">called id
called id
- : int * bool = (1, true)
</div></pre>
</div>
<h2 class="section" id="sec13">1.6  Exceptions</h2>
<p>OCaml provides exceptions for signalling and handling exceptional
conditions. Exceptions can also be used as a general-purpose non-local
control structure. Exceptions are declared with the <span class="c003">exception</span>
construct, and signalled with the <span class="c003">raise</span> operator. For instance, the
function below for taking the head of a list uses an exception to
signal the case where an empty list is given.
</p><div class="caml-example">
<pre><div class="caml-input"> exception Empty_list;;
</div><div class="caml-output ok">exception Empty_list
</div></pre>
<pre><div class="caml-input"> let head l =
match l with
[] -> raise Empty_list
| hd :: tl -> hd;;
</div><div class="caml-output ok">val head : 'a list -> 'a = <fun>
</div></pre>
<pre><div class="caml-input"> head [1;2];;
</div><div class="caml-output ok">- : int = 1
</div></pre>
<pre><div class="caml-input"> head [];;
</div><div class="caml-output ok">Exception: Empty_list.
</div></pre>
</div><p>Exceptions are used throughout the standard library to signal cases
where the library functions cannot complete normally. For instance,
the <span class="c003">List.assoc</span> function, which returns the data associated with a
given key in a list of (key, data) pairs, raises the predefined
exception <span class="c003">Not_found</span> when the key does not appear in the list:
</p><div class="caml-example">
<pre><div class="caml-input"> List.assoc 1 [(0, "zero"); (1, "one")];;
</div><div class="caml-output ok">- : string = "one"
</div></pre>
<pre><div class="caml-input"> List.assoc 2 [(0, "zero"); (1, "one")];;
</div><div class="caml-output ok">Exception: Not_found.
</div></pre>
</div><p>Exceptions can be trapped with the <span class="c003">try</span>…<span class="c003">with</span> construct:
</p><div class="caml-example">
<pre><div class="caml-input"> let name_of_binary_digit digit =
try
List.assoc digit [0, "zero"; 1, "one"]
with Not_found ->
"not a binary digit";;
</div><div class="caml-output ok">val name_of_binary_digit : int -> string = <fun>
</div></pre>
<pre><div class="caml-input"> name_of_binary_digit 0;;
</div><div class="caml-output ok">- : string = "zero"
</div></pre>
<pre><div class="caml-input"> name_of_binary_digit (-1);;
</div><div class="caml-output ok">- : string = "not a binary digit"
</div></pre>
</div><p>The <span class="c003">with</span> part is actually a regular pattern-matching on the
exception value. Thus, several exceptions can be caught by one
<span class="c003">try</span>…<span class="c003">with</span> construct. Also, finalization can be performed by
trapping all exceptions, performing the finalization, then raising
again the exception:
</p><div class="caml-example">
<pre><div class="caml-input"> let temporarily_set_reference ref newval funct =
let oldval = !ref in
try
ref := newval;
let res = funct () in
ref := oldval;
res
with x ->
ref := oldval;
raise x;;
</div><div class="caml-output ok">val temporarily_set_reference : 'a ref -> 'a -> (unit -> 'b) -> 'b = <fun>
</div></pre>
</div>
<h2 class="section" id="sec14">1.7  Symbolic processing of expressions</h2>
<p>We finish this introduction with a more complete example
representative of the use of OCaml for symbolic processing: formal
manipulations of arithmetic expressions containing variables. The
following variant type describes the expressions we shall manipulate:
</p><div class="caml-example">
<pre><div class="caml-input"> type expression =
Const of float
| Var of string
| Sum of expression * expression (* e1 + e2 *)
| Diff of expression * expression (* e1 - e2 *)
| Prod of expression * expression (* e1 * e2 *)
| Quot of expression * expression (* e1 / e2 *)
;;
</div><div class="caml-output ok">type expression =
Const of float
| Var of string
| Sum of expression * expression
| Diff of expression * expression
| Prod of expression * expression
| Quot of expression * expression
</div></pre>
</div><p>We first define a function to evaluate an expression given an
environment that maps variable names to their values. For simplicity,
the environment is represented as an association list.
</p><div class="caml-example">
<pre><div class="caml-input"> exception Unbound_variable of string;;
</div><div class="caml-output ok">exception Unbound_variable of string
</div></pre>
<pre><div class="caml-input"> let rec eval env exp =
match exp with
Const c -> c
| Var v ->
(try List.assoc v env with Not_found -> raise (Unbound_variable v))
| Sum(f, g) -> eval env f +. eval env g
| Diff(f, g) -> eval env f -. eval env g
| Prod(f, g) -> eval env f *. eval env g
| Quot(f, g) -> eval env f /. eval env g;;
</div><div class="caml-output ok">val eval : (string * float) list -> expression -> float = <fun>
</div></pre>
<pre><div class="caml-input"> eval [("x", 1.0); ("y", 3.14)] (Prod(Sum(Var "x", Const 2.0), Var "y"));;
</div><div class="caml-output ok">- : float = 9.42
</div></pre>
</div><p>Now for a real symbolic processing, we define the derivative of an
expression with respect to a variable <span class="c003">dv</span>:
</p><div class="caml-example">
<pre><div class="caml-input"> let rec deriv exp dv =
match exp with
Const c -> Const 0.0
| Var v -> if v = dv then Const 1.0 else Const 0.0
| Sum(f, g) -> Sum(deriv f dv, deriv g dv)
| Diff(f, g) -> Diff(deriv f dv, deriv g dv)
| Prod(f, g) -> Sum(Prod(f, deriv g dv), Prod(deriv f dv, g))
| Quot(f, g) -> Quot(Diff(Prod(deriv f dv, g), Prod(f, deriv g dv)),
Prod(g, g))
;;
</div><div class="caml-output ok">val deriv : expression -> string -> expression = <fun>
</div></pre>
<pre><div class="caml-input"> deriv (Quot(Const 1.0, Var "x")) "x";;
</div><div class="caml-output ok">- : expression =
Quot (Diff (Prod (Const 0., Var "x"), Prod (Const 1., Const 1.)),
Prod (Var "x", Var "x"))
</div></pre>
</div>
<h2 class="section" id="sec15">1.8  Pretty-printing</h2>
<p>As shown in the examples above, the internal representation (also
called <em>abstract syntax</em>) of expressions quickly becomes hard to
read and write as the expressions get larger. We need a printer and a
parser to go back and forth between the abstract syntax and the <em>concrete syntax</em>, which in the case of expressions is the familiar
algebraic notation (e.g. <span class="c003">2*x+1</span>).</p><p>For the printing function, we take into account the usual precedence
rules (i.e. <span class="c003">*</span> binds tighter than <span class="c003">+</span>) to avoid printing unnecessary
parentheses. To this end, we maintain the current operator precedence
and print parentheses around an operator only if its precedence is
less than the current precedence.
</p><div class="caml-example">
<pre><div class="caml-input"> let print_expr exp =
(* Local function definitions *)
let open_paren prec op_prec =
if prec > op_prec then print_string "(" in
let close_paren prec op_prec =
if prec > op_prec then print_string ")" in
let rec print prec exp = (* prec is the current precedence *)
match exp with
Const c -> print_float c
| Var v -> print_string v
| Sum(f, g) ->
open_paren prec 0;
print 0 f; print_string " + "; print 0 g;
close_paren prec 0
| Diff(f, g) ->
open_paren prec 0;
print 0 f; print_string " - "; print 1 g;
close_paren prec 0
| Prod(f, g) ->
open_paren prec 2;
print 2 f; print_string " * "; print 2 g;
close_paren prec 2
| Quot(f, g) ->
open_paren prec 2;
print 2 f; print_string " / "; print 3 g;
close_paren prec 2
in print 0 exp;;
</div><div class="caml-output ok">val print_expr : expression -> unit = <fun>
</div></pre>
<pre><div class="caml-input"> let e = Sum(Prod(Const 2.0, Var "x"), Const 1.0);;
</div><div class="caml-output ok">val e : expression = Sum (Prod (Const 2., Var "x"), Const 1.)
</div></pre>
<pre><div class="caml-input"> print_expr e; print_newline ();;
</div><div class="caml-output ok">2. * x + 1.
- : unit = ()
</div></pre>
<pre><div class="caml-input"> print_expr (deriv e "x"); print_newline ();;
</div><div class="caml-output ok">2. * 1. + 0. * x + 0.
- : unit = ()
</div></pre>
</div>
<h2 class="section" id="sec16">1.9  Standalone OCaml programs</h2>
<p>All examples given so far were executed under the interactive system.
OCaml code can also be compiled separately and executed
non-interactively using the batch compilers <span class="c003">ocamlc</span> and <span class="c003">ocamlopt</span>.
The source code must be put in a file with extension <span class="c003">.ml</span>. It
consists of a sequence of phrases, which will be evaluated at runtime
in their order of appearance in the source file. Unlike in interactive
mode, types and values are not printed automatically; the program must
call printing functions explicitly to produce some output. Here is a
sample standalone program to print Fibonacci numbers:
</p><pre>(* File fib.ml *)
let rec fib n =
if n < 2 then 1 else fib (n-1) + fib (n-2);;
let main () =
let arg = int_of_string Sys.argv.(1) in
print_int (fib arg);
print_newline ();
exit 0;;
main ();;
</pre><p><span class="c003">Sys.argv</span> is an array of strings containing the command-line
parameters. <span class="c003">Sys.argv.(1)</span> is thus the first command-line parameter.
The program above is compiled and executed with the following shell
commands:
</p><pre>$ ocamlc -o fib fib.ml
$ ./fib 10
89
$ ./fib 20
10946
</pre><p>
More complex standalone OCaml programs are typically composed of
multiple source files, and can link with precompiled libraries.
Chapters <a href="comp.html#c%3Acamlc">8</a> and <a href="native.html#c%3Anativecomp">11</a> explain how to use the
batch compilers <span class="c003">ocamlc</span> and <span class="c003">ocamlopt</span>. Recompilation of
multi-file OCaml projects can be automated using third-party
build systems, such as the
<a href="https://github.com/ocaml/ocamlbuild/">ocamlbuild</a>
compilation manager.
</p>
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