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intro_ocaml.html
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<div id="content">
<h1 class="title">Introduction to OCaml</h1>
<div id="outline-container-org004ef66" class="outline-2">
<h2 id="org004ef66"><span class="section-number-2">1</span> Background</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-orgab0a78e" class="outline-3">
<h3 id="orgab0a78e"><span class="section-number-3">1.1</span> The Categorical Abstract Machine Language</h3>
<div class="outline-text-3" id="text-1-1">
<p>
OCaml is part of the ML family, like SML (big brother) or F# (little brother).
</p>
<dl class="org-dl">
<dt>1973</dt><dd>(classic) ML <a class='org-ref-reference' href="#ClassicML">ClassicML</a></dd>
<dt>1987-1992</dt><dd>Heavy CAML (LISP-based implementation)</dd>
<dt>1990-1991</dt><dd>Caml Light</dd>
<dt>1996</dt><dd>Objective Caml <code>1.00</code></dd>
<dt>2011</dt><dd>Objective Caml becomes OCaml</dd>
<dt>2020</dt><dd>OCaml <code>4.10.0</code> (Feb 21)</dd>
</dl>
</div>
</div>
<div id="outline-container-orgb7be8f6" class="outline-3">
<h3 id="orgb7be8f6"><span class="section-number-3">1.2</span> OCaml : an open-minded functional language</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-center">
<p>
OCaml is <b>not</b> a pure functional language
</p>
</div>
<ul class="org-ul">
<li>imperative programming is very much part of the nominal toolbox</li>
<li>OOP too when it is the right fit.</li>
</ul>
</div>
</div>
<div id="outline-container-orgd151add" class="outline-3">
<h3 id="orgd151add"><span class="section-number-3">1.3</span> Bytecode and native code support</h3>
<div class="outline-text-3" id="text-1-3">
<p>
2 compilers for the price of one:
</p>
<dl class="org-dl">
<dt><code>ocamlc</code></dt><dd>a bytecode compiler to a stack-based
<ul class="org-ul">
<li>its interpreter <code>ocamlrun</code> works anywhere you have a C compiler</li>
</ul></dd>
<dt><code>ocamlopt</code></dt><dd>a native code compiler
<ul class="org-ul">
<li>supports x86 (32/64), ARM (v5-v8), PowerPC (32/64) and … SPARC !</li>
<li>RISC-V will be in <code>4.11</code></li>
</ul></dd>
</dl>
</div>
</div>
<div id="outline-container-orga01b54b" class="outline-3">
<h3 id="orga01b54b"><span class="section-number-3">1.4</span> Users</h3>
<div class="outline-text-3" id="text-1-4">
<ul class="org-ul">
<li>Academic circles
<dl class="org-dl">
<dt>academia</dt><dd><b>INRIA</b>, Berkeley, CEA, CMU, UArizona, UPenn</dd>
<dt>SMEs</dt><dd>OCamlPro/Origin Labs, Nomadic Labs, TrustInSoft, Tarides,</dd>
</dl></li>
<li>Financial "institutions" – Bloomberg, Jane Street, Lexifi, SimCorp</li>
<li>Facebook (ReasonML, Infer)</li>
<li>Atos, AbsInt</li>
<li>Indirect users: Airbus (Astrée, Frama-C, Fluctuat), EDF, …</li>
<li>…</li>
</ul>
</div>
<ol class="org-ol">
<li><a id="orgd28215d"></a>:B<sub>note</sub>:<br />
<div class="outline-text-4" id="text-1-4-1">
<p>
Its french origin shows in the community. The financial application have
increased recently but Lexifi started 20 years ago (ICFP 2000)
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-org2355b3a" class="outline-3">
<h3 id="org2355b3a"><span class="section-number-3">1.5</span> Natural application fields</h3>
<div class="outline-text-3" id="text-1-5">
<ul class="org-ul">
<li>compilers</li>
<li>program analysis</li>
<li>theorem proving</li>
<li>symbolic computations</li>
</ul>
</div>
</div>
<div id="outline-container-org56b988f" class="outline-3">
<h3 id="org56b988f"><span class="section-number-3">1.6</span> Tooling (as of 2020)</h3>
<div class="outline-text-3" id="text-1-6">
<dl class="org-dl">
<dt><a href="https://github.com/ocaml/ocaml">compiler</a></dt><dd>last release is <code>4.10</code> (2020-02-21)</dd>
<dt><a href="https://github.com/ocaml/merlin">merlin</a></dt><dd><p>
context-sensitive completion for OCaml (in Vim, Emacs, VsCode, …)
</p>
<p>
A <b>very</b> nice tool which has changed the life of most OCaml developers,
and it's editor-agnostic !
</p></dd>
<dt><a href="https://github.com/ocaml/dune">dune</a></dt><dd><p>
newest contender in dedicated build systems
</p>
<p>
Subsumes <code>OCamlMakefile</code>, <code>omake</code>, <code>ocamlbuild</code>.
</p></dd>
<dt><a href="https://github.com/ocaml/opam">OPAM</a></dt><dd><p>
<code>1.0</code> in 2013, current is <code>2.0.7</code> (2020-04-21)
</p>
<p>
A source-based package manager for OCaml software.
</p></dd>
<dt>Emacs</dt><dd>or another editor</dd>
</dl>
<div class="org-center">
<p>
<a href="https://opam.ocaml.org/blog/turn-your-editor-into-an-ocaml-ide/">https://opam.ocaml.org/blog/turn-your-editor-into-an-ocaml-ide/</a>
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgd7f3111" class="outline-2">
<h2 id="orgd7f3111"><span class="section-number-2">2</span> Building blocks</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org2969803" class="outline-3">
<h3 id="org2969803"><span class="section-number-3">2.1</span> let-bindings</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-ocaml">let add x y = x + y (* or let add = ( + ) *)
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val add : int -> int -> int = <fun>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">let simple_main () =
let x = read_int () in
let y = read_int () in
print_int (add x y);
print_newline ()
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val simple_main : unit -> unit = <fun>
</pre>
</div>
</div>
<ol class="org-ol">
<li><a id="orgd179e5b"></a>:B<sub>note</sub>:<br />
<div class="outline-text-4" id="text-2-1-1">
<p>
Name bindings are introduced by <code>let</code>. <code>let .. in</code> is a locally scoped binding.
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-orgd038ebc" class="outline-3">
<h3 id="orgd038ebc"><span class="section-number-3">2.2</span> Functions: curried by default</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Functions are <b>curried</b> (unlike SML functions).
</p>
<p>
<code>add x y</code> actually is <code>(add(x))(y)</code>
</p>
<p>
<code>add</code> can be partially applied, as <code>add x</code>.
</p>
<div class="org-src-container">
<pre class="src src-ocaml">let add1 = add 1 ;;
add1 2
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">- : int = 3
</pre>
</div>
</div>
<ol class="org-ol">
<li><a id="org7bdad46"></a>:B<sub>note</sub>:<br />
<div class="outline-text-4" id="text-2-2-1">
<p>
Currying is taking a multiple argument functions and converting it to n
1-arg funs
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-orgc19f6a4" class="outline-3">
<h3 id="orgc19f6a4"><span class="section-number-3">2.3</span> Recursivity</h3>
<div class="outline-text-3" id="text-2-3">
<p>
Recursive functions are explicitly qualified by the <b>rec</b> keyword.
</p>
<div class="org-src-container">
<pre class="src src-ocaml">(** [foldlf v l] is f ... (f (f v a0) a1) ... an)
** assuming [l] is [a0; a1; ...; an].
** [foldl] is sometimes called reduce ,*)
let rec foldl f acc = function
| [] -> acc
| x :: xs -> foldl f (f acc x) xs ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val foldl : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a = <fun>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">foldl (+) 0 [1;2;3;4] ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">- : int = 10
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">(** [( |-> ) n m] is an infix operator computing
** the list of elements from [n] included to [m] included. *)
let ( |-> ) lo hi =
let rec loop acc n =
if n > hi then List.rev acc
else loop (n :: acc) (n + 1) in
loop [] lo
;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val ( |-> ) : int -> int -> int list = <fun>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">1 |-> 10 ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">- : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
</pre>
</div>
</div>
<ol class="org-ol">
<li><a id="orgffffe62"></a>:B<sub>note</sub>:<br />
<div class="outline-text-4" id="text-2-3-1">
<ul class="org-ul">
<li>We can define functions inside functions</li>
<li>We'll see later that closures (reference to outer env) are done automatically</li>
<li>The pattern inside is very common to get tail-recursion (accumulate then reverse)</li>
</ul>
</div>
</li>
</ol>
</div>
<div id="outline-container-orgcdbe572" class="outline-3">
<h3 id="orgcdbe572"><span class="section-number-3">2.4</span> Corollary</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-center">
<p>
Functions are <b>not recursive</b> by default.
</p>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">(* This second declaration hides the first.*)
let ( |-> ) lo hi =
assert (hi >= lo);
lo |-> hi
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val ( |-> ) : int -> int -> int list = <fun>
</pre>
</div>
</div>
<ol class="org-ol">
<li><a id="org3b41d26"></a>:B<sub>note</sub>:<br />
<div class="outline-text-4" id="text-2-4-1">
<p>
Assertions are checked at runtime and trigger (catchable) exceptions
</p>
<p>
<code>-noassert</code> do not compile time, except the <code>assert false</code> special form.
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-orgb04fe61" class="outline-3">
<h3 id="orgb04fe61"><span class="section-number-3">2.5</span> Functions are first-class citizens</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-ocaml">(** [max cmp l] computes the maximun element of a list [l] provided a [cmp]
** function conforming to the following specification:
** - cmp x y = 0 if x is equivalent to y
** - cmp x y > 0 if x is bigger than y
** - cmp x y < 0 if x if smaller than y **)
let max cmp l =
let rec loop vmax = function
| [] -> vmax
| x :: xs ->
let vmax' =
match vmax with
| None -> Some x
| Some y -> if cmp x y > 0 then Some x else vmax in
loop vmax' xs
in loop None l
;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val max : ('a -> 'a -> int) -> 'a list -> 'a option = <fun>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">max Stdlib.compare [1; 2; 3;] ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">- : int option = Some 3
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">(* We just hid [Stdlib.max] behind another definition !*)
Stdlib.max ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">- : 'a -> 'a -> 'a = <fun>
</pre>
</div>
</div>
</div>
<div id="outline-container-org18c87ca" class="outline-3">
<h3 id="org18c87ca"><span class="section-number-3">2.6</span> Evaluation is strict</h3>
<div class="outline-text-3" id="text-2-6">
<p>
Laziness (call-by-name / call-by-need) is not the default evaluation mode.
</p>
<p>
OCaml is said to be <b>strict</b> (call-by-value).
</p>
<div class="org-src-container">
<pre class="src src-ocaml">let double x = print_int x; 2 * x ;;
(* We forgot to use x ... *)
let dadd _x y =
let x' = double y
and y' = double y in
(* Infix operators are prefixed ones that are treated specially
by the parser. Have fun and create your owns. *)
( + ) x' y' ;;
dadd (double 1) (double 2) ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">2144- : int = 16
</pre>
</div>
<p>
… well except for binary Boolean operators – of course ;-).
</p>
</div>
<ol class="org-ol">
<li><a id="orgda3400e"></a>:B<sub>note</sub>:<br />
<div class="outline-text-4" id="text-2-6-1">
<p>
We see not only that all arguments are evaluated (even unused ones), but
that <code>double y</code> is evaluated twice. Not much optimization is done by default.
</p>
<p>
The <code>_</code> prefix notation avoid unused variable warning
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-orgbac9467" class="outline-3">
<h3 id="orgbac9467"><span class="section-number-3">2.7</span> Evaluation Oddity</h3>
<div class="outline-text-3" id="text-2-7">
<p>
Evaluation order for function arguments is <b>unspecified</b>.
</p>
<p>
It is usually right-to-left, as exemplified by the snippet below.
</p>
<div class="org-src-container">
<pre class="src src-ocaml">add (print_string "foo!"; 1) (print_string "bar!"; 2) ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">bar!foo!- : int = 3
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">( || ) (print_string "foo!"; false) (print_string "bar!"; true) ;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">foo!bar!- : bool = true
</pre>
</div>
</div>
</div>
<div id="outline-container-org581642e" class="outline-3">
<h3 id="org581642e"><span class="section-number-3">2.8</span> Grouping information : Tuples   <span class="tag"><span class="proofreading">proofreading</span></span></h3>
<div class="outline-text-3" id="text-2-8">
<div class="org-src-container">
<pre class="src src-ocaml">let a = 1, 2 in
let x, y = a in
x + y
;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">- : int = 3
</pre>
</div>
<p>
can also be written with <code>( .. )</code> as
</p>
<div class="org-src-container">
<pre class="src src-ocaml">let a = (1, 2) in
let (x, y) = a in
x + y
;;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">- : int = 3
</pre>
</div>
</div>
</div>
<div id="outline-container-org8f4ecee" class="outline-3">
<h3 id="org8f4ecee"><span class="section-number-3">2.9</span> Everything is a pattern</h3>
<div class="outline-text-3" id="text-2-9">
<div class="org-src-container">
<pre class="src src-ocaml">let create x y z = x, y, z
(* FP arithmetic operations have a dedicated syntax *)
let square a = a *. a
let dist (x1, y1, z1) p =
let x2, y2, z2 = p in
let xdiff = x2 -. x1
and ydiff = y2 -. y1
and zdiff = z2 -. z1 in
square xdiff +. square ydiff +. square zdiff |> sqrt
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val dist : float * float * float -> float * float * float -> float = <fun>
</pre>
</div>
</div>
</div>
<div id="outline-container-orga820526" class="outline-3">
<h3 id="orga820526"><span class="section-number-3">2.10</span> <code>dist</code>: another version</h3>
<div class="outline-text-3" id="text-2-10">
<div class="org-src-container">
<pre class="src src-ocaml">let dist p1 p2 =
match p1, p2 with
(* The | can also be used as a separator instead of as a starting
annotation. *)
| (x1, y1, z1), (x2, y2, z2) ->
let xdiff = x2 -. x1
and ydiff = y2 -. y1
and zdiff = z2 -. z1 in
sqrt @@ square xdiff +. square ydiff +. square zdiff
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val dist : float * float * float -> float * float * float -> float = <fun>
</pre>
</div>
</div>
<ol class="org-ol">
<li><a id="org05f276e"></a>:B<sub>note</sub>:<br />
<div class="outline-text-4" id="text-2-10-1">
<p>
I've deliberately used <code>@@</code> instead of <code>|></code> to show yet another infix operator
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-org4c66452" class="outline-3">
<h3 id="org4c66452"><span class="section-number-3">2.11</span> Grouping information : Records (aka named tuples)</h3>
<div class="outline-text-3" id="text-2-11">
<div class="org-src-container">
<pre class="src src-ocaml">type point_2d = { x : float; y: float; } ;;
(* C-like . notations for field access *)
let dist p1 p2 =
let xdiff = p1.x -. p2.x
and ydiff = p1.y -. p2.y in
sqrt (xdiff *. xdiff +. ydiff *. ydiff)
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val dist : point_2d -> point_2d -> float = <fun>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">(* Using pattern-matching *)
let dist p1 p2 =
match p1, p2 with
| { x; y; }, { x = x'; y = y';} ->
let xdiff = x -. x'
and ydiff = y -. y' in
sqrt (xdiff *. xdiff +. ydiff *. ydiff)
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val dist : point_2d -> point_2d -> float = <fun>
</pre>
</div>
</div>
</div>
<div id="outline-container-org76982ca" class="outline-3">
<h3 id="org76982ca"><span class="section-number-3">2.12</span> Building / destructing records</h3>
<div class="outline-text-3" id="text-2-12">
<div class="org-src-container">
<pre class="src src-ocaml">(* Record can be built/destructed using a shortcut notation.
[let create x y = { x; y; }] is a shortcut for
[let create x y = { x = x; y = y; }].
Choose your field names wisely and unleash your inner procrastinator !
*)
let create x y = { x; y; }
let of_int myx myy = { x = float myx; y = float myy; }
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">val create : float -> float -> point_2d = <fun>
val of_int : int -> int -> point_2d = <fun>
</pre>
</div>
</div>
<ol class="org-ol">
<li><a id="orge52ef5b"></a>Record size   <span class="tag"><span class="B_ignoreheading">B_ignoreheading</span></span><br />
<div class="outline-text-4" id="text-2-12-1">
<p>
Records are limited to 2<sup>22</sup> − 1 fields (aka max <code>Array</code> size)
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-org71a0959" class="outline-3">
<h3 id="org71a0959"><span class="section-number-3">2.13</span> ADT & pattern matching</h3>
<div class="outline-text-3" id="text-2-13">
</div>
<ol class="org-ol">
<li><a id="orgefb7915"></a>Exhustiveness   <span class="tag"><span class="B_ignoreheading">B_ignoreheading</span></span><br />
<div class="outline-text-4" id="text-2-13-1">
<p>
Exhaustiveness and fragility of pattern-matchings are reported by default.
</p>
</div>
</li>
<li><a id="org6c470a5"></a>Example ADT (continue in next slide)   <span class="tag"><span class="B_ignoreheading">B_ignoreheading</span></span><br />
<div class="outline-text-4" id="text-2-13-2">
<div class="org-src-container">
<pre class="src src-ocaml">type prop = (* inductively defined types do not need a rec keyword *)
| Pcst of bool
| Pvar of string
| Pand of prop * prop
| Por of prop * prop
| Pnot of prop
</pre>
</div>
</div>
</li>
</ol>
</div>
<div id="outline-container-orge14c9d2" class="outline-3">
<h3 id="orge14c9d2"><span class="section-number-3">2.14</span> Lack of exhaustiveness   <span class="tag"><span class="B_frame">B_frame</span></span></h3>
<div class="outline-text-3" id="text-2-14">
<div class="org-src-container">
<pre class="src src-ocaml">let free_variables =
(* The pattern matching in [loop] is well-typed but not exhaustive *)
let rec loop vars = function
| Pvar s -> if List.mem s vars then vars else s :: vars
| Pand (p1, p2) ->
let vars' = loop vars p1 in
loop vars' p2
in loop []
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml">Line 3, characters 22-169:
3 | ......................function
4 | | Pvar s -> if List.mem s vars then vars else s :: vars
5 | | Pand (p1, p2) ->
6 | let vars' = loop vars p1 in
7 | loop vars' p2
Warning 8: this pattern-matching is not exhaustive.
Here is an example of a case that is not matched:
(Pcst _|Por (_, _)|Pnot _)
val free_variables : prop -> string list = <fun>
</pre>
</div>
</div>
</div>
<div id="outline-container-org5b44763" class="outline-3">
<h3 id="org5b44763"><span class="section-number-3">2.15</span> Fragility   <span class="tag"><span class="B_frame">B_frame</span></span></h3>
<div class="outline-text-3" id="text-2-15">
<div class="org-src-container">
<pre class="src src-ocaml">let free_variables =
(* Now it is exhaustive, but ... fragile *)
let rec loop vars = function
| Pvar s -> if List.mem s vars then vars else s :: vars
| Pand (p1, p2) ->
let vars' = loop vars p1 in loop vars' p2