Learn X in Y minutes

# let inc x = x + 1 ;;
val inc : int -> int = <fun>
# let a = 99 ;;
val a : int = 99

$ cat sigtest.ml
let inc x = x + 1
let add x y = x + y

let a = 1

$ ocamlc -i ./sigtest.ml
val inc : int -> int
val add : int -> int -> int
val a : int

(*** Comments ***)

(* Comments are enclosed in (* and *). It's fine to nest comments. *)

(* There are no single-line comments. *)


(*** Variables and functions ***)

(* Expressions can be separated by a double semicolon ";;".
   In many cases it's redundant, but in this tutorial we use it after
   every expression for easy pasting into the interpreter shell.
   Unnecessary use of expression separators in source code files
   is often considered to be a bad style. *)

(* Variable and function declarations use the "let" keyword. *)
(* Variables are immutable by default in OCaml *)
let x = 10 ;;

(* OCaml allows single quote characters in identifiers.
   Single quote doesn't have a special meaning in this case, it's often used
   in cases when in other languages one would use names like "foo_tmp". *)
let foo = 1 ;;
let foo' = foo * 2 ;;

(* Since OCaml compiler infers types automatically, you normally don't need to
   specify argument types explicitly. However, you can do it if
   you want or need to. *)
let inc_int (x: int) : int = x + 1 ;;

(* One of the cases when explicit type annotations may be needed is
   resolving ambiguity between two record types that have fields with
   the same name. The alternative is to encapsulate those types in
   modules, but both topics are a bit out of scope of this
   tutorial. *)

(* You need to mark recursive function definitions as such with "rec" keyword. *)
let rec factorial n =
    if n = 0 then 1
    else n * factorial (n-1)
;;

(* Function application usually doesn't need parentheses around arguments *)
let fact_5 = factorial 5 ;;

(* ...unless the argument is an expression. *)
let fact_4 = factorial (5-1) ;;
let sqr2 = sqr (-2) ;;

(* Every function must have at least one argument.
   Since some functions naturally don't take any arguments, there's
   "unit" type for it that has the only one value written as "()" *)
let print_hello () = print_endline "hello world" ;;

(* Note that you must specify "()" as the argument when calling it. *)
print_hello () ;;

(* Calling a function with an insufficient number of arguments
   does not cause an error, it produces a new function. *)
let make_inc x y = x + y ;; (* make_inc is int -> int -> int *)
let inc_2 = make_inc 2 ;;   (* inc_2 is int -> int *)
inc_2 3 ;; (* Evaluates to 5 *)

(* You can use multiple expressions in the function body.
   The last expression becomes the return value. All other
   expressions must be of the "unit" type.
   This is useful when writing in imperative style, the simplest
   form of which is inserting a debug print. *)
let print_and_return x =
    print_endline (string_of_int x);
    x
;;

(* Since OCaml is a functional language, it lacks "procedures".
   Every function must return something. So functions that do not
   really return anything and are called solely for their side
   effects, like print_endline, return a value of "unit" type. *)


(* Definitions can be chained with the "let ... in" construct.
   This is roughly the same as assigning values to multiple
   variables before using them in expressions in imperative
   languages. *)
let x = 10 in
let y = 20 in
x + y ;;

(* Alternatively you can use the "let ... and ... in" construct.
   This is especially useful for mutually recursive functions,
   with ordinary "let ... in" the compiler will complain about
   unbound values. *)
let rec
  is_even = function
  | 0 -> true
  | n -> is_odd (n-1)
and
  is_odd = function
  | 0 -> false
  | n -> is_even (n-1)
;;

(* Anonymous functions use the following syntax: *)
let my_lambda = fun x -> x * x ;;

(*** Operators ***)

(* There is little distinction between operators and functions.
   Every operator can be called as a function. *)

(+) 3 4  (* Same as 3 + 4 *)

(* There's a number of built-in operators. One unusual feature is
   that OCaml doesn't just refrain from any implicit conversions
   between integers and floats, it also uses different operators
   for floats. *)
12 + 3 ;; (* Integer addition. *)
12.0 +. 3.0 ;; (* Floating point addition. *)

12 / 3 ;; (* Integer division. *)
12.0 /. 3.0 ;; (* Floating point division. *)
5 mod 2 ;; (* Remainder. *)

(* Unary minus is a notable exception, it's polymorphic.
   However, it also has "pure" integer and float forms. *)
- 3 ;; (* Polymorphic, integer *)
- 4.5 ;; (* Polymorphic, float *)
~- 3 (* Integer only *)
~- 3.4 (* Type error *)
~-. 3.4 (* Float only *)

(* You can define your own operators or redefine existing ones.
   Unlike Standard ML or Haskell, only certain symbols can be
   used for operator names and the operator's first symbol determines
   its associativity and precedence rules. *)
let (+) a b = a - b ;; (* Surprise maintenance programmers. *)

(* More useful: a reciprocal operator for floats.
   Unary operators must start with "~". *)
let (~/) x = 1.0 /. x ;;
~/4.0 (* = 0.25 *)


(*** Built-in data structures ***)

(* Lists are enclosed in square brackets, items are separated by
   semicolons. *)
let my_list = [1; 2; 3] ;; (* Has type "int list". *)

(* Tuples are (optionally) enclosed in parentheses, items are separated
   by commas. *)
let first_tuple = 3, 4 ;; (* Has type "int * int". *)
let second_tuple = (4, 5) ;;

(* Corollary: if you try to separate list items by commas, you get a list
   with a tuple inside, probably not what you want. *)
let bad_list = [1, 2] ;; (* Becomes [(1, 2)] *)

(* You can access individual list items with the List.nth function. *)
List.nth my_list 1 ;;

(* There are higher-order functions for lists such as map and filter. *)
List.map (fun x -> x * 2) [1; 2; 3] ;;
List.filter (fun x -> x mod 2 = 0) [1; 2; 3; 4] ;;

(* You can add an item to the beginning of a list with the "::" constructor
   often referred to as "cons". *)
1 :: [2; 3] ;; (* Gives [1; 2; 3] *)

(* Remember that the cons :: constructor can only cons a single item to the front
   of a list. To combine two lists use the append @ operator *)
[1; 2] @ [3; 4] ;; (* Gives [1; 2; 3; 4] *)

(* Arrays are enclosed in [| |] *)
let my_array = [| 1; 2; 3 |] ;;

(* You can access array items like this: *)
my_array.(0) ;;


(*** Strings and characters ***)

(* Use double quotes for string literals. *)
let my_str = "Hello world" ;;

(* Use single quotes for character literals. *)
let my_char = 'a' ;;

(* Single and double quotes are not interchangeable. *)
let bad_str = 'syntax error' ;; (* Syntax error. *)

(* This will give you a single character string, not a character. *)
let single_char_str = "w" ;;

(* Strings can be concatenated with the "^" operator. *)
let some_str = "hello" ^ "world" ;;

(* Strings are not arrays of characters.
   You can't mix characters and strings in expressions.
   You can convert a character to a string with "String.make 1 my_char".
   There are more convenient functions for this purpose in additional
   libraries such as Core.Std that may not be installed and/or loaded
   by default. *)
let ocaml = (String.make 1 'O') ^ "Caml" ;;

(* There is a printf function. *)
Printf.printf "%d %s" 99 "bottles of beer" ;;

(* There's also unformatted read and write functions. *)
print_string "hello world\n" ;;
print_endline "hello world" ;;
let line = read_line () ;;


(*** User-defined data types ***)

(* You can define types with the "type some_type =" construct. Like in this
   useless type alias: *)
type my_int = int ;;

(* More interesting types include so called type constructors.
   Constructors must start with a capital letter. *)
type ml = OCaml | StandardML ;;
let lang = OCaml ;;  (* Has type "ml". *)

(* Type constructors don't need to be empty. *)
type my_number = PlusInfinity | MinusInfinity | Real of float ;;
let r0 = Real (-3.4) ;; (* Has type "my_number". *)

(* Can be used to implement polymorphic arithmetics. *)
type number = Int of int | Float of float ;;

(* Point on a plane, essentially a type-constrained tuple *)
type point2d = Point of float * float ;;
let my_point = Point (2.0, 3.0) ;;

(* Types can be parameterized, like in this type for "list of lists
   of anything". 'a can be substituted with any type. *)
type 'a list_of_lists = 'a list list ;;
type int_list_list = int list_of_lists ;;

(* These features allow for useful optional types *)
type 'a option = Some of 'a | None ;;
let x = Some x ;;
let y = None ;;

(* Types can also be recursive. Like in this type analogous to
   a built-in list of integers. *)
type my_int_list = EmptyList | IntList of int * my_int_list ;;
let l = IntList (1, EmptyList) ;;

(* or Trees *)
type 'a tree =
   | Empty
   | Node of 'a tree * 'a * 'a tree

let example_tree: int tree =
   Node (
      Node (Empty, 7, Empty),
      5,
      Node (Empty, 9, Empty)
   )
(*
   5
  / \
 7   9
*)

(*** Records ***)

(* A collection of values with named fields *)

type animal = 
   {
      name: string;
      color: string;
      legs: int;
   }
;;

let cow = 
   {  name: "cow";
      color: "black and white";
      legs: 4; 
   }
;;
val cow : animal

cow.name ;;
- : string = "cow"

(*** Pattern matching ***)

(* Pattern matching is somewhat similar to the switch statement in imperative
   languages, but offers a lot more expressive power.

   Even though it may look complicated, it really boils down to matching
   an argument against an exact value, a predicate, or a type constructor.
   The type system is what makes it so powerful. *)

(** Matching exact values.  **)

let is_zero x =
    match x with
    | 0 -> true
    | _ -> false  (* The "_" means "anything else". *)
;;

(* Alternatively, you can use the "function" keyword. *)
let is_one = function
| 1 -> true
| _ -> false
;;

(* Matching predicates, aka "guarded pattern matching". *)
let abs x =
    match x with
    | x when x < 0 -> -x
    | _ -> x
;;

abs 5 ;; (* 5 *)
abs (-5) (* 5 again *)

(** Matching type constructors **)

type animal = Dog of string | Cat of string ;;

let say x =
    match x with
    | Dog x -> x ^ " says woof"
    | Cat x -> x ^ " says meow"
;;

say (Cat "Fluffy") ;; (* "Fluffy says meow". *)

(* However, pattern matching must be exhaustive *)
type color = Red | Blue | Green ;;
let what_color x = 
   match x with 
   | Red -> "color is red"
   | Blue -> "color is blue"
   (* Won't compile! You have to add a _ case or a Green case 
      to ensure all possibilities are accounted for *)
;;
(* Also, the match statement checks each case in order.
   So, if a _ case appears first, none of the 
   following cases will be reached! *)

(** Traversing data structures with pattern matching **)

(* Recursive types can be traversed with pattern matching easily.
   Let's see how we can traverse a data structure of the built-in list type.
   Even though the built-in cons ("::") looks like an infix operator,
   it's actually a type constructor and can be matched like any other. *)
let rec sum_list l =
    match l with
    | [] -> 0
    | head :: tail -> head + (sum_list tail)
;;

sum_list [1; 2; 3] ;; (* Evaluates to 6 *)

(* Built-in syntax for cons obscures the structure a bit, so we'll make
   our own list for demonstration. *)

type int_list = Nil | Cons of int * int_list ;;
let rec sum_int_list l =
  match l with
      | Nil -> 0
      | Cons (head, tail) -> head + (sum_int_list tail)
;;

let t = Cons (1, Cons (2, Cons (3, Nil))) ;;
sum_int_list t ;;

(* Heres a function to tell if a list is sorted *)
let rec is_sorted l = 
   match l with 
   | x :: y :: tail -> x <= y && is_sorted (y :: tail)
   | _ -> true
;;

is_sorted [1; 2; 3] ;; (* True *)
(* OCaml's powerful type inference guesses that l is of type int list
   since the <= operator is used on elements of l *)

(* And another to reverse a list *)
let rec rev (l: 'a list) : 'a list = 
  match l with 
  | [] -> []
  | x::tl -> (rev tl) @ [x]
;;

rev [1; 2; 3] ;; (* Gives [3; 2; 1] *)
(* This function works on lists of any element type *)

(*** Higher Order Functions ***)

(* Functions are first class in OCaml *)

let rec transform (f: 'a -> 'b) (l: 'a list) : 'b list =
  match l with
  | [] -> []
  | head :: tail -> (f head) :: transform f tail
;;

transform (fun x -> x + 1) [1; 2; 3] ;; (* Gives [2; 3; 4] *)

(** Lets combine everything we learned! **)
let rec filter (pred: 'a -> bool) (l: 'a list) : 'a list =
  begin match l with
  | [] -> []
  | x :: xs ->
     let rest = filter pred xs in
     if pred x then x :: rest else rest
  end
;;

filter (fun x -> x < 4) [3; 1; 4; 1; 5] ;; (* Gives [3; 1; 1]) *)

(*** Mutability ***)

(* Records and variables are immutable: you cannot change where a variable points to *)

(* However, you can create mutable polymorphic fields *)
type counter = { mutable num : int } ;;

let c = { num: 0 } ;;
c.num ;; (* Gives 0 *)
c.num <- 1 ;; (* <- operator can set mutable record fields *)
c.num ;; (* Gives 1 *)

(* OCaml's standard library provides a ref type to make single field mutability easier *)
type 'a ref = { mutable contents : 'a } ;;
let counter = ref 0 ;;
!counter ;; (* ! operator returns x.contents *)
counter := !counter + 1 ;; (* := can be used to set contents *)