The listing sheet, as PDF, can be found here, or as a single column portrait, while below is an unruly html rendition.
This reference sheet is built from a CheatSheets with Org-mode system.
- Emacs Setup:HTML:
- Arithmetic
- Functions & Variables
- Booleans
- Strings
- Records
- Variants and Pattern Matching
- Tuples and Lists
- Options
- Imperative Programming —Sequencing &
main - Imperative Programming —Arrays
- Imperative Programming —Unit Type
- Imperative programming —Mutable records
- Imperative Programming —References
- Modules
- Functors
- First-Class Modules
- Locally Abstract Types & ‘[un]bundling’
- Metaprogramming with MetaOCaml
- Reads
OCaml is a strict language; it is strongly typed where types are inferred.
I may write explicit type annotations below for demonstration or clarity purposes.
(* Using explicit type annotations *)
let x : int = 3;;
let f (x : int) (y : string) (r : 'a) : float = 3.14;;
Only when interacting with the top-level interpreter,
commands must be terminated by ;;.
OCaml uses ; as an expression separator —not a terminator!
My Emacs setup for OCaml can be found on this CheatSheet's repo.
First, let's get [Meta]OCaml.
;; Easiest on my machine.
;; (async-shell-command "brew install ocaml")
;; The OCaml package manager: https://opam.ocaml.org/
(async-shell-command "brew install opam") ;; version 2.0.4
;; (async-shell-command "opam switch create 4.07.1") ;; install ocaml
(async-shell-command "opam switch create 4.07.1+BER") ;; install metaocaml
Let's set this up for Emacs.
(use-package tuareg :demand t) ;; Emacs’ OCaml mode
(setq tuareg-support-metaocaml t) ;; Only handles metaocaml syntax
(setq org-babel-ocaml-command "metaocaml") ;; Different command for metaocaml
Let's obtain ocp-indent —OCaml's indentation tool that indents the same even if
co-workers use a different editor— and merlin which provides interactive feedback
including context-aware completion and jumping to definitions.
(async-shell-command "time opam install ocp-indent merlin") ;; real 1m33.636s
(use-package merlin)
(add-hook 'tuareg-mode-hook #'merlin-mode)
(with-eval-after-load 'merlin (setq merlin-command 'opam))
Now entering, say, List. brings a pop-up completion menu for the
contents of the list module.
—In org-src blocks, you need to enter the ocaml mode, via C-c '.
Operations on floats have a ‘.’ suffix.
8 / 3;; (* 2 *)
8 /. 3;; (* Type error: /. is for floats *)
8.0 /. 3.0;; (* 2.6666… *)
A function is declared with the let keyword
—variables are functions of zero arguments.
Function & varaible names must begin with a lowercase letter, and may use _ or '.
- They cannot begin with capital letters or numbers, or contain dashes!
- Functions are like variables, but with arguments, so the same syntax applies.
(* Function application *)
let result = f 10 (2 * 6)
(* Partial application *)
let g x = f x 2
(* We can re-bind variables *)
let x = 123
let x = string_of_int x
Recursive functions are marked with the rec keyword.
let rec fact n = if n = 0
then 1
else n * fact (n - 1)
Here's an example of a higher-order function & multiple local functions & an infix operator & an anonymous function & the main method is parametricly polymorphic.
let try_add (bop : 'a -> 'a -> 'a) (test : 'a -> bool)
(default : 'a) (x : 'a) (y : 'a)
= let (/@/) x y = bop x y
(* Only select symbols can be used as infix operators *)
(* (/@/) x y = x /@/ y *)
and wrap a = if test a then a else default
in wrap x /@/ wrap y;;
699 = try_add (+) (fun a -> a mod 3 = 0) (666) (~-1) 33;;
(* The anonymouse function uses ‘=’ as Boolean equality. *)
~- 2 = ~- 2 mod 3;; (* /Remainder/ after dividing out 3s *)
Inequality is expressed with <>.
(* false, true, false, true, false, true, true, 1 *)
true = false , true || false, true && false, true >= false
, 12 < 2, "abc" <= "abd", 1 <> 2
, if true then 1 else 2
OCaml strings are not arrays, or lists, of characters as in C or Haskell.
"string catenation" = "string " ^ "catenation"
Printf.printf "%d %s" 1972 "taxi";;
let input = read_line ();;
Records: Products with named, rather than positional, components.
type point2d = {x : float; y : float};;
(* Construction *)
let p = {y = 2.0; x = 3.4};;
(* Pattern matching for deconstruction *)
let {x = px; y = py} = p;;
let go {x = qx; y = qy} = qx +. qy;;
(* More tersely, using “field punning”: Variables must coincide with field names. *)
let erroenous ({xx; y} : point2d )= x +. y;;
let works {x; y} = 0.0;;
(* Or we can use dot notation *)
let go q = q.x +. q.y;;
Variant types: A unified way to combine different types into a single type; each case is distinuighed by a capitalised tag.
(* Constructors must start with a capital letter, like in Haskell *)
type 'a fancy_num = Nothing | Boring of int | Fancy of 'a
| Point of point2d | Pair of 'a fancy_num * 'a fancy_num
let example = Pair (Fancy "twenty", Point {x = 1.2; y = 3.14})
The tags allow us to extract components of a variant value as well as to case against values by inspecting their tags. This is pattern matching.
(* Destructuring a value *)
let Pair(head, _) = example;;
(* Guarded pattern matching, with in-line casing via ‘match’ *)
let rec sum acc = function
| Nothing -> 0 + (match acc with true -> 1 | false -> 0)
| Fancy x when x <= "nine" -> 0
| (Fancy "twenty") as p -> failwith "Evil!"
| Pair(l, r) -> sum acc l + sum acc r
| _ -> 2 (* Default case *)
let res = sum true example (* Exception: Failure "Evil!" *)
(* Type aliases can also be formed this way *)
type myints = int
Note that we can give a pattern a name; above we mentioned p,
but did not use it.
-
Repeated & non-exhaustive patterns trigger a warning; e.g., remove the default case above.
-
You can pattern match on arrays too; e.g.,
[| x ; y ; z|] -> y.
The above mechanisms apply to all variants —including tuples, lists, and options.
Tuples: Parentheses are optional, comma is the main operator.
let mytuple : int * string * float = (3, "three", 3.0);;
(* Pattern matching & projection *)
let (woah0, woah1, woah2) = mytuple;;
let add_1and4 (w, x, y, z) = w + z;;
let that = fst ("that", false)
(* A singelton list of one tuple !!!! *)
let zs = [ 1, "two", true ]
(* Lists: type 'a list = [] | (::) of 'a * 'a list *)
let xs = [1; 2; 3]
[1; 2; 3] = 1 :: 2 :: 3 :: [];; (* Syntactic sugar *)
(* List catenation *)
[1;2;4;6] = [1;2] @ [4;6];;
(* Pattern matching example; Only works on lists of length 3 *)
let go [x; y; z] = x + y + z;;
14 = go [2;5;7];;
(* Labelled arguments, using ‘~’, means position is irrelevant *)
[1; 2; 3] = List.map ["a", "ab", "abc"] ~f:String.length;;
[1; 2; 3] = List.map ~f:String.length ["a", "ab", "abc"];;
\columnbreak
Option: Expressing whether a value is present or not.
(* type 'a option = None | Some of 'a *)
let divide x y : int option = if y = 0 then None else Some (x / y);;
let getInt ox = match ox with None -> 0 | Some x -> x;;
0 = getInt None;;
2 = getInt (Some 2);;
We may use begin/end or parentheses to group expressions together.
(* Parentheses *)
( print_string "a"
; () (* This is the unit value *)
; 9
);;
(* Begin-end block *)
begin
print_string "nice";
"bye";
true;
10
end;;
Remember: Single semicolon ; is for sequencing whereas double ;; is for termination.
OCaml programs don't have a unique main function as in C, instead the entire file
is evaluated sequentially at startup, which may contain arbitrary expressions not just functional declarations,
and so in some sense the full codebase is one big main function.
Zero-indexed Arrays: Indexing with .(i) and update with <-.
let nums : int array = [| 1; 2; 3 |];;
nums.(0) <- 12;;
12 = nums.(0);;
[|12; 2; 3|] = nums;;
What is the type of update, <-? A function that returns the unit type!
—see myupdate below.
Operations whose use produces a side-effect return the unit type.
This’ akin to the role played by void in C.
A function is a sequence of expressions; its return value
is the value of the final expression —all other expressions
are of unit type.
let myupdate (arr : 'a array) (e : 'a)
(i : int) : unit
= arr.(i) <- e;;
myupdate nums 33 1;;
[|12; 33; 3|] = nums;;
let my_io () = print_endline "Hello!" ;;
let const x y
= my_io();
y;
x;;
let res = const 1972 12;;
Record fields are immutable by default, but can be declared mutable.
type running_sum = {mutable sum : int; mutable more : int};;
let create () = {sum = 0; more = 0};;
let update rs x = rs.sum <- rs.sum + rs.more
; rs.more <- x;;
let res = create ()
in update res 12
; {sum = 0; more = 12} = res ;;
References: Single mutable values; i.e., a record with a single mutable field named contents.
let x : int ref = {contents = 0}
in x.contents <- x.contents + 1; {contents = 1} = x;;
Refs come with a handful of convenience methods; here's their re-implementation:
(* Alias *) type 'a ref = {mutable contents : 'a};;
(* Creation *) let ref v = {contents = v};;
(* Access *) let (!) r = r.contents;; (* “value of” *)
(* Update *) let (:=) r e = r.contents <- e;;
Notice that ref is overloaded: As a type former and as a function forming values.
(* Summing the first 10 numbers *)
let sum = ref 0
in for i = 0 to 10 do sum := !sum + i done
; 55 = !sum;;
true
\columnbreak
OCaml files not only store & manage code, but also correspond to (second-class) ‘modules’, which act as boundaries that divide a program into conceptual units.
-
At its simplest, a module is a collection of definitions that are stored within a namespace.
-
Implementation details of a module can be hidden by using an interface, module type, signature —all are aliases.
valdeclarations specify values in a signature:val ⟪identifier⟫ : ⟪type⟫.- A type is abstract if its name is exposed in the interface but its definition is not:
type t.- It is conventional to use
tfor the name of such types.
- It is conventional to use
- Including the type definition in the interface makes the type concrete.
-
E.g., module names are derived, with capitalisation, automatically from file names. An interface for
myfile.mlto constrain exposed interface is placed inmyfile.mli.This is nearly how C header and implementation files work.
-
Modules & signatures can be nested inside other modules.
Modules names always begin with a capital; their contents are accessed with dot notation. Here is the general syntax:
(* Module declaration *)
module ‘Name’ : ‘signature’ = struct ‘implementation’ end
(* Signature declaration *)
module type ‘Name’ = sig ‘sig_decls’ end
(* sig_decls are a space-separated sequence of “type” or “val : ‘name’ : ‘type’”
declarations. A “type” declaration with no “= ⋯” is an abstract type. *)
Without constructors type creates aliases, if we want to treat a type in two different
ways and have the compiler ensure we don't mess-up, we produce single-constructor new
types:
let jasim : person = P "jasim";;
let home : address = A "the farm";;
(* Type error *)
let this : person = home;;
(* If needed, we could make coercions *)
let person_to_string : person -> string
= function P s -> s
let address_of_string : string -> address
= fun s -> A s
However, if the underlying type were the same, this repetition could be error-prone.
Instead, we could use generative modules: Distinct types with the same underlying implementation.
Being ‘generative’ is akin to the new keyword in Java:
Each use of the BasicImplementation module below makes a new type.
module BasicImplementaion
: EssentiallyString = struct
type t = string
let to_string x = x
let from_string x = x
let (=) l r = String.(l = r)
end
Note that BasicImplemention is just a namespace where, e.g., t is an alias for string.
(* Here we get to reuse the above, thereby avoiding repetition *)
module Person : EssentiallyString = BasicImplementaion
module Address : EssentiallyString = BasicImplementaion
let jasim : Person.t = Person.from_string "jasim";;
let home : Address.t = Address.from_string "the farmlands";;
(* Type error: Expected a Person.t, but have a Address.t *)
let uhoh : Person.t = home;;
Note that we could have placed the definitions of EssentiallyString
and \newline BasicImplementaion in-line for the Person and Address module
declarations —without syntactic alterations— but that would have
defeated our purpose of avoiding repetition.
Without the type annotation, we could accidentally forget to implement
part of the interface & OCaml would infer a different module type.
Use the module type of operator to see what was inferred.
module ErroneousImplementation = struct
type t = string let (=) l r = String.(l = r)
end
module type S = (module type of ErroneousImplementation)
(* module type S = sig type t = string val ( = ) : 'a -> 'a -> bool end *)
Many equivalent ways to use module contents —the third is for small expressions.
-
Note the dot!
let qasim = Person.(from_string "jasim") in (let open Person in qasim = jasim) , Person.(=) qasim jasim , Person.(from_string "jasim" = jasim) (* Rebind module name to a shorter name *) , let module P = Person in P.(qasim = jasim) ;;
While opening a module [type] affects the environment used to search for identifiers,
including a module is a way of adding new identifiers to a module [type] proper
—it is a copy-paste of constituents.
For example, we could re-organise EssentialyString into a hierarchy:
module type Type = sig type t end
module type Relation = sig include Type val (=) : t -> t -> bool end
(* module type Relation = sig type t val ( = ) : t -> t -> bool end *)
module type PingPong = sig
include Type val from_string : string -> t val to_string : t -> string end
This allows us to form extensions to modules, akin to C#:
To extend, say, the List module with a new function f so that
List.f is valid, we make and open module List = struct let f = ⋯ include List.
If we wanted to override an existing f, we put its definition after the include.
The interface would be sig val f : ⋯ include (module type of List) end.
When we have multiple declarations of a type or we have type that is too abstract to be
of use, expect to see:
Error: This expression has type 𝓉 but an expression was expected of type M.t; instead maybe use M.t with type t = 𝓉, where:
(* “Constraint Sharing”: Declaration of t stays as an alias. *)
sig type t val ⋯ end with type t = imp
≈ sig type t = imp val ⋯ end
(* “Destructive Substitution”: Declaration of t is gone. *)
sig type t val ⋯t⋯ end with type t := imp
≈ sig val ⋯imp⋯ end
We may now continue our EssentiallyString hierarchy:
module type IntRelation = sig include Relation with type t := int end
(* Desugars: module type IntRelation = sig val ( = ) : int -> int -> bool end *)
module type EssentiallyStr = sig include Type include Relation with type t := t end
Warning! The order of constructor declarations for a concrete type variant must be the same in the implementation as in the interface, likewise for record fields and function arguments.
Functors are, roughly speaking, functions from modules to modules. — There's no “modules to module types” thing, instead we return a module that contains a module type ;-) —
\room Functors provide the same abstraction features as functions do but also allow the implementation of one module to vary depending on another module. In contrast to functions, functors require explicit type annotation —otherwise how would we know what constituents the input module contains— and their arguments must be enclosed in parentheses.
In a sense, these are parameterised modules —as in Agda— and that is how they may be treated syntactically in OCaml:
(* Example functor that takes a namespace having ‘x’
and yields a namspace with ‘x’ incremented. *)
module type OneInt = sig val x : int end;;
module IncrementFunctor (M : OneInt) : OneInt = struct let x = M.x + 1 end;;
module Three : OneInt = struct let x = 3 end;;
module Four : OneInt = IncrementFunctor(Three);;
Four.x = Three.x + 1;;
A functor may be applied to any module that satisfies the functor's input interface:
module Point = struct let x = 0 let y = 1 end;;
module One = IncrementFunctor(Point);;
One.x = Point.x + 1;;
Modules can contain types & values, but ordinary values can't contain modules or module types. In order to define variables whose value is a module, or a function that takes a module as an argument, OCaml provides first-class modules which are ordinary values that can be created from and converted back to regular modules.
A first-class module is created by packaging up a module with a signature that
it satisfies by using the module keyword:
let three : (module OneInt) = (module Three : OneInt);;
let three' = (module Three);; (* Error: Signature couldn't be inferred *)
let three'' : (module OneInt) = (module Three);;
let three''' = (module Three : OneInt);; (* Most terse ^_^ *)
(* Lists are homogeneous, whence latters' type inferred from formers' *)
let list_of_modules = [three; (module Three); (module Four)];;
Dot notation only works for records and modules, so we access contents of a
first-class module by turning it into an ordinary module with val:
let x : int = let module M = (val three : OneInt) in M.x;;
let x : int = (val three : OneInt).x;; (* Error: Invalid syntax. *)
Warning! The parentheses for these module, val keywords are important!
Rule of thumb: Use the forms (module M : T) and (val M : T) always.
We can create ordinary functions which consume and create first-class modules.
let unpack (m : (module OneInt)) : int = let module M = (val m) in M.x;;
let pack (n : int) : (module OneInt) = (module struct let x = n end);;
3 = unpack three;;
3 = unpack (pack 3);;
pack 3 = three;; (* Woah! Equality of modules! *)
(* “Module pattern matching” *)
(* unpack' : (module OneInt) -> int *)
let unpack' (module M : OneInt) = M.x;;
true
\columnbreak
Type variables are generally implicit, but we can treat them as abstract types in a function body yet still not pass them in explicitly at use-sites.
(* Where did the 'a come from? *)
let wrap (x : 'a) : 'a list = [x];;
(* Let's explicitly declare it! *)
let wrap' (type a) (x : a) : a list = [x];;
(* Usage doesn't change. *)
wrap 1 = wrap' 1
One use is to connect the abstract types of a first-class module with other types we're working with —by using constraint sharing. That is, we ‘unbundle’ the type from ‘inside’ the module to its ‘type’. This is a prime reason to use first-class modules!
Here's an example where we approximate C#'s default keyword:
module type Pointed = sig type t val point : t end;;
(* Error: The hidden type of M is exposed!
“The type constructor M.t would escape its scope.”
“here : (M:Pointed) → M.t” *)
let default (module M : Pointed) = M.point;;
(* default : (module Pointed with type t = 'a) -> 'a *)
let default (type a) (module M : Pointed with type t = a) = M.point;;
module Nat : Pointed with type t = int = struct type t = int let point = 0 end;;
(* module Nat = struct type t = int let point = 0 end;; *)
(* ‘default’ works on first-class modules *)
0 = default(module Nat)
Conversely, this allows us to ‘bundle’ up data to form a module!
(* make_pointed : 'a -> (module Pointed with type t = 'a) *)
let make_pointed (type a) (x : a) : (module Pointed with type t = a)
= (module struct type t = a let point = x end)
Metaprogramming with MetaOCaml
Quasi-quote expressions with ‘brackets’ .< expr >.
to delay their execution
and splice quoted items into such an expression with ‘escape’ .~expr.
Finally, code can be ‘run’ with Runcode.run expr.
Warning! You must use the metaocaml command rather than the ocaml command.
open Runcode;;
(* Addition is not performed right now, but transformed into ‘code’ *)
let x : int code = .<1 + 2>.;; (* .<1 + 2>. *)
(* Actually execute the addition *)
let y : int = run x;;
(* Example using escape *)
let z : int code = .< let res = .~x in res + res >.;;
6 = run z;;
(* A more complicated example *)
(* Desugars using a fresh name: .<fun x_4 -> 2 * x_4>. *)
let ff = let c = 2 in .< fun x -> c * x >.;;
let six = .< .~ff 3 >.;; (* .<(fun x_14 -> 2 * x_14) 3>. *)
The traditional ‘staging of the power function’ example can be found here —as a Jupyter Notebook.
For more, see A Gentle Introduction to Multi-stage Programming
- The deprecated
!.is replaced withRuncode.run. - A Haskell rendition can be found here.
\columnbreak