OCaml operator cheatsheet

One of the hardest parts of learning OCaml is figuring out what the infix operators do, since they're just a string of symbols and you can't find them with a Google search. This is my attempt to make a cheatsheet for whenever you're wondering what a random series of symbols means. Doing a search on this page should find basic info about any of the common OCaml operators.

Note that some libraries define their own operators, like how Jane Street's Command.Spec¹ defines ++, +>, and +<. In cases like that, hopefully the library you're using will make it clear what the infix operators do.

General info about infix functions

In OCaml, a function is infix if its name starts with one of these characters:

= @ ^ | & + - * / $ %

Followed by zero or more of these characters:

! $ % & * + - . / : ? @ ^ | ~

When defining an infix function, you need to put () around the "name".

For example, in utop²:

# let (=<>@^|&~+-*/$%!?:.) a b =
a + b ;;
val ( =<>@^|&~+-*/$%!?:. ) : int -> int -> int = <fun>

# 1 =<>@^|&~+-*/$%!?:. 2 ;;
- : int = 3

Also, you can see the type of an infix operator in utop by again wrapping the function name in parentheses:

# (=<>@^|&~+-*/$%!?:.);;
val ( =<>@^|&~+-*/$%!?:. ) : int -> int -> int = <fun>

The official documentation for this is here³, although this blog⁴ has a more accessible explanation.

Built-in infix operators

The built-in operators are defined in Pervasives⁵:

Refer to the documentation for the magic involved in functions that work on multiple types (=, <>, <, >, etc).

Jane Street

Numbers

Jane Street generally defines arithmetic operators in modules where they make sense, so you can do things like:

Bigint.(of_int 1 + of_int 3 / of_int 5)

The documentation for this interface is under Int_intf.S_common⁷, although most of them are defined for floating point numbers too.

Monads

Jane Street's libraries (Core, Async, Base, etc.) consistently define infix operators under Monad_infix modules⁹.

map and bind are documented assuming that you're familiar with monads¹⁵, and you may find this StackOverflow answer¹⁶ useful if you need more information.

>>= and >>| show up most commonly in Async, but they can also be used with Option, List, Result, etc.

Lwt

See the Lwt documentation¹⁷.

Lwt doesn't have Async's >>=? or >>|? because Lwt.t can contain errors without having a separate Or_error module.

See the Jane Street Monad section above if you need info about map and bind actually do.