\section{s:binding-operators}{Binding operators}
%HEVEA\cutname{bindingops.html}

(Introduced in 4.08.0)

\begin{syntax}
let-operator:
 | 'let' (core-operator-char || '<') { dot-operator-char }
;
and-operator:
 | 'and' (core-operator-char || '<') { dot-operator-char }
;
operator-name :
          ...
        | let-operator
        | and-operator
;
letop-binding :
          pattern '=' expr
        | value-name
;
expr:
          ...
        | let-operator letop-binding { and-operator letop-binding } in expr
;
\end{syntax}

Binding operators offer syntactic sugar to expose library functions
under (a variant of) the familiar syntax of standard keywords.
Currently supported ``binding operators'' are "let<op>" and "and<op>",
where "<op>" is an operator symbol, for example "and+$".

Binding operators were introduced to offer convenient syntax for
working with monads and applicative functors; for those, we propose
conventions using operators "*" and "+" respectively. They may be used
for other purposes, but one should keep in mind that each new
unfamiliar notation introduced makes programs harder to understand for
non-experts. We expect that new conventions will be developed over
time on other families of operator.

\subsection{ss:letop-examples}{Examples}

Users can define {\em let operators}:

\begin{caml_example}{verbatim}
let ( let* ) o f =
  match o with
  | None -> None
  | Some x -> f x

let return x = Some x
\end{caml_example}

and then apply them using this convenient syntax:

\begin{caml_example}{verbatim}
let find_and_sum tbl k1 k2 =
  let* x1 = Hashtbl.find_opt tbl k1 in
  let* x2 = Hashtbl.find_opt tbl k2 in
    return (x1 + x2)
\end{caml_example}

which is equivalent to this expanded form:

\begin{caml_example}{verbatim}
let find_and_sum tbl k1 k2 =
  ( let* ) (Hashtbl.find_opt tbl k1)
    (fun x1 ->
       ( let* ) (Hashtbl.find_opt tbl k2)
         (fun x2 -> return (x1 + x2)))
\end{caml_example}

Users can also define {\em and operators}:

\begin{caml_example}{verbatim}
module ZipSeq = struct

  type 'a t = 'a Seq.t

  open Seq

  let rec return x =
    fun () -> Cons(x, return x)

  let rec prod a b =
    fun () ->
      match a (), b () with
      | Nil, _ | _, Nil -> Nil
      | Cons(x, a), Cons(y, b) -> Cons((x, y), prod a b)

  let ( let+ ) f s = map s f
  let ( and+ ) a b = prod a b

end
\end{caml_example}

to support the syntax:

\begin{caml_example}{verbatim}
open ZipSeq
let sum3 z1 z2 z3 =
  let+ x1 = z1
  and+ x2 = z2
  and+ x3 = z3 in
    x1 + x2 + x3
\end{caml_example}

which is equivalent to this expanded form:

\begin{caml_example}{verbatim}
open ZipSeq
let sum3 z1 z2 z3 =
  ( let+ ) (( and+ ) (( and+ ) z1 z2) z3)
    (fun ((x1, x2), x3) -> x1 + x2 + x3)
\end{caml_example}

\subsection{ss:letops-conventions}{Conventions}

An applicative functor should provide a module implementing the following
interface:

\begin{caml_example*}{verbatim}
module type Applicative_syntax = sig
  type 'a t
  val ( let+ ) : 'a t -> ('a -> 'b) -> 'b t
  val ( and+ ): 'a t -> 'b t -> ('a * 'b) t
end
\end{caml_example*}

where "(let+)" is bound to the "map" operation and "(and+)" is bound to
the monoidal product operation.

A monad should provide a module implementing the following interface:

\begin{caml_example*}{verbatim}
module type Monad_syntax = sig
  include Applicative_syntax
  val ( let* ) : 'a t -> ('a -> 'b t) -> 'b t
  val ( and* ): 'a t -> 'b t -> ('a * 'b) t
end
\end{caml_example*}

where "(let*)" is bound to the "bind" operation, and "(and*)" is also
bound to the monoidal product operation.

\subsection{ss:letop-rules}{General desugaring rules}

The form

\begin{verbatim}
let<op0>
  x1 = e1
and<op1>
  x2 = e2
and<op2>
  x3 = e3
in e
\end{verbatim}

desugars into

\begin{verbatim}
( let<op0> )
  (( and<op2> )
    (( and<op1> )
      e1
      e2)
    e3)
  (fun ((x1, x2), x3) -> e)
\end{verbatim}

This of course works for any number of nested "and"-operators. One can
express the general rule by repeating the following simplification
steps:
\begin{itemize}
\item
The first "and"-operator in
\begin{center}
"let<op0> x1 = e1 and<op1> x2 = e2 and... in e"
\end{center}
can be desugared into a function application
\begin{center}
"let<op0> (x1, x2) = ( and<op1> ) e1 e2 and... in e".
\end{center}

\item
Once all "and"-operators have been simplified away,
the "let"-operator in
\begin{center}
"let<op> x1 = e1 in e"
\end{center}
can be desugared into an application
\begin{center}
"( let<op> ) e1 (fun x1 -> e)".
\end{center}
\end{itemize}

Note that the grammar allows mixing different operator symbols in the
same binding ("<op0>", "<op1>", "<op2>" may be distinct), but we
strongly recommend APIs where let-operators and and-operators working
together use the same symbol.

\subsection{ss:letops-punning}{Short notation for variable bindings (let-punning)}

(Introduced in 4.13.0)

When the expression being bound is a variable, it can be convenient to
use the shorthand notation "let+ x in ...", which expands to "let+ x =
x in ...".  This notation, also known as let-punning, allows the
"sum3" function above can be written more concisely as:

\begin{caml_example}{verbatim}
open ZipSeq
let sum3 z1 z2 z3 =
  let+ z1 and+ z2 and+ z3 in
  z1 + z2 + z3
\end{caml_example}

This notation is also supported for extension nodes, expanding
"let%foo x in ..." to "let%foo x = x in ...". However, to avoid
confusion, this notation is not supported for plain "let" bindings.