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<title>8.23 Binding operators</title>
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<h2 class="section" id="s:binding-operators"><a class="section-anchor" href="#s:binding-operators" aria-hidden="true"></a>8.23 Binding operators</h2>
<ul>
<li><a href="bindingops.html#ss%3Aletops-rationale">8.23.1 Rationale</a>
</li></ul>
<p>
(Introduced in 4.08.0)</p><div class="syntax"><table class="display dcenter"><tr class="c019"><td class="dcell"><table class="c001 cellpading0"><tr><td class="c018">
<a class="syntax" id="let-operator"><span class="c010">let-operator</span></a></td><td class="c015">::=</td><td class="c017">
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <span class="c004">let</span> (<a class="syntax" href="lex.html#core-operator-char"><span class="c010">core-operator-char</span></a> ∣ <span class="c004"><</span>) { <a class="syntax" href="indexops.html#dot-operator-char"><span class="c010">dot-operator-char</span></a> }
</td></tr>
<tr><td class="c018"> </td></tr>
<tr><td class="c018">
<a class="syntax" id="and-operator"><span class="c010">and-operator</span></a></td><td class="c015">::=</td><td class="c017">
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <span class="c004">and</span> (<a class="syntax" href="lex.html#core-operator-char"><span class="c010">core-operator-char</span></a> ∣ <span class="c004"><</span>) { <a class="syntax" href="indexops.html#dot-operator-char"><span class="c010">dot-operator-char</span></a> }
</td></tr>
<tr><td class="c018"> </td></tr>
<tr><td class="c018">
<span class="c010">operator-name</span> </td><td class="c015">::=</td><td class="c017">
...
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <a class="syntax" href="#let-operator"><span class="c010">let-operator</span></a>
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <a class="syntax" href="#and-operator"><span class="c010">and-operator</span></a>
</td></tr>
<tr><td class="c018"> </td></tr>
<tr><td class="c018">
<a class="syntax" href="expr.html#expr"><span class="c010">expr</span></a></td><td class="c015">::=</td><td class="c017">
...
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <a class="syntax" href="#let-operator"><span class="c010">let-operator</span></a> <a class="syntax" href="expr.html#let-binding"><span class="c010">let-binding</span></a> { <a class="syntax" href="#and-operator"><span class="c010">and-operator</span></a> <a class="syntax" href="expr.html#let-binding"><span class="c010">let-binding</span></a> } <span class="c010">in</span> <a class="syntax" href="expr.html#expr"><span class="c010">expr</span></a>
</td></tr>
<tr><td class="c018"> </td></tr>
</table></td></tr>
</table></div><p>Users can define <em>let operators</em>:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">let</span> ( <span class="ocamlkeyword">let</span>* ) o f =
<span class="ocamlkeyword">match</span> o <span class="ocamlkeyword">with</span>
| None -> None
| Some x -> f x
<span class="ocamlkeyword">let</span> return x = Some x</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">val</span> ( <span class="ocamlkeyword">let</span>* ) : 'a option -> ('a -> 'b option) -> 'b option = <<span class="ocamlkeyword">fun</span>>
<span class="ocamlkeyword">val</span> return : 'a -> 'a option = <<span class="ocamlkeyword">fun</span>></div></div>
</div><p>and then apply them using this convenient syntax:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">let</span> find_and_sum tbl k1 k2 =
<span class="ocamlkeyword">let</span>* x1 = Hashtbl.find_opt tbl k1 <span class="ocamlkeyword">in</span>
<span class="ocamlkeyword">let</span>* x2 = Hashtbl.find_opt tbl k2 <span class="ocamlkeyword">in</span>
return (x1 + x2)</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">val</span> find_and_sum : ('a, int) Hashtbl.t -> 'a -> 'a -> int option = <<span class="ocamlkeyword">fun</span>></div></div>
</div><p>which is equivalent to this expanded form:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">let</span> find_and_sum tbl k1 k2 =
( <span class="ocamlkeyword">let</span>* ) (Hashtbl.find_opt tbl k1)
(<span class="ocamlkeyword">fun</span> x1 ->
( <span class="ocamlkeyword">let</span>* ) (Hashtbl.find_opt tbl k2)
(<span class="ocamlkeyword">fun</span> x2 -> return (x1 + x2)))</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">val</span> find_and_sum : ('a, int) Hashtbl.t -> 'a -> 'a -> int option = <<span class="ocamlkeyword">fun</span>></div></div>
</div><p>Users can also define <em>and operators</em>:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> ZipSeq = <span class="ocamlkeyword">struct</span>
<span class="ocamlkeyword">type</span> 'a t = 'a Seq.t
<span class="ocamlkeyword">open</span> Seq
<span class="ocamlkeyword">let</span> <span class="ocamlkeyword">rec</span> return x =
<span class="ocamlkeyword">fun</span> () -> Cons(x, return x)
<span class="ocamlkeyword">let</span> <span class="ocamlkeyword">rec</span> prod a b =
<span class="ocamlkeyword">fun</span> () ->
<span class="ocamlkeyword">match</span> a (), b () <span class="ocamlkeyword">with</span>
| Nil, _ | _, Nil -> Nil
| Cons(x, a), Cons(y, b) -> Cons((x, y), prod a b)
<span class="ocamlkeyword">let</span> ( <span class="ocamlkeyword">let</span>+ ) f s = map s f
<span class="ocamlkeyword">let</span> ( <span class="ocamlkeyword">and</span>+ ) a b = prod a b
<span class="ocamlkeyword">end</span></div>
<div class="pre caml-output ok"><span class="ocamlkeyword">module</span> ZipSeq :
<span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> 'a t = 'a Seq.t
<span class="ocamlkeyword">val</span> return : 'a -> 'a Seq.t
<span class="ocamlkeyword">val</span> prod : 'a Seq.t -> 'b Seq.t -> ('a * 'b) Seq.t
<span class="ocamlkeyword">val</span> ( <span class="ocamlkeyword">let</span>+ ) : 'a Seq.t -> ('a -> 'b) -> 'b Seq.t
<span class="ocamlkeyword">val</span> ( <span class="ocamlkeyword">and</span>+ ) : 'a Seq.t -> 'b Seq.t -> ('a * 'b) Seq.t
<span class="ocamlkeyword">end</span></div></div>
</div><p>to support the syntax:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">open</span> ZipSeq
<span class="ocamlkeyword">let</span> sum3 z1 z2 z3 =
<span class="ocamlkeyword">let</span>+ x1 = z1
<span class="ocamlkeyword">and</span>+ x2 = z2
<span class="ocamlkeyword">and</span>+ x3 = z3 <span class="ocamlkeyword">in</span>
x1 + x2 + x3</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">val</span> sum3 : int Seq.t -> int Seq.t -> int Seq.t -> int Seq.t = <<span class="ocamlkeyword">fun</span>></div></div>
</div><p>which is equivalent to this expanded form:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">open</span> ZipSeq
<span class="ocamlkeyword">let</span> sum3 z1 z2 z3 =
( <span class="ocamlkeyword">let</span>+ ) (( <span class="ocamlkeyword">and</span>+ ) (( <span class="ocamlkeyword">and</span>+ ) z1 z2) z3)
(<span class="ocamlkeyword">fun</span> ((x1, x2), x3) -> x1 + x2 + x3)</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">val</span> sum3 : int Seq.t -> int Seq.t -> int Seq.t -> int Seq.t = <<span class="ocamlkeyword">fun</span>></div></div>
</div>
<h3 class="subsection" id="ss:letops-rationale"><a class="section-anchor" href="#ss:letops-rationale" aria-hidden="true"></a>8.23.1 Rationale</h3>
<p>This extension is intended to provide a convenient syntax for working
with monads and applicatives.</p><p>An applicative should provide a module implementing the following
interface:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> Applicative_syntax = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> 'a t
<span class="ocamlkeyword">val</span> ( <span class="ocamlkeyword">let</span>+ ) : 'a t -> ('a -> 'b) -> 'b t
<span class="ocamlkeyword">val</span> ( <span class="ocamlkeyword">and</span>+ ): 'a t -> 'b t -> ('a * 'b) t
<span class="ocamlkeyword">end</span></div></div>
</div><p>where <span class="c003">(let+)</span> is bound to the <span class="c003">map</span> operation and <span class="c003">(and+)</span> is bound to
the monoidal product operation.</p><p>A monad should provide a module implementing the following interface:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> Monad_syntax = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">include</span> Applicative_syntax
<span class="ocamlkeyword">val</span> ( <span class="ocamlkeyword">let</span>* ) : 'a t -> ('a -> 'b t) -> 'b t
<span class="ocamlkeyword">val</span> ( <span class="ocamlkeyword">and</span>* ): 'a t -> 'b t -> ('a * 'b) t
<span class="ocamlkeyword">end</span></div></div>
</div><p>where <span class="c003">(let*)</span> is bound to the <span class="c003">bind</span> operation, and <span class="c003">(and*)</span> is also
bound to the monoidal product operation.</p><hr>
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