A ppx rewriter for monadic and applicative let bindings, match expressions, and
if expressions.

Overview
--------

The aim of this rewriter is to make monadic and applicative code look nicer by
writing custom binders the same way that we normally bind variables. In OCaml,
the common way to bind the result of a computation to a variable is:

```ocaml
let VAR = EXPR in BODY
```

ppx\_let simply adds two new binders: `let%bind` and `let%map`. These are
rewritten into calls to the `bind` and `map` functions respectively. These
functions are expected to have

```ocaml
val map  : 'a t -> f:('a -> 'b)   -> 'b t
val bind : 'a t -> f:('a -> 'b t) -> 'b t
```

for some type `t`, as one might expect.

These functions are to be provided by the user, and are generally expected to be
part of the signatures of monads and applicatives modules. This is the case for
all monads and applicatives defined by the Jane Street's Core suite of
libraries. (see the section below on getting the right names into scope).

### Parallel bindings

ppx\_let understands parallel bindings as well. i.e.:

```ocaml
let%bind VAR1 = EXPR1 and VAR2 = EXPR2 and VAR3 = EXPR3 in BODY
```

The `and` keyword is seen as a binding combination operator. To do so it expects
the presence of a `both` function, that lifts the OCaml pair operation to the
type `t` in question:

```ocaml
val both : 'a t -> 'b t -> ('a * 'b) t
```

### Match statements

We found that this form was quite useful for match statements as well. So for
convenience ppx\_let also accepts `%bind` and `%map` on the `match` keyword.
Morally `match%bind expr with cases` is seen as `let%bind x = expr in match x
with cases`.

### If statements

As a further convenience, ppx\_let accepts `%bind` and `%map` on the `if`
keyword. The expression `if%bind expr1 then expr2 else expr3` is morally
equivalent to `let%bind p = expr1 in if p then expr2 else expr3`.

Syntactic forms and actual rewriting
------------------------------------

`ppx_let` adds six syntactic forms

```ocaml
let%bind P = M in E

let%map  P = M in E

match%bind M with P1 -> E1 | P2 -> E2 | ...

match%map  M with P1 -> E1 | P2 -> E2 | ...

if%bind M then E1 else E2

if%map  M then E1 else E2
```

that expand into

```ocaml
bind M ~f:(fun P -> E)

map  M ~f:(fun P -> E)

bind M ~f:(function P1 -> E1 | P2 -> E2 | ...)

map  M ~f:(function P1 -> E1 | P2 -> E2 | ...)

bind M ~f:(function true -> E1 | false -> E2)

map  M ~f:(function true -> E1 | false -> E2)
```

respectively.

As with `let`, `let%bind` and `let%map` also support multiple *parallel*
bindings via the `and` keyword:

```ocaml
let%bind P1 = M1 and P2 = M2 and P3 = M3 and P4 = M4 in E

let%map  P1 = M1 and P2 = M2 and P3 = M3 and P4 = M4 in E
```

that expand into

```ocaml
let x1 = M1 and x2 = M2 and x3 = M3 and x4 = M4 in
bind
  (both x1 (both x2 (both x3 x4)))
  ~f:(fun (P1, (P2, (P3, P4))) -> E)

let x1 = M1 and x2 = M2 and x3 = M3 and x4 = M4 in
map
  (both x1 (both x2 (both x3 x4)))
  ~f:(fun (P1, (P2, (P3, P4))) -> E)
```

respectively. (Instead of `x1`, `x2`, ... ppx\_let uses variable names that are
unlikely to clash with other names)

As with `let`, names introduced by left-hand sides of the let bindings are not
available in subsequent right-hand sides of the same sequence.

Getting the right names in scope
--------------------------------

The description of how the `%bind` and `%map` syntax extensions expand left out
the fact that the names `bind`, `map`, `both`, and `return` are not used
directly, but rather qualified by `Let_syntax`. For example, we use
`Let_syntax.bind` rather than merely `bind`. This means one just needs to get a
properly loaded `Let_syntax` module in scope to use `%bind` and `%map`.

For monads, `Core.Std.Monad.Make` produces a submodule `Let_syntax` of the
appropriate form.

For applicatives. The convention for these modules is to have a submodule
`Let_syntax` of the form

```ocaml
module Let_syntax : sig
  val return : 'a -> 'a t
  val map    : 'a t -> f:('a -> 'b) -> 'b t
  val both   : 'a t -> 'b t -> ('a * 'b) t
  module Open_on_rhs : << some signature >>
end
```

The `Open_on_rhs` submodule is used by variants of `%map` and `%bind` called
`%map_open` and `%bind_open`. It is locally opened on the right hand sides of
the rewritten let bindings in `%map_open` and `%bind_open` expressions. For
`match%map_open` and `match%bind_open` expressions, `Open_on_rhs` is opened for
the expression being matched on.

`Open_on_rhs` is useful when programming with applicatives, which operate in a
staged manner where the operators used to construct the applicatives are
distinct from the operators used to manipulate the values those applicatives
produce. For monads, `Open_on_rhs` contains `return`.