ppx_monadic

ppx_monadic is a PPX syntax extension for monadic bind syntactic sugar. It provides:

• do_ sequence and p <-- e notation for monadic bind

• Extension to when to support pattern guards

• [%comp e || ..] for list (and other monadic) comprehensions

• let%m p = e in' for monadic bind, equivalent with p <-- e

• match%m e with ..' for monadic bind+match, equivalent with p <-- e; match p with ..

• [%do ..] and begin%do .. end, other forms for do_ sequence

ppx_monadic follows the tradition of pa_monad, a CamlP4 syntax extension for do notation. Basically almost of all the code with pa_monad should work with ppx_monadic only by replacing perform by do_;. (I find perform is bit too long to type.)

Syntax of do-sequence

Do-sequence phs is a non-empty sequence of the following phrases ph seprated by ;:

phs ::= ph
      | ph ; phs
      | let .. in phs
      | [%x phs]

ph ::= p <-- e
     | e
     | ()

Bind p <-- e

p is a pattern to bind the result of e. The syntax of the pattern p is limited to those which are parsable as OCaml expressions. For example, you cannot write

(Foo x as y) <-- e

since Foo x as y is not a valid OCaml expression. You can still write such complex patterns wrapping them with [%p? ..]:

[%p? (Foo x as y)] <-- e

is a valid phrase.

Action e

Action e in a do-sequence is an arbitrary expression except in the form of p <-- e.

Escape by ()

ppx_monadic overrides the original meaning of ; operator in do-sequence, but we often want to use the original meaning of ; for sequential execution in order to perform side effects. For this purpose, we have a sugar to escape the override:

(); e; phs

If an expression e is prefixed by (); in do-sequence, e; phs is desguared simply to e; <phs> using OCaml's original sequential execution, where <phs> is the desugar of phs.

If you do not like this syntax, you can always define:

let escape e = e; return ()

and use it inside do_:

do_;
  ...;
  escape @@ e;
  ...;

Lets let .. in phs

A do-sequence can be a let-binding such as the normal let and let rec, let module, etc.

let .. in phs is always desugared to let .. in <phs> where <phs> is the desugar of phs.

Extension [%x phs]

A do-sequence can be an extension [%x phs] which contains another do-sequence.

[%x phs] is always desugared to [%x <phs>] where <phs> is the desugar of phs.

Monadic do_ notation

do_ (and also M.do_ for a module path M) is treated as a new keyword in ppx_monadic. It can only appear at the head of an expresison. do_ introduces syntactic sugar for the monadic operations against the expressions followed by it as far as they are sequenced using ;. A do_ clause looks like:

do_
; ph1
; ..
; phn

or

M.do_
; ph1
; ..
; phn

You cannot omit ; after do_. This is since do_ x <-- e is parsed as (do_ x) <-- e by OCaml and usually this is not what you want.

Desugaring inside do_

<phs>, the desguaring of do-sequence do_; phs is defined as follows:

< p <-- e; phs >   =  bind e (fun p -> <phs>)
< p <-- e >        =  THIS IS ERROR
< e; phs >         =  bind e (fun () -> <phs>)
< e >              =  e
<(); e; phs>       =  e; <phs>
<(); e>            =  e
<let .. in phs>    =  let .. in <phs>
<[%x phs]>         =  [%x <phs>]

bind must be available in the scope so that the desugared expression can be properly compiled.

With a module path: M.do_

do_ clause with a module path, M.do_, has the same syntactic sugar as do_ but adds let bind = M.bind and return = M.return in at the head of the desugared expression in addition. For example, Option.do_; x <-- e1; phs is desugared to:

let bind = Option.bind
and return = Optin.return
in
bind e1 (fun x -> <phs>)

when phs is desugared to <phs>. This is convenient when bind and other monadic operators are defined in the module specified by the module path.

Incompatibility with pa_monad

• do_; instead of perform

• M.do_; instead of perform with M

• Refutable patterns such as 1 <-- exp are simply translated to non-exhaustive pattern matches, where pa_monad inserts failwith to the default case. In ppx_monadic, we recommend to use bind + multi-case pattern match: match%m exp with 1 -> ... | _ -> ....

• Recursive monad bindings are not supported.

Difference between Haskell's do notation

ppx_monadic is different from Haskell's do notation in the following points:

• do_: We cannot use do since it is a keyword in OCaml which cannot be used at the head of expressions.

• <--: We cannot use <- since it is for record/object field mutation in OCaml.

• (); e; phs: OCaml is impure and side effects are often used even inside do_. (); e; is to escape the desugaring and regain the original meaning of ;.

Pattern guards

ppx_monadic extends when clause so that it can take pattern guards pattern guards. The expression inside when is parsed as a do-sequence.

The meaning of do-sequence phrases inside when is as follows:

Bind p <-- e

The result of e is pattern-matched with p.

If the match of p fails, the match case immediately fails, then the next match case is tried.

If the match of p succeeds, then the next pharse is tested keeping the variable bindings in p. If there is no more phrase, then the match action is executed with all the variable bindings of p <-- e inside when.

Action e

If the result of e is false, the match case immediately fails and the next case is tested.

If the result of e is true, then the next phrase is tested. If there is no more phrase, the match action is executed with all the variable bindings of p <-- e inside when.

Escape (); e

Simply executed e, then test the next phrase.

Let let .. in phs

Binds variables inside let binding then tests phs.

Extension [%x phs]

Desugared to [%x <phs>], where <phs> is the desugar of phs.

Incompatibility

ppx_monadic changes the semantics of when clause. If some existing code has code like when e1; e2 -> .., this e1; e2 is no longer considered as a sequential execution but do-sequence.

Normally such uses of ; inside when should be found by the type-checker, since in ppx_monadic e1 should have type bool in e1; e2, instead of unit. Therefore I believe the impact is negligble.

List (and monadic) comprehensions

ppx_monadic introduces list comprehension syntax [%comp e || phs]. (Unfortunatelly | is not usable here.)

ppx_monadic also introduces general monad comprehension [%M.comp e || phs]. It uses M.return, M.bind and M.mzero inside the desugaring, therefore they must be defined inside module M.

Syntax of list comprehension could be as simple as [e || phs], but in that case the || symbol would become ambiguous: we cannot tell it is the separator of the list comprehension or normal boolean "OR". In addition, I personally feel [ e || phs ] is too confusing with the normal list expression [ e1; ..; en ], though their semantics are pretty different.

Notation let%m

let%m p = e1 in e2 is another form of p <-- e1; e2 and desugared to

bind e1 (fun p -> e2')

when e2 is desugared to e2'. let%m is not required inside do_. You can also write let%M.m p = e1 in e2 which uses M.bind.

In side do_, you can use let%m p = e as an alternative of p <-- e, it is useful when pattern p is too complex and you cannot simply write p <-- e.

Multi bindings of let%m

Note that

let%m p1 = e1
and   p2 = e2
in
e

is equivalent with

let fresh_var1 = e1
and fresh_var2 = e2
in
bind fresh_var1 (fun p1 ->
  bind fresh_var2 (fun p2 ->
    e))

This is not equal to the following sequence of two let%m bindings:

let%m p1 = e1 in
let%m p2 = e2 in
e

Notation match%m

match%m e with .. is equivalent with

bind e (function ..)

You can simplify bind-then-match sequences using match%m. For example,

do_;
  x <-- e
  match x with
  | ...

can be simplified to:

match%m e with
| ...

Notations [%do ..], begin %do .. end

Notations [%do <e>] and begin %do <e> end are other forms of do_; <e>. You can use them if you do not like do_; ...

Like M.do_; .., you can qualifiy do in [%do ..] and begin%do .. end like [%M.do ..] and begin%M.do .. end.

To see the output of ppx_monadic

$ ppx_monadic -debug x.ml

prints out desugared source code. This should be convenient if you feel the desugaring is buggy.