* Re: [Caml-list] [ANN] New release of visitors
[not found] ` <CACVN0Vvw_oxj9bpEUJe0QBo5ZNC7pVE2b5LJQ+e7hSx-HnMa7A@mail.gmail.com>
@ 2017-03-09 18:33 ` François Pottier
2017-03-09 19:17 ` Gabriel Scherer
0 siblings, 1 reply; 5+ messages in thread
From: François Pottier @ 2017-03-09 18:33 UTC (permalink / raw)
To: KC Sivaramakrishnan; +Cc: caml users
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Dear KC,
On 09/03/2017 12:53, KC Sivaramakrishnan wrote:
> Thanks for the wonderful library and the excellent documentation. I have
> a feature request. Could you provide a python-style generator for
> traversing the data structure on demand? For a binary tree:
>
> type 'a t = Leaf | Node of 'a t * 'a * 'a t
>
> I envision a `mk_gen` function:
>
> val mk_gen : 'a t -> (unit -> 'a option)
> (** [mk_gen t] returns a generator function [f], which when invoked
> performs 1-step of the traversal and returns [Some v], where [v]
> is the node value. [f] returns [None] when the traversal is done. *)
Thanks for this excellent question, which I had not thought about.
A quick answer might be that, if you are using OCaml + effect handlers,
it should be fairly easy for you to perform control inversion and turn
a producer-controlled traversal (as performed by an [iter] visitor) into
a consumer-controlled traversal.
That said, I was able to come up with a solution in pure OCaml. It is
somewhat
unexpected and (I think) quite nice, so I am posting it (with comments)
on the
list (see attached file). If there is demand, most of this code could be
made
part of the VisitorsRuntime library.
Best regards,
--
François Pottier
francois.pottier@inria.fr
http://gallium.inria.fr/~fpottier/
[-- Attachment #2: delayed_tree.ml --]
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(* To play with this code in an OCaml toplevel, launch [ocaml] and type this:
#use "topfind";;
#require "visitors.ppx";;
#require "visitors.runtime";;
*)
(* -------------------------------------------------------------------------- *)
(* Suppose we have an arbitrary data structure that contains elements
of type ['a]. Here, it is a binary tree, but it could be anything: *)
type 'a sometree =
| Leaf
| Node of 'a sometree * 'a * 'a sometree
(* We would like to enumerate the elements of this data structure.
More precisely, we would like to construct an iterator, that is,
an an on-demand producer of elements. Here is a simple definition
of a stateful iterator: *)
type 'a iterator =
unit -> 'a option
(* The question is, can we construct an iterator for the type ['a sometree],
based on an automatically-generated visitor, so that the construction is
entirely independent of the type ['a sometree]? *)
(* -------------------------------------------------------------------------- *)
(* For starters, let us first define cascades, which are a more pleasant kind
of iterators. A cascade is a persistent (stateless) iterator. It can be
thought of as a delayed list, that is, a list whose elements are computed
only on demand. *)
(* Cascades could (should) be part of a separate library. There is in fact a
proposal to add them to OCaml's standard library: see the discussion at
https://github.com/ocaml/ocaml/pull/1002 *)
type 'a cascade =
unit -> 'a head
and 'a head =
| Nil
| Cons of 'a * 'a cascade
(* A delayed computation is represented as a function of type [unit -> _].
Thus, no memoization takes place. It is easy to implement a function
[memo: 'a cascade -> 'a cascade] that turns a nonmemoizing cascade into
a memoizing one, so memoization can be requested a posteriori, if
desired. *)
(* The empty cascade. *)
let nil : 'a cascade =
fun () -> Nil
(* Forcing a cascade reveals its head. *)
let force xs =
xs()
(* A cascade can be easily converted to a stateful iterator. *)
let cascade_to_iterator (xs : 'a cascade) : 'a iterator =
let s = ref xs in
fun () ->
match force !s with
| Nil ->
(* Writing [nil] into [s] may seem superfluous, but is in fact
necessary to guarantee that the computation that just led to
a [Nil] outcome is not repeated in the future. *)
s := nil;
None
| Cons (x, xs) ->
s := xs;
Some x
(* Because cascades are close cousins of lists, they are easy to work with.
Constructing a cascade for a tree-like data structure is straightforward,
whereas directly constructing a stateful iterator would be more involved. *)
(* -------------------------------------------------------------------------- *)
(* Now, can we use some kind of visitor to turn a tree of type ['a sometree]
into a cascade of type ['a cascade]? *)
(* At first sight, this does not seem very easy, for two reasons: 1- a visitor
usually traverses a tree in an eager manner, whereas we need the traversal
to make progress only as cascade elements are demanded; and 2- a visitor
performs a bottom-up computation, without a left-to-right bias (assuming
mutable state is not used), whereas a cascade enumerates elements in a
left-to-right manner. (Or in a right-to-left manner. As will be apparent
below, both directions are possible.) *)
(* The trick is to use another intermediate step. Instead of turning a tree
directly into a cascade, we first transform it into a generic tree-like
structure: a *delayed tree*. Problem 1 is solved because, by introducing
delays into the new tree, we allow its construction to be carried out on
demand. Problem 2 is solved because this tree-to-tree transformation can be
carried out in a purely bottom-up manner by a [reduce] visitor. Then,
finally, it is straightforward to transform a delayed tree into a
cascade. *)
(* -------------------------------------------------------------------------- *)
(* A delayed tree contains ordinary nodes of arity 0, 1, and 2. Furthermore,
it contains [DTDelay] nodes, of arity 1, whose child is delayed, that is,
computed only on demand. *)
type 'a delayed_tree =
| DTZero
| DTOne of 'a
| DTTwo of 'a delayed_tree * 'a delayed_tree
| DTDelay of (unit -> 'a delayed_tree)
(* A delayed tree is converted to a cascade as follows. We may choose, at this
point, between left-to-right and right-to-left traversals. As usual, when
building a cascade, one must take a continuation [k] as an argument, so as
to avoid naive and costly cascade concatenation operations. *)
let rec delayed_tree_to_cascade (dt : 'a delayed_tree) (k : 'a cascade)
: 'a cascade =
fun () -> delayed_tree_to_head dt k
and delayed_tree_to_head (dt : 'a delayed_tree) (k : 'a cascade) : 'a head =
match dt with
| DTZero ->
force k
| DTOne x ->
Cons (x, k)
| DTTwo (dt1, dt2) ->
delayed_tree_to_head dt1 (delayed_tree_to_cascade dt2 k)
| DTDelay dt ->
delayed_tree_to_head (force dt) k
let delayed_tree_to_cascade (dt : 'a delayed_tree) : 'a cascade =
delayed_tree_to_cascade dt nil
let delayed_tree_to_iterator (dt : 'a delayed_tree) : 'a iterator =
cascade_to_iterator (delayed_tree_to_cascade dt)
(* -------------------------------------------------------------------------- *)
(* We now set up four constructor functions and constructor methods, which
construct delayed trees, and which we will use in a [reduce] visitor. *)
(* The type ['a delay] is a synonym for ['a]. It is used as a decoration, in a
type definition, to indicate that a call to the method [visit_delay] is
desired. *)
type 'a delay = 'a
class ['self] delayed_tree_monoid = object (_ : 'self)
(* Delayed trees form a monoid, in the sense that we concatenate them using
[DTTwo], and the neutral element is [DTZero]. We package these two data
constructors in the methods [zero] and [plus], which are automatically
called in an automatically-generated [reduce] visitor. *)
method zero =
DTZero
method plus s1 s2 =
match s1, s2 with
| DTZero, s
| s, DTZero ->
(* This optimization is not mandatory. It helps allocate fewer nodes. *)
s
| _, _ ->
DTTwo (s1, s2)
(* The visitor method [visit_delay] delays the visit of a subtree by
constructing and returning a [DTDelay] node, which carries a delayed
recursive call to a visitor. *)
method visit_delay: 'env 'a .
('env -> 'a -> 'b delayed_tree) ->
'env -> 'a delay -> 'b delayed_tree
= fun visit_'a env x ->
DTDelay (fun () -> visit_'a env x)
end
(* The visitor function [yield] will be invoked at elements of type ['a].
It constructs a one-element delayed tree. *)
let yield _env x =
DTOne x
(* -------------------------------------------------------------------------- *)
(* It is now time to generate a [reduce] visitor for the type ['a sometree].
This is the only part of the code which is specific of [sometree].
Everything else is generic. *)
(* We must insert [delay]s into the structure of the type ['a sometree] so as
to indicate where [visit_delay] should be called and (therefore) where
[DTDelay] nodes should be allocated. To do this, we write a copy of the
definition of the type ['a sometree], with extra delays in it. The new type
is actually considered equal to ['a sometree] by OCaml. Its role is purely
to carry a [@@deriving visitors] annotation. *)
(* In the data constructor [Node], the left-hand [delay] is in fact
superfluous. With or without it, our iterators will eagerly descend along
the leftmost branch of a tree, anyway. *)
type 'a mytree = 'a sometree =
| Leaf
| Node of 'a mytree delay * 'a * 'a mytree delay
and 'a mytree_delay =
'a mytree delay
[@@deriving visitors { variety = "reduce"; polymorphic = true;
concrete = true; ancestors = ["delayed_tree_monoid"] }]
(* -------------------------------------------------------------------------- *)
(* For demonstration purposes, let us make our visitor verbose. *)
class ['self] verbose_reduce = object (_ : 'self)
inherit [_] reduce as super
method! visit_Leaf visit_'a env =
Printf.printf "Visiting a leaf.\n%!";
super#visit_Leaf visit_'a env
method! visit_Node visit_'a env t1 x t2 =
Printf.printf "Visiting a node.\n%!";
super#visit_Node visit_'a env t1 x t2
end
(* In production, one should remove [verbose_reduce] and use [reduce]
instead. *)
let sometree_to_delayed_tree (t : 'a sometree) =
new verbose_reduce # visit_mytree_delay yield () t
(* We use [visit_mytree_delay], even though [visit_mytree] would work
just as well, so as to ensure that we get a delayed tree whose root
is a [DTDelay] node. *)
(* Problem solved! *)
let sometree_to_iterator (t : 'a sometree) : 'a iterator =
delayed_tree_to_iterator (sometree_to_delayed_tree t)
(* -------------------------------------------------------------------------- *)
(* Demo. *)
let t : int sometree =
Node (Node (Leaf, 1, Leaf), 2, Node (Leaf, 3, Leaf))
let i : int iterator =
sometree_to_iterator t
(* Transcript of an OCaml toplevel session:
# i();;
Visiting a node.
Visiting a node.
Visiting a leaf.
- : int option = Some 1
# i();;
Visiting a leaf.
- : int option = Some 2
# i();;
Visiting a node.
Visiting a leaf.
- : int option = Some 3
# i();;
Visiting a leaf.
- : int option = None
# i();;
- : int option = None
*)
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