1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Generic dnet implementation over non-recursive types *)
module type Datatype =
sig
type 'a t
val map : ('a -> 'b) -> 'a t -> 'b t
val map2 : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a
val fold2 : ('a -> 'b -> 'c -> 'a) -> 'a -> 'b t -> 'c t -> 'a
val compare : unit t -> unit t -> int
val terminal : 'a t -> bool
val choose : ('a -> 'b) -> 'a t -> 'b
end
module type S =
sig
type t
type ident
type meta
type 'a structure
module Idset : Set.S with type elt=ident
type term_pattern =
| Term of term_pattern structure
| Meta of meta
val empty : t
val add : t -> term_pattern -> ident -> t
val find_all : t -> Idset.t
val fold_pattern :
('a -> (Idset.t * meta * t) -> 'a) -> 'a -> term_pattern -> t -> Idset.t option * 'a
val find_match : term_pattern -> t -> Idset.t
val inter : t -> t -> t
val union : t -> t -> t
val map : (ident -> ident) -> (unit structure -> unit structure) -> t -> t
val map_metas : (meta -> meta) -> t -> t
end
module Make =
functor (T:Datatype) ->
functor (Ident:Set.OrderedType) ->
functor (Meta:Set.OrderedType) ->
struct
type ident = Ident.t
type meta = Meta.t
type 'a structure = 'a T.t
type term_pattern =
| Term of term_pattern structure
| Meta of meta
module Idset = Set.Make(Ident)
module Mmap = Map.Make(Meta)
module Tmap = Map.Make(struct type t = unit structure
let compare = T.compare end)
type idset = Idset.t
(* we store identifiers at the leaf of the dnet *)
type node =
| Node of t structure
| Terminal of t structure * idset
(* at each node, we have a bunch of nodes (actually a map between
the bare node and a subnet) and a bunch of metavariables *)
and t = Nodes of node Tmap.t * idset Mmap.t
let empty : t = Nodes (Tmap.empty, Mmap.empty)
(* the head of a data is of type unit structure *)
let head w = T.map (fun c -> ()) w
(* given a node of the net and a word, returns the subnet with the
same head as the word (with the rest of the nodes) *)
let split l (w:'a structure) : node * node Tmap.t =
let elt : node = Tmap.find (head w) l in
(elt, Tmap.remove (head w) l)
let select l w = Tmap.find (head w) l
let rec add (Nodes (t,m):t) (w:term_pattern) (id:ident) : t =
match w with Term w ->
( try
let (n,tl) = split t w in
let new_node = match n with
| Terminal (e,is) -> Terminal (e,Idset.add id is)
| Node e -> Node (T.map2 (fun t p -> add t p id) e w) in
Nodes ((Tmap.add (head w) new_node tl), m)
with Not_found ->
let new_content = T.map (fun p -> add empty p id) w in
let new_node =
if T.terminal w then
Terminal (new_content, Idset.singleton id)
else Node new_content in
Nodes ((Tmap.add (head w) new_node t), m) )
| Meta i ->
let m =
try Mmap.add i (Idset.add id (Mmap.find i m)) m
with Not_found -> Mmap.add i (Idset.singleton id) m in
Nodes (t, m)
let add t w id = add t w id
let rec find_all (Nodes (t,m)) : idset =
Idset.union
(Mmap.fold (fun _ -> Idset.union) m Idset.empty)
(Tmap.fold
( fun _ n acc ->
let s2 = match n with
| Terminal (_,is) -> is
| Node e -> T.choose find_all e in
Idset.union acc s2
) t Idset.empty)
(* (\* optimization hack: Not_found is caught in fold_pattern *\) *)
(* let fast_inter s1 s2 = *)
(* if Idset.is_empty s1 || Idset.is_empty s2 then raise Not_found *)
(* else Idset.inter s1 s2 *)
(* let option_any2 f s1 s2 = match s1,s2 with *)
(* | Some s1, Some s2 -> f s1 s2 *)
(* | (Some s, _ | _, Some s) -> s *)
(* | _ -> raise Not_found *)
(* let fold_pattern ?(complete=true) f acc pat dn = *)
(* let deferred = ref [] in *)
(* let leafs,metas = ref None, ref None in *)
(* let leaf s = leafs := match !leafs with *)
(* | None -> Some s *)
(* | Some s' -> Some (fast_inter s s') in *)
(* let meta s = metas := match !metas with *)
(* | None -> Some s *)
(* | Some s' -> Some (Idset.union s s') in *)
(* let defer c = deferred := c::!deferred in *)
(* let rec fp_rec (p:term_pattern) (Nodes(t,m) as dn:t) = *)
(* Mmap.iter (fun _ -> meta) m; (\* TODO: gérer patterns nonlin ici *\) *)
(* match p with *)
(* | Meta m -> defer (m,dn) *)
(* | Term w -> *)
(* try match select t w with *)
(* | Terminal (_,is) -> leaf is *)
(* | Node e -> *)
(* if complete then T.fold2 (fun _ -> fp_rec) () w e else *)
(* if T.fold2 *)
(* (fun b p dn -> match p with *)
(* | Term _ -> fp_rec p dn; false *)
(* | Meta _ -> b *)
(* ) true w e *)
(* then T.choose (T.choose fp_rec w) e *)
(* with Not_found -> *)
(* if Mmap.is_empty m then raise Not_found else () *)
(* in try *)
(* fp_rec pat dn; *)
(* (try Some (option_any2 Idset.union !leafs !metas) with Not_found -> None), *)
(* List.fold_left (fun acc (m,dn) -> f m dn acc) acc !deferred *)
(* with Not_found -> None,acc *)
(* Sets with a neutral element for inter *)
module OSet (S:Set.S) = struct
type t = S.t option
let union s1 s2 : t = match s1,s2 with
| (None, _ | _, None) -> None
| Some a, Some b -> Some (S.union a b)
let inter s1 s2 : t = match s1,s2 with
| (None, a | a, None) -> a
| Some a, Some b -> Some (S.inter a b)
let is_empty : t -> bool = function
| None -> false
| Some s -> S.is_empty s
(* optimization hack: Not_found is caught in fold_pattern *)
let fast_inter s1 s2 =
if is_empty s1 || is_empty s2 then raise Not_found
else let r = inter s1 s2 in
if is_empty r then raise Not_found else r
let full = None
let empty = Some S.empty
end
module OIdset = OSet(Idset)
let fold_pattern ?(complete=true) f acc pat dn =
let deferred = ref [] in
let defer c = deferred := c::!deferred in
let rec fp_rec metas p (Nodes(t,m) as dn:t) =
(* TODO gérer les dnets non-linéaires *)
let metas = Mmap.fold (fun _ -> Idset.union) m metas in
match p with
| Meta m -> defer (metas,m,dn); OIdset.full
| Term w ->
let curm = Mmap.fold (fun _ -> Idset.union) m Idset.empty in
try match select t w with
| Terminal (_,is) -> Some (Idset.union curm is)
| Node e ->
let ids = if complete then T.fold2
(fun acc w e ->
OIdset.fast_inter acc (fp_rec metas w e)
) OIdset.full w e
else
let (all_metas, res) = T.fold2
(fun (b,acc) w e -> match w with
| Term _ -> false, OIdset.fast_inter acc (fp_rec metas w e)
| Meta _ -> b, acc
) (true,OIdset.full) w e in
if all_metas then T.choose (T.choose (fp_rec metas) w) e
else res in
OIdset.union ids (Some curm)
with Not_found ->
if Idset.is_empty metas then raise Not_found else Some curm in
let cand =
try fp_rec Idset.empty pat dn
with Not_found -> OIdset.empty in
let res = List.fold_left f acc !deferred in
cand, res
(* intersection of two dnets. keep only the common pairs *)
let rec inter (t1:t) (t2:t) : t =
let inter_map f (Nodes (t1,m1):t) (Nodes (t2,m2):t) : t =
Nodes
(Tmap.fold
( fun k e acc ->
try Tmap.add k (f e (Tmap.find k t2)) acc
with Not_found -> acc
) t1 Tmap.empty,
Mmap.fold
( fun m s acc ->
try Mmap.add m (Idset.inter s (Mmap.find m m2)) acc
with Not_found -> acc
) m1 Mmap.empty
) in
inter_map
(fun n1 n2 -> match n1,n2 with
| Terminal (e1,s1), Terminal (_,s2) -> Terminal (e1,Idset.inter s1 s2)
| Node e1, Node e2 -> Node (T.map2 inter e1 e2)
| _ -> assert false
) t1 t2
let rec union (t1:t) (t2:t) : t =
let union_map f (Nodes (t1,m1):t) (Nodes (t2,m2):t) : t =
Nodes
(Tmap.fold
( fun k e acc ->
try Tmap.add k (f e (Tmap.find k acc)) acc
with Not_found -> Tmap.add k e acc
) t1 t2,
Mmap.fold
( fun m s acc ->
try Mmap.add m (Idset.inter s (Mmap.find m acc)) acc
with Not_found -> Mmap.add m s acc
) m1 m2
) in
union_map
(fun n1 n2 -> match n1,n2 with
| Terminal (e1,s1), Terminal (_,s2) -> Terminal (e1,Idset.union s1 s2)
| Node e1, Node e2 -> Node (T.map2 union e1 e2)
| _ -> assert false
) t1 t2
let find_match (p:term_pattern) (t:t) : idset =
let metas = ref Mmap.empty in
let (mset,lset) = fold_pattern ~complete:false
(fun acc (mset,m,t) ->
let all = OIdset.fast_inter acc
(Some(let t = try inter t (Mmap.find m !metas) with Not_found -> t in
metas := Mmap.add m t !metas;
find_all t)) in
OIdset.union (Some mset) all
) None p t in
Option.get (OIdset.inter mset lset)
let fold_pattern f acc p dn = fold_pattern ~complete:true f acc p dn
let idset_map f is = Idset.fold (fun e acc -> Idset.add (f e) acc) is Idset.empty
let tmap_map f g m = Tmap.fold (fun k e acc -> Tmap.add (f k) (g e) acc) m Tmap.empty
let rec map sidset sterm (Nodes (t,m)) : t =
let snode = function
| Terminal (e,is) -> Terminal (e,idset_map sidset is)
| Node e -> Node (T.map (map sidset sterm) e) in
Nodes (tmap_map sterm snode t, Mmap.map (idset_map sidset) m)
let rec map_metas f (Nodes (t, m)) : t =
let f_node = function
| Terminal (e, is) -> Terminal (T.map (map_metas f) e, is)
| Node e -> Node (T.map (map_metas f) e)
in
let m' = Mmap.fold (fun m s acc -> Mmap.add (f m) s acc) m Mmap.empty in
let t' = Tmap.fold (fun k n acc -> Tmap.add k (f_node n) acc) t Tmap.empty in
Nodes (t', m')
end
|
