aboutsummaryrefslogtreecommitdiffhomepage
path: root/pretyping/pattern.ml
blob: 9acdd15855aba444b0472fafafbe4706d7514fce (plain)
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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* $Id$ *)

open Util
open Names
open Libnames
open Nameops
open Term
open Rawterm
open Environ
open Nametab
open Pp
open Mod_subst

(* Metavariables *)

type patvar_map = (patvar * constr) list
let pr_patvar = pr_id

(* Patterns *)

type constr_pattern =
  | PRef of global_reference
  | PVar of identifier
  | PEvar of existential_key * constr_pattern array
  | PRel of int
  | PApp of constr_pattern * constr_pattern array
  | PSoApp of patvar * constr_pattern list
  | PLambda of name * constr_pattern * constr_pattern
  | PProd of name * constr_pattern * constr_pattern
  | PLetIn of name * constr_pattern * constr_pattern
  | PSort of rawsort
  | PMeta of patvar option
  | PIf of constr_pattern * constr_pattern * constr_pattern
  | PCase of (case_style * int array * inductive option * (int * int) option)
      * constr_pattern * constr_pattern * constr_pattern array
  | PFix of fixpoint
  | PCoFix of cofixpoint

let rec occur_meta_pattern = function
  | PApp (f,args) ->
      (occur_meta_pattern f) or (array_exists occur_meta_pattern args)
  | PLambda (na,t,c)  -> (occur_meta_pattern t) or (occur_meta_pattern c)
  | PProd (na,t,c)  -> (occur_meta_pattern t) or (occur_meta_pattern c)
  | PLetIn (na,t,c)  -> (occur_meta_pattern t) or (occur_meta_pattern c)
  | PIf (c,c1,c2)  ->
      (occur_meta_pattern c) or
      (occur_meta_pattern c1) or (occur_meta_pattern c2)
  | PCase(_,p,c,br) ->
      (occur_meta_pattern p) or
      (occur_meta_pattern c) or (array_exists occur_meta_pattern br)
  | PMeta _ | PSoApp _ -> true
  | PEvar _ | PVar _ | PRef _ | PRel _ | PSort _ | PFix _ | PCoFix _ -> false

type constr_label =
  | ConstNode of constant
  | IndNode of inductive
  | CstrNode of constructor
  | VarNode of identifier

exception BoundPattern;;

let rec head_pattern_bound t =
  match t with
    | PProd (_,_,b)  -> head_pattern_bound b
    | PLetIn (_,_,b) -> head_pattern_bound b
    | PApp (c,args)  -> head_pattern_bound c
    | PIf (c,_,_)  -> head_pattern_bound c
    | PCase (_,p,c,br) -> head_pattern_bound c
    | PRef r         -> r
    | PVar id        -> VarRef id
    | PEvar _ | PRel _ | PMeta _ | PSoApp _  | PSort _ | PFix _
	-> raise BoundPattern
    (* Perhaps they were arguments, but we don't beta-reduce *)
    | PLambda _ -> raise BoundPattern
    | PCoFix _ -> anomaly "head_pattern_bound: not a type"

let head_of_constr_reference c = match kind_of_term c with
  | Const sp -> ConstRef sp
  | Construct sp -> ConstructRef sp
  | Ind sp -> IndRef sp
  | Var id -> VarRef id
  | _ -> anomaly "Not a rigid reference"

let rec pattern_of_constr t =
  match kind_of_term t with
    | Rel n  -> PRel n
    | Meta n -> PMeta (Some (id_of_string ("META" ^ string_of_int n)))
    | Var id -> PVar id
    | Sort (Prop c) -> PSort (RProp c)
    | Sort (Type _) -> PSort (RType None)
    | Cast (c,_,_)      -> pattern_of_constr c
    | LetIn (na,c,_,b) -> PLetIn (na,pattern_of_constr c,pattern_of_constr b)
    | Prod (na,c,b)   -> PProd (na,pattern_of_constr c,pattern_of_constr b)
    | Lambda (na,c,b) -> PLambda (na,pattern_of_constr c,pattern_of_constr b)
    | App (f,a) -> PApp (pattern_of_constr f,Array.map pattern_of_constr a)
    | Const sp         -> PRef (ConstRef (constant_of_kn(canonical_con sp)))
    | Ind sp        -> PRef (canonical_gr (IndRef sp))
    | Construct sp -> PRef (canonical_gr (ConstructRef sp))
    | Evar (n,ctxt) -> PEvar (n,Array.map pattern_of_constr ctxt)
    | Case (ci,p,a,br) ->
	let cip = ci.ci_pp_info in
	let no = Some (ci.ci_npar,cip.ind_nargs) in
	PCase ((cip.style,ci.ci_cstr_nargs,Some ci.ci_ind,no),
	       pattern_of_constr p,pattern_of_constr a,
	       Array.map pattern_of_constr br)
    | Fix f -> PFix f
    | CoFix f -> PCoFix f

(* To process patterns, we need a translation without typing at all. *)

let map_pattern_with_binders g f l = function
  | PApp (p,pl) -> PApp (f l p, Array.map (f l) pl)
  | PSoApp (n,pl) -> PSoApp (n, List.map (f l) pl)
  | PLambda (n,a,b) -> PLambda (n,f l a,f (g l) b)
  | PProd (n,a,b) -> PProd (n,f l a,f (g l) b)
  | PLetIn (n,a,b) -> PLetIn (n,f l a,f (g l) b)
  | PIf (c,b1,b2) -> PIf (f l c,f l b1,f l b2)
  | PCase (ci,po,p,pl) -> PCase (ci,f l po,f l p,Array.map (f l) pl)
  (* Non recursive *)
  | (PVar _ | PEvar _ | PRel _ | PRef _  | PSort _  | PMeta _
  (* Bound to terms *)
  | PFix _ | PCoFix _ as x) -> x

let map_pattern f = map_pattern_with_binders (fun () -> ()) (fun () -> f) ()

let rec instantiate_pattern lvar = function
  | PVar id as x -> (try Lazy.force(List.assoc id lvar) with Not_found -> x)
  | (PFix _ | PCoFix _) -> error ("Non instantiable pattern.")
  | c -> map_pattern (instantiate_pattern lvar) c

let rec liftn_pattern k n = function
  | PRel i as x -> if i >= n then PRel (i+k) else x
  | PFix x -> PFix (destFix (liftn k n (mkFix x)))
  | PCoFix x -> PCoFix (destCoFix (liftn k n (mkCoFix x)))
  | c -> map_pattern_with_binders succ (liftn_pattern k) n c

let lift_pattern k = liftn_pattern k 1

let rec subst_pattern subst pat = match pat with
  | PRef ref ->
      let ref',t = subst_global subst ref in
	if ref' == ref then pat else
	 pattern_of_constr t
  | PVar _
  | PEvar _
  | PRel _ -> pat
  | PApp (f,args) ->
      let f' = subst_pattern subst f in
      let args' = array_smartmap (subst_pattern subst) args in
	if f' == f && args' == args then pat else
	  PApp (f',args')
  | PSoApp (i,args) ->
      let args' = list_smartmap (subst_pattern subst) args in
	if args' == args then pat else
	  PSoApp (i,args')
  | PLambda (name,c1,c2) ->
      let c1' = subst_pattern subst c1 in
      let c2' = subst_pattern subst c2 in
	if c1' == c1 && c2' == c2 then pat else
	  PLambda (name,c1',c2')
  | PProd (name,c1,c2) ->
      let c1' = subst_pattern subst c1 in
      let c2' = subst_pattern subst c2 in
	if c1' == c1 && c2' == c2 then pat else
	  PProd (name,c1',c2')
  | PLetIn (name,c1,c2) ->
      let c1' = subst_pattern subst c1 in
      let c2' = subst_pattern subst c2 in
	if c1' == c1 && c2' == c2 then pat else
	  PLetIn (name,c1',c2')
  | PSort _
  | PMeta _ -> pat
  | PIf (c,c1,c2) ->
      let c' = subst_pattern subst c in
      let c1' = subst_pattern subst c1 in
      let c2' = subst_pattern subst c2 in
	if c' == c && c1' == c1 && c2' == c2 then pat else
	  PIf (c',c1',c2')
  | PCase ((a,b,ind,n as cs),typ,c,branches) ->
      let ind' = Option.smartmap (Inductiveops.subst_inductive subst) ind in
      let typ' = subst_pattern subst typ in
      let c' = subst_pattern subst c in
      let branches' = array_smartmap (subst_pattern subst) branches in
      let cs' = if ind == ind' then cs else (a,b,ind',n) in
	if typ' == typ && c' == c && branches' == branches then pat else
	  PCase(cs',typ', c', branches')
  | PFix fixpoint ->
      let cstr = mkFix fixpoint in
      let fixpoint' = destFix (subst_mps subst cstr) in
	if fixpoint' == fixpoint then pat else
	  PFix fixpoint'
  | PCoFix cofixpoint ->
      let cstr = mkCoFix cofixpoint in
      let cofixpoint' = destCoFix (subst_mps subst cstr) in
	if cofixpoint' == cofixpoint then pat else
	  PCoFix cofixpoint'

let mkPLambda na b = PLambda(na,PMeta None,b)
let rev_it_mkPLambda = List.fold_right mkPLambda

let rec pat_of_raw metas vars = function
  | RVar (_,id) ->
      (try PRel (list_index (Name id) vars)
       with Not_found -> PVar id)
  | RPatVar (_,(false,n)) ->
      metas := n::!metas; PMeta (Some n)
  | RRef (_,gr) ->
      PRef (canonical_gr gr)
  (* Hack pour ne pas réécrire une interprétation complète des patterns*)
  | RApp (_, RPatVar (_,(true,n)), cl) ->
      metas := n::!metas; PSoApp (n, List.map (pat_of_raw metas vars) cl)
  | RApp (_,c,cl) ->
      PApp (pat_of_raw metas vars c,
	    Array.of_list (List.map (pat_of_raw metas vars) cl))
  | RLambda (_,na,bk,c1,c2) ->
      name_iter (fun n -> metas := n::!metas) na;
      PLambda (na, pat_of_raw metas vars c1,
	       pat_of_raw metas (na::vars) c2)
  | RProd (_,na,bk,c1,c2) ->
      name_iter (fun n -> metas := n::!metas) na;
      PProd (na, pat_of_raw metas vars c1,
	       pat_of_raw metas (na::vars) c2)
  | RLetIn (_,na,c1,c2) ->
      name_iter (fun n -> metas := n::!metas) na;
      PLetIn (na, pat_of_raw metas vars c1,
	       pat_of_raw metas (na::vars) c2)
  | RSort (_,s) ->
      PSort s
  | RHole _ ->
      PMeta None
  | RCast (_,c,_) ->
      Flags.if_verbose
        Pp.warning "Cast not taken into account in constr pattern";
      pat_of_raw metas vars c
  | RIf (_,c,(_,None),b1,b2) ->
      PIf (pat_of_raw metas vars c,
           pat_of_raw metas vars b1,pat_of_raw metas vars b2)
  | RLetTuple (loc,nal,(_,None),b,c) ->
      let mkRLambda c na = RLambda (loc,na,Explicit,RHole (loc,Evd.InternalHole),c) in
      let c = List.fold_left mkRLambda c nal in
      PCase ((LetStyle,[|1|],None,None),PMeta None,pat_of_raw metas vars b,
             [|pat_of_raw metas vars c|])
  | RCases (loc,sty,p,[c,(na,indnames)],brs) ->
      let pred,ind_nargs, ind = match p,indnames with
	| Some p, Some (_,ind,n,nal) ->
	    rev_it_mkPLambda nal (mkPLambda na (pat_of_raw metas vars p)),
	    Some (n,List.length nal),Some ind
	| _ -> PMeta None, None, None in
      let ind = match ind with Some _ -> ind | None ->
	match brs with
	  | (_,_,[PatCstr(_,(ind,_),_,_)],_)::_ -> Some ind
	  | _ -> None in
      let cbrs =
	Array.init (List.length brs) (pat_of_raw_branch loc metas vars ind brs)
      in
      let cstr_nargs,brs = (Array.map fst cbrs, Array.map snd cbrs) in
      PCase ((sty,cstr_nargs,ind,ind_nargs), pred,
             pat_of_raw metas vars c, brs)

  | r ->
      let loc = loc_of_rawconstr r in
      user_err_loc (loc,"pattern_of_rawconstr", Pp.str"Non supported pattern.")

and pat_of_raw_branch loc metas vars ind brs i =
  let bri = List.filter
    (function
        (_,_,[PatCstr(_,c,lv,Anonymous)],_) -> snd c = i+1
      | (loc,_,_,_) ->
          user_err_loc (loc,"pattern_of_rawconstr",
                        Pp.str "Non supported pattern.")) brs in
  match bri with
    | [(_,_,[PatCstr(_,(indsp,_),lv,_)],br)] ->
	if ind <> None & ind <> Some indsp then
          user_err_loc (loc,"pattern_of_rawconstr",
            Pp.str "All constructors must be in the same inductive type.");
        let lna =
          List.map
            (function PatVar(_,na) -> na
              | PatCstr(loc,_,_,_) ->
                  user_err_loc (loc,"pattern_of_rawconstr",
                                Pp.str "Non supported pattern.")) lv in
        let vars' = List.rev lna @ vars in
	List.length lv, rev_it_mkPLambda lna (pat_of_raw metas vars' br)
    | _ -> user_err_loc (loc,"pattern_of_rawconstr",
                         str "No unique branch for " ++ int (i+1) ++
                         str"-th constructor.")

let pattern_of_rawconstr c =
  let metas = ref [] in
  let p = pat_of_raw metas [] c in	
  (!metas,p)