summaryrefslogtreecommitdiff
path: root/plugins/quote/quote.ml
blob: fbb754204c507100848fc02a38d2c2ad6f873499 (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
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* The `Quote' tactic *)

(* The basic idea is to automatize the inversion of interpetation functions
   in 2-level approach

   Examples are given in \texttt{theories/DEMOS/DemoQuote.v}

   Suppose you have a langage \texttt{L} of 'abstract terms'
   and a type \texttt{A} of 'concrete terms'
   and a function \texttt{f : L -> (varmap A L) -> A}.

   Then, the tactic \texttt{quote f} will replace an
   expression \texttt{e} of type \texttt{A} by \texttt{(f vm t)}
   such that \texttt{e} and \texttt{(f vm t)} are convertible.

   The problem is then inverting the function \texttt{f}.

   The tactic works when:

   \begin{itemize}
   \item L is a simple inductive datatype. The constructors of L may
     have one of the three following forms:

     \begin{enumerate}
     \item ordinary recursive constructors like: \verb|Cplus : L -> L -> L|
     \item variable leaf like: \verb|Cvar : index -> L|
     \item constant leaf like \verb|Cconst : A -> L|
     \end{enumerate}

     The definition of \texttt{L} must contain at most one variable
     leaf and at most one constant leaf.

     When there are both a variable leaf and a constant leaf, there is
     an ambiguity on inversion. The term t can be either the
     interpretation of \texttt{(Cconst t)} or the interpretation of
     (\texttt{Cvar}~$i$) in a variable map containing the binding $i
     \rightarrow$~\texttt{t}. How to discriminate between these
     choices?

     To solve the dilemma, one gives to \texttt{quote} a list of
     \emph{constant constructors}: a term will be considered as a
     constant if it is either a constant constructor or the
     application of a constant constructor to constants. For example
     the list \verb+[S, O]+ defines the closed natural
     numbers. \texttt{(S (S O))} is a constant when \texttt{(S x)} is
     not.

     The definition of constants vary for each application of the
     tactic, so it can even be different for two applications of
     \texttt{quote} with the same function.

   \item \texttt{f} is a quite simple fixpoint on
     \texttt{L}. In particular, \texttt{f} must verify:

\begin{verbatim}
     (f (Cvar i)) = (varmap_find vm default_value i)
\end{verbatim}
\begin{verbatim}
     (f (Cconst c)) = c
\end{verbatim}

     where \texttt{index} and \texttt{varmap\_find} are those defined
     the \texttt{Quote} module. \emph{The tactic won't work with
     user's own variables map!!}  It is mandatory to use the
     variable map defined in module \texttt{Quote}.

   \end{itemize}

   The method to proceed is then clear:

   \begin{itemize}
   \item Start with an empty hashtable of "registed leafs"
      that maps constr to integers and a "variable counter" equal to 0.
    \item Try to match the term with every right hand side of the
      definition of \texttt{f}.

      If there is one match, returns the correponding left hand
      side and call yourself recursively to get the arguments of this
      left hand side.

      If there is no match, we are at a leaf. That is the
      interpretation of either a variable or a constant.

      If it is a constant, return \texttt{Cconst} applied to that
      constant.

      If not, it is a variable. Look in the hashtable
      if this leaf has been already encountered. If not, increment
      the variable counter and add an entry to the hashtable; then
      return \texttt{(Cvar !variables\_counter)}
   \end{itemize}
*)


(*i*)
open Pp
open Util
open Names
open Term
open Pattern
open Matching
open Tacmach
open Tactics
open Tacexpr
(*i*)

(*s First, we need to access some Coq constants
  We do that lazily, because this code can be linked before
  the constants are loaded in the environment *)

let constant dir s = Coqlib.gen_constant "Quote" ("quote"::dir) s

let coq_Empty_vm = lazy (constant ["Quote"] "Empty_vm")
let coq_Node_vm = lazy (constant ["Quote"] "Node_vm")
let coq_varmap_find = lazy (constant ["Quote"] "varmap_find")
let coq_Right_idx = lazy (constant ["Quote"] "Right_idx")
let coq_Left_idx = lazy (constant ["Quote"] "Left_idx")
let coq_End_idx = lazy (constant ["Quote"] "End_idx")

(*s Then comes the stuff to decompose the body of interpetation function
  and pre-compute the inversion data.

For a function like:

\begin{verbatim}
  Fixpoint interp (vm:varmap Prop) (f:form) :=
     match f with
       | f_and f1 f1 f2 => (interp f1) /\ (interp f2)
       | f_or f1 f1 f2 => (interp f1) \/ (interp f2)
       | f_var i => varmap_find Prop default_v i vm
       | f_const c => c
     end.
\end{verbatim}

With the constant constructors \texttt{C1}, \dots, \texttt{Cn}, the
corresponding scheme will be:

\begin{verbatim}
  {normal_lhs_rhs =
     [ "(f_and ?1 ?2)", "?1 /\ ?2";
       "(f_or ?1 ?2)", " ?1 \/ ?2";];
   return_type = "Prop";
   constants = Some [C1,...Cn];
   variable_lhs = Some "(f_var ?1)";
   constant_lhs = Some "(f_const ?1)"
  }
\end{verbatim}

If there is no constructor for variables in the type \texttt{form},
then [variable_lhs] is [None]. Idem for constants and
[constant_lhs]. Both cannot be equal to [None].

The metas in the RHS must correspond to those in the LHS (one cannot
exchange ?1 and ?2 in the example above)

*)

module ConstrSet = Set.Make(
  struct
    type t = constr
    let compare = constr_ord
  end)

type inversion_scheme = {
  normal_lhs_rhs : (constr * constr_pattern) list;
  variable_lhs : constr option;
  return_type : constr;
  constants : ConstrSet.t;
  constant_lhs : constr option }

(*s [compute_ivs gl f cs] computes the inversion scheme associated to
  [f:constr] with constants list [cs:constr list] in the context of
  goal [gl]. This function uses the auxiliary functions
  [i_can't_do_that], [decomp_term], [compute_lhs] and [compute_rhs]. *)

let i_can't_do_that () = error "Quote: not a simple fixpoint"

let decomp_term c = kind_of_term (strip_outer_cast c)

(*s [compute_lhs typ i nargsi] builds the term \texttt{(C ?nargsi ...
  ?2 ?1)}, where \texttt{C} is the [i]-th constructor of inductive
  type [typ] *)

let coerce_meta_out id =
  let s = string_of_id id in
  int_of_string (String.sub s 1 (String.length s - 1))
let coerce_meta_in n =
  id_of_string ("M" ^ string_of_int n)

let compute_lhs typ i nargsi =
  match kind_of_term typ with
    | Ind(sp,0) ->
        let argsi = Array.init nargsi (fun j -> mkMeta (nargsi - j)) in
        mkApp (mkConstruct ((sp,0),i+1), argsi)
    | _ -> i_can't_do_that ()

(*s This function builds the pattern from the RHS. Recursive calls are
  replaced by meta-variables ?i corresponding to those in the LHS *)

let compute_rhs bodyi index_of_f =
  let rec aux c =
    match kind_of_term c with
      | App (j, args) when isRel j && destRel j = index_of_f (* recursive call *) ->
          let i = destRel (array_last args) in
	  PMeta (Some (coerce_meta_in i))
      | App (f,args) ->
          PApp (snd (pattern_of_constr Evd.empty f), Array.map aux args)
      | Cast (c,_,_) -> aux c
      | _ -> snd (pattern_of_constr Evd.empty c)
  in
  aux bodyi

(*s Now the function [compute_ivs] itself *)

let compute_ivs gl f cs =
  let cst = try destConst f with _ -> i_can't_do_that () in
  let body = Environ.constant_value (Global.env()) cst in
  match decomp_term body with
    | Fix(([| len |], 0), ([| name |], [| typ |], [| body2 |])) ->
        let (args3, body3) = decompose_lam body2 in
        let nargs3 = List.length args3 in
        begin match decomp_term body3 with
          | Case(_,p,c,lci) -> (* <p> Case c of c1 ... cn end *)
              let n_lhs_rhs = ref []
              and v_lhs = ref (None : constr option)
              and c_lhs = ref (None : constr option) in
              Array.iteri
                (fun i ci ->
                   let argsi, bodyi = decompose_lam ci in
                   let nargsi = List.length argsi in
           (* REL (narg3 + nargsi + 1) is f *)
           (* REL nargsi+1 to REL nargsi + nargs3 are arguments of f *)
           (* REL 1 to REL nargsi are argsi (reverse order) *)
           (* First we test if the RHS is the RHS for constants *)
                   if isRel bodyi && destRel bodyi = 1 then
                     c_lhs := Some (compute_lhs (snd (List.hd args3))
                                      i nargsi)
           (* Then we test if the RHS is the RHS for variables *)
                   else begin match decompose_app bodyi with
                     | vmf, [_; _; a3; a4 ]
                         when isRel a3 & isRel a4 &
			   pf_conv_x gl vmf
                           (Lazy.force coq_varmap_find)->
                             v_lhs := Some (compute_lhs
                                              (snd (List.hd args3))
                                              i nargsi)
           (* Third case: this is a normal LHS-RHS *)
                     | _ ->
                         n_lhs_rhs :=
                         (compute_lhs (snd (List.hd args3)) i nargsi,
                          compute_rhs bodyi (nargs3 + nargsi + 1))
                         :: !n_lhs_rhs
                   end)
                lci;

              if !c_lhs = None & !v_lhs = None then i_can't_do_that ();

	      (* The Cases predicate is a lambda; we assume no dependency *)
	      let p = match kind_of_term p with
		| Lambda (_,_,p) -> Termops.pop p
		| _ -> p
	      in

              { normal_lhs_rhs = List.rev !n_lhs_rhs;
                variable_lhs = !v_lhs;
                return_type = p;
                constants = List.fold_right ConstrSet.add cs ConstrSet.empty;
                constant_lhs = !c_lhs }

          | _ -> i_can't_do_that ()
        end
    |_ -> i_can't_do_that ()

(* TODO for that function:
\begin{itemize}
\item handle the case where the return type is an argument of the
  function
\item handle the case of simple mutual inductive (for example terms
  and lists of terms) formulas with the corresponding mutual
  recursvive interpretation functions.
\end{itemize}
*)

(*s Stuff to build variables map, currently implemented as complete
binary search trees (see file \texttt{Quote.v}) *)

(* First the function to distinghish between constants (closed terms)
   and variables (open terms) *)

let rec closed_under cset t =
  (ConstrSet.mem t cset) or
  (match (kind_of_term t) with
     | Cast(c,_,_) -> closed_under cset c
     | App(f,l) -> closed_under cset f && array_for_all (closed_under cset) l
     | _ -> false)

(*s [btree_of_array [| c1; c2; c3; c4; c5 |]] builds the complete
   binary search tree containing the [ci], that is:

\begin{verbatim}
                  c1
                 /  \
               c2    c3
              /  \
             c4  c5
\end{verbatim}

The second argument is a constr (the common type of the [ci])
*)

let btree_of_array a ty =
  let size_of_a = Array.length a in
  let semi_size_of_a = size_of_a lsr 1 in
  let node = Lazy.force coq_Node_vm
  and empty = mkApp (Lazy.force coq_Empty_vm, [| ty |]) in
  let rec aux n =
    if n > size_of_a
    then empty
    else if  n > semi_size_of_a
    then mkApp (node, [| ty; a.(n-1); empty; empty |])
    else mkApp (node, [| ty; a.(n-1); aux (2*n); aux (2*n+1) |])
  in
  aux 1

(*s [btree_of_array] and [path_of_int] verify the following invariant:\\
   {\tt (varmap\_find A dv }[(path_of_int n)] [(btree_of_array a ty)]
  = [a.(n)]\\
  [n] must be [> 0] *)

let path_of_int n =
  (* returns the list of digits of n in reverse order with
     initial 1 removed *)
  let rec digits_of_int n =
    if n=1 then []
    else (n mod 2 = 1)::(digits_of_int (n lsr 1))
  in
  List.fold_right
    (fun b c -> mkApp ((if b then Lazy.force coq_Right_idx
                         else Lazy.force coq_Left_idx),
                         [| c |]))
    (List.rev (digits_of_int n))
    (Lazy.force coq_End_idx)

(*s The tactic works with a list of subterms sharing the same
  variables map. We need to sort terms in order to avoid than
  strange things happen during replacement of terms by their
  'abstract' counterparties. *)

(* [subterm t t'] tests if constr [t'] occurs in [t] *)
(* This function does not descend under binders (lambda and Cases) *)

let rec subterm gl (t : constr) (t' : constr) =
  (pf_conv_x gl t t') or
  (match (kind_of_term t) with
     | App (f,args) -> array_exists (fun t -> subterm gl t t') args
     | Cast(t,_,_) -> (subterm gl t t')
     | _ -> false)

(*s We want to sort the list according to reverse subterm order. *)
(* Since it's a partial order the algoritm of Sort.list won't work !! *)

let rec sort_subterm gl l =
  let rec insert c = function
    | [] -> [c]
    | (h::t as l) when eq_constr c h -> l (* Avoid doing the same work twice *)
    | h::t -> if subterm gl c h then c::h::t else h::(insert c t)
  in
  match l with
    | [] -> []
    | h::t -> insert h (sort_subterm gl t)

module Constrhash = Hashtbl.Make
  (struct type t = constr
	  let equal = eq_constr
	  let hash = hash_constr
   end)

(*s Now we are able to do the inversion itself.
  We destructurate the term and use an imperative hashtable
  to store leafs that are already encountered.
  The type of arguments is:\\
  [ivs : inversion_scheme]\\
  [lc: constr list]\\
  [gl: goal sigma]\\ *)
let quote_terms ivs lc gl =
  Coqlib.check_required_library ["Coq";"quote";"Quote"];
  let varhash  = (Constrhash.create 17 : constr Constrhash.t) in
  let varlist = ref ([] : constr list) in (* list of variables *)
  let counter = ref 1 in (* number of variables created + 1 *)
  let rec aux c =
    let rec auxl l =
      match l with
        | (lhs, rhs)::tail ->
            begin try
              let s1 = matches rhs c in
              let s2 = List.map (fun (i,c_i) -> (coerce_meta_out i,aux c_i)) s1
	      in
              Termops.subst_meta s2 lhs
            with PatternMatchingFailure -> auxl tail
            end
        |  [] ->
             begin match ivs.variable_lhs with
               | None ->
                   begin match ivs.constant_lhs with
                     | Some c_lhs -> Termops.subst_meta [1, c] c_lhs
                     | None -> anomaly "invalid inversion scheme for quote"
                   end
               | Some var_lhs ->
                   begin match ivs.constant_lhs with
                     | Some c_lhs when closed_under ivs.constants c ->
			 Termops.subst_meta [1, c] c_lhs
                     | _ ->
			 begin
                           try Constrhash.find varhash c
                           with Not_found ->
                             let newvar =
                               Termops.subst_meta [1, (path_of_int !counter)]
				 var_lhs in
                             begin
                               incr counter;
                               varlist := c :: !varlist;
                               Constrhash.add varhash c newvar;
                               newvar
                             end
			 end
                   end
             end
    in
    auxl ivs.normal_lhs_rhs
  in
  let lp = List.map aux lc in
  (lp, (btree_of_array (Array.of_list (List.rev !varlist))
          ivs.return_type ))

(*s actually we could "quote" a list of terms instead of a single
  term. Ring for example needs that, but Ring doesn't use Quote
  yet. *)

let quote f lid gl =
  let f = pf_global gl f in
  let cl = List.map (pf_global gl) lid in
  let ivs = compute_ivs gl f cl in
  let (p, vm) = match quote_terms ivs [(pf_concl gl)] gl with
    | [p], vm -> (p,vm)
    | _ -> assert false
  in
  match ivs.variable_lhs with
    | None -> Tactics.convert_concl (mkApp (f, [| p |])) DEFAULTcast gl
    | Some _ -> Tactics.convert_concl (mkApp (f, [| vm; p |])) DEFAULTcast gl

let gen_quote cont c f lid gl =
  let f = pf_global gl f in
  let cl = List.map (pf_global gl) lid in
  let ivs = compute_ivs gl f cl in
  let (p, vm) = match quote_terms ivs [c] gl with
    | [p], vm -> (p,vm)
    | _ -> assert false
  in
  match ivs.variable_lhs with
    | None -> cont (mkApp (f, [| p |])) gl
    | Some _ -> cont (mkApp (f, [| vm; p |])) gl

(*i

Just testing ...

#use "include.ml";;
open Quote;;

let r = glob_constr_of_string;;

let ivs = {
  normal_lhs_rhs =
   [ r "(f_and ?1 ?2)", r "?1/\?2";
     r "(f_not ?1)", r "~?1"];
  variable_lhs = Some (r "(f_atom ?1)");
  return_type = r "Prop";
  constants = ConstrSet.empty;
  constant_lhs = (r "nat")
};;

let t1 = r "True/\(True /\ ~False)";;
let t2 = r "True/\~~False";;

quote_term ivs () t1;;
quote_term ivs () t2;;

let ivs2 =
  normal_lhs_rhs =
   [ r "(f_and ?1 ?2)", r "?1/\?2";
     r "(f_not ?1)", r "~?1"
     r "True", r "f_true"];
  variable_lhs = Some (r "(f_atom ?1)");
  return_type = r "Prop";
  constants = ConstrSet.empty;
  constant_lhs = (r "nat")

i*)