File: cic.mli

package info (click to toggle)
coq 8.9.0-1
  • links: PTS, VCS
  • area: main
  • in suites: bullseye, buster, sid
  • size: 30,604 kB
  • sloc: ml: 192,230; sh: 2,585; python: 2,206; ansic: 1,878; makefile: 818; lisp: 202; xml: 24; sed: 2
file content (469 lines) | stat: -rw-r--r-- 15,777 bytes parent folder | download
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
(************************************************************************)
(*         *   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)         *)
(************************************************************************)

(** Type definitions for the Calculus of Inductive Constructions *)

(** We regroup here the type definitions for structures of the Coq kernel
    that are present in .vo files. Here is everything the Checker needs
    to know about these structures for verifying a .vo. Note that this
    isn't an exact copy of the kernel code :

    - there isn't any abstraction here (see e.g. [constr] or [lazy_constr])
    - some types are left undefined when they aren't used by the Checker
    - some types have less constructors when the final constructors aren't
      supposed to appear in .vo (see [REVERTcast] and [Direct]).

    The following types are also described in a reified manner in values.ml,
    for validating the layout of structures after de-marshalling. So:

    IF YOU ADAPT THIS FILE, YOU SHOULD MODIFY values.ml ACCORDINGLY !
*)

open Names

(*************************************************************************)
(** {4 From term.ml} *)

(** {6 The sorts of CCI. } *)

type sorts =
  | Prop
  | Set
  | Type of Univ.universe

(** {6 The sorts family of CCI. } *)

type sorts_family = InProp | InSet | InType

(** {6 Useful types } *)

(** {6 Existential variables } *)
type existential_key = int

(** {6 Existential variables } *)
type metavariable = int

(** {6 Case annotation } *)
type case_style = LetStyle | IfStyle | LetPatternStyle | MatchStyle
  | RegularStyle (** infer printing form from number of constructor *)
type case_printing =
  { ind_tags : bool list; (* tell whether letin or lambda in the arity of the inductive type *)
    cstr_tags : bool list array; (* whether each pattern var of each constructor is a let-in (true) or not (false) *)
    style     : case_style }

(** the integer is the number of real args, needed for reduction *)
type case_info =
  { ci_ind        : inductive;
    ci_npar       : int;
    ci_cstr_ndecls : int array; (* number of pattern vars of each constructor (with let's)*)
    ci_cstr_nargs : int array; (* number of pattern vars of each constructor (w/o let's) *)
    ci_pp_info    : case_printing (** not interpreted by the kernel *)
  }

(** This defines the strategy to use for verifiying a Cast. *)
type cast_kind = VMcast | NATIVEcast | DEFAULTcast (* | REVERTcast *)

(** {6 The type of constructions } *)

(** [constr array] is an instance matching definitional [named_context] in
    the same order (i.e. last argument first) *)
type 'constr pexistential = existential_key * 'constr array
type 'constr prec_declaration =
    Name.t array * 'constr array * 'constr array
type 'constr pfixpoint =
    (int array * int) * 'constr prec_declaration
type 'constr pcofixpoint =
    int * 'constr prec_declaration
type 'a puniverses = 'a Univ.puniverses
type pconstant = Constant.t puniverses
type pinductive = inductive puniverses
type pconstructor = constructor puniverses

type constr =
  | Rel       of int
  | Var       of Id.t (** Shouldn't occur in a .vo *)
  | Meta      of metavariable (** Shouldn't occur in a .vo *)
  | Evar      of constr pexistential (** Shouldn't occur in a .vo *)
  | Sort      of sorts
  | Cast      of constr * cast_kind * constr
  | Prod      of Name.t * constr * constr
  | Lambda    of Name.t * constr * constr
  | LetIn     of Name.t * constr * constr * constr
  | App       of constr * constr array
  | Const     of pconstant
  | Ind       of pinductive
  | Construct of pconstructor
  | Case      of case_info * constr * constr * constr array
  | Fix       of constr pfixpoint
  | CoFix     of constr pcofixpoint
  | Proj      of Projection.t * constr

type existential = constr pexistential
type rec_declaration = constr prec_declaration
type fixpoint = constr pfixpoint
type cofixpoint = constr pcofixpoint

(** {6 Type of assumptions and contexts}  *)

type rel_declaration = LocalAssum of Name.t * constr          (* name, type *)
                     | LocalDef of Name.t * constr * constr   (* name, value, type *)
type rel_context = rel_declaration list

(** The declarations below in .vo should be outside sections,
    so we expect there a value compatible with an empty list *)
type section_context = unit


(*************************************************************************)
(** {4 From mod_susbt.ml and lazyconstr.ml} *)

(** {6 Substitutions} *)

type delta_hint =
  | Inline of int * (Univ.AUContext.t * constr) option
  | Equiv of KerName.t

type delta_resolver = ModPath.t MPmap.t * delta_hint KNmap.t

type 'a umap_t = 'a MPmap.t * 'a MBImap.t
type substitution = (ModPath.t * delta_resolver) umap_t

(** {6 Delayed constr} *)

type 'a substituted = {
  mutable subst_value : 'a;
  mutable subst_subst : substitution list;
}

type constr_substituted = constr substituted

(** Nota : in coqtop, the [lazy_constr] type also have a [Direct]
    constructor, but it shouldn't occur inside a .vo, so we ignore it *)

type lazy_constr =
  | Indirect of substitution list * DirPath.t * int
(* | Direct of constr_substituted *)


(*************************************************************************)
(** {4 From declarations.mli} *)

(** Some types unused in the checker, hence left undefined *)

(** Bytecode *)
type reloc_table
type to_patch_substituted
(** Native code *)
type native_name
(** Retroknowledge *)
type action

(** Engagements *)

type set_predicativity = ImpredicativeSet | PredicativeSet

type engagement = set_predicativity

(** {6 Conversion oracle} *)

type level = Expand | Level of int | Opaque

type oracle = {
  var_opacity : level Id.Map.t;
  cst_opacity : level Cmap.t;
  var_trstate : Id.Pred.t;
  cst_trstate : Cpred.t;
}

(** {6 Representation of constants (Definition/Axiom) } *)


type template_arity = {
  template_param_levels : Univ.universe_level option list;
  template_level : Univ.universe;
}

type ('a, 'b) declaration_arity = 
  | RegularArity of 'a
  | TemplateArity of 'b

(** Inlining level of parameters at functor applications.
    This is ignored by the checker. *)

type inline = int option

(** A constant can have no body (axiom/parameter), or a
    transparent body, or an opaque one *)

type constant_def =
  | Undef of inline
  | Def of constr_substituted
  | OpaqueDef of lazy_constr

type constant_universes =
  | Monomorphic_const of Univ.ContextSet.t
  | Polymorphic_const of Univ.abstract_universe_context

(** The [typing_flags] are instructions to the type-checker which
    modify its behaviour. The typing flags used in the type-checking
    of a constant are tracked in their {!constant_body} so that they
    can be displayed to the user. *)
type typing_flags = {
  check_guarded : bool; (** If [false] then fixed points and co-fixed
                            points are assumed to be total. *)
  check_universes : bool; (** If [false] universe constraints are not checked *)
  conv_oracle : oracle; (** Unfolding strategies for conversion *)
  share_reduction : bool; (** Use by-need reduction algorithm *)
}

type constant_body = {
    const_hyps : section_context; (** New: younger hyp at top *)
    const_body : constant_def;
    const_type : constr;
    const_body_code : to_patch_substituted;
    const_universes : constant_universes;
    const_inline_code : bool;
    const_typing_flags : typing_flags;
}

(** {6 Representation of mutual inductive types } *)

type recarg =
  | Norec
  | Mrec of inductive
  | Imbr of inductive

type wf_paths = recarg Rtree.t

type record_info =
| NotRecord
| FakeRecord
| PrimRecord of (Id.t * Label.t array * constr array) array

type regular_inductive_arity = {
  mind_user_arity : constr;
  mind_sort : sorts;
}

type recursivity_kind =
  | Finite (** = inductive *)
  | CoFinite (** = coinductive *)
  | BiFinite (** = non-recursive, like in "Record" definitions *)

type inductive_arity = (regular_inductive_arity, template_arity) declaration_arity

type one_inductive_body = {
(** {8 Primitive datas } *)

    mind_typename : Id.t; (** Name of the type: [Ii] *)

    mind_arity_ctxt : rel_context; (** Arity context of [Ii] with parameters: [forall params, Ui] *)

    mind_arity : inductive_arity; (** Arity sort and original user arity if monomorphic *)

    mind_consnames : Id.t array; (** Names of the constructors: [cij] *)

    mind_user_lc : constr array;
 (** Types of the constructors with parameters:  [forall params, Tij],
     where the Ik are replaced by de Bruijn index in the
     context I1:forall params, U1 ..  In:forall params, Un *)

(** {8 Derived datas } *)

    mind_nrealargs : int; (** Number of expected real arguments of the type (no let, no params) *)

    mind_nrealdecls : int; (** Length of realargs context (with let, no params) *)

    mind_kelim : sorts_family list; (** List of allowed elimination sorts *)

    mind_nf_lc : constr array; (** Head normalized constructor types so that their conclusion is atomic *)

    mind_consnrealargs : int array;
 (** Length of the signature of the constructors (w/o let, w/o params)
    (not used in the kernel) *)

    mind_consnrealdecls : int array;
 (** Length of the signature of the constructors (with let, w/o params)
    (not used in the kernel) *)

    mind_recargs : wf_paths; (** Signature of recursive arguments in the constructors *)

(** {8 Datas for bytecode compilation } *)

    mind_nb_constant : int; (** number of constant constructor *)

    mind_nb_args : int; (** number of no constant constructor *)

    mind_reloc_tbl : reloc_table;
  }

type abstract_inductive_universes =
  | Monomorphic_ind of Univ.ContextSet.t
  | Polymorphic_ind of Univ.abstract_universe_context
  | Cumulative_ind of Univ.abstract_cumulativity_info

type mutual_inductive_body = {

    mind_packets : one_inductive_body array;  (** The component of the mutual inductive block *)

    mind_record : record_info; (** Whether the inductive type has been declared as a record. *)

    mind_finite : recursivity_kind;  (** Whether the type is inductive or coinductive *)

    mind_ntypes : int;  (** Number of types in the block *)

    mind_hyps : section_context;  (** Section hypotheses on which the block depends *)

    mind_nparams : int;  (** Number of expected parameters *)

    mind_nparams_rec : int;  (** Number of recursively uniform (i.e. ordinary) parameters *)

    mind_params_ctxt : rel_context;  (** The context of parameters (includes let-in declaration) *)

    mind_universes : abstract_inductive_universes; (** Local universe variables and constraints together with subtyping constraints *)

    mind_private : bool option; (** allow pattern-matching: Some true ok, Some false blocked *)

    mind_typing_flags : typing_flags; (** typing flags at the time of the inductive creation *)
  }

(** {6 Module declarations } *)

(** Functor expressions are forced to be on top of other expressions *)

type ('ty,'a) functorize =
  | NoFunctor of 'a
  | MoreFunctor of MBId.t * 'ty * ('ty,'a) functorize

(** The fully-algebraic module expressions : names, applications, 'with ...'.
    They correspond to the user entries of non-interactive modules.
    They will be later expanded into module structures in [Mod_typing],
    and won't play any role into the kernel after that : they are kept
    only for short module printing and for extraction. *)

type with_declaration

type module_alg_expr =
  | MEident of ModPath.t
  | MEapply of module_alg_expr * ModPath.t
  | MEwith of module_alg_expr * with_declaration

(** A component of a module structure *)

type structure_field_body =
  | SFBconst of constant_body
  | SFBmind of mutual_inductive_body
  | SFBmodule of module_body
  | SFBmodtype of module_type_body

(** A module structure is a list of labeled components.

    Note : we may encounter now (at most) twice the same label in
    a [structure_body], once for a module ([SFBmodule] or [SFBmodtype])
    and once for an object ([SFBconst] or [SFBmind]) *)

and structure_body = (Label.t * structure_field_body) list

(** A module signature is a structure, with possibly functors on top of it *)

and module_signature = (module_type_body,structure_body) functorize

(** A module expression is an algebraic expression, possibly functorized. *)

and module_expression = (module_type_body,module_alg_expr) functorize

and module_implementation =
  | Abstract (** no accessible implementation (keep this constructor first!) *)
  | Algebraic of module_expression (** non-interactive algebraic expression *)
  | Struct of module_signature (** interactive body *)
  | FullStruct (** special case of [Struct] : the body is exactly [mod_type] *)

and 'a generic_module_body =
  { mod_mp : ModPath.t; (** absolute path of the module *)
    mod_expr : 'a; (** implementation *)
    mod_type : module_signature; (** expanded type *)
    (** algebraic type, kept if it's relevant for extraction *)
    mod_type_alg : module_expression option;
    (** set of all constraints in the module  *)
    mod_constraints : Univ.ContextSet.t;
    (** quotiented set of equivalent constants and inductive names *)
    mod_delta : delta_resolver;
    mod_retroknowledge : 'a module_retroknowledge; }

and module_body = module_implementation generic_module_body

(** A [module_type_body] is just a [module_body] with no
    implementation and also an empty [mod_retroknowledge] *)

and module_type_body = unit generic_module_body

and _ module_retroknowledge =
| ModBodyRK :
  action list -> module_implementation module_retroknowledge
| ModTypeRK : unit module_retroknowledge

(*************************************************************************)
(** {4 From safe_typing.ml} *)

type nativecode_symb_array

type compilation_unit_name = DirPath.t

type vodigest =
  | Dvo of Digest.t              (* The digest of the seg_lib part *)
  | Dviovo of Digest.t * Digest.t (* The digest of the seg_lib+seg_univ part *)

type library_info = compilation_unit_name * vodigest

type library_deps = library_info array

type compiled_library = {
  comp_name : compilation_unit_name;
  comp_mod : module_body;
  comp_deps : library_deps;
  comp_enga : engagement;
  comp_natsymbs : nativecode_symb_array
}


(*************************************************************************)
(** {4 From library.ml} *)

type library_objects

type summary_disk = {
  md_name : compilation_unit_name;
  md_imports : compilation_unit_name array;
  md_deps : library_deps;
}

type library_disk = {
  md_compiled : compiled_library;
  md_objects : library_objects;
}

type opaque_table = constr Future.computation array
type univ_table =
  (Univ.universe_context_set Future.computation array * Univ.universe_context_set * bool) option

(** A .vo file is currently made of :

    1) a magic number (4 bytes, cf output_binary_int)
    2) a marshalled [library_disk] structure
    3) a [Digest.t] string (16 bytes)
    4) a marshalled [univ_table] (* Some if vo was obtained from vi *)
    5) a [Digest.t] string (16 bytes)
    6) a marshalled [None] discharge_table (* Some in vi files *)
    7) a [Digest.t] string (16 bytes)
    8) a marshalled [None] todo_table (* Some in vi files *)
    9) a [Digest.t] string (16 bytes)
   10) a marshalled [opaque_table]
   11) a [Digest.t] string (16 bytes)
*)