1 (* Copyright (C) 2003-2005, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
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13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 * GNU General Public License for more details.
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19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
27 module E = CicEnvironment
29 module TC = CicTypeChecker
30 module UM = UriManager
31 module Rd = CicReduction
32 module PEH = ProofEngineHelpers
33 module PT = PrimitiveTactics
34 module DTI = DoubleTypeInference
36 module H = ProceduralHelpers
38 (* helpers ******************************************************************)
40 let rec list_sub start length = function
41 | _ :: tl when start > 0 -> list_sub (pred start) length tl
42 | hd :: tl when length > 0 -> hd :: list_sub start (pred length) tl
45 (* proof construction *******************************************************)
48 let rec iter_xns k (uri, t) = uri, iter_term k t
49 and iter_ms k = function
51 | Some t -> Some (iter_term k t)
52 and iter_fix len k (id, name, i, ty, bo) =
53 id, name, i, iter_term k ty, iter_term (k + len) bo
54 and iter_cofix len k (id, name, ty, bo) =
55 id, name, iter_term k ty, iter_term (k + len) bo
56 and iter_term k = function
58 | C.AImplicit _ as t -> t
59 | C.ARel (id, rid, m, b) as t ->
60 if m < k then t else f k id rid m b
61 | C.AConst (id, uri, xnss) -> C.AConst (id, uri, List.map (iter_xns k) xnss)
62 | C.AVar (id, uri, xnss) -> C.AVar (id, uri, List.map (iter_xns k) xnss)
63 | C.AMutInd (id, uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (iter_xns k) xnss)
64 | C.AMutConstruct (id, uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (iter_xns k) xnss)
65 | C.AMeta (id, i, mss) -> C.AMeta(id, i, List.map (iter_ms k) mss)
66 | C.AAppl (id, ts) -> C.AAppl (id, List.map (iter_term k) ts)
67 | C.ACast (id, te, ty) -> C.ACast (id, iter_term k te, iter_term k ty)
68 | C.AMutCase (id, sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, iter_term k outty, iter_term k t, List.map (iter_term k) pl)
69 | C.AProd (id, n, s, t) -> C.AProd (id, n, iter_term k s, iter_term (succ k) t)
70 | C.ALambda (id, n, s, t) -> C.ALambda (id, n, iter_term k s, iter_term (succ k) t)
71 | C.ALetIn (id, n, ty, s, t) -> C.ALetIn (id, n, iter_term k ty, iter_term k s, iter_term (succ k) t)
72 | C.AFix (id, i, fl) -> C.AFix (id, i, List.map (iter_fix (List.length fl) k) fl)
73 | C.ACoFix (id, i, fl) -> C.ACoFix (id, i, List.map (iter_cofix (List.length fl) k) fl)
79 if m + n > 0 then C.ARel (id, rid, m + n, b) else
81 HLog.error (Printf.sprintf "ProceduralConversion.lift: %i %i" m n);
89 if m = k then lift 1 (pred k) v else C.ARel (id, rid, pred m, b)
93 let fake_annotate id c =
95 try match List.nth c (pred m) with
96 | Some (C.Name s, _) -> s
99 | Invalid_argument _ -> assert false
101 let mk_decl n v = Some (n, C.Decl v) in
102 let mk_def n v ty = Some (n, C.Def (v, ty)) in
103 let mk_fix (name, _, ty, bo) = mk_def (C.Name name) bo ty in
104 let mk_cofix (name, ty, bo) = mk_def (C.Name name) bo ty in
105 let rec ann_xns c (uri, t) = uri, ann_term c t
106 and ann_ms c = function
108 | Some t -> Some (ann_term c t)
109 and ann_fix newc c (name, i, ty, bo) =
110 id, name, i, ann_term c ty, ann_term (List.rev_append newc c) bo
111 and ann_cofix newc c (name, ty, bo) =
112 id, name, ann_term c ty, ann_term (List.rev_append newc c) bo
113 and ann_term c = function
114 | C.Sort sort -> C.ASort (id, sort)
115 | C.Implicit ann -> C.AImplicit (id, ann)
116 | C.Rel m -> C.ARel (id, id, m, get_binder c m)
117 | C.Const (uri, xnss) -> C.AConst (id, uri, List.map (ann_xns c) xnss)
118 | C.Var (uri, xnss) -> C.AVar (id, uri, List.map (ann_xns c) xnss)
119 | C.MutInd (uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (ann_xns c) xnss)
120 | C.MutConstruct (uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (ann_xns c) xnss)
121 | C.Meta (i, mss) -> C.AMeta(id, i, List.map (ann_ms c) mss)
122 | C.Appl ts -> C.AAppl (id, List.map (ann_term c) ts)
123 | C.Cast (te, ty) -> C.ACast (id, ann_term c te, ann_term c ty)
124 | C.MutCase (sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, ann_term c outty, ann_term c t, List.map (ann_term c) pl)
125 | C.Prod (n, s, t) -> C.AProd (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
126 | C.Lambda (n, s, t) -> C.ALambda (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
127 | C.LetIn (n, s, ty, t) -> C.ALetIn (id, n, ann_term c s, ann_term c ty, ann_term (mk_def n s ty :: c) t)
128 | C.Fix (i, fl) -> C.AFix (id, i, List.map (ann_fix (List.rev_map mk_fix fl) c) fl)
129 | C.CoFix (i, fl) -> C.ACoFix (id, i, List.map (ann_cofix (List.rev_map mk_cofix fl) c) fl)
133 let mk_arel k = C.ARel ("", "", k, "")
135 let mk_aappl ts = C.AAppl ("", ts)
137 let rec clear_absts f n k = function
138 | t when n = 0 -> f k t
139 | C.ALambda (_, _, _, t) -> clear_absts f (pred n) (succ k) t
141 let u = match mk_aappl [lift (succ k) 1 t; mk_arel (succ k)] with
142 | C.AAppl (_, [ C.AAppl (id, ts); t]) -> C.AAppl (id, ts @ [t])
145 clear_absts f (pred n) (succ k) u
147 let hole id = C.AImplicit (id, Some `Hole)
149 let meta id = C.AImplicit (id, None)
151 let anon = C.Anonymous
156 | C.AImplicit (_, None) when b -> b
159 List.fold_left map true
161 let rec gen_fix len k (id, name, i, ty, bo) =
162 id, name, i, gen_term k ty, gen_term (k + len) bo
163 and gen_cofix len k (id, name, ty, bo) =
164 id, name, gen_term k ty, gen_term (k + len) bo
165 and gen_term k = function
167 | C.AImplicit (id, _)
168 | C.AConst (id, _, _)
170 | C.AMutInd (id, _, _, _)
171 | C.AMutConstruct (id, _, _, _, _)
172 | C.AMeta (id, _, _) -> meta id
173 | C.ARel (id, _, m, _) ->
174 if succ (k - n) <= m && m <= k then hole id else meta id
175 | C.AAppl (id, ts) ->
176 let ts = List.map (gen_term k) ts in
177 if is_meta ts then meta id else C.AAppl (id, ts)
178 | C.ACast (id, te, ty) ->
179 let te, ty = gen_term k te, gen_term k ty in
180 if is_meta [te; ty] then meta id else C.ACast (id, te, ty)
181 | C.AMutCase (id, sp, i, outty, t, pl) ->
182 let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
183 if is_meta (outty :: t :: pl) then meta id else hole id (* C.AMutCase (id, sp, i, outty, t, pl) *)
184 | C.AProd (id, _, s, t) ->
185 let s, t = gen_term k s, gen_term (succ k) t in
186 if is_meta [s; t] then meta id else C.AProd (id, anon, s, t)
187 | C.ALambda (id, _, s, t) ->
188 let s, t = gen_term k s, gen_term (succ k) t in
189 if is_meta [s; t] then meta id else C.ALambda (id, anon, s, t)
190 | C.ALetIn (id, _, s, ty, t) ->
191 let s, ty, t = gen_term k s, gen_term k ty, gen_term (succ k) t in
192 if is_meta [s; t] then meta id else C.ALetIn (id, anon, s, ty, t)
193 | C.AFix (id, i, fl) -> C.AFix (id, i, List.map (gen_fix (List.length fl) k) fl)
194 | C.ACoFix (id, i, fl) -> C.ACoFix (id, i, List.map (gen_cofix (List.length fl) k) fl)
198 let convert g ety k predicate =
199 let rec aux = function
200 | C.ALambda (_, _, b, ety), C.ALambda (id, n, u, pred) ->
201 C.ALambda (id, n, aux (b, u), aux (ety, pred))
202 | C.AProd (_, _, b, ety), C.AProd (id, n, u, pred) ->
203 C.AProd (id, n, aux (b, u), aux (ety, pred))
204 | C.ALetIn (_, _, a, b, ety), C.ALetIn (id, n, v, u, pred) ->
205 C.ALetIn (id, n, aux (a, v), aux (b, u), aux (ety, pred))
206 | C.AAppl (_, bs), C.AAppl (id, us) when List.length bs = List.length us ->
207 let map b u = aux (b,u) in
208 C.AAppl (id, List.map2 map bs us)
209 | C.ACast (_, ety, b), C.ACast (id, pred, u) ->
210 C.ACast (id, aux (ety, pred), aux (b, u))
211 | ety, C.AAppl (_, C.ALambda (_, _, _, pred) :: v :: []) ->
212 aux (ety, subst 1 v pred)
213 | ety, C.AAppl (id, C.ALambda (_, _, _, pred) :: v :: vs) ->
214 aux (ety, C.AAppl (id, subst 1 v pred :: vs))
217 g k (aux (ety, predicate))
219 let mk_pattern psno ety predicate =
220 clear_absts (convert (generalize psno) ety) psno 0 predicate
222 let get_clears c p xtypes =
223 let meta = C.Implicit None in
224 let rec aux c names p it et = function
226 List.rev c, List.rev names
227 | Some (C.Name name as n, C.Decl v) as hd :: tl ->
229 if DTI.does_not_occur 1 p && DTI.does_not_occur 1 it && DTI.does_not_occur 1 et then
230 Some (C.Anonymous, C.Decl v), name :: names, meta
234 let p = C.Lambda (n, v, p) in
235 let it = C.Prod (n, v, it) in
236 let et = C.Prod (n, v, et) in
237 aux (hd :: c) names p it et tl
238 | Some (C.Name name as n, C.Def (v, x)) as hd :: tl ->
240 if DTI.does_not_occur 1 p && DTI.does_not_occur 1 it && DTI.does_not_occur 1 et then
241 Some (C.Anonymous, C.Def (v, x)), name :: names, meta
245 let p = C.LetIn (n, v, x, p) in
246 let it = C.LetIn (n, v, x, it) in
247 let et = C.LetIn (n, v, x, et) in
248 aux (hd :: c) names p it et tl
249 | Some (C.Anonymous as n, C.Decl v) as hd :: tl ->
250 let p = C.Lambda (n, meta, p) in
251 let it = C.Lambda (n, meta, it) in
252 let et = C.Lambda (n, meta, et) in
253 aux (hd :: c) names p it et tl
254 | Some (C.Anonymous as n, C.Def (v, _)) as hd :: tl ->
255 let p = C.LetIn (n, meta, meta, p) in
256 let it = C.LetIn (n, meta, meta, it) in
257 let et = C.LetIn (n, meta, meta, et) in
258 aux (hd :: c) names p it et tl
259 | None :: tl -> assert false
262 | Some (it, et) -> aux [] [] p it et c
266 let rec aux c = function
268 | Some (C.Name name, entry) :: tail when name = hyp ->
269 aux (Some (C.Anonymous, entry) :: c) tail
270 | entry :: tail -> aux (entry :: c) tail
274 let elim_inferred_type context goal arg using cpattern =
275 let metasenv, ugraph = [], Un.default_ugraph in
276 let ety = H.get_type "elim_inferred_type" context using in
277 let _splits, args_no = PEH.split_with_whd (context, ety) in
278 let _metasenv, _subst, predicate, _arg, actual_args =
279 PT.mk_predicate_for_elim
280 ~context ~metasenv ~subst:[] ~ugraph ~goal ~arg ~using ~cpattern ~args_no
282 let ty = C.Appl (predicate :: actual_args) in
283 let upto = List.length actual_args in
284 Rd.head_beta_reduce ~delta:false ~upto ty
286 let does_not_occur = function
287 | C.AImplicit (_, None) -> true