1 (* Copyright (C) 2002, 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
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
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18 * along with HELM; if not, write to the Free Software
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/.
28 exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
29 exception NotAnInductiveTypeToEliminate
33 fun msg -> if debug then prerr_endline (Lazy.force msg) else ()
36 let inside_obj = function
37 | Cic.InductiveDefinition (l,params, nleft, _) ->
39 | _ -> raise (Invalid_argument "Errore in inside_obj")
41 let term_to_list = function
43 | _ -> raise (Invalid_argument "Errore in term_to_list")
46 let rec baseuri_of_term = function
47 | Cic.Appl l -> baseuri_of_term (List.hd l)
48 | Cic.MutInd (baseuri, tyno, []) -> baseuri
49 | _ -> raise (Invalid_argument "baseuri_of_term")
52 (* prende il numero dei parametri sinistri, la lista dei parametri, la lista
53 dei tipi dei parametri, il tipo del GOAL e costruisce il termine per la cut
54 ossia DX1 = DX1 -> ... DXn=DXn -> GOALTY *)
56 let rec foo_cut nleft l param_ty_l body uri_of_eq =
57 if nleft > 0 then foo_cut (nleft-1) (List.tl l) (List.tl param_ty_l) body
60 | hd::tl -> Cic.Prod (Cic.Anonymous, Cic.Appl[Cic.MutInd (uri_of_eq ,0,[]);
61 (List.hd param_ty_l) ; hd; hd], foo_cut nleft
62 (List.map (CicSubstitution.lift 1) tl) (List.tl param_ty_l)
63 (CicSubstitution.lift 1 body) uri_of_eq )
67 (* da una catena di prod costruisce una lista dei termini che lo compongono.*)
68 let rec list_of_prod term =
70 | Cic.Prod (Cic.Anonymous,src,tgt) -> [src] @ (list_of_prod tgt)
75 let rec cut_first n l =
78 | hd::tl -> cut_first (n-1) tl
86 | hd::tl when tl != [] -> hd:: (cut_last tl)
91 let foo_appl nleft nright_consno term uri =
95 a := !a @ [(Cic.Implicit None)]
98 for n = 1 to nright_consno do
99 a := !a @ [(Cic.Implicit None)]
101 Cic.Appl ([Cic.Const(uri,[])] @ !a @ [Cic.Rel 1]) (*L'ipotesi e' sempre Rel 1. (?) *)
105 let rec foo_prod nright param_ty_l l l2 base_rel body uri_of_eq nleft termty
107 match param_ty_l with
108 | hd::tl -> Cic.Prod (
110 Cic.Appl[Cic.MutInd(uri_of_eq,0,[]); hd; (List.hd l); Cic.Rel base_rel],
111 foo_prod (nright-1) tl (List.map (CicSubstitution.lift 1) (List.tl l))
112 (List.map (CicSubstitution.lift 1) l2)
113 base_rel (CicSubstitution.lift 1 body)
114 uri_of_eq nleft (CicSubstitution.lift 1 termty)
115 isSetType (CicSubstitution.lift 1 term))
116 | [] -> ProofEngineReduction.replace_lifting
117 ~equality:(ProofEngineReduction.alpha_equivalence)
119 then ((cut_first (1+nleft) (term_to_list termty) ) @ [term] )
120 else (cut_first (1+nleft) (term_to_list termty) ) )
121 ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
123 (*TODO lo stesso sottotermine di body puo' essere sia sx che dx!*)
126 let rec foo_lambda nright param_ty_l nright_ param_ty_l_ l l2 base_rel body
127 uri_of_eq nleft termty isSetType ty_indty term =
128 (*assert nright >0 *)
129 match param_ty_l with
130 | hd::tl ->Cic.Lambda (
131 (Cic.Name ("lambda" ^ (string_of_int nright))),
133 foo_lambda (nright-1) tl nright_ param_ty_l_
134 (List.map (CicSubstitution.lift 1) l)
135 (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1]))
136 base_rel (CicSubstitution.lift 1 body)
138 (CicSubstitution.lift 1 termty)
140 (CicSubstitution.lift 1 term))
141 | [] when isSetType -> Cic.Lambda (
142 (Cic.Name ("lambda" ^ (string_of_int nright))),
143 (ProofEngineReduction.replace_lifting
144 ~equality:(ProofEngineReduction.alpha_equivalence)
145 ~what: (cut_first (1+nleft) (term_to_list termty) )
146 ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
147 ~where:termty), (* tipo di H con i parametri destri sostituiti *)
148 foo_prod nright_ param_ty_l_ (List.map (CicSubstitution.lift 1) l)
149 (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1]))
150 (base_rel+1) (CicSubstitution.lift 1 body)
152 (CicSubstitution.lift 1 termty) isSetType
153 (CicSubstitution.lift 1 term))
154 | [] -> foo_prod nright_ param_ty_l_ l l2 base_rel body uri_of_eq nleft
155 termty isSetType term
158 let inversion_tac ~term =
159 let module T = CicTypeChecker in
160 let module R = CicReduction in
161 let module C = Cic in
162 let module P = PrimitiveTactics in
163 let module PET = ProofEngineTypes in
164 let module PEH = ProofEngineHelpers in
165 let inversion_tac ~term (proof, goal) =
166 let (_,metasenv,_,_) = proof in
167 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
168 let uri_of_eq = HelmLibraryObjects.Logic.eq_URI in
170 (* dall'indice che indentifica il goal nel metasenv, ritorna il suo tipo, che
171 e' la terza componente della relativa congettura *)
172 let (_,_,body) = CicUtil.lookup_meta goal metasenv in
173 (* estrae il tipo del termine(ipotesi) oggetto di inversion,
174 di solito un Cic.Appl *)
175 let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
176 let uri = baseuri_of_term termty in
177 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
178 let l,params,nleft = inside_obj o in
181 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
182 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
183 (uri,exp_named_subst,typeno,args)
184 | _ -> raise NotAnInductiveTypeToEliminate
187 let buri = UriManager.buri_of_uri uri in
190 C.InductiveDefinition (tys,_,_,_) ->
191 let (name,_,_,_) = List.nth tys typeno in
196 UriManager.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
198 (* il tipo del tipo induttivo da cui viene l'ipotesi oggetto di inversione *)
199 let (_,_,ty_indty,cons_list) = (List.hd l) in
200 (*la lista di Cic.term ricavata dal tipo del tipo induttivo. *)
201 let param_ty_l = list_of_prod ty_indty in
202 let consno = List.length cons_list in
203 let nright= (List.length param_ty_l)- (nleft+1) in
204 let isSetType = ((Pervasives.compare
205 (List.nth param_ty_l ((List.length param_ty_l)-1))
206 (Cic.Sort Cic.Prop)) != 0)
208 (* eliminiamo la testa di termty, in quanto e' il nome del predicato e non un parametro.*)
209 let cut_term = foo_cut nleft (List.tl (term_to_list termty))
210 (list_of_prod ty_indty) body uri_of_eq in
211 (* cut DXn=DXn \to GOAL *)
212 let proof1,gl1 = PET.apply_tactic (P.cut_tac cut_term) (proof,goal) in
213 (* apply Hcut ; reflexivity (su tutti i goals aperti da apply_tac) *)
214 let proof2, gl2 = PET.apply_tactic
216 ~start: (P.apply_tac (C.Rel 1)) (* apply Hcut *)
217 ~continuation: (EqualityTactics.reflexivity_tac)
218 ) (proof1, (List.hd gl1))
220 (* apply (ledx_ind( lambda x. lambda y, ...)) *)
221 let (t1,metasenv,t3,t4) = proof2 in
222 let goal2 = List.hd (List.tl gl1) in
223 let (metano,context,_) = CicUtil.lookup_meta goal2 metasenv in
224 let cut_param_ty_l = (cut_first nleft (cut_last param_ty_l)) in
225 (* la lista dei soli parametri destri *)
226 let l= cut_first (1+nleft) (term_to_list termty) in
227 let lambda_t = foo_lambda nright cut_param_ty_l nright cut_param_ty_l l []
228 nright body uri_of_eq nleft termty isSetType ty_indty term in
229 let t = foo_appl nleft (nright+consno) lambda_t eliminator_uri in
230 debug_print (lazy ("Lambda_t: " ^ (CicPp.ppterm t)));
231 debug_print (lazy ("Term: " ^ (CicPp.ppterm termty)));
232 debug_print (lazy ("Body: " ^ (CicPp.ppterm body)));
233 debug_print (lazy ("Right param: " ^ (CicPp.ppterm (Cic.Appl l))));
235 let (ref_t,_,metasenv'',_) = CicRefine.type_of_aux' metasenv context t
238 let proof2 = (t1,metasenv'',t3,t4) in
239 let proof3,gl3 = PET.apply_tactic (P.apply_tac ref_t) (proof2, goal2) in
240 let new_goals = ProofEngineHelpers.compare_metasenvs
241 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
243 let patched_new_goals =
244 let (_,metasenv''',_,_) = proof3 in
245 List.filter (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
248 (*prerr_endline ("METASENV: " ^ CicMetaSubst.ppmetasenv metasenv []); DEBUG*)
249 (proof3, patched_new_goals)
251 ProofEngineTypes.mk_tactic (inversion_tac ~term)