+++ /dev/null
-(* Copyright (C) 2002, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-(* $Id$ *)
-
-module C = Cic
-module U = UriManager
-module P = PrimitiveTactics
-module T = Tacticals
-module CR = CicReduction
-module PST = ProofEngineStructuralRules
-module PET = ProofEngineTypes
-module CTC = CicTypeChecker
-module CU = CicUniv
-module S = CicSubstitution
-module RT = ReductionTactics
-module PEH = ProofEngineHelpers
-module ET = EqualityTactics
-
-let debug = false
-let debug_print =
- if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
-
-(* funzione generale di rilocazione dei riferimenti locali *)
-
-let relocate_term map t =
- let rec map_xnss k xnss =
- let imap (uri, t) = uri, map_term k t in
- List.map imap xnss
- and map_mss k mss =
- let imap = function
- | None -> None
- | Some t -> Some (map_term k t)
- in
- List.map imap mss
- and map_fs len k fs =
- let imap (name, i, ty, bo) = name, i, map_term k ty, map_term (k + len) bo in
- List.map imap fs
- and map_cfs len k cfs =
- let imap (name, ty, bo) = name, map_term k ty, map_term (k + len) bo in
- List.map imap cfs
- and map_term k = function
- | C.Rel m -> if m < k then C.Rel m else C.Rel (map (m - k))
- | C.Sort _ as t -> t
- | C.Implicit _ as t -> t
- | C.Var (uri, xnss) -> C.Var (uri, map_xnss k xnss)
- | C.Const (uri, xnss) -> C.Const (uri, map_xnss k xnss)
- | C.MutInd (uri, tyno, xnss) -> C.MutInd (uri, tyno, map_xnss k xnss)
- | C.MutConstruct (uri, tyno, consno, xnss) ->
- C.MutConstruct (uri, tyno, consno, map_xnss k xnss)
- | C.Meta (i, mss) -> C.Meta(i, map_mss k mss)
- | C.Cast (te, ty) -> C.Cast (map_term k te, map_term k ty)
- | C.Appl ts -> C.Appl (List.map (map_term k) ts)
- | C.MutCase (sp, i, outty, t, pl) ->
- C.MutCase (sp, i, map_term k outty, map_term k t, List.map (map_term k) pl)
- | C.Prod (n, s, t) -> C.Prod (n, map_term k s, map_term (succ k) t)
- | C.Lambda (n, s, t) -> C.Lambda (n, map_term k s, map_term (succ k) t)
- | C.LetIn (n, s, t) -> C.LetIn (n, map_term k s, map_term (succ k) t)
- | C.Fix (i, fs) -> C.Fix (i, map_fs (List.length fs) k fs)
- | C.CoFix (i, cfs) -> C.CoFix (i, map_cfs (List.length cfs) k cfs)
- in
- map_term 0 t
-
-let id n = n
-
-let after continuation aftermap beforemap =
- continuation ~map:(fun n -> aftermap (beforemap n))
-
-let after2 continuation aftermap beforemap ~map =
- continuation ~map:(fun n -> map (aftermap (beforemap n)))
-
-(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
-diversi *)
-
-let discriminate_tac ~term =
- let true_URI =
- match LibraryObjects.true_URI () with
- Some uri -> uri
- | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
- let false_URI =
- match LibraryObjects.false_URI () with
- Some uri -> uri
- | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
- let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
- let find_discriminating_consno t1 t2 =
- let rec aux t1 t2 =
- match t1, t2 with
- | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
- | C.Appl ((C.MutConstruct _ as constr1) :: args1),
- C.Appl ((C.MutConstruct _ as constr2) :: args2)
- when constr1 = constr2 ->
- let rec aux_list l1 l2 =
- match l1, l2 with
- | [], [] -> None
- | hd1 :: tl1, hd2 :: tl2 ->
- (match aux hd1 hd2 with
- | None -> aux_list tl1 tl2
- | Some _ as res -> res)
- | _ -> (* same constructor applied to a different number of args *)
- assert false
- in
- aux_list args1 args2
- | ((C.MutConstruct (_,_,consno1,subst1)),
- (C.MutConstruct (_,_,consno2,subst2)))
- | ((C.MutConstruct (_,_,consno1,subst1)),
- (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
- | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
- (C.MutConstruct (_,_,consno2,subst2)))
- | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
- (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
- when (consno1 <> consno2) || (subst1 <> subst2) ->
- Some consno2
- | _ -> fail "not a discriminable equality"
- in
- aux t1 t2
- in
- let mk_branches_and_outtype turi typeno consno context args =
- (* a list of "True" except for the element in position consno which
- * is "False" *)
- match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
- | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
- let _,_,rty,constructor_list = List.nth ind_type_list typeno in
- let false_constr_id,_ = List.nth constructor_list (consno - 1) in
- let branches =
- List.map
- (fun (id,cty) ->
- (* dubbio: e' corretto ridurre in questo context ??? *)
- let red_ty = CR.whd context cty in
- let rec aux t k =
- match t with
- | C.Prod (_,_,target) when (k <= paramsno) ->
- S.subst (List.nth args (k-1))
- (aux target (k+1))
- | C.Prod (binder,source,target) when (k > paramsno) ->
- C.Lambda (binder, source, (aux target (k+1)))
- | _ ->
- if (id = false_constr_id)
- then (C.MutInd(false_URI,0,[]))
- else (C.MutInd(true_URI,0,[]))
- in
- (S.lift 1 (aux red_ty 1)))
- constructor_list in
- let outtype =
- let seed = ref 0 in
- let rec mk_lambdas rev_left_args =
- function
- 0, args, C.Prod (_,so,ta) ->
- C.Lambda
- (C.Name (incr seed; "x" ^ string_of_int !seed),
- so,
- mk_lambdas rev_left_args (0,args,ta))
- | 0, args, C.Sort _ ->
- let rec mk_rels =
- function
- 0 -> []
- | n -> C.Rel n :: mk_rels (n - 1) in
- let argsno = List.length args in
- C.Lambda
- (C.Name "x",
- (if argsno + List.length rev_left_args > 0 then
- C.Appl
- (C.MutInd (turi, typeno, []) ::
- (List.map
- (S.lift (argsno + 1))
- (List.rev rev_left_args)) @
- mk_rels argsno)
- else
- C.MutInd (turi,typeno,[])),
- C.Sort C.Prop)
- | 0, _, _ -> assert false (* seriously screwed up *)
- | n, he::tl, C.Prod (_,_,ta) ->
- mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
- | n,_,_ ->
- assert false (* we should probably reduce in some context *)
- in
- mk_lambdas [] (paramsno, args, rty)
- in
- branches, outtype
- | _ -> assert false
- in
- let discriminate'_tac ~term status =
- let (proof, goal) = status in
- let _,metasenv,_subst,_,_, _ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let termty,_ =
- CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
- in
- match termty with
- | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
- when LibraryObjects.is_eq_URI equri ->
- let turi,typeno,exp_named_subst,args =
- match tty with
- | (C.MutInd (turi,typeno,exp_named_subst)) ->
- turi,typeno,exp_named_subst,[]
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
- turi,typeno,exp_named_subst,args
- | _ -> fail "not a discriminable equality"
- in
- let consno =
- match find_discriminating_consno t1 t2 with
- | Some consno -> consno
- | None -> fail "discriminating terms are structurally equal"
- in
- let branches,outtype =
- mk_branches_and_outtype turi typeno consno context args
- in
- PET.apply_tactic
- (T.then_
- ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
- ~continuation:
- (T.then_
- ~start:
- (RT.change_tac
- ~pattern:(PET.conclusion_pattern None)
- (fun _ m u ->
- C.Appl [
- C.Lambda ( C.Name "x", tty,
- C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
- t2 ],
- m, u))
- ~continuation:
- (T.then_
- ~start:
- (ET.rewrite_simpl_tac
- ~direction:`RightToLeft
- ~pattern:(PET.conclusion_pattern None)
- term [])
- ~continuation:
- (IntroductionTactics.constructor_tac ~n:1)))) status
- | _ -> fail "not an equality"
- in
- PET.mk_tactic (discriminate'_tac ~term)
-
-let exn_nonproj =
- PET.Fail (lazy "Injection: not a projectable equality")
-let exn_noneq =
- PET.Fail (lazy "Injection: not an equality")
-let exn_nothingtodo =
- PET.Fail (lazy "Nothing to do")
-let exn_discrnonind =
- PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
-let exn_injwronggoal =
- PET.Fail (lazy "Injection: goal after cut is not correct")
-let exn_noneqind =
- PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
-
-let pp ctx t =
- let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
- CicPp.pp t names
-
-let clear_term first_time context term =
- let g () = if first_time then raise exn_nothingtodo else T.id_tac in
- match term with
- | C.Rel n ->
- begin match List.nth context (pred n) with
- | Some (C.Name id, _) -> PST.clear ~hyps:[id]
- | _ -> assert false
- end
- | _ -> g ()
-
-let simpl_in_term context = function
- | Cic.Rel i ->
- let name = match List.nth context (pred i) with
- | Some (Cic.Name s, Cic.Def _) -> s
- | Some (Cic.Name s, Cic.Decl _) -> s
- | _ -> assert false
- in
- RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None)
- | _ -> raise exn_nonproj
-
-(* ~term vive nel contesto della tattica una volta ~mappato
- * ~continuation riceve la mappa assoluta
- *)
-let rec injection_tac ~map ~term ~i ~continuation =
- let give_name seed = function
- | C.Name _ as name -> name
- | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
- in
- let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
- let injection_tac status =
- let (proof, goal) = status in
- (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
- * differiscono (o potrebbero differire?) nell'i-esimo parametro
- * del costruttore *)
- let _,metasenv,_subst,_,_, _ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let term = relocate_term map term in
- let termty,_ =
- CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
- in
- debug_print (lazy ("\ninjection su : " ^ pp context termty));
- match termty with (* an equality *)
- | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
- when LibraryObjects.is_eq_URI equri ->
- let turi,typeno,ens,params =
- match tty with (* some inductive type *)
- | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
- | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
- | _ -> raise exn_noneqind
- in
- let t1',t2',consno = (* sono i due sottotermini che differiscono *)
- match t1,t2 with
- | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
- C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
- when (uri1 = uri2) && (typeno1 = typeno2) &&
- (consno1 = consno2) && (ens1 = ens2) ->
- (* controllo ridondante *)
- List.nth applist1 (pred i),List.nth applist2 (pred i),consno2
- | _ -> assert false
- in
- let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
- let patterns,outtype =
- match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
- | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
- let left_params, right_params = HExtlib.split_nth paramsno params in
- let _,_,_,constructor_list = List.nth ind_type_list typeno in
- let i_constr_id,_ = List.nth constructor_list (consno - 1) in
- let patterns =
- let seed = ref 0 in
- List.map
- (function (id,cty) ->
- let reduced_cty = CR.whd context cty in
- let rec aux k = function
- | C.Prod (_,_,tgt) when k <= paramsno ->
- let left = List.nth left_params (k-1) in
- aux (k+1) (S.subst left tgt)
- | C.Prod (binder,source,target) when k > paramsno ->
- let binder' = give_name seed binder in
- C.Lambda (binder',source,(aux (k+1) target))
- | _ ->
- let nr_param_constr = k - paramsno - 1 in
- if id = i_constr_id then C.Rel (k - i)
- else S.lift nr_param_constr t1'
- (* + 1 per liftare anche il lambda aggiunto
- * esternamente al case *)
- in S.lift 1 (aux 1 reduced_cty))
- constructor_list
- in
- (* this code should be taken from cases_tac *)
- let outtype =
- let seed = ref 0 in
- let rec to_lambdas te head =
- match CR.whd context te with
- | C.Prod (binder,so,ta) ->
- let binder' = give_name seed binder in
- C.Lambda (binder',so,to_lambdas ta head)
- | _ -> head
- in
- let rec skip_prods params te =
- match params, CR.whd context te with
- | [], _ -> te
- | left::tl, C.Prod (_,_,ta) ->
- skip_prods tl (S.subst left ta)
- | _, _ -> assert false
- in
- let abstracted_tty =
- let tty =
- List.fold_left (fun x y -> S.subst y x) tty left_params
- in
- (* non lift, ma subst coi left! *)
- match S.lift 1 tty with
- | C.MutInd _ as tty' -> tty'
- | C.Appl l ->
- let keep,abstract = HExtlib.split_nth (paramsno +1) l in
- let keep = List.map (S.lift paramsno) keep in
- C.Appl (keep@mk_rels (List.length abstract))
- | _ -> assert false
- in
- match ind_type_list with
- | [] -> assert false
- | (_,_,ty,_)::_ ->
- (* this is in general wrong, do as in cases_tac *)
- to_lambdas (skip_prods left_params ty)
- (C.Lambda
- (C.Name "cased", abstracted_tty,
- (* here we should capture right parameters *)
- (* 1 for his Lambda, one for the Lambda outside the match
- * and then one for each to_lambda *)
- S.lift (2+List.length right_params) tty'))
- in
- patterns,outtype
- | _ -> raise exn_discrnonind
- in
- let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
- let changed =
- C.Appl [ C.Lambda (C.Name "x", tty,
- C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
- in
- (* check if cutted and changed are well typed and if t1' ~ changed *)
- let go_on =
- try
- let _,g = CTC.type_of_aux' metasenv context cutted
- CicUniv.empty_ugraph
- in
- let _,g = CTC.type_of_aux' metasenv context changed g in
- fst (CR.are_convertible ~metasenv context t1' changed g)
- with
- | CTC.TypeCheckerFailure _ -> false
- in
- if not go_on then
- PET.apply_tactic (continuation ~map) status
- else
- let tac term =
- let tac status =
- debug_print (lazy "riempio il cut");
- let (proof, goal) = status in
- let _,metasenv,_subst,_,_, _ = proof in
- let _,context,gty = CicUtil.lookup_meta goal metasenv in
- let gty = Unshare.unshare gty in
- let new_t1' = match gty with
- | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
- | _ -> raise exn_injwronggoal
- in
- debug_print (lazy ("metto: " ^ pp context changed));
- debug_print (lazy ("al posto di: " ^ pp context new_t1'));
- debug_print (lazy ("nel goal: " ^ pp context gty));
- debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
- debug_print (lazy ("e poi rewrite con: "^pp context term));
- let tac = T.seq ~tactics:[
- RT.change_tac
- ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
- (fun _ m u -> changed,m,u);
- ET.rewrite_simpl_tac
- ~direction:`LeftToRight
- ~pattern:(PET.conclusion_pattern None)
- term [];
- ET.reflexivity_tac
- ] in
- PET.apply_tactic tac status
- in
- PET.mk_tactic tac
- in
- debug_print (lazy ("CUT: " ^ pp context cutted));
- PET.apply_tactic
- (T.thens ~start: (P.cut_tac cutted)
- ~continuations:[
- (destruct ~first_time:false ~term:(C.Rel 1) ~map:id
- ~continuation:(after2 continuation succ map)
- );
- tac term]
- ) status
- | _ -> raise exn_noneq
- in
- PET.mk_tactic injection_tac
-
-(* ~term vive nel contesto della tattica una volta ~mappato
- * ~continuation riceve la mappa assoluta
- *)
-and subst_tac ~map ~term ~direction ~where ~continuation =
- let fail_tactic = continuation ~map in
- let subst_tac status =
- let term = relocate_term map term in
- let tactic = match where with
- | None ->
- let pattern = PET.conclusion_pattern None in
- let tactic = ET.rewrite_tac ~direction ~pattern term [] in
- T.then_ ~start:(T.try_tactic ~tactic)
- ~continuation:fail_tactic
- | Some name ->
- let pattern = None, [name, PET.hole], None in
- let start = ET.rewrite_tac ~direction ~pattern term [] in
- let continuation =
- destruct ~first_time:false ~term:(C.Rel 1) ~map:id
- ~continuation:(after2 continuation succ map)
- in
- T.if_ ~start ~continuation ~fail:fail_tactic
- in
- PET.apply_tactic tactic status
- in
- PET.mk_tactic subst_tac
-
-(* ~term vive nel contesto della tattica una volta ~mappato
- * ~continuation riceve la mappa assoluta
- *)
-and destruct ~first_time ~map ~term ~continuation =
- let are_convertible hd1 hd2 metasenv context =
- fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph)
- in
- let destruct status =
- let (proof, goal) = status in
- let _,metasenv,_subst, _,_, _ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let term = relocate_term map term in
- debug_print (lazy ("\nqnify di: " ^ pp context term));
- debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
- let termty,_ =
- CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
- in
- debug_print (lazy ("\nqnify su: " ^ pp context termty));
- let tac = match termty with
- | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
- when LibraryObjects.is_eq_URI equri -> begin
- match (CR.whd ~delta:true context tty) with
- | C.MutInd _
- | C.Appl (C.MutInd _ :: _) ->
- begin match t1,t2 with
- | C.MutConstruct _,
- C.MutConstruct _
- when t1 = t2 ->
- T.then_ ~start:(clear_term first_time context term)
- ~continuation:(continuation ~map)
- | C.Appl (C.MutConstruct _ as mc1 :: applist1),
- C.Appl (C.MutConstruct _ as mc2 :: applist2)
- when mc1 = mc2 ->
- let rec traverse_list first_time i l1 l2 =
- match l1, l2 with
- | [], [] ->
- fun ~map:aftermap ->
- T.then_ ~start:(clear_term first_time context term)
- ~continuation:(after continuation aftermap map)
- | hd1 :: tl1, hd2 :: tl2 ->
- if are_convertible hd1 hd2 metasenv context then
- traverse_list first_time (succ i) tl1 tl2
- else
- injection_tac ~i ~term ~continuation:
- (traverse_list false (succ i) tl1 tl2)
- | _ -> assert false
- (* i 2 termini hanno in testa lo stesso costruttore,
- * ma applicato a un numero diverso di termini *)
- in
- traverse_list first_time 1 applist1 applist2 ~map:id
- | C.MutConstruct (_,_,consno1,ens1),
- C.MutConstruct (_,_,consno2,ens2)
- | C.MutConstruct (_,_,consno1,ens1),
- C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
- | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
- C.MutConstruct (_,_,consno2,ens2)
- | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
- C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
- when (consno1 <> consno2) || (ens1 <> ens2) ->
- discriminate_tac ~term
- | _ when not first_time -> continuation ~map
- | _ (* when first_time *) ->
- T.then_ ~start:(simpl_in_term context term)
- ~continuation:(destruct ~first_time:false ~term ~map ~continuation)
- end
- | _ when not first_time -> continuation ~map
- | _ (* when first_time *) -> raise exn_nonproj
- end
- | _ -> raise exn_nonproj
- in
- PET.apply_tactic tac status
- in
- PET.mk_tactic destruct
-
-(* destruct performs either injection or discriminate *)
-(* equivalent to Coq's "analyze equality" *)
-let destruct_tac =
- destruct
- ~first_time:true ~map:id ~continuation:(fun ~map -> T.id_tac)
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