--- /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/.
+ *)
+
+(* $Id$ *)
+
+exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
+exception NotAnInductiveTypeToEliminate
+
+let debug = false;;
+let debug_print =
+ fun msg -> if debug then prerr_endline (Lazy.force msg) else ()
+
+
+let inside_obj = function
+ | Cic.InductiveDefinition (type_list,params, nleft, _) ->
+ (type_list,params,nleft)
+ | _ -> raise (Invalid_argument "Errore in inside_obj")
+
+let term_to_list = function
+ | Cic.Appl l -> l
+ | _ -> raise (Invalid_argument "Errore in term_to_list")
+
+
+let rec baseuri_of_term = function
+ | Cic.Appl l -> baseuri_of_term (List.hd l)
+ | Cic.MutInd (baseuri, tyno, []) -> baseuri
+ | _ -> raise (Invalid_argument "baseuri_of_term")
+
+(* returns DX1 = DX1 -> ... DXn=DXn -> GOALTY *)
+let rec foo_cut nleft parameters parameters_ty body uri_of_eq =
+ if nleft > 0
+ then
+ foo_cut (nleft-1) (List.tl parameters) (List.tl parameters_ty) body
+ uri_of_eq
+ else
+ match parameters with
+ | hd::tl ->
+ Cic.Prod (
+ Cic.Anonymous,
+ Cic.Appl[Cic.MutInd (uri_of_eq ,0,[]);
+ (List.hd parameters_ty) ; hd; hd],
+ foo_cut nleft (List.map (CicSubstitution.lift 1) tl)
+ (List.map (CicSubstitution.lift 1) (List.tl parameters_ty))
+ (CicSubstitution.lift 1 body) uri_of_eq )
+ | [] -> body
+;;
+
+(* from a complex Cic.Prod term, return the list of its components *)
+let rec get_sort_type term =
+ match term with
+ | Cic.Prod (_,src,tgt) -> (get_sort_type tgt)
+ | _ -> term
+;;
+
+
+let rec cut_first n l =
+ if n>0 then
+ match l with
+ | hd::tl -> cut_first (n-1) tl
+ | [] -> []
+ else l
+;;
+
+
+let rec cut_last l =
+ match l with
+ | hd::tl when tl != [] -> hd:: (cut_last tl)
+ | _ -> []
+;;
+
+(* returns the term to apply*)
+let foo_appl nleft nright_consno term uri =
+ let l = [] in
+ let a = ref l in
+ for n = 1 to nleft do
+ a := !a @ [(Cic.Implicit None)]
+ done;
+ a:= !a @ [term];
+ for n = 1 to nright_consno do
+ a := !a @ [(Cic.Implicit None)]
+ done;
+ (* apply i_ind ? ... ? H *)
+ Cic.Appl ([Cic.Const(uri,[])] @ !a @ [Cic.Rel 1])
+;;
+
+
+let rec foo_prod nright right_param_tys rightparameters l2 base_rel goalty
+ uri_of_eq rightparameters_ termty isSetType term =
+ match right_param_tys with
+ | hd::tl -> Cic.Prod (
+ Cic.Anonymous,
+ Cic.Appl
+ [Cic.MutInd(uri_of_eq,0,[]); hd; (List.hd rightparameters);
+ Cic.Rel base_rel],
+ foo_prod (nright-1)
+ (List.map (CicSubstitution.lift 1) tl)
+ (List.map (CicSubstitution.lift 1) (List.tl rightparameters))
+ (List.map (CicSubstitution.lift 1) l2)
+ base_rel (CicSubstitution.lift 1 goalty) uri_of_eq
+ (List.map (CicSubstitution.lift 1) rightparameters_)
+ (CicSubstitution.lift 1 termty)
+ isSetType (CicSubstitution.lift 1 term))
+ | [] -> ProofEngineReduction.replace_lifting
+ ~equality:(fun _ -> CicUtil.alpha_equivalence)
+ ~context:[]
+ ~what: (if isSetType
+ then (rightparameters_ @ [term] )
+ else (rightparameters_ ) )
+ ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
+ ~where:goalty
+(* the same subterm of goalty could be simultaneously sx and dx!*)
+;;
+
+let rec foo_lambda nright right_param_tys nright_ right_param_tys_
+ rightparameters created_vars base_rel goalty uri_of_eq rightparameters_
+ termty isSetType term =
+ match right_param_tys with
+ | hd::tl -> Cic.Lambda (
+ (Cic.Name ("lambda" ^ (string_of_int nright))),
+ hd, (* type *)
+ foo_lambda (nright-1)
+ (List.map (CicSubstitution.lift 1) tl) nright_
+ (List.map (CicSubstitution.lift 1) right_param_tys_)
+ (List.map (CicSubstitution.lift 1) rightparameters)
+ (List.map (CicSubstitution.lift 1) (created_vars @ [Cic.Rel 1]))
+ base_rel (CicSubstitution.lift 1 goalty) uri_of_eq
+ (List.map (CicSubstitution.lift 1) rightparameters_)
+ (CicSubstitution.lift 1 termty) isSetType
+ (CicSubstitution.lift 1 term))
+ | [] when isSetType -> Cic.Lambda (
+ (Cic.Name ("lambda" ^ (string_of_int nright))),
+ (ProofEngineReduction.replace_lifting
+ ~equality:(fun _ -> CicUtil.alpha_equivalence)
+ ~context:[]
+ ~what: (rightparameters_ )
+ ~with_what: (List.map (CicSubstitution.lift (-1)) created_vars)
+ ~where:termty), (* type of H with replaced right parameters *)
+ foo_prod nright_ (List.map (CicSubstitution.lift 1) right_param_tys_)
+ (List.map (CicSubstitution.lift 1) rightparameters)
+ (List.map (CicSubstitution.lift 1) (created_vars @ [Cic.Rel 1]))
+ (base_rel+1) (CicSubstitution.lift 1 goalty) uri_of_eq
+ (List.map (CicSubstitution.lift 1) rightparameters_)
+ (CicSubstitution.lift 1 termty) isSetType
+ (CicSubstitution.lift 1 term))
+ | [] -> foo_prod nright_ right_param_tys_ rightparameters created_vars
+ base_rel goalty uri_of_eq rightparameters_
+ termty isSetType term
+;;
+
+let isSetType paramty = ((Pervasives.compare
+ (get_sort_type paramty)
+ (Cic.Sort Cic.Prop)) != 0)
+
+exception EqualityNotDefinedYet
+let private_inversion_tac ~term =
+ let module T = CicTypeChecker in
+ let module R = CicReduction in
+ let module C = Cic in
+ let module P = PrimitiveTactics in
+ let module PET = ProofEngineTypes in
+ let private_inversion_tac ~term (proof, goal) =
+
+ (*DEBUG*) debug_print (lazy ("private inversion begins"));
+ let _,metasenv,_subst,_,_, _ = proof in
+ let uri_of_eq =
+ match LibraryObjects.eq_URI () with
+ None -> raise EqualityNotDefinedYet
+ | Some uri -> uri
+ in
+ let (_,context,goalty) = CicUtil.lookup_meta goal metasenv in
+ let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let uri = baseuri_of_term termty in
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ let (_,_,typeno,_) =
+ match termty with
+ C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
+ | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
+ (uri,exp_named_subst,typeno,args)
+ | _ -> raise NotAnInductiveTypeToEliminate
+ in
+ let buri = UriManager.buri_of_uri uri in
+ let name,nleft,paramty,cons_list =
+ match o with
+ C.InductiveDefinition (tys,_,nleft,_) ->
+ let (name,_,paramty,cons_list) = List.nth tys typeno in
+ (name,nleft,paramty,cons_list)
+ |_ -> assert false
+ in
+ let eliminator_uri =
+ UriManager.uri_of_string (buri ^ "/" ^ name ^ "_ind" ^ ".con")
+ in
+ let parameters = (List.tl (term_to_list termty)) in
+ let parameters_tys =
+ (List.map
+ (fun t -> (
+ match (T.type_of_aux' metasenv context t CicUniv.empty_ugraph) with
+ (term,graph) -> term))
+ parameters)
+ in
+ let consno = List.length cons_list in
+ let nright= ((List.length parameters)- nleft) in
+ let isSetType = isSetType paramty in
+ let cut_term = foo_cut nleft parameters
+ parameters_tys goalty uri_of_eq in
+ (*DEBUG*) debug_print (lazy ("cut term " ^ CicPp.ppterm cut_term));
+ debug_print (lazy ("CONTEXT before apply HCUT: " ^
+ (CicMetaSubst.ppcontext ~metasenv [] context )));
+ debug_print (lazy ("termty " ^ CicPp.ppterm termty));
+ (* cut DXn=DXn \to GOAL *)
+ let proof1,gl1 = PET.apply_tactic (P.cut_tac cut_term) (proof,goal) in
+ (* apply Hcut ; reflexivity *)
+ let proof2, gl2 = PET.apply_tactic
+ (Tacticals.then_
+ ~start: (P.apply_tac (C.Rel 1)) (* apply Hcut *)
+ ~continuation: (EqualityTactics.reflexivity_tac)
+ ) (proof1, (List.hd gl1))
+ in
+ (*DEBUG*) debug_print (lazy ("after apply HCUT;reflexivity
+ in private inversion"));
+ (* apply (ledx_ind( lambda x. lambda y, ...)) *)
+ let t1,metasenv,_subst,t3,t4, attrs = proof2 in
+ let goal2 = List.hd (List.tl gl1) in
+ let (_,context,_) = CicUtil.lookup_meta goal2 metasenv in
+ (* rightparameters type list *)
+ let rightparam_ty_l = (cut_first nleft parameters_tys) in
+ (* rightparameters list *)
+ let rightparameters= cut_first nleft parameters in
+ let lambda_t = foo_lambda nright rightparam_ty_l nright rightparam_ty_l
+ rightparameters [] nright goalty uri_of_eq rightparameters termty isSetType
+ term in
+ let t = foo_appl nleft (nright+consno) lambda_t eliminator_uri in
+ debug_print (lazy ("Lambda_t: " ^ (CicPp.ppterm t)));
+ debug_print (lazy ("Term: " ^ (CicPp.ppterm termty)));
+ debug_print (lazy ("Body: " ^ (CicPp.ppterm goalty)));
+ debug_print
+ (lazy ("Right param: " ^ (CicPp.ppterm (Cic.Appl rightparameters))));
+ debug_print (lazy ("CONTEXT before refinement: " ^
+ (CicMetaSubst.ppcontext ~metasenv [] context )));
+ (*DEBUG*) debug_print (lazy ("private inversion: term before refinement: " ^
+ CicPp.ppterm t));
+ let (ref_t,_,metasenv'',_) = CicRefine.type_of_aux' metasenv context t
+ CicUniv.empty_ugraph
+ in
+ (*DEBUG*) debug_print (lazy ("private inversion: termine after refinement: "
+ ^ CicPp.ppterm ref_t));
+ let proof2 = (t1,metasenv'',_subst,t3,t4, attrs) in
+ let my_apply_tac =
+ let my_apply_tac status =
+ let proof,goals =
+ ProofEngineTypes.apply_tactic (P.apply_tac ref_t) status in
+ let patched_new_goals =
+ let (_,metasenv''',_subst,_,_, _) = proof in
+ let new_goals = ProofEngineHelpers.compare_metasenvs
+ ~oldmetasenv:metasenv ~newmetasenv:metasenv''
+ in
+ List.filter (function i -> List.exists (function (j,_,_) -> j=i)
+ metasenv''') new_goals @ goals
+ in
+ proof,patched_new_goals
+ in
+ ProofEngineTypes.mk_tactic my_apply_tac
+ in
+ let proof3,gl3 =
+ PET.apply_tactic
+ (Tacticals.then_
+ ~start:my_apply_tac
+ ~continuation:
+ (ReductionTactics.simpl_tac (ProofEngineTypes.conclusion_pattern(None))))
+ (proof2,goal2)
+ in
+
+ (proof3, gl3)
+in
+ProofEngineTypes.mk_tactic (private_inversion_tac ~term)
+;;
+
+
+let inversion_tac ~term =
+ let module T = CicTypeChecker in
+ let module R = CicReduction in
+ let module C = Cic in
+ let module P = PrimitiveTactics in
+ let module PET = ProofEngineTypes in
+ let inversion_tac ~term (proof, goal) =
+ (*DEBUG*) debug_print (lazy ("inversion begins"));
+ let _,metasenv,_subst,_,_, _ = proof in
+ let (_,context,goalty) = CicUtil.lookup_meta goal metasenv in
+ let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let uri, typeno =
+ match termty with
+ | Cic.MutInd (uri,typeno,_)
+ | Cic.Appl(Cic.MutInd (uri,typeno,_)::_) -> uri,typeno
+ | _ -> assert false
+ in
+ (* let uri = baseuri_of_term termty in *)
+ let obj,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ let name,nleft,arity,cons_list =
+ match obj with
+ Cic.InductiveDefinition (tys,_,nleft,_) ->
+ let (name,_,arity,cons_list) = List.nth tys typeno in
+ (name,nleft,arity,cons_list)
+ |_ -> assert false
+ in
+ let buri = UriManager.buri_of_uri uri in
+ let inversor_uri =
+ UriManager.uri_of_string (buri ^ "/" ^ name ^ "_inv" ^ ".con") in
+ (* arity length = number of parameters plus 1 *)
+ let arity_length = (List.length (term_to_list termty)) in
+ (* Check the existence of any right parameter. *)
+ assert (arity_length > (nleft + 1));
+ let appl_term arity_consno uri =
+ let l = [] in
+ let a = ref l in
+ for n = 1 to arity_consno do
+ a := (Cic.Implicit None)::(!a)
+ done;
+ (* apply i_inv ? ...? H). *)
+ Cic.Appl ([Cic.Const(uri,[])] @ !a @ [term])
+ in
+ let t = appl_term (arity_length + (List.length cons_list)) inversor_uri in
+ let (t1,metasenv,_subst,t3,t4, attrs) = proof in
+ let (ref_t,_,metasenv'',_) = CicRefine.type_of_aux' metasenv context t
+ CicUniv.empty_ugraph
+ in
+ let proof = (t1,metasenv'',_subst,t3,t4, attrs) in
+ let proof3,gl3 =
+ ProofEngineTypes.apply_tactic (P.apply_tac ref_t) (proof,goal) in
+ let patched_new_goals =
+ let (_,metasenv''',_subst,_,_, _) = proof3 in
+ let new_goals = ProofEngineHelpers.compare_metasenvs
+ ~oldmetasenv:metasenv ~newmetasenv:metasenv''
+ in
+ List.filter (function i -> List.exists (function (j,_,_) -> j=i)
+ metasenv''') new_goals @ gl3
+ in
+ (proof3, patched_new_goals)
+ in
+ProofEngineTypes.mk_tactic (inversion_tac ~term)
+;;
projects / helm.git / blobdiff