exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
exception NotAnInductiveTypeToEliminate
-let debug = false;;
+let debug = false;;
let debug_print =
fun msg -> if debug then prerr_endline (Lazy.force msg) else ()
+
let inside_obj = function
| Cic.InductiveDefinition (l,params, nleft, _) ->
(l,params,nleft)
| _ -> raise (Invalid_argument "baseuri_of_term")
-(*prende il numero dei parametri sinistri, la lista dei parametri, la lista dei tipi dei parametri,
-il tipo del GOAL e costruisce il termine per la cut ossia DX1 = DX1 -> ... DXn=DXn -> GOALTY *)
-let rec foo_cut nleft l param_ty_l body uri_of_eq =
+(* prende il numero dei parametri sinistri, la lista dei parametri, la lista
+dei tipi dei parametri, il tipo del GOAL e costruisce il termine per la cut
+ossia DX1 = DX1 -> ... DXn=DXn -> GOALTY *)
- if nleft >0 then foo_cut (nleft-1) (List.tl l) (List.tl param_ty_l) body uri_of_eq
- else match l with
- | hd::tl -> Cic.Prod (Cic.Anonymous,
- Cic.Appl[Cic.MutInd (uri_of_eq ,0,[]);
- (List.hd param_ty_l) ;
- hd;
- hd],
- foo_cut nleft (List.map (CicSubstitution.lift 1) tl) (List.tl param_ty_l) (CicSubstitution.lift 1 body) uri_of_eq
- )
- | [] -> body
+let rec foo_cut nleft l param_ty_l body uri_of_eq =
+ if nleft > 0 then foo_cut (nleft-1) (List.tl l) (List.tl param_ty_l) body
+ uri_of_eq
+ else match l with
+ | hd::tl -> Cic.Prod (Cic.Anonymous, Cic.Appl[Cic.MutInd (uri_of_eq ,0,[]);
+ (List.hd param_ty_l) ; hd; hd], foo_cut nleft
+ (List.map (CicSubstitution.lift 1) tl) (List.tl param_ty_l)
+ (CicSubstitution.lift 1 body) uri_of_eq )
+ | [] -> body
;;
(* da una catena di prod costruisce una lista dei termini che lo compongono.*)
match term with
| Cic.Prod (Cic.Anonymous,src,tgt) -> [src] @ (list_of_prod tgt)
| _ -> [term]
-
;;
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;
;;
-
-let rec foo_prod nright param_ty_l l l2 base_rel body uri_of_eq nleft termty isSetType term =
- match param_ty_l with
- | hd::tl -> Cic.Prod (Cic.Anonymous,
- Cic.Appl[Cic.MutInd(uri_of_eq,0,[]);
- hd;
- (List.hd l);
- Cic.Rel base_rel
- ],
- foo_prod (nright-1) tl (List.map (CicSubstitution.lift 1) (List.tl l))
- (List.map (CicSubstitution.lift 1) l2)
- base_rel
- (CicSubstitution.lift 1 body)
- uri_of_eq nleft
- (CicSubstitution.lift 1 termty)
- isSetType
- (CicSubstitution.lift 1 term))
-
-
- | [] -> ProofEngineReduction.replace_lifting ~equality:(ProofEngineReduction.alpha_equivalence)
- ~what: (if isSetType then ((cut_first (1+nleft) (term_to_list termty) ) @ [term] )
- else (cut_first (1+nleft) (term_to_list termty) ) )
- ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
- ~where:body
- (*TODO lo stesso sottotermine di body puo' essere sia sx che dx!*)
+let rec foo_prod nright param_ty_l l l2 base_rel body uri_of_eq nleft termty
+ isSetType term =
+ match param_ty_l with
+ | hd::tl -> Cic.Prod (
+ Cic.Anonymous,
+ Cic.Appl[Cic.MutInd(uri_of_eq,0,[]); hd; (List.hd l); Cic.Rel base_rel],
+ foo_prod (nright-1) tl (List.map (CicSubstitution.lift 1) (List.tl l))
+ (List.map (CicSubstitution.lift 1) l2)
+ base_rel (CicSubstitution.lift 1 body)
+ uri_of_eq nleft (CicSubstitution.lift 1 termty)
+ isSetType (CicSubstitution.lift 1 term))
+ | [] -> ProofEngineReduction.replace_lifting
+ ~equality:(ProofEngineReduction.alpha_equivalence)
+ ~what: (if isSetType
+ then ((cut_first (1+nleft) (term_to_list termty) ) @ [term] )
+ else (cut_first (1+nleft) (term_to_list termty) ) )
+ ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
+ ~where:body
+(*TODO lo stesso sottotermine di body puo' essere sia sx che dx!*)
;;
-
-let rec foo_lambda nright param_ty_l nright_ param_ty_l_ l l2 base_rel body uri_of_eq nleft termty isSetType ty_indty term =
+let rec foo_lambda nright param_ty_l nright_ param_ty_l_ l l2 base_rel body
+ uri_of_eq nleft termty isSetType ty_indty term =
(*assert nright >0 *)
match param_ty_l with
- | hd::tl ->Cic.Lambda ((Cic.Name ("lambda" ^ (string_of_int nright))),
- hd, (* typ *)
- foo_lambda (nright-1) tl
- nright_ param_ty_l_
- (List.map (CicSubstitution.lift 1) l)
- (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1]))
- base_rel
- (CicSubstitution.lift 1 body)
- uri_of_eq nleft
- (CicSubstitution.lift 1 termty)
- isSetType ty_indty
- (CicSubstitution.lift 1 term))
- | [] when isSetType -> Cic.Lambda (
- (Cic.Name ("lambda" ^ (string_of_int nright))),
- (ProofEngineReduction.replace_lifting ~equality:(ProofEngineReduction.alpha_equivalence)
- ~what: (cut_first (1+nleft) (term_to_list termty) )
- ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
- ~where:termty), (* tipo di H con i parametri destri sostituiti *)
- foo_prod nright_ param_ty_l_
- (List.map (CicSubstitution.lift 1) l)
- (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1]))
- (base_rel+1) (CicSubstitution.lift 1 body)
- uri_of_eq nleft
- (CicSubstitution.lift 1 termty) isSetType
- (CicSubstitution.lift 1 term))
- | [] -> foo_prod nright_ param_ty_l_ l l2
- base_rel body uri_of_eq
- nleft termty isSetType term
+ | hd::tl ->Cic.Lambda (
+ (Cic.Name ("lambda" ^ (string_of_int nright))),
+ hd, (* typ *)
+ foo_lambda (nright-1) tl nright_ param_ty_l_
+ (List.map (CicSubstitution.lift 1) l)
+ (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1]))
+ base_rel (CicSubstitution.lift 1 body)
+ uri_of_eq nleft
+ (CicSubstitution.lift 1 termty)
+ isSetType ty_indty
+ (CicSubstitution.lift 1 term))
+ | [] when isSetType -> Cic.Lambda (
+ (Cic.Name ("lambda" ^ (string_of_int nright))),
+ (ProofEngineReduction.replace_lifting
+ ~equality:(ProofEngineReduction.alpha_equivalence)
+ ~what: (cut_first (1+nleft) (term_to_list termty) )
+ ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
+ ~where:termty), (* tipo di H con i parametri destri sostituiti *)
+ foo_prod nright_ param_ty_l_ (List.map (CicSubstitution.lift 1) l)
+ (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1]))
+ (base_rel+1) (CicSubstitution.lift 1 body)
+ uri_of_eq nleft
+ (CicSubstitution.lift 1 termty) isSetType
+ (CicSubstitution.lift 1 term))
+ | [] -> foo_prod nright_ param_ty_l_ l l2 base_rel body uri_of_eq nleft
+ termty isSetType 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 module PEH = ProofEngineHelpers in
let inversion_tac ~term (proof, goal) =
let (_,metasenv,_,_) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let (newproof, metasenv') = ProofEngineHelpers.subst_meta_in_proof proof metano term [] in
+ let (newproof, metasenv') = PEH.subst_meta_in_proof proof metano term [] in
let uri_of_eq = HelmLibraryObjects.Logic.eq_URI in
-(* dall'indice che indentifica il goal nel metasenv, ritorna il suo tipo, che e' la terza componente
-della relativa congettura *)
-let (_,_,body) = CicUtil.lookup_meta goal metasenv in
-
-(* estrae il tipo del termine oggetto di inversion, di solito un Cic.Appl list, ma..*)
-
- let termty,_ = CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ (* dall'indice che indentifica il goal nel metasenv, ritorna il suo tipo, che
+ e' la terza componente della relativa congettura *)
+ let (_,_,body) = CicUtil.lookup_meta goal metasenv in
+ (* estrae il tipo del termine(ipotesi) oggetto di inversion,
+ di solito un Cic.Appl *)
+ 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 l,params,nleft = inside_obj o 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
+ 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 eliminator_uri =
-
- let buri = UriManager.buri_of_uri uri in
- let name =
- match o with
- C.InductiveDefinition (tys,_,_,_) ->
- let (name,_,_,_) = List.nth tys typeno in
- name
- |_ -> assert false
- in
-
-
-(* let ty_ty,_ = T.type_of_aux' metasenv context termty CicUniv.empty_ugraph in
- let ext =
- match ty_ty with
- C.Sort C.Prop -> "_ind"
- | C.Sort C.Set -> "_rec"
- | C.Sort C.CProp -> "_rec"
- | C.Sort (C.Type _)-> "_rect"
- | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
- | _ -> assert false
- in
-*)
-
- let ext = "_ind" in
- UriManager.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
-in
-
- (* il tipo del tipo induttivo oggetto di inversione *)
-
+ let buri = UriManager.buri_of_uri uri in
+ let name =
+ match o with
+ C.InductiveDefinition (tys,_,_,_) ->
+ let (name,_,_,_) = List.nth tys typeno in
+ name
+ |_ -> assert false
+ in
+ let ext = "_ind" in
+ UriManager.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
+ in
+ (* il tipo del tipo induttivo da cui viene l'ipotesi oggetto di inversione *)
let (_,_,ty_indty,cons_list) = (List.hd l) in
- (*la lista ricavata dal tipo del tipo induttivo. *)
+ (*la lista di Cic.term ricavata dal tipo del tipo induttivo. *)
let param_ty_l = list_of_prod ty_indty in
let consno = List.length cons_list in
let nright= (List.length param_ty_l)- (nleft+1) in
-
let isSetType = ((Pervasives.compare
- (List.nth param_ty_l ((List.length param_ty_l)-1))
- (Cic.Sort Cic.Prop)
- ) != 0) in
-
-
-
-
-(* eliminiamo la testa di termty, in quanto e' il nome del predicato e non un parametro.*)
-let cut_term = foo_cut nleft (List.tl (term_to_list termty)) (list_of_prod ty_indty) body uri_of_eq in
-
-
-
-(* cut DXn=DXn \to GOAL *)
-let proof1,gl1 = PET.apply_tactic (P.cut_tac cut_term) (proof,goal) in
-
-(* apply Hcut ; reflexivity (su tutti i goals aperti da apply_tac) *)
-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))
-
+ (List.nth param_ty_l ((List.length param_ty_l)-1))
+ (Cic.Sort Cic.Prop)) != 0)
+ in
+ (* eliminiamo la testa di termty, in quanto e' il nome del predicato e non un parametro.*)
+ let cut_term = foo_cut nleft (List.tl (term_to_list termty))
+ (list_of_prod ty_indty) body uri_of_eq in
+ (* cut DXn=DXn \to GOAL *)
+ let proof1,gl1 = PET.apply_tactic (P.cut_tac cut_term) (proof,goal) in
+ (* apply Hcut ; reflexivity (su tutti i goals aperti da apply_tac) *)
+ 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
-
-
-
-(* apply (ledx_ind( lambda x. lambda y, ...)) *)
-
-let (t1,metasenv,t3,t4) = proof2 in
-let goal2 = List.hd (List.tl gl1) in
-let (metano,context,_) = CicUtil.lookup_meta goal2 metasenv in
-
-let cut_param_ty_l = (cut_first nleft (cut_last param_ty_l)) in
-
-(* la lista dei soli parametri destri *)
-let l= cut_first (1+nleft) (term_to_list termty) in
-
-let lambda_t = foo_lambda nright cut_param_ty_l nright cut_param_ty_l l [] nright body uri_of_eq nleft termty isSetType ty_indty term in
-let t = foo_appl nleft (nright+consno) lambda_t eliminator_uri in
-
-debug_print (lazy ("Lambda_t: " ^ (CicPp.ppterm t)));
-prerr_endline ("Term: " ^ (CicPp.ppterm termty));
-prerr_endline ("Body: " ^ (CicPp.ppterm body));
-prerr_endline ("Right param: " ^ (CicPp.ppterm (Cic.Appl l)));
-
-
-
-
-
-
-let (ref_t,_,metasenv'',_) = CicRefine.type_of_aux' metasenv context t CicUniv.empty_ugraph in
-
-let proof2 = (t1,metasenv'',t3,t4) in
-
-let proof3,gl3 = PET.apply_tactic (P.apply_tac ref_t)
- (proof2, goal2) in
-
-let new_goals =
- ProofEngineHelpers.compare_metasenvs
- ~oldmetasenv:metasenv ~newmetasenv:metasenv''
- in
-
-let patched_new_goals =
- let (_,metasenv''',_,_) = proof3 in
- List.filter
- (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
- ) new_goals @ gl3
- in
-
-
-
-
-(*prerr_endline ("METASENV: " ^ CicMetaSubst.ppmetasenv metasenv []); DEBUG*)
-
-
-(proof3, patched_new_goals)
-
+ (* apply (ledx_ind( lambda x. lambda y, ...)) *)
+ let (t1,metasenv,t3,t4) = proof2 in
+ let goal2 = List.hd (List.tl gl1) in
+ let (metano,context,_) = CicUtil.lookup_meta goal2 metasenv in
+ let cut_param_ty_l = (cut_first nleft (cut_last param_ty_l)) in
+ (* la lista dei soli parametri destri *)
+ let l= cut_first (1+nleft) (term_to_list termty) in
+ let lambda_t = foo_lambda nright cut_param_ty_l nright cut_param_ty_l l []
+ nright body uri_of_eq nleft termty isSetType ty_indty 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 body)));
+ debug_print (lazy ("Right param: " ^ (CicPp.ppterm (Cic.Appl l))));
+
+ let (ref_t,_,metasenv'',_) = CicRefine.type_of_aux' metasenv context t
+ CicUniv.empty_ugraph
+ in
+ let proof2 = (t1,metasenv'',t3,t4) in
+ let proof3,gl3 = PET.apply_tactic (P.apply_tac ref_t) (proof2, goal2) in
+ let new_goals = ProofEngineHelpers.compare_metasenvs
+ ~oldmetasenv:metasenv ~newmetasenv:metasenv''
+ in
+ let patched_new_goals =
+ let (_,metasenv''',_,_) = proof3 in
+ List.filter (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
+ new_goals @ gl3
+ in
+ (*prerr_endline ("METASENV: " ^ CicMetaSubst.ppmetasenv metasenv []); DEBUG*)
+ (proof3, patched_new_goals)
in
-
ProofEngineTypes.mk_tactic (inversion_tac ~term)
;;
projects / helm.git / commitdiff