- | C.Anonimous -> C.Name "fresh_name"
- in
- ((Declaration,n',s)::ctx,ty,C.Lambda(n',s,bo))
- | C.LetIn (n,s,t) ->
- let (ctx,ty,bo) = collect_context t in
- ((Definition,n,s)::ctx,ty,C.LetIn(n,s,bo))
- | _ as t -> [], t, (C.Meta newmeta)
- in
- let revcontext',ty',bo' = collect_context ty in
- let context'' = (List.rev revcontext') @ context in
- refine_meta metano bo' [newmeta,ty'] ;
- goal := Some (newmeta,(context'',ty'))
-;;
-
-(* The term bo must be closed in the current context *)
-let exact bo =
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let metasenv =
- match !proof with
- None -> assert false
- | Some (_,metasenv,_,_) -> metasenv
- in
- let (metano,context,ty) =
- match !goal with
- None -> assert false
- | Some (metano,(context,ty)) ->
- assert (ty = List.assoc metano metasenv) ;
- (* Invariant: context is the actual context of the meta in the proof *)
- metano,context,ty
- in
- (*CSC: deve sparire! *)
- let context = cic_context_of_context context in
- if R.are_convertible (T.type_of_aux' metasenv context bo) ty then
- begin
- refine_meta metano bo [] ;
- goal := None
- end
- else
- raise (Fail "The type of the provided term is not the one expected.")
-;;
-
-let fix_andreas_meta mgu mgut =
- let mgul = Array.to_list mgu in
- let mgutl = Array.to_list mgut in
- let applymetas_to_metas =
- let newmeta = new_meta () in
- (* WARNING: here we are using the invariant that above the most *)
- (* recente new_meta() there are no used metas. *)
- Array.init (List.length mgul) (function i -> newmeta + i) in
- (* WARNING!!!!!!!!!!!!!!!!!!!!!!!!!!!!! *)
- (* Here we assume that either a META has been instantiated with *)
- (* a close term or with itself. *)
- let uninstantiatedmetas =
- List.fold_right2
- (fun bo ty newmetas ->
- let module C = Cic in
- match bo with
- Cic.Meta i ->
- let newmeta = applymetas_to_metas.(i) in
- (*CSC: se ty contiene metas, queste hanno il numero errato!!! *)
- let ty_with_newmetas =
- (* Substitues (META n) with (META (applymetas_to_metas.(n))) *)
- let rec aux =
- function
- C.Rel _
- | C.Var _ as t -> t
- | C.Meta n -> C.Meta (applymetas_to_metas.(n))
- | C.Sort _
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, aux s, aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, aux s, aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, aux s, aux t)
- | C.Appl l -> C.Appl (List.map aux l)
- | C.Const _ as t -> t
- | C.Abst _ -> assert false
- | C.MutInd _
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux outt, aux t,
- List.map aux pl)
- | C.Fix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux ty, aux bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux ty, aux bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- in
- aux ty
- in
- (newmeta,ty_with_newmetas)::newmetas
- | _ -> newmetas
- ) mgul mgutl []
- in
- let mgul' =
- List.map
- (function
- Cic.Meta i -> Cic.Meta (applymetas_to_metas.(i))
- | _ as t -> t
- ) mgul
- in
- mgul',uninstantiatedmetas
-;;
-
-(* The term bo must be closed in the current context *)
-let apply term =
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let module C = Cic in
- let metasenv =
- match !proof with
- None -> assert false
- | Some (_,metasenv,_,_) -> metasenv
- in
- let (metano,context,ty) =
- match !goal with
- None -> assert false
- | Some (metano,(context,ty)) ->
- assert (ty = List.assoc metano metasenv) ;
- (* Invariant: context is the actual context of the meta in the proof *)
- metano,context,ty
- in
- (*CSC: deve sparire! *)
- let ciccontext = cic_context_of_context context in
- let mgu,mgut = CicUnification.apply metasenv ciccontext term ty in
- let mgul',uninstantiatedmetas = fix_andreas_meta mgu mgut in
- let bo' =
- if List.length mgul' = 0 then
- term
- else
- Cic.Appl (term::mgul')
- in
- refine_meta metano bo' uninstantiatedmetas ;
- match uninstantiatedmetas with
- (n,ty)::tl -> goal := Some (n,(context,ty))
- | [] -> goal := None
-;;
-
-
-let eta_expand metasenv ciccontext t arg =
- let module T = CicTypeChecker in
- let module S = CicSubstitution in
- let module C = Cic in
- let rec aux n =
- function
- t' when t' = S.lift n arg -> C.Rel (1 + n)
- | C.Rel m -> if m <= n then C.Rel m else C.Rel (m+1)
- | C.Var _
- | C.Meta _
- | C.Sort _
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
- | C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
- | C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
- | C.LetIn (nn,s,t) -> C.LetIn (nn, aux n s, aux (n+1) t)
- | C.Appl l -> C.Appl (List.map (aux n) l)
- | C.Const _ as t -> t
- | C.Abst _ -> assert false
- | C.MutInd _
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux n outt, aux n t,
- List.map (aux n) pl)
- | C.Fix (i,fl) ->
- let tylen = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let tylen = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- in
- let argty =
- T.type_of_aux' metasenv ciccontext arg
- in
- (C.Appl [C.Lambda ((C.Name "dummy"),argty,aux 0 t) ; arg])
-;;
-
-exception NotAnInductiveTypeToEliminate;;
-exception NotTheRightEliminatorShape;;
-exception NoHypothesesFound;;
-
-let elim term =
- let module T = CicTypeChecker in
- let module U = UriManager in
- let module R = CicReduction in
- let module C = Cic in
- let curi,metasenv =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,_,_) -> curi,metasenv
- in
- let (metano,context,ty) =
- match !goal with
- None -> assert false
- | Some (metano,(context,ty)) ->
- assert (ty = List.assoc metano metasenv) ;
- (* Invariant: context is the actual context of the meta in the proof *)
- metano,context,ty
- in
- (*CSC: deve sparire! *)
- let ciccontext = cic_context_of_context context in
- let termty = T.type_of_aux' metasenv ciccontext term in
- let uri,cookingno,typeno,args =
- match termty with
- C.MutInd (uri,cookingno,typeno) -> (uri,cookingno,typeno,[])
- | C.Appl ((C.MutInd (uri,cookingno,typeno))::args) ->
- (uri,cookingno,typeno,args)
- | _ -> raise NotAnInductiveTypeToEliminate
- in
- let eliminator_uri =
- let buri = U.buri_of_uri uri in
- let name =
- match CicEnvironment.get_cooked_obj uri cookingno with
- C.InductiveDefinition (tys,_,_) ->
- let (name,_,_,_) = List.nth tys typeno in
- name
- | _ -> assert false
- in
- let ext =
- match T.type_of_aux' metasenv ciccontext ty with
- C.Sort C.Prop -> "_ind"
- | C.Sort C.Set -> "_rec"
- | C.Sort C.Type -> "_rect"
- | _ -> assert false
- in
- U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
- in
- let eliminator_cookingno =
- UriManager.relative_depth curi eliminator_uri 0
- in
- let eliminator_ref = C.Const (eliminator_uri,eliminator_cookingno) in
- let ety =
- T.type_of_aux' [] [] eliminator_ref
- in
-
- let earity = CicUnification.get_arity ety in
- let mgu = Array.init earity (fun i -> (C.Meta i)) in
- let mgut = Array.make earity C.Implicit in
- (* Here we assume that we have only one inductive hypothesis to *)
- (* eliminate and that it is the last hypothesis of the theorem. *)
- (* A better approach would be fingering the hypotheses in some *)
- (* way. *)
- let hypothesis_to_eliminate,econclusion =
- (* aux n h t *)
- (* traverses the backbone [t] looking for the last hypothesis *)
- (* and substituting Pi-abstractions with META declarations. *)
- (* [h] is the last hypothesis met up to now. [n] is the next *)
- (* unused META. *)
- let rec aux n h =
- function
- C.Prod (_,s,t) ->
- mgut.(n) <- s ;
- aux (n+1) (Some s) (CicSubstitution.subst (C.Meta n) t)
- | C.Cast (te,_) -> aux n h te
- | t -> match h with
- None -> raise NoHypothesesFound
- | Some h' -> h',t
- in
- aux 0 None ety
- in
-prerr_endline ("HTOELIM: " ^ CicPp.ppterm hypothesis_to_eliminate) ;
-prerr_endline ("ECONCLUSION: " ^ CicPp.ppterm econclusion) ;
-flush stderr ;
- ignore (CicUnification.fo_unif_mgu 0 hypothesis_to_eliminate termty mgu) ;
- ignore (CicUnification.fo_unif_mgu 0 term (C.Meta (earity - 1)) mgu) ;
- let mgu = CicUnification.unwind mgu in
-prerr_endline "Dopo l'unwind dell'mgu"; flush stderr ;
- let mark = Array.make earity 1 in
- let ueconclusion =
- CicUnification.unwind_meta mgu mark econclusion
- in
-prerr_endline ("ECONCLUSION DOPO UNWIND: " ^ CicPp.ppterm ueconclusion) ;
-flush stderr ;
- (* The conclusion of our elimination principle is *)
- (* (?i farg1 ... fargn) *)
- (* The conclusion of our goal is ty. So, we can *)
- (* eta-expand ty w.r.t. farg1 .... fargn to get *)
- (* a new ty equal to (P farg1 ... fargn). Now *)
- (* ?i can be instantiated with P and we are ready *)
- (* to refine the term. *)
- let emeta, fargs =
- match ueconclusion with
- C.Appl ((C.Meta emeta)::fargs) -> emeta,fargs
- | _ -> raise NotTheRightEliminatorShape
- in
- let eta_expanded_ty =
-(*CSC: metasenv e ?????????????*)
- List.fold_left (eta_expand metasenv ciccontext) ty fargs
- in
-(*CSC: 0????????*)
-prerr_endline ("ETAEXPANDEDTY:" ^ CicPp.ppterm eta_expanded_ty) ; flush stdout ;
- ignore (CicUnification.fo_unif_mgu 0 ueconclusion eta_expanded_ty mgu) ;
-prerr_endline "Dopo la seconda unificazione" ; flush stdout ;
- let mgu = CicUnification.unwind mgu in
- print_endline "unwind"; flush stdout;
- (* When unwinding the META that corresponds to the elimination *)
- (* predicate (which is emeta), we must also perform one-step *)
- (* beta-reduction. *)
- let mgut =
- let mark = Array.make (Array.length mgu) 1 in
- Array.map
- (CicUnification.unwind_meta_reducing mgu mark (Some emeta))
- mgut ;
- in
- print_endline "unwind_array"; flush stdout;
- let mgu' = Array.copy mgu in
- let mgut' = CicUnification.list_of_array mgut in
- print_endline "list"; flush stdout;
- Array.iteri
- (fun i ty ->
-prerr_endline ("META " ^ string_of_int i ^ ": " ^ CicPp.ppterm mgu'.(i) ^
- " == " ^ CicPp.ppterm ty) ; flush stderr ;
- let ty' =
- CicTypeChecker.type_of_aux' mgut' ciccontext mgu'.(i)
- in
- ignore (CicUnification.fo_unif_mgu 0 ty ty' mgu)
- ) mgut ;
- let mgu = CicUnification.unwind mgu in
- let mgut = CicUnification.unwind_array mgu mgut in
-prerr_endline "Dopo le unwind dell'mgut" ; flush stdout ;
- let mgul',uninstantiatedmetas = fix_andreas_meta mgu mgut in
-prerr_endline "Dopo il fissaggio" ; flush stdout ;
- let bo' = Cic.Appl (eliminator_ref::mgul') in
-prerr_endline ("BODY': " ^ CicPp.ppterm bo') ; flush stdout ;
- refine_meta metano bo' uninstantiatedmetas ;
-prerr_endline "dopo refine meta" ; flush stdout ;
- match uninstantiatedmetas with
- (n,ty)::tl -> goal := Some (n,(context,ty))
- | [] -> goal := None
-;;
-
-let elim_intros term =
- elim term ;
- intros ()
-;;