+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department, University of Bologna, Italy.
+ ||I||
+ ||T|| HELM is free software; you can redistribute it and/or
+ ||A|| modify it under the terms of the GNU General Public License
+ \ / version 2 or (at your option) any later version.
+ \ / This software is distributed as is, NO WARRANTY.
+ V_______________________________________________________________ *)
+
+(* $Id: nCicReduction.ml 8250 2008-03-25 17:56:20Z tassi $ *)
exception TypeCheckerFailure of string Lazy.t
exception AssertFailure of string Lazy.t
-(* typechecks the object, raising an exception if illtyped *)
-let typecheck_obj obj = match obj with _ -> ()
+(* $Id: cicTypeChecker.ml 8213 2008-03-13 18:48:26Z sacerdot $ *)
+
+(*
+let debrujin_constructor ?(cb=fun _ _ -> ()) uri number_of_types =
+ let rec aux k t =
+ let module C = Cic in
+ let res =
+ match t with
+ C.Rel n as t when n <= k -> t
+ | C.Rel _ ->
+ raise (TypeCheckerFailure (lazy "unbound variable found in constructor type"))
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.Var (uri,exp_named_subst')
+ | C.Meta (i,l) ->
+ let l' = List.map (function None -> None | Some t -> Some (aux k t)) l in
+ C.Meta (i,l')
+ | C.Sort _
+ | C.Implicit _ as t -> t
+ | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty)
+ | C.Prod (n,s,t) -> C.Prod (n, aux k s, aux (k+1) t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, aux k s, aux (k+1) t)
+ | C.LetIn (n,s,ty,t) -> C.LetIn (n, aux k s, aux k ty, aux (k+1) t)
+ | C.Appl l -> C.Appl (List.map (aux k) l)
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.Const (uri,exp_named_subst')
+ | C.MutInd (uri',tyno,exp_named_subst) when UriManager.eq uri uri' ->
+ if exp_named_subst != [] then
+ raise (TypeCheckerFailure
+ (lazy ("non-empty explicit named substitution is applied to "^
+ "a mutual inductive type which is being defined"))) ;
+ C.Rel (k + number_of_types - tyno) ;
+ | C.MutInd (uri',tyno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.MutInd (uri',tyno,exp_named_subst')
+ | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.MutConstruct (uri,tyno,consno,exp_named_subst')
+ | C.MutCase (sp,i,outty,t,pl) ->
+ C.MutCase (sp, i, aux k outty, aux k t,
+ List.map (aux k) pl)
+ | C.Fix (i, fl) ->
+ let len = List.length fl in
+ let liftedfl =
+ List.map
+ (fun (name, i, ty, bo) -> (name, i, aux k ty, aux (k+len) bo))
+ fl
+ in
+ C.Fix (i, liftedfl)
+ | C.CoFix (i, fl) ->
+ let len = List.length fl in
+ let liftedfl =
+ List.map
+ (fun (name, ty, bo) -> (name, aux k ty, aux (k+len) bo))
+ fl
+ in
+ C.CoFix (i, liftedfl)
+ in
+ cb t res;
+ res
+ in
+ aux 0
+;;
+
+exception CicEnvironmentError;;
+
+(*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
+(*CSC questa funzione e' simile alla are_all_occurrences_positive, ma fa *)
+(*CSC dei controlli leggermente diversi. Viene invocata solamente dalla *)
+(*CSC strictly_positive *)
+(*CSC definizione (giusta???) tratta dalla mail di Hugo ;-) *)
+and weakly_positive context n nn uri te =
+ let module C = Cic in
+(*CSC: Che schifo! Bisogna capire meglio e trovare una soluzione ragionevole!*)
+ let dummy_mutind =
+ C.MutInd (HelmLibraryObjects.Datatypes.nat_URI,0,[])
+ in
+ (*CSC: mettere in cicSubstitution *)
+ let rec subst_inductive_type_with_dummy_mutind =
+ function
+ C.MutInd (uri',0,_) when UriManager.eq uri' uri ->
+ dummy_mutind
+ | C.Appl ((C.MutInd (uri',0,_))::tl) when UriManager.eq uri' uri ->
+ dummy_mutind
+ | C.Cast (te,ty) -> subst_inductive_type_with_dummy_mutind te
+ | C.Prod (name,so,ta) ->
+ C.Prod (name, subst_inductive_type_with_dummy_mutind so,
+ subst_inductive_type_with_dummy_mutind ta)
+ | C.Lambda (name,so,ta) ->
+ C.Lambda (name, subst_inductive_type_with_dummy_mutind so,
+ subst_inductive_type_with_dummy_mutind ta)
+ | C.Appl tl ->
+ C.Appl (List.map subst_inductive_type_with_dummy_mutind tl)
+ | C.MutCase (uri,i,outtype,term,pl) ->
+ C.MutCase (uri,i,
+ subst_inductive_type_with_dummy_mutind outtype,
+ subst_inductive_type_with_dummy_mutind term,
+ List.map subst_inductive_type_with_dummy_mutind pl)
+ | C.Fix (i,fl) ->
+ C.Fix (i,List.map (fun (name,i,ty,bo) -> (name,i,
+ subst_inductive_type_with_dummy_mutind ty,
+ subst_inductive_type_with_dummy_mutind bo)) fl)
+ | C.CoFix (i,fl) ->
+ C.CoFix (i,List.map (fun (name,ty,bo) -> (name,
+ subst_inductive_type_with_dummy_mutind ty,
+ subst_inductive_type_with_dummy_mutind bo)) fl)
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map
+ (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t))
+ exp_named_subst
+ in
+ C.Const (uri,exp_named_subst')
+ | C.MutInd (uri,typeno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map
+ (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t))
+ exp_named_subst
+ in
+ C.MutInd (uri,typeno,exp_named_subst')
+ | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map
+ (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t))
+ exp_named_subst
+ in
+ C.MutConstruct (uri,typeno,consno,exp_named_subst')
+ | t -> t
+ in
+ match CicReduction.whd context te with
+(*
+ C.Appl ((C.MutInd (uri',0,_))::tl) when UriManager.eq uri' uri -> true
+*)
+ C.Appl ((C.MutInd (uri',_,_))::tl) when UriManager.eq uri' uri -> true
+ | C.MutInd (uri',0,_) when UriManager.eq uri' uri -> true
+ | C.Prod (C.Anonymous,source,dest) ->
+ strictly_positive context n nn
+ (subst_inductive_type_with_dummy_mutind source) &&
+ weakly_positive ((Some (C.Anonymous,(C.Decl source)))::context)
+ (n + 1) (nn + 1) uri dest
+ | C.Prod (name,source,dest) when
+ does_not_occur ((Some (name,(C.Decl source)))::context) 0 n dest ->
+ (* dummy abstraction, so we behave as in the anonimous case *)
+ strictly_positive context n nn
+ (subst_inductive_type_with_dummy_mutind source) &&
+ weakly_positive ((Some (name,(C.Decl source)))::context)
+ (n + 1) (nn + 1) uri dest
+ | C.Prod (name,source,dest) ->
+ does_not_occur context n nn
+ (subst_inductive_type_with_dummy_mutind source)&&
+ weakly_positive ((Some (name,(C.Decl source)))::context)
+ (n + 1) (nn + 1) uri dest
+ | _ ->
+ raise (TypeCheckerFailure (lazy "Malformed inductive constructor type"))
+
+(* instantiate_parameters ps (x1:T1)...(xn:Tn)C *)
+(* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *)
+and instantiate_parameters params c =
+ let module C = Cic in
+ match (c,params) with
+ (c,[]) -> c
+ | (C.Prod (_,_,ta), he::tl) ->
+ instantiate_parameters tl
+ (CicSubstitution.subst he ta)
+ | (C.Cast (te,_), _) -> instantiate_parameters params te
+ | (t,l) -> raise (AssertFailure (lazy "1"))
+
+and strictly_positive context n nn te =
+ let module C = Cic in
+ let module U = UriManager in
+ match CicReduction.whd context te with
+ | t when does_not_occur context n nn t -> true
+ | C.Rel _ -> true
+ | C.Cast (te,ty) ->
+ (*CSC: bisogna controllare ty????*)
+ strictly_positive context n nn te
+ | C.Prod (name,so,ta) ->
+ does_not_occur context n nn so &&
+ strictly_positive ((Some (name,(C.Decl so)))::context) (n+1) (nn+1) ta
+ | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
+ List.fold_right (fun x i -> i && does_not_occur context n nn x) tl true
+ | C.Appl ((C.MutInd (uri,i,exp_named_subst))::tl) ->
+ let (ok,paramsno,ity,cl,name) =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tl,_,paramsno,_) ->
+ let (name,_,ity,cl) = List.nth tl i in
+ (List.length tl = 1, paramsno, ity, cl, name)
+ (* (true, paramsno, ity, cl, name) *)
+ | _ ->
+ raise
+ (TypeCheckerFailure
+ (lazy ("Unknown inductive type:" ^ U.string_of_uri uri)))
+ in
+ let (params,arguments) = split tl paramsno in
+ let lifted_params = List.map (CicSubstitution.lift 1) params in
+ let cl' =
+ List.map
+ (fun (_,te) ->
+ instantiate_parameters lifted_params
+ (CicSubstitution.subst_vars exp_named_subst te)
+ ) cl
+ in
+ ok &&
+ List.fold_right
+ (fun x i -> i && does_not_occur context n nn x)
+ arguments true &&
+ (*CSC: MEGAPATCH3 (sara' quella giusta?)*)
+ List.fold_right
+ (fun x i ->
+ i &&
+ weakly_positive
+ ((Some (C.Name name,(Cic.Decl ity)))::context) (n+1) (nn+1) uri
+ x
+ ) cl' true
+ | t -> false
+
+(* the inductive type indexes are s.t. n < x <= nn *)
+and are_all_occurrences_positive context uri indparamsno i n nn te =
+ let module C = Cic in
+ match CicReduction.whd context te with
+ C.Appl ((C.Rel m)::tl) when m = i ->
+ (*CSC: riscrivere fermandosi a 0 *)
+ (* let's check if the inductive type is applied at least to *)
+ (* indparamsno parameters *)
+ let last =
+ List.fold_left
+ (fun k x ->
+ if k = 0 then 0
+ else
+ match CicReduction.whd context x with
+ C.Rel m when m = n - (indparamsno - k) -> k - 1
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy
+ ("Non-positive occurence in mutual inductive definition(s) [1]" ^
+ UriManager.string_of_uri uri)))
+ ) indparamsno tl
+ in
+ if last = 0 then
+ List.fold_right (fun x i -> i && does_not_occur context n nn x) tl true
+ else
+ raise (TypeCheckerFailure
+ (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^
+ UriManager.string_of_uri uri)))
+ | C.Rel m when m = i ->
+ if indparamsno = 0 then
+ true
+ else
+ raise (TypeCheckerFailure
+ (lazy ("Non-positive occurence in mutual inductive definition(s) [3]"^
+ UriManager.string_of_uri uri)))
+ | C.Prod (C.Anonymous,source,dest) ->
+ let b = strictly_positive context n nn source in
+ b &&
+ are_all_occurrences_positive
+ ((Some (C.Anonymous,(C.Decl source)))::context) uri indparamsno
+ (i+1) (n + 1) (nn + 1) dest
+ | C.Prod (name,source,dest) when
+ does_not_occur ((Some (name,(C.Decl source)))::context) 0 n dest ->
+ (* dummy abstraction, so we behave as in the anonimous case *)
+ strictly_positive context n nn source &&
+ are_all_occurrences_positive
+ ((Some (name,(C.Decl source)))::context) uri indparamsno
+ (i+1) (n + 1) (nn + 1) dest
+ | C.Prod (name,source,dest) ->
+ does_not_occur context n nn source &&
+ are_all_occurrences_positive ((Some (name,(C.Decl source)))::context)
+ uri indparamsno (i+1) (n + 1) (nn + 1) dest
+ | _ ->
+ raise
+ (TypeCheckerFailure (lazy ("Malformed inductive constructor type " ^
+ (UriManager.string_of_uri uri))))
+
+(* Main function to checks the correctness of a mutual *)
+(* inductive block definition. This is the function *)
+(* exported to the proof-engine. *)
+and typecheck_mutual_inductive_defs ~logger uri (itl,_,indparamsno) ugraph =
+ let module U = UriManager in
+ (* let's check if the arity of the inductive types are well *)
+ (* formed *)
+ let ugrap1 = List.fold_left
+ (fun ugraph (_,_,x,_) -> let _,ugraph' =
+ type_of ~logger x ugraph in ugraph')
+ ugraph itl in
+
+ (* let's check if the types of the inductive constructors *)
+ (* are well formed. *)
+ (* In order not to use type_of_aux we put the types of the *)
+ (* mutual inductive types at the head of the types of the *)
+ (* constructors using Prods *)
+ let len = List.length itl in
+ let tys =
+ List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl in
+ let _,ugraph2 =
+ List.fold_right
+ (fun (_,_,_,cl) (i,ugraph) ->
+ let ugraph'' =
+ List.fold_left
+ (fun ugraph (name,te) ->
+ let debrujinedte = debrujin_constructor uri len te in
+ let augmented_term =
+ List.fold_right
+ (fun (name,_,ty,_) i -> Cic.Prod (Cic.Name name, ty, i))
+ itl debrujinedte
+ in
+ let _,ugraph' = type_of ~logger augmented_term ugraph in
+ (* let's check also the positivity conditions *)
+ if
+ not
+ (are_all_occurrences_positive tys uri indparamsno i 0 len
+ debrujinedte)
+ then
+ begin
+ prerr_endline (UriManager.string_of_uri uri);
+ prerr_endline (string_of_int (List.length tys));
+ raise
+ (TypeCheckerFailure
+ (lazy ("Non positive occurence in " ^ U.string_of_uri uri))) end
+ else
+ ugraph'
+ ) ugraph cl in
+ (i + 1),ugraph''
+ ) itl (1,ugrap1)
+ in
+ ugraph2
+
+(* Main function to checks the correctness of a mutual *)
+(* inductive block definition. *)
+and check_mutual_inductive_defs uri obj ugraph =
+ match obj with
+ Cic.InductiveDefinition (itl, params, indparamsno, _) ->
+ typecheck_mutual_inductive_defs uri (itl,params,indparamsno) ugraph
+ | _ ->
+ raise (TypeCheckerFailure (
+ lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+
+and recursive_args context n nn te =
+ let module C = Cic in
+ match CicReduction.whd context te with
+ C.Rel _ -> []
+ | C.Var _
+ | C.Meta _
+ | C.Sort _
+ | C.Implicit _
+ | C.Cast _ (*CSC ??? *) ->
+ raise (AssertFailure (lazy "3")) (* due to type-checking *)
+ | C.Prod (name,so,de) ->
+ (not (does_not_occur context n nn so)) ::
+ (recursive_args ((Some (name,(C.Decl so)))::context) (n+1) (nn + 1) de)
+ | C.Lambda _
+ | C.LetIn _ ->
+ raise (AssertFailure (lazy "4")) (* due to type-checking *)
+ | C.Appl _ -> []
+ | C.Const _ -> raise (AssertFailure (lazy "5"))
+ | C.MutInd _
+ | C.MutConstruct _
+ | C.MutCase _
+ | C.Fix _
+ | C.CoFix _ -> raise (AssertFailure (lazy "6")) (* due to type-checking *)
+
+and get_new_safes ~subst context p c rl safes n nn x =
+ let module C = Cic in
+ let module U = UriManager in
+ let module R = CicReduction in
+ match (R.whd ~subst context c, R.whd ~subst context p, rl) with
+ (C.Prod (_,so,ta1), C.Lambda (name,_,ta2), b::tl) ->
+ (* we are sure that the two sources are convertible because we *)
+ (* have just checked this. So let's go along ... *)
+ let safes' =
+ List.map (fun x -> x + 1) safes
+ in
+ let safes'' =
+ if b then 1::safes' else safes'
+ in
+ get_new_safes ~subst ((Some (name,(C.Decl so)))::context)
+ ta2 ta1 tl safes'' (n+1) (nn+1) (x+1)
+ | (C.Prod _, (C.MutConstruct _ as e), _)
+ | (C.Prod _, (C.Rel _ as e), _)
+ | (C.MutInd _, e, [])
+ | (C.Appl _, e, []) -> (e,safes,n,nn,x,context)
+ | (c,p,l) ->
+ (* CSC: If the next exception is raised, it just means that *)
+ (* CSC: the proof-assistant allows to use very strange things *)
+ (* CSC: as a branch of a case whose type is a Prod. In *)
+ (* CSC: particular, this means that a new (C.Prod, x,_) case *)
+ (* CSC: must be considered in this match. (e.g. x = MutCase) *)
+ raise
+ (AssertFailure (lazy
+ (Printf.sprintf "Get New Safes: c=%s ; p=%s"
+ (CicPp.ppterm c) (CicPp.ppterm p))))
+
+and split_prods ~subst context n te =
+ let module C = Cic in
+ let module R = CicReduction in
+ match (n, R.whd ~subst context te) with
+ (0, _) -> context,te
+ | (n, C.Prod (name,so,ta)) when n > 0 ->
+ split_prods ~subst ((Some (name,(C.Decl so)))::context) (n - 1) ta
+ | (_, _) -> raise (AssertFailure (lazy "8"))
+
+and eat_lambdas ~subst context n te =
+ let module C = Cic in
+ let module R = CicReduction in
+ match (n, R.whd ~subst context te) with
+ (0, _) -> (te, 0, context)
+ | (n, C.Lambda (name,so,ta)) when n > 0 ->
+ let (te, k, context') =
+ eat_lambdas ~subst ((Some (name,(C.Decl so)))::context) (n - 1) ta
+ in
+ (te, k + 1, context')
+ | (n, te) ->
+ raise (AssertFailure (lazy (sprintf "9 (%d, %s)" n (CicPp.ppterm te))))
+
+(*CSC: Tutto quello che segue e' l'intuzione di luca ;-) *)
+and check_is_really_smaller_arg ~subst context n nn kl x safes te =
+ (*CSC: forse la whd si puo' fare solo quando serve veramente. *)
+ (*CSC: cfr guarded_by_destructors *)
+ let module C = Cic in
+ let module U = UriManager in
+ match CicReduction.whd ~subst context te with
+ C.Rel m when List.mem m safes -> true
+ | C.Rel _ -> false
+ | C.Var _
+ | C.Meta _
+ | C.Sort _
+ | C.Implicit _
+ | C.Cast _
+(* | C.Cast (te,ty) ->
+ check_is_really_smaller_arg ~subst n nn kl x safes te &&
+ check_is_really_smaller_arg ~subst n nn kl x safes ty*)
+(* | C.Prod (_,so,ta) ->
+ check_is_really_smaller_arg ~subst n nn kl x safes so &&
+ check_is_really_smaller_arg ~subst (n+1) (nn+1) kl (x+1)
+ (List.map (fun x -> x + 1) safes) ta*)
+ | C.Prod _ -> raise (AssertFailure (lazy "10"))
+ | C.Lambda (name,so,ta) ->
+ check_is_really_smaller_arg ~subst context n nn kl x safes so &&
+ check_is_really_smaller_arg ~subst ((Some (name,(C.Decl so)))::context)
+ (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
+ | C.LetIn (name,so,ty,ta) ->
+ check_is_really_smaller_arg ~subst context n nn kl x safes so &&
+ check_is_really_smaller_arg ~subst context n nn kl x safes ty &&
+ check_is_really_smaller_arg ~subst ((Some (name,(C.Def (so,ty))))::context)
+ (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
+ | C.Appl (he::_) ->
+ (*CSC: sulla coda ci vogliono dei controlli? secondo noi no, ma *)
+ (*CSC: solo perche' non abbiamo trovato controesempi *)
+ check_is_really_smaller_arg ~subst context n nn kl x safes he
+ | C.Appl [] -> raise (AssertFailure (lazy "11"))
+ | C.Const _
+ | C.MutInd _ -> raise (AssertFailure (lazy "12"))
+ | C.MutConstruct _ -> false
+ | C.MutCase (uri,i,outtype,term,pl) ->
+ (match term with
+ C.Rel m when List.mem m safes || m = x ->
+ let (lefts_and_tys,len,isinductive,paramsno,cl) =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tl,_,paramsno,_) ->
+ let tys =
+ List.map
+ (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) tl
+ in
+ let (_,isinductive,_,cl) = List.nth tl i in
+ let cl' =
+ List.map
+ (fun (id,ty) ->
+ (id, snd (split_prods ~subst tys paramsno ty))) cl in
+ let lefts =
+ match tl with
+ [] -> assert false
+ | (_,_,ty,_)::_ ->
+ fst (split_prods ~subst [] paramsno ty)
+ in
+ (tys@lefts,List.length tl,isinductive,paramsno,cl')
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ in
+ if not isinductive then
+ List.fold_right
+ (fun p i ->
+ i && check_is_really_smaller_arg ~subst context n nn kl x safes p)
+ pl true
+ else
+ let pl_and_cl =
+ try
+ List.combine pl cl
+ with
+ Invalid_argument _ ->
+ raise (TypeCheckerFailure (lazy "not enough patterns"))
+ in
+ (*CSC: supponiamo come prima che nessun controllo sia necessario*)
+ (*CSC: sugli argomenti di una applicazione *)
+ List.fold_right
+ (fun (p,(_,c)) i ->
+ let rl' =
+ let debrujinedte = debrujin_constructor uri len c in
+ recursive_args lefts_and_tys 0 len debrujinedte
+ in
+ let (e,safes',n',nn',x',context') =
+ get_new_safes ~subst context p c rl' safes n nn x
+ in
+ i &&
+ check_is_really_smaller_arg ~subst context' n' nn' kl x' safes' e
+ ) pl_and_cl true
+ | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
+ let (lefts_and_tys,len,isinductive,paramsno,cl) =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tl,_,paramsno,_) ->
+ let (_,isinductive,_,cl) = List.nth tl i in
+ let tys =
+ List.map (fun (n,_,ty,_) ->
+ Some(Cic.Name n,(Cic.Decl ty))) tl
+ in
+ let cl' =
+ List.map
+ (fun (id,ty) ->
+ (id, snd (split_prods ~subst tys paramsno ty))) cl in
+ let lefts =
+ match tl with
+ [] -> assert false
+ | (_,_,ty,_)::_ ->
+ fst (split_prods ~subst [] paramsno ty)
+ in
+ (tys@lefts,List.length tl,isinductive,paramsno,cl')
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ in
+ if not isinductive then
+ List.fold_right
+ (fun p i ->
+ i && check_is_really_smaller_arg ~subst context n nn kl x safes p)
+ pl true
+ else
+ let pl_and_cl =
+ try
+ List.combine pl cl
+ with
+ Invalid_argument _ ->
+ raise (TypeCheckerFailure (lazy "not enough patterns"))
+ in
+ (*CSC: supponiamo come prima che nessun controllo sia necessario*)
+ (*CSC: sugli argomenti di una applicazione *)
+ List.fold_right
+ (fun (p,(_,c)) i ->
+ let rl' =
+ let debrujinedte = debrujin_constructor uri len c in
+ recursive_args lefts_and_tys 0 len debrujinedte
+ in
+ let (e,safes',n',nn',x',context') =
+ get_new_safes ~subst context p c rl' safes n nn x
+ in
+ i &&
+ check_is_really_smaller_arg ~subst context' n' nn' kl x' safes' e
+ ) pl_and_cl true
+ | _ ->
+ List.fold_right
+ (fun p i ->
+ i && check_is_really_smaller_arg ~subst context n nn kl x safes p
+ ) pl true
+ )
+ | C.Fix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,_,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,_,ty,bo) i ->
+ i &&
+ check_is_really_smaller_arg ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+ | C.CoFix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,ty,bo) i ->
+ i &&
+ check_is_really_smaller_arg ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+
+and guarded_by_destructors ~subst context n nn kl x safes =
+ let module C = Cic in
+ let module U = UriManager in
+ function
+ C.Rel m when m > n && m <= nn -> false
+ | C.Rel m ->
+ (match List.nth context (n-1) with
+ Some (_,C.Decl _) -> true
+ | Some (_,C.Def (bo,_)) ->
+ guarded_by_destructors ~subst context m nn kl x safes
+ (CicSubstitution.lift m bo)
+ | None -> raise (TypeCheckerFailure (lazy "Reference to deleted hypothesis"))
+ )
+ | C.Meta _
+ | C.Sort _
+ | C.Implicit _ -> true
+ | C.Cast (te,ty) ->
+ guarded_by_destructors ~subst context n nn kl x safes te &&
+ guarded_by_destructors ~subst context n nn kl x safes ty
+ | C.Prod (name,so,ta) ->
+ guarded_by_destructors ~subst context n nn kl x safes so &&
+ guarded_by_destructors ~subst ((Some (name,(C.Decl so)))::context)
+ (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
+ | C.Lambda (name,so,ta) ->
+ guarded_by_destructors ~subst context n nn kl x safes so &&
+ guarded_by_destructors ~subst ((Some (name,(C.Decl so)))::context)
+ (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
+ | C.LetIn (name,so,ty,ta) ->
+ guarded_by_destructors ~subst context n nn kl x safes so &&
+ guarded_by_destructors ~subst context n nn kl x safes ty &&
+ guarded_by_destructors ~subst ((Some (name,(C.Def (so,ty))))::context)
+ (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
+ | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
+ let k = List.nth kl (m - n - 1) in
+ if not (List.length tl > k) then false
+ else
+ List.fold_right
+ (fun param i ->
+ i && guarded_by_destructors ~subst context n nn kl x safes param
+ ) tl true &&
+ check_is_really_smaller_arg ~subst context n nn kl x safes (List.nth tl k)
+ | C.Appl tl ->
+ List.fold_right
+ (fun t i -> i && guarded_by_destructors ~subst context n nn kl x safes t)
+ tl true
+ | C.Var (_,exp_named_subst)
+ | C.Const (_,exp_named_subst)
+ | C.MutInd (_,_,exp_named_subst)
+ | C.MutConstruct (_,_,_,exp_named_subst) ->
+ List.fold_right
+ (fun (_,t) i -> i && guarded_by_destructors ~subst context n nn kl x safes t)
+ exp_named_subst true
+ | C.MutCase (uri,i,outtype,term,pl) ->
+ (match CicReduction.whd ~subst context term with
+ C.Rel m when List.mem m safes || m = x ->
+ let (lefts_and_tys,len,isinductive,paramsno,cl) =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tl,_,paramsno,_) ->
+ let len = List.length tl in
+ let (_,isinductive,_,cl) = List.nth tl i in
+ let tys =
+ List.map (fun (n,_,ty,_) ->
+ Some(Cic.Name n,(Cic.Decl ty))) tl
+ in
+ let cl' =
+ List.map
+ (fun (id,ty) ->
+ let debrujinedty = debrujin_constructor uri len ty in
+ (id, snd (split_prods ~subst tys paramsno ty),
+ snd (split_prods ~subst tys paramsno debrujinedty)
+ )) cl in
+ let lefts =
+ match tl with
+ [] -> assert false
+ | (_,_,ty,_)::_ ->
+ fst (split_prods ~subst [] paramsno ty)
+ in
+ (tys@lefts,len,isinductive,paramsno,cl')
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ in
+ if not isinductive then
+ guarded_by_destructors ~subst context n nn kl x safes outtype &&
+ guarded_by_destructors ~subst context n nn kl x safes term &&
+ (*CSC: manca ??? il controllo sul tipo di term? *)
+ List.fold_right
+ (fun p i ->
+ i && guarded_by_destructors ~subst context n nn kl x safes p)
+ pl true
+ else
+ let pl_and_cl =
+ try
+ List.combine pl cl
+ with
+ Invalid_argument _ ->
+ raise (TypeCheckerFailure (lazy "not enough patterns"))
+ in
+ guarded_by_destructors ~subst context n nn kl x safes outtype &&
+ (*CSC: manca ??? il controllo sul tipo di term? *)
+ List.fold_right
+ (fun (p,(_,c,brujinedc)) i ->
+ let rl' = recursive_args lefts_and_tys 0 len brujinedc in
+ let (e,safes',n',nn',x',context') =
+ get_new_safes ~subst context p c rl' safes n nn x
+ in
+ i &&
+ guarded_by_destructors ~subst context' n' nn' kl x' safes' e
+ ) pl_and_cl true
+ | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
+ let (lefts_and_tys,len,isinductive,paramsno,cl) =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tl,_,paramsno,_) ->
+ let (_,isinductive,_,cl) = List.nth tl i in
+ let tys =
+ List.map
+ (fun (n,_,ty,_) -> Some(Cic.Name n,(Cic.Decl ty))) tl
+ in
+ let cl' =
+ List.map
+ (fun (id,ty) ->
+ (id, snd (split_prods ~subst tys paramsno ty))) cl in
+ let lefts =
+ match tl with
+ [] -> assert false
+ | (_,_,ty,_)::_ ->
+ fst (split_prods ~subst [] paramsno ty)
+ in
+ (tys@lefts,List.length tl,isinductive,paramsno,cl')
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ in
+ if not isinductive then
+ guarded_by_destructors ~subst context n nn kl x safes outtype &&
+ guarded_by_destructors ~subst context n nn kl x safes term &&
+ (*CSC: manca ??? il controllo sul tipo di term? *)
+ List.fold_right
+ (fun p i ->
+ i && guarded_by_destructors ~subst context n nn kl x safes p)
+ pl true
+ else
+ let pl_and_cl =
+ try
+ List.combine pl cl
+ with
+ Invalid_argument _ ->
+ raise (TypeCheckerFailure (lazy "not enough patterns"))
+ in
+ guarded_by_destructors ~subst context n nn kl x safes outtype &&
+ (*CSC: manca ??? il controllo sul tipo di term? *)
+ List.fold_right
+ (fun t i ->
+ i && guarded_by_destructors ~subst context n nn kl x safes t)
+ tl true &&
+ List.fold_right
+ (fun (p,(_,c)) i ->
+ let rl' =
+ let debrujinedte = debrujin_constructor uri len c in
+ recursive_args lefts_and_tys 0 len debrujinedte
+ in
+ let (e, safes',n',nn',x',context') =
+ get_new_safes ~subst context p c rl' safes n nn x
+ in
+ i &&
+ guarded_by_destructors ~subst context' n' nn' kl x' safes' e
+ ) pl_and_cl true
+ | _ ->
+ guarded_by_destructors ~subst context n nn kl x safes outtype &&
+ guarded_by_destructors ~subst context n nn kl x safes term &&
+ (*CSC: manca ??? il controllo sul tipo di term? *)
+ List.fold_right
+ (fun p i -> i && guarded_by_destructors ~subst context n nn kl x safes p)
+ pl true
+ )
+ | C.Fix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,_,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,_,ty,bo) i ->
+ i && guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
+ guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+ | C.CoFix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,ty,bo) i ->
+ i &&
+ guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
+ guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+
+(* the boolean h means already protected *)
+(* args is the list of arguments the type of the constructor that may be *)
+(* found in head position must be applied to. *)
+and guarded_by_constructors ~subst context n nn h te args coInductiveTypeURI =
+ let module C = Cic in
+ (*CSC: There is a lot of code replication between the cases X and *)
+ (*CSC: (C.Appl X tl). Maybe it will be better to define a function *)
+ (*CSC: that maps X into (C.Appl X []) when X is not already a C.Appl *)
+ match CicReduction.whd ~subst context te with
+ C.Rel m when m > n && m <= nn -> h
+ | C.Rel _ -> true
+ | C.Meta _
+ | C.Sort _
+ | C.Implicit _
+ | C.Cast _
+ | C.Prod _
+ | C.LetIn _ ->
+ (* the term has just been type-checked *)
+ raise (AssertFailure (lazy "17"))
+ | C.Lambda (name,so,de) ->
+ does_not_occur ~subst context n nn so &&
+ guarded_by_constructors ~subst ((Some (name,(C.Decl so)))::context)
+ (n + 1) (nn + 1) h de args coInductiveTypeURI
+ | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
+ h &&
+ List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) tl true
+ | C.Appl ((C.MutConstruct (uri,i,j,exp_named_subst))::tl) ->
+ let consty =
+ let obj,_ =
+ try
+ CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri
+ with Not_found -> assert false
+ in
+ match obj with
+ C.InductiveDefinition (itl,_,_,_) ->
+ let (_,_,_,cl) = List.nth itl i in
+ let (_,cons) = List.nth cl (j - 1) in
+ CicSubstitution.subst_vars exp_named_subst cons
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^ UriManager.string_of_uri uri)))
+ in
+ let rec analyse_branch context ty te =
+ match CicReduction.whd ~subst context ty with
+ C.Meta _ -> raise (AssertFailure (lazy "34"))
+ | C.Rel _
+ | C.Var _
+ | C.Sort _ ->
+ does_not_occur ~subst context n nn te
+ | C.Implicit _
+ | C.Cast _ ->
+ raise (AssertFailure (lazy "24"))(* due to type-checking *)
+ | C.Prod (name,so,de) ->
+ analyse_branch ((Some (name,(C.Decl so)))::context) de te
+ | C.Lambda _
+ | C.LetIn _ ->
+ raise (AssertFailure (lazy "25"))(* due to type-checking *)
+ | C.Appl ((C.MutInd (uri,_,_))::_) when uri == coInductiveTypeURI ->
+ guarded_by_constructors ~subst context n nn true te []
+ coInductiveTypeURI
+ | C.Appl ((C.MutInd (uri,_,_))::_) ->
+ guarded_by_constructors ~subst context n nn true te tl
+ coInductiveTypeURI
+ | C.Appl _ ->
+ does_not_occur ~subst context n nn te
+ | C.Const _ -> raise (AssertFailure (lazy "26"))
+ | C.MutInd (uri,_,_) when uri == coInductiveTypeURI ->
+ guarded_by_constructors ~subst context n nn true te []
+ coInductiveTypeURI
+ | C.MutInd _ ->
+ does_not_occur ~subst context n nn te
+ | C.MutConstruct _ -> raise (AssertFailure (lazy "27"))
+ (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
+ (*CSC: in head position. *)
+ | C.MutCase _
+ | C.Fix _
+ | C.CoFix _ ->
+ raise (AssertFailure (lazy "28"))(* due to type-checking *)
+ in
+ let rec analyse_instantiated_type context ty l =
+ match CicReduction.whd ~subst context ty with
+ C.Rel _
+ | C.Var _
+ | C.Meta _
+ | C.Sort _
+ | C.Implicit _
+ | C.Cast _ -> raise (AssertFailure (lazy "29"))(* due to type-checking *)
+ | C.Prod (name,so,de) ->
+ begin
+ match l with
+ [] -> true
+ | he::tl ->
+ analyse_branch context so he &&
+ analyse_instantiated_type
+ ((Some (name,(C.Decl so)))::context) de tl
+ end
+ | C.Lambda _
+ | C.LetIn _ ->
+ raise (AssertFailure (lazy "30"))(* due to type-checking *)
+ | C.Appl _ ->
+ List.fold_left
+ (fun i x -> i && does_not_occur ~subst context n nn x) true l
+ | C.Const _ -> raise (AssertFailure (lazy "31"))
+ | C.MutInd _ ->
+ List.fold_left
+ (fun i x -> i && does_not_occur ~subst context n nn x) true l
+ | C.MutConstruct _ -> raise (AssertFailure (lazy "32"))
+ (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
+ (*CSC: in head position. *)
+ | C.MutCase _
+ | C.Fix _
+ | C.CoFix _ ->
+ raise (AssertFailure (lazy "33"))(* due to type-checking *)
+ in
+ let rec instantiate_type args consty =
+ function
+ [] -> true
+ | tlhe::tltl as l ->
+ let consty' = CicReduction.whd ~subst context consty in
+ match args with
+ he::tl ->
+ begin
+ match consty' with
+ C.Prod (_,_,de) ->
+ let instantiated_de = CicSubstitution.subst he de in
+ (*CSC: siamo sicuri che non sia troppo forte? *)
+ does_not_occur ~subst context n nn tlhe &
+ instantiate_type tl instantiated_de tltl
+ | _ ->
+ (*CSC:We do not consider backbones with a MutCase, a *)
+ (*CSC:FixPoint, a CoFixPoint and so on in head position.*)
+ raise (AssertFailure (lazy "23"))
+ end
+ | [] -> analyse_instantiated_type context consty' l
+ (* These are all the other cases *)
+ in
+ instantiate_type args consty tl
+ | C.Appl ((C.CoFix (_,fl))::tl) ->
+ List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl &&
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ in
+ List.fold_right
+ (fun (_,ty,bo) i ->
+ i && does_not_occur ~subst context n nn ty &&
+ guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len
+ h bo args coInductiveTypeURI
+ ) fl true
+ | C.Appl ((C.MutCase (_,_,out,te,pl))::tl) ->
+ List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl &&
+ does_not_occur ~subst context n nn out &&
+ does_not_occur ~subst context n nn te &&
+ List.fold_right
+ (fun x i ->
+ i &&
+ guarded_by_constructors ~subst context n nn h x args
+ coInductiveTypeURI
+ ) pl true
+ | C.Appl l ->
+ List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) l true
+ | C.Var (_,exp_named_subst)
+ | C.Const (_,exp_named_subst) ->
+ List.fold_right
+ (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
+ | C.MutInd _ -> assert false
+ | C.MutConstruct (_,_,_,exp_named_subst) ->
+ List.fold_right
+ (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
+ | C.MutCase (_,_,out,te,pl) ->
+ does_not_occur ~subst context n nn out &&
+ does_not_occur ~subst context n nn te &&
+ List.fold_right
+ (fun x i ->
+ i &&
+ guarded_by_constructors ~subst context n nn h x args
+ coInductiveTypeURI
+ ) pl true
+ | C.Fix (_,fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,_,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ in
+ List.fold_right
+ (fun (_,_,ty,bo) i ->
+ i && does_not_occur ~subst context n nn ty &&
+ does_not_occur ~subst (tys@context) n_plus_len nn_plus_len bo
+ ) fl true
+ | C.CoFix (_,fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ in
+ List.fold_right
+ (fun (_,ty,bo) i ->
+ i && does_not_occur ~subst context n nn ty &&
+ guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len
+ h bo
+ args coInductiveTypeURI
+ ) fl true
+
+and type_of_branch ~subst context argsno need_dummy outtype term constype =
+ let module C = Cic in
+ let module R = CicReduction in
+ match R.whd ~subst context constype with
+ C.MutInd (_,_,_) ->
+ if need_dummy then
+ outtype
+ else
+ C.Appl [outtype ; term]
+ | C.Appl (C.MutInd (_,_,_)::tl) ->
+ let (_,arguments) = split tl argsno
+ in
+ if need_dummy && arguments = [] then
+ outtype
+ else
+ C.Appl (outtype::arguments@(if need_dummy then [] else [term]))
+ | C.Prod (name,so,de) ->
+ let term' =
+ match CicSubstitution.lift 1 term with
+ C.Appl l -> C.Appl (l@[C.Rel 1])
+ | t -> C.Appl [t ; C.Rel 1]
+ in
+ C.Prod (name,so,type_of_branch ~subst
+ ((Some (name,(C.Decl so)))::context) argsno need_dummy
+ (CicSubstitution.lift 1 outtype) term' de)
+ | _ -> raise (AssertFailure (lazy "20"))
+
+ and returns_a_coinductive ~subst context ty =
+ let module C = Cic in
+ match CicReduction.whd ~subst context ty with
+ C.MutInd (uri,i,_) ->
+ (*CSC: definire una funzioncina per questo codice sempre replicato *)
+ let obj,_ =
+ try
+ CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri
+ with Not_found -> assert false
+ in
+ (match obj with
+ C.InductiveDefinition (itl,_,_,_) ->
+ let (_,is_inductive,_,_) = List.nth itl i in
+ if is_inductive then None else (Some uri)
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ )
+ | C.Appl ((C.MutInd (uri,i,_))::_) ->
+ (let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (itl,_,_,_) ->
+ let (_,is_inductive,_,_) = List.nth itl i in
+ if is_inductive then None else (Some uri)
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ )
+ | C.Prod (n,so,de) ->
+ returns_a_coinductive ~subst ((Some (n,C.Decl so))::context) de
+ | _ -> None
+
+ in
+ type_of_aux ~logger context t ugraph
+
+;;
+
+(** wrappers which instantiate fresh loggers *)
+
+(* check_allowed_sort_elimination uri i s1 s2
+ This function is used outside the kernel to determine in advance whether
+ a MutCase will be allowed or not.
+ [uri,i] is the type of the term to match
+ [s1] is the sort of the term to eliminate (i.e. the head of the arity
+ of the inductive type [uri,i])
+ [s2] is the sort of the goal (i.e. the head of the type of the outtype
+ of the MutCase) *)
+let check_allowed_sort_elimination uri i s1 s2 =
+ fst (check_allowed_sort_elimination ~subst:[] ~metasenv:[]
+ ~logger:(new CicLogger.logger) [] uri i true
+ (Cic.Implicit None) (* never used *) (Cic.Sort s1) (Cic.Sort s2)
+ CicUniv.empty_ugraph)
+;;
+
+Deannotate.type_of_aux' := fun context t -> fst (type_of_aux' [] context t CicUniv.oblivion_ugraph);;
+
+*)
+
+module C = NCic
+module R = NCicReduction
+module Ref = NReference
+module S = NCicSubstitution
+module U = NCicUtils
+module E = NCicEnvironment
+
+let rec split_prods ~subst context n te =
+ match (n, R.whd ~subst context te) with
+ | (0, _) -> context,te
+ | (n, C.Prod (name,so,ta)) when n > 0 ->
+ split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
+ | (_, _) -> raise (AssertFailure (lazy "split_prods"))
+;;
+
+let sort_of_prod ~subst context (name,s) (t1, t2) =
+ let t1 = R.whd ~subst context t1 in
+ let t2 = R.whd ~subst ((name,C.Decl s)::context) t2 in
+ match t1, t2 with
+ | C.Sort s1, C.Sort C.Prop -> t2
+ | C.Sort (C.Type u1), C.Sort (C.Type u2) -> C.Sort (C.Type (max u1 u2))
+ | C.Sort _,C.Sort (C.Type _) -> t2
+ | C.Sort (C.Type _) , C.Sort C.CProp -> t1
+ | C.Sort _, C.Sort C.CProp -> t2
+ | C.Meta _, C.Sort _
+ | C.Meta _, C.Meta _
+ | C.Sort _, C.Meta _ when U.is_closed t2 -> t2
+ | _ ->
+ raise (TypeCheckerFailure (lazy (Printf.sprintf
+ "Prod: expected two sorts, found = %s, %s"
+ (NCicPp.ppterm t1) (NCicPp.ppterm t2))))
+;;
+
+let eat_prods ~subst ~metasenv context ty_he args_with_ty =
+ let rec aux ty_he = function
+ | [] -> ty_he
+ | (arg, ty_arg)::tl ->
+ (match R.whd ~subst context ty_he with
+ | C.Prod (n,s,t) ->
+ if R.are_convertible ~subst ~metasenv context ty_arg s then
+ aux (S.subst ~avoid_beta_redexes:true arg t) tl
+ else
+ raise
+ (TypeCheckerFailure
+ (lazy (Printf.sprintf
+ ("Appl: wrong parameter-type, expected %s, found %s")
+ (NCicPp.ppterm ty_arg) (NCicPp.ppterm s))))
+ | _ ->
+ raise
+ (TypeCheckerFailure
+ (lazy "Appl: this is not a function, it cannot be applied")))
+ in
+ aux ty_he args_with_ty
+;;
+
+exception DoesOccur;;
+
+let does_not_occur ~subst context n nn t =
+ let rec aux (context,n,nn as k) _ = function
+ | C.Rel m when m > n && m <= nn -> raise DoesOccur
+ | C.Rel m ->
+ (try (match List.nth context (m-1) with
+ | _,C.Def (bo,_) -> aux k () (S.lift m bo)
+ | _ -> ())
+ with Failure _ -> assert false)
+ | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))) -> (* closed meta *) ()
+ | C.Meta (mno,(s,l)) ->
+ (try
+ let _,_,term,_ = U.lookup_subst mno subst in
+ aux (context,n+s,nn+s) () (S.subst_meta (0,l) term)
+ with CicUtil.Subst_not_found _ -> match l with
+ | C.Irl len -> if not (n >= s+len || s > nn) then raise DoesOccur
+ | C.Ctx lc -> List.iter (aux (context,n+s,nn+s) ()) lc)
+ | t -> U.fold (fun e (ctx,n,nn) -> (e::ctx,n+1,nn+1)) k aux () t
+ in
+ try aux (context,n,nn) () t; true
+ with DoesOccur -> false
+;;
+
+let rec typeof ~subst ~metasenv context term =
+ let rec typeof_aux context = function
+ | C.Rel n ->
+ (try
+ match List.nth context (n - 1) with
+ | (_,C.Decl ty) -> S.lift n ty
+ | (_,C.Def (_,ty)) -> S.lift n ty
+ with Failure _ -> raise (TypeCheckerFailure (lazy "unbound variable")))
+ | C.Sort (C.Type i) -> C.Sort (C.Type (i+1))
+ | C.Sort s -> C.Sort (C.Type 0)
+ | C.Implicit _ -> raise (AssertFailure (lazy "Implicit found"))
+ | C.Meta (n,l) as t ->
+ let canonical_context,ty =
+ try
+ let _,c,_,ty = U.lookup_subst n subst in c,ty
+ with U.Subst_not_found _ -> try
+ let _,_,c,ty = U.lookup_meta n metasenv in c,ty
+ with U.Meta_not_found _ ->
+ raise (AssertFailure (lazy (Printf.sprintf
+ "%s not found" (NCicPp.ppterm t))))
+ in
+ check_metasenv_consistency t context canonical_context l;
+ S.subst_meta l ty
+ | C.Const ref -> type_of_constant ref
+ | C.Prod (name,s,t) ->
+ let sort1 = typeof_aux context s in
+ let sort2 = typeof_aux ((name,(C.Decl s))::context) t in
+ sort_of_prod ~subst context (name,s) (sort1,sort2)
+ | C.Lambda (n,s,t) ->
+ let sort = typeof_aux context s in
+ (match R.whd ~subst context sort with
+ | C.Meta _ | C.Sort _ -> ()
+ | _ ->
+ raise
+ (TypeCheckerFailure (lazy (Printf.sprintf
+ ("Not well-typed lambda-abstraction: " ^^
+ "the source %s should be a type; instead it is a term " ^^
+ "of type %s") (NCicPp.ppterm s) (NCicPp.ppterm sort)))));
+ let ty = typeof_aux ((n,(C.Decl s))::context) t in
+ C.Prod (n,s,ty)
+ | C.LetIn (n,ty,t,bo) ->
+ let ty_t = typeof_aux context t in
+ if not (R.are_convertible ~subst ~metasenv context ty ty_t) then
+ raise
+ (TypeCheckerFailure
+ (lazy (Printf.sprintf
+ "The type of %s is %s but it is expected to be %s"
+ (NCicPp.ppterm t) (NCicPp.ppterm ty_t) (NCicPp.ppterm ty))))
+ else
+ let ty_bo = typeof_aux ((n,C.Def (t,ty))::context) bo in
+ S.subst ~avoid_beta_redexes:true t ty_bo
+ | C.Appl (he::(_::_ as args)) ->
+ let ty_he = typeof_aux context he in
+ let args_with_ty = List.map (fun t -> t, typeof_aux context t) args in
+ eat_prods ~subst ~metasenv context ty_he args_with_ty
+ | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2"))
+ | C.Match (Ref.Ref (dummy_depth,uri,Ref.Ind tyno) as r,outtype,term,pl) ->
+ let outsort = typeof_aux context outtype in
+ let leftno = E.get_indty_leftno r in
+ let parameters, arguments =
+ let ty = R.whd ~subst context (typeof_aux context term) in
+ let r',tl =
+ match ty with
+ C.Const (Ref.Ref (_,_,Ref.Ind _) as r') -> r',[]
+ | C.Appl (C.Const (Ref.Ref (_,_,Ref.Ind _) as r') :: tl) -> r',tl
+ | _ ->
+ raise
+ (TypeCheckerFailure (lazy (Printf.sprintf
+ "Case analysis: analysed term %s is not an inductive one"
+ (NCicPp.ppterm term)))) in
+ if not (Ref.eq r r') then
+ raise
+ (TypeCheckerFailure (lazy (Printf.sprintf
+ ("Case analysys: analysed term type is %s, but is expected " ^^
+ "to be (an application of) %s")
+ (NCicPp.ppterm ty) (NCicPp.ppterm (C.Const r')))))
+ else
+ try HExtlib.split_nth leftno tl
+ with
+ Failure _ ->
+ raise (TypeCheckerFailure (lazy (Printf.sprintf
+ "%s is partially applied" (NCicPp.ppterm ty)))) in
+ (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
+ let sort_of_ind_type =
+ if parameters = [] then C.Const r
+ else C.Appl ((C.Const r)::parameters) in
+ let type_of_sort_of_ind_ty = typeof_aux context sort_of_ind_type in
+ if not (check_allowed_sort_elimination ~subst ~metasenv r context
+ sort_of_ind_type type_of_sort_of_ind_ty outsort)
+ then raise (TypeCheckerFailure (lazy ("Sort elimination not allowed")));
+ (* let's check if the type of branches are right *)
+ let leftno,constructorsno =
+ let inductive,leftno,itl,_,i = E.get_checked_indtys r in
+ let _,name,ty,cl = List.nth itl i in
+ let cl_len = List.length cl in
+ leftno, cl_len
+ in
+ if List.length pl <> constructorsno then
+ raise (TypeCheckerFailure (lazy ("Wrong number of cases in a match")));
+ let j,branches_ok =
+ List.fold_left
+ (fun (j,b) p ->
+ if b then
+ let cons =
+ let cons = Ref.Ref (dummy_depth, uri, Ref.Con (tyno, j)) in
+ if parameters = [] then C.Const cons
+ else C.Appl (C.Const cons::parameters)
+ in
+ let ty_p = typeof_aux context p in
+ let ty_cons = typeof_aux context cons in
+ let ty_branch =
+ type_of_branch ~subst context leftno outtype cons ty_cons in
+ j+1, R.are_convertible ~subst ~metasenv context ty_p ty_branch
+ else
+ j,false
+ ) (1,true) pl
+ in
+ if not branches_ok then
+ raise
+ (TypeCheckerFailure
+ (lazy (Printf.sprintf "Branch for constructor %s has wrong type"
+ (NCicPp.ppterm (C.Const
+ (Ref.Ref (dummy_depth, uri, Ref.Con (tyno, j))))))));
+ let res = outtype::arguments@[term] in
+ R.head_beta_reduce (C.Appl res)
+ | C.Match _ -> assert false
+
+ and type_of_branch ~subst context leftno outty cons tycons = assert false
+
+ (* check_metasenv_consistency checks that the "canonical" context of a
+ metavariable is consitent - up to relocation via the relocation list l -
+ with the actual context *)
+ and check_metasenv_consistency term context canonical_context l =
+ match l with
+ | shift, NCic.Irl n ->
+ let context = snd (HExtlib.split_nth shift context) in
+ let rec compare = function
+ | 0,_,[] -> ()
+ | 0,_,_::_
+ | _,_,[] ->
+ raise (AssertFailure (lazy (Printf.sprintf
+ "Local and canonical context %s have different lengths"
+ (NCicPp.ppterm term))))
+ | m,[],_::_ ->
+ raise (TypeCheckerFailure (lazy (Printf.sprintf
+ "Unbound variable -%d in %s" m (NCicPp.ppterm term))))
+ | m,t::tl,ct::ctl ->
+ (match t,ct with
+ (_,C.Decl t1), (_,C.Decl t2)
+ | (_,C.Def (t1,_)), (_,C.Def (t2,_))
+ | (_,C.Def (_,t1)), (_,C.Decl t2) ->
+ if not (R.are_convertible ~subst ~metasenv tl t1 t2) then
+ raise
+ (TypeCheckerFailure
+ (lazy (Printf.sprintf
+ ("Not well typed metavariable local context for %s: " ^^
+ "%s expected, which is not convertible with %s")
+ (NCicPp.ppterm term) (NCicPp.ppterm t2) (NCicPp.ppterm t1)
+ )))
+ | _,_ ->
+ raise
+ (TypeCheckerFailure
+ (lazy (Printf.sprintf
+ ("Not well typed metavariable local context for %s: " ^^
+ "a definition expected, but a declaration found")
+ (NCicPp.ppterm term)))));
+ compare (m - 1,tl,ctl)
+ in
+ compare (n,context,canonical_context)
+ | shift, lc_kind ->
+ (* we avoid useless lifting by shortening the context*)
+ let l,context = (0,lc_kind), snd (HExtlib.split_nth shift context) in
+ let lifted_canonical_context =
+ let rec lift_metas i = function
+ | [] -> []
+ | (n,C.Decl t)::tl ->
+ (n,C.Decl (S.subst_meta l (S.lift i t)))::(lift_metas (i+1) tl)
+ | (n,C.Def (t,ty))::tl ->
+ (n,C.Def ((S.subst_meta l (S.lift i t)),
+ S.subst_meta l (S.lift i ty)))::(lift_metas (i+1) tl)
+ in
+ lift_metas 1 canonical_context in
+ let l = U.expand_local_context lc_kind in
+ try
+ List.iter2
+ (fun t ct ->
+ match (t,ct) with
+ | t, (_,C.Def (ct,_)) ->
+ (*CSC: the following optimization is to avoid a possibly expensive
+ reduction that can be easily avoided and that is quite
+ frequent. However, this is better handled using levels to
+ control reduction *)
+ let optimized_t =
+ match t with
+ | C.Rel n ->
+ (try
+ match List.nth context (n - 1) with
+ | (_,C.Def (te,_)) -> S.lift n te
+ | _ -> t
+ with Failure _ -> t)
+ | _ -> t
+ in
+ if not (R.are_convertible ~subst ~metasenv context optimized_t ct)
+ then
+ raise
+ (TypeCheckerFailure
+ (lazy (Printf.sprintf
+ ("Not well typed metavariable local context: " ^^
+ "expected a term convertible with %s, found %s")
+ (NCicPp.ppterm ct) (NCicPp.ppterm t))))
+ | t, (_,C.Decl ct) ->
+ let type_t = typeof_aux context t in
+ if not (R.are_convertible ~subst ~metasenv context type_t ct) then
+ raise (TypeCheckerFailure
+ (lazy (Printf.sprintf
+ ("Not well typed metavariable local context: "^^
+ "expected a term of type %s, found %s of type %s")
+ (NCicPp.ppterm ct) (NCicPp.ppterm t) (NCicPp.ppterm type_t))))
+ ) l lifted_canonical_context
+ with
+ Invalid_argument _ ->
+ raise (AssertFailure (lazy (Printf.sprintf
+ "Local and canonical context %s have different lengths"
+ (NCicPp.ppterm term))))
+
+ and is_non_informative context paramsno c =
+ let rec aux context c =
+ match R.whd context c with
+ | C.Prod (n,so,de) ->
+ let s = typeof_aux context so in
+ s = C.Sort C.Prop && aux ((n,(C.Decl so))::context) de
+ | _ -> true in
+ let context',dx = split_prods ~subst:[] context paramsno c in
+ aux context' dx
+
+ and check_allowed_sort_elimination ~subst ~metasenv r =
+ let mkapp he arg =
+ match he with
+ | C.Appl l -> C.Appl (l @ [arg])
+ | t -> C.Appl [t;arg] in
+ let rec aux context ind arity1 arity2 =
+ let arity1 = R.whd ~subst context arity1 in
+ let arity2 = R.whd ~subst context arity2 in
+ match arity1,arity2 with
+ | C.Prod (name,so1,de1), C.Prod (_,so2,de2) ->
+ R.are_convertible ~subst ~metasenv context so1 so2 &&
+ aux ((name, C.Decl so1)::context)
+ (mkapp (S.lift 1 ind) (C.Rel 1)) de1 de2
+ | C.Sort _, C.Prod (name,so,ta) ->
+ (R.are_convertible ~subst ~metasenv context so ind &&
+ match arity1,ta with
+ | (C.Sort (C.CProp | C.Type _), C.Sort _)
+ | (C.Sort C.Prop, C.Sort C.Prop) -> true
+ | (C.Sort C.Prop, C.Sort (C.CProp | C.Type _)) ->
+ let inductive,leftno,itl,_,i = E.get_checked_indtys r in
+ let itl_len = List.length itl in
+ let _,name,ty,cl = List.nth itl i in
+ let cl_len = List.length cl in
+ (* is it a singleton or empty non recursive and non informative
+ definition? *)
+ cl_len = 0 ||
+ (itl_len = 1 && cl_len = 1 &&
+ is_non_informative [name,C.Decl ty] leftno
+ (let _,_,x = List.nth cl 0 in x))
+ | _,_ -> false)
+ | _,_ -> false
+ in
+ aux
+
+ in
+ typeof_aux context term
+
+and check_mutual_inductive_defs _ = assert false
+and eat_lambdas ~subst _ _ _ = assert false
+and guarded_by_constructors ~subst _ _ _ _ _ _ _ = assert false
+and guarded_by_destructors ~subst _ _ _ _ _ _ _ = assert false
+and returns_a_coinductive ~subst _ _ = assert false
+
+and type_of_constant ref = assert false (* USARE typecheck_obj0 *)
+(* ALIAS typecheck *)
+(*
+ let cobj,ugraph1 =
+ match CicEnvironment.is_type_checked ~trust:true ugraph uri with
+ CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph'
+ | CicEnvironment.UncheckedObj uobj ->
+ logger#log (`Start_type_checking uri) ;
+ let ugraph1_dust =
+ typecheck_obj0 ~logger uri CicUniv.empty_ugraph uobj in
+ try
+ CicEnvironment.set_type_checking_info uri ;
+ logger#log (`Type_checking_completed uri) ;
+ (match CicEnvironment.is_type_checked ~trust:false ugraph uri with
+ CicEnvironment.CheckedObj (cobj,ugraph') -> (cobj,ugraph')
+ | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
+ )
+ with
+ (*
+ this is raised if set_type_checking_info is called on an object
+ that has no associated universe file. If we are in univ_maker
+ phase this is OK since univ_maker will properly commit the
+ object.
+ *)
+ Invalid_argument s ->
+ (*debug_print (lazy s);*)
+ uobj,ugraph1_dust
+ in
+CASO COSTRUTTORE
+ match cobj with
+ C.InductiveDefinition (dl,_,_,_) ->
+ let (_,_,arity,_) = List.nth dl i in
+ arity,ugraph1
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^ U.string_of_uri uri)))
+CASO TIPO INDUTTIVO
+ match cobj with
+ C.InductiveDefinition (dl,_,_,_) ->
+ let (_,_,_,cl) = List.nth dl i in
+ let (_,ty) = List.nth cl (j-1) in
+ ty,ugraph1
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^ UriManager.string_of_uri uri)))
+CASO COSTANTE
+CASO FIX/COFIX
+*)
+
+and typecheck_obj0 (uri,height,metasenv,subst,kind) =
+ (* CSC: here we should typecheck the metasenv and the subst *)
+ assert (metasenv = [] && subst = []);
+ match kind with
+ | C.Constant (_,_,Some te,ty,_) ->
+ let _ = typeof ~subst ~metasenv [] ty in
+ let ty_te = typeof ~subst ~metasenv [] te in
+ if not (R.are_convertible ~subst ~metasenv [] ty_te ty) then
+ raise (TypeCheckerFailure (lazy (Printf.sprintf
+ "the type of the body is not the one expected:\n%s\nvs\n%s"
+ (NCicPp.ppterm ty_te) (NCicPp.ppterm ty))))
+ | C.Constant (_,_,None,ty,_) -> ignore (typeof ~subst ~metasenv [] ty)
+ | C.Inductive _ as obj -> check_mutual_inductive_defs uri obj
+ | C.Fixpoint (inductive,fl,_) ->
+ let types,kl,len =
+ List.fold_left
+ (fun (types,kl,len) (_,n,k,ty,_) ->
+ let _ = typeof ~subst ~metasenv [] ty in
+ ((n,(C.Decl (S.lift len ty)))::types, k::kl,len+1)
+ ) ([],[],0) fl
+ in
+ List.iter (fun (_,name,x,ty,bo) ->
+ let ty_bo = typeof ~subst ~metasenv types bo in
+ if not (R.are_convertible ~subst ~metasenv types ty_bo (S.lift len ty))
+ then raise (TypeCheckerFailure (lazy ("(Co)Fix: ill-typed bodies")))
+ else
+ if inductive then begin
+ let m, eaten, context =
+ eat_lambdas ~subst types (x + 1) bo
+ in
+ (* guarded by destructors conditions D{f,k,x,M} *)
+ if not (guarded_by_destructors ~subst context eaten
+ (len + eaten) kl 1 [] m)
+ then
+ raise(TypeCheckerFailure(lazy("Fix: not guarded by destructors")))
+ end else
+ match returns_a_coinductive ~subst [] ty with
+ | None ->
+ raise (TypeCheckerFailure
+ (lazy "CoFix: does not return a coinductive type"))
+ | Some uri ->
+ (* guarded by constructors conditions C{f,M} *)
+ if not (guarded_by_constructors ~subst
+ types 0 len false bo [] uri)
+ then
+ raise (TypeCheckerFailure
+ (lazy "CoFix: not guarded by constructors"))
+ ) fl
+
+let typecheck_obj (*uri*) obj = assert false (*
+ let ugraph = typecheck_obj0 ~logger uri CicUniv.empty_ugraph obj in
+ let ugraph, univlist, obj = CicUnivUtils.clean_and_fill uri obj ugraph in
+ CicEnvironment.add_type_checked_obj uri (obj,ugraph,univlist)
+*)
+;;