(* ||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 (* $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;; and does_not_occur ?(subst=[]) context n nn te = let module C = Cic in match te with C.Rel m when m > n && m <= nn -> false | C.Rel m -> (try (match List.nth context (m-1) with Some (_,C.Def (bo,_)) -> does_not_occur ~subst context n nn (CicSubstitution.lift m bo) | _ -> true) with Failure _ -> assert false) | C.Sort _ | C.Implicit _ -> true | C.Meta (_,l) -> List.fold_right (fun x i -> match x with None -> i | Some x -> i && does_not_occur ~subst context n nn x) l true && (try let (canonical_context,term,ty) = CicUtil.lookup_subst n subst in does_not_occur ~subst context n nn (CicSubstitution.subst_meta l term) with CicUtil.Subst_not_found _ -> true) | C.Cast (te,ty) -> does_not_occur ~subst context n nn te && does_not_occur ~subst context n nn ty | C.Prod (name,so,dest) -> does_not_occur ~subst context n nn so && does_not_occur ~subst ((Some (name,(C.Decl so)))::context) (n + 1) (nn + 1) dest | C.Lambda (name,so,dest) -> does_not_occur ~subst context n nn so && does_not_occur ~subst ((Some (name,(C.Decl so)))::context) (n + 1) (nn + 1) dest | C.LetIn (name,so,ty,dest) -> does_not_occur ~subst context n nn so && does_not_occur ~subst context n nn ty && does_not_occur ~subst ((Some (name,(C.Def (so,ty))))::context) (n + 1) (nn + 1) dest | 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) | C.MutInd (_,_,exp_named_subst) | 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 && does_not_occur ~subst context n nn x) pl true | C.Fix (_,fl) -> let len = List.length fl in let n_plus_len = n + len in let nn_plus_len = nn + len in let 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 in let nn_plus_len = nn + len in let 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 (*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 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 ;; 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 = NCicUtils.lookup_subst n subst in c,ty with NCicUtils.Subst_not_found _ -> try let _,_,c,ty = NCicUtils.lookup_meta n metasenv in c,ty with NCicUtils.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 = NCicUtils.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 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))) *) and typecheck_obj0 = function obj -> assert false (* | C.Constant (_,Some te,ty,_,_) -> let _,ugraph = type_of ~logger ty ugraph in let ty_te,ugraph = type_of ~logger te ugraph in let b,ugraph = (CicReduction.are_convertible [] ty_te ty ugraph) in if not b then raise (TypeCheckerFailure (lazy ("the type of the body is not the one expected:\n" ^ CicPp.ppterm ty_te ^ "\nvs\n" ^ CicPp.ppterm ty))) else ugraph | C.Constant (_,None,ty,_,_) -> (* only to check that ty is well-typed *) let _,ugraph = type_of ~logger ty ugraph in ugraph | C.CurrentProof (_,conjs,te,ty,_,_) -> let _,ugraph = List.fold_left (fun (metasenv,ugraph) ((_,context,ty) as conj) -> let _,ugraph = type_of_aux' ~logger metasenv context ty ugraph in metasenv @ [conj],ugraph ) ([],ugraph) conjs in let _,ugraph = type_of_aux' ~logger conjs [] ty ugraph in let type_of_te,ugraph = type_of_aux' ~logger conjs [] te ugraph in let b,ugraph = CicReduction.are_convertible [] type_of_te ty ugraph in if not b then raise (TypeCheckerFailure (lazy (sprintf "the current proof is not well typed because the type %s of the body is not convertible to the declared type %s" (CicPp.ppterm type_of_te) (CicPp.ppterm ty)))) else ugraph | (C.InductiveDefinition _ as obj) -> check_mutual_inductive_defs ~logger uri obj ugraph | C.Fix (i,fl) -> let types,kl,ugraph1,len = List.fold_left (fun (types,kl,ugraph,len) (n,k,ty,_) -> let _,ugraph1 = type_of_aux ~logger context ty ugraph in (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, k::kl,ugraph1,len+1) ) ([],[],ugraph,0) fl in let ugraph2 = List.fold_left (fun ugraph (name,x,ty,bo) -> let ty_bo,ugraph1 = type_of_aux ~logger (types@context) bo ugraph in let b,ugraph2 = R.are_convertible ~subst ~metasenv (types@context) ty_bo (CicSubstitution.lift len ty) ugraph1 in if b then begin let (m, eaten, context') = eat_lambdas ~subst (types @ context) (x + 1) bo in (* let's control the 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"))) else ugraph2 end else raise (TypeCheckerFailure (lazy ("Fix: ill-typed bodies"))) ) ugraph1 fl in (*CSC: controlli mancanti solo su D{f,k,x,M} *) let (_,_,ty,_) = List.nth fl i in ty,ugraph2 | C.CoFix (i,fl) -> let types,ugraph1,len = List.fold_left (fun (l,ugraph,len) (n,ty,_) -> let _,ugraph1 = type_of_aux ~logger context ty ugraph in (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::l, ugraph1,len+1) ) ([],ugraph,0) fl in let ugraph2 = List.fold_left (fun ugraph (_,ty,bo) -> let ty_bo,ugraph1 = type_of_aux ~logger (types @ context) bo ugraph in let b,ugraph2 = R.are_convertible ~subst ~metasenv (types @ context) ty_bo (CicSubstitution.lift len ty) ugraph1 in if b then begin (* let's control that the returned type is coinductive *) match returns_a_coinductive ~subst context ty with None -> raise (TypeCheckerFailure (lazy "CoFix: does not return a coinductive type")) | Some uri -> (* let's control the guarded by constructors conditions C{f,M} *) if not (guarded_by_constructors ~subst (types @ context) 0 len false bo [] uri) then raise (TypeCheckerFailure (lazy "CoFix: not guarded by constructors")) else ugraph2 end else raise (TypeCheckerFailure (lazy "CoFix: ill-typed bodies")) ) ugraph1 fl in let (_,ty,_) = List.nth fl i in ty,ugraph2 *) 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) *) ;;