X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fcomponents%2Fng_kernel%2FnCicTypeChecker.ml;h=fd7e756ce9a0552f6ce0ccaa8b85aecc8f970ffc;hb=507636cbb473500f40d0969a30e7afc7ddd88f2d;hp=30bde93171e9a6e999a4d6ce87edc8dec5e4e0f2;hpb=a981dd18ae8ad9e9da79615fb80fe85dfe609f05;p=helm.git diff --git a/helm/software/components/ng_kernel/nCicTypeChecker.ml b/helm/software/components/ng_kernel/nCicTypeChecker.ml index 30bde9317..fd7e756ce 100644 --- a/helm/software/components/ng_kernel/nCicTypeChecker.ml +++ b/helm/software/components/ng_kernel/nCicTypeChecker.ml @@ -1,6 +1,1617 @@ +(* + ||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) +*) +;;