X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fcic_proof_checking%2FcicTypeChecker.ml;fp=helm%2Focaml%2Fcic_proof_checking%2FcicTypeChecker.ml;h=0000000000000000000000000000000000000000;hb=c7514aaa249a96c5fdd39b1123fbdb38d92f20b6;hp=48d8b2ea925450736c9be0d60288c351df233751;hpb=1c7fb836e2af4f2f3d18afd0396701f2094265ff;p=helm.git diff --git a/helm/ocaml/cic_proof_checking/cicTypeChecker.ml b/helm/ocaml/cic_proof_checking/cicTypeChecker.ml deleted file mode 100644 index 48d8b2ea9..000000000 --- a/helm/ocaml/cic_proof_checking/cicTypeChecker.ml +++ /dev/null @@ -1,1785 +0,0 @@ -(* Copyright (C) 2000, HELM Team. - * - * This file is part of HELM, an Hypertextual, Electronic - * Library of Mathematics, developed at the Computer Science - * Department, University of Bologna, Italy. - * - * HELM is free software; you can redistribute it and/or - * modify it under the terms of the GNU General Public License - * as published by the Free Software Foundation; either version 2 - * of the License, or (at your option) any later version. - * - * HELM is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * You should have received a copy of the GNU General Public License - * along with HELM; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place - Suite 330, Boston, - * MA 02111-1307, USA. - * - * For details, see the HELM World-Wide-Web page, - * http://cs.unibo.it/helm/. - *) - -type type_checker_exn = - Impossible of int - | NotWellTyped of string - | WrongUriToConstant of string - | WrongUriToVariable of string - | WrongUriToMutualInductiveDefinitions of string - | ListTooShort - | NotPositiveOccurrences of string - | NotWellFormedTypeOfInductiveConstructor of string - | WrongRequiredArgument of string - | RelToHiddenHypothesis - | MetasenvInconsistency;; - -(* This is the only exception that will be raised *) -exception TypeCheckerFailure of type_checker_exn;; - -let fdebug = ref 0;; -let debug t context = - let rec debug_aux t i = - let module C = Cic in - let module U = UriManager in - CicPp.ppobj (C.Variable ("DEBUG", None, t, [])) ^ "\n" ^ i - in - if !fdebug = 0 then - raise - (TypeCheckerFailure - (NotWellTyped ("\n" ^ List.fold_right debug_aux (t::context) ""))) - (*print_endline ("\n" ^ List.fold_right debug_aux (t::context) "") ; flush stdout*) -;; - -let rec split l n = - match (l,n) with - (l,0) -> ([], l) - | (he::tl, n) -> let (l1,l2) = split tl (n-1) in (he::l1,l2) - | (_,_) -> raise (TypeCheckerFailure ListTooShort) -;; - -let debrujin_constructor uri number_of_types = - let rec aux k = - let module C = Cic in - function - C.Rel n as t when n <= k -> t - | C.Rel _ -> - raise (TypeCheckerFailure (NotWellTyped ("Debrujin: open term found"))) - | 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 _ -> assert false - | 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,t) -> C.LetIn (n, aux k s, 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 - (NotWellTyped - ("Debrujin: a 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 - aux 0 -;; - -exception CicEnvironmentError;; - -let rec type_of_constant uri = - let module C = Cic in - let module R = CicReduction in - let module U = UriManager in - let cobj = - match CicEnvironment.is_type_checked ~trust:true uri with - CicEnvironment.CheckedObj cobj -> cobj - | CicEnvironment.UncheckedObj uobj -> - Logger.log (`Start_type_checking uri) ; - (* let's typecheck the uncooked obj *) - (match uobj with - C.Constant (_,Some te,ty,_) -> - let _ = type_of ty in - if not (R.are_convertible [] (type_of te) ty) then - raise - (TypeCheckerFailure - (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))) - | C.Constant (_,None,ty,_) -> - (* only to check that ty is well-typed *) - let _ = type_of ty in () - | C.CurrentProof (_,conjs,te,ty,_) -> - let _ = - List.fold_left - (fun metasenv ((_,context,ty) as conj) -> - ignore (type_of_aux' metasenv context ty) ; - metasenv @ [conj] - ) [] conjs - in - let _ = type_of_aux' conjs [] ty in - if not (R.are_convertible [] (type_of_aux' conjs [] te) ty) - then - raise - (TypeCheckerFailure - (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))) - | _ -> - raise (TypeCheckerFailure (WrongUriToConstant (U.string_of_uri uri))) - ) ; - CicEnvironment.set_type_checking_info uri ; - Logger.log (`Type_checking_completed uri) ; - match CicEnvironment.is_type_checked ~trust:false uri with - CicEnvironment.CheckedObj cobj -> cobj - | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError - in - match cobj with - C.Constant (_,_,ty,_) -> ty - | C.CurrentProof (_,_,_,ty,_) -> ty - | _ -> raise (TypeCheckerFailure (WrongUriToConstant (U.string_of_uri uri))) - -and type_of_variable uri = - let module C = Cic in - let module R = CicReduction in - let module U = UriManager in - (* 0 because a variable is never cooked => no partial cooking at one level *) - match CicEnvironment.is_type_checked ~trust:true uri with - CicEnvironment.CheckedObj (C.Variable (_,_,ty,_)) -> ty - | CicEnvironment.UncheckedObj (C.Variable (_,bo,ty,_)) -> - Logger.log (`Start_type_checking uri) ; - (* only to check that ty is well-typed *) - let _ = type_of ty in - (match bo with - None -> () - | Some bo -> - if not (R.are_convertible [] (type_of bo) ty) then - raise - (TypeCheckerFailure - (NotWellTyped ("Variable " ^ (U.string_of_uri uri)))) - ) ; - CicEnvironment.set_type_checking_info uri ; - Logger.log (`Type_checking_completed uri) ; - ty - | _ -> - raise - (TypeCheckerFailure (WrongUriToVariable (UriManager.string_of_uri uri))) - -and does_not_occur context n nn te = - let module C = Cic in - (*CSC: whd sembra essere superflua perche' un caso in cui l'occorrenza *) - (*CSC: venga mangiata durante la whd sembra presentare problemi di *) - (*CSC: universi *) - match CicReduction.whd context te with - C.Rel m when m > n && m <= nn -> false - | C.Rel _ - | C.Meta _ - | C.Sort _ - | C.Implicit -> true - | C.Cast (te,ty) -> - does_not_occur context n nn te && does_not_occur context n nn ty - | C.Prod (name,so,dest) -> - does_not_occur context n nn so && - does_not_occur((Some (name,(C.Decl so)))::context) (n + 1) (nn + 1) dest - | C.Lambda (name,so,dest) -> - does_not_occur context n nn so && - does_not_occur((Some (name,(C.Decl so)))::context) (n + 1) (nn + 1) dest - | C.LetIn (name,so,dest) -> - does_not_occur context n nn so && - does_not_occur ((Some (name,(C.Def so)))::context) (n + 1) (nn + 1) dest - | C.Appl l -> - List.fold_right (fun x i -> i && does_not_occur 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 context n nn x) - exp_named_subst true - | C.MutCase (_,_,out,te,pl) -> - does_not_occur context n nn out && does_not_occur context n nn te && - List.fold_right (fun x i -> i && does_not_occur 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.map (fun (n,_,ty,_) -> Some (C.Name n,(Cic.Decl ty))) fl - in - List.fold_right - (fun (_,_,ty,bo) i -> - i && does_not_occur context n nn ty && - does_not_occur (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.map (fun (n,ty,_) -> Some (C.Name n,(Cic.Decl ty))) fl - in - List.fold_right - (fun (_,ty,bo) i -> - i && does_not_occur context n nn ty && - does_not_occur (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 (UriManager.uri_of_string "cic:/Coq/Init/Datatypes/nat.ind",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.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 - (NotWellFormedTypeOfInductiveConstructor - ("Guess where the error is ;-)"))) - -(* 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 (TypeCheckerFailure (Impossible 1)) - -and strictly_positive context n nn te = - let module C = Cic in - let module U = UriManager in - match CicReduction.whd context te with - 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) = - match CicEnvironment.get_obj uri with - C.InductiveDefinition (tl,_,paramsno) -> - let (name,_,ity,cl) = List.nth tl i in - (List.length tl = 1, paramsno, ity, cl, name) - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions(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 -> does_not_occur context n nn t - -(*CSC l'indice x dei tipi induttivi e' t.c. 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 - (WrongRequiredArgument (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 - (WrongRequiredArgument (UriManager.string_of_uri uri))) - | C.Rel m when m = i -> - if indparamsno = 0 then - true - else - raise - (TypeCheckerFailure - (WrongRequiredArgument (UriManager.string_of_uri uri))) - | C.Prod (C.Anonymous,source,dest) -> - strictly_positive context n nn source && - 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 - (NotWellFormedTypeOfInductiveConstructor (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 uri (itl,_,indparamsno) = - let module U = UriManager in - (* let's check if the arity of the inductive types are well *) - (* formed *) - List.iter (fun (_,_,x,_) -> let _ = type_of x in ()) itl ; - - (* 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 _ = - List.fold_right - (fun (_,_,_,cl) i -> - List.iter - (fun (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 _ = type_of augmented_term in - (* let's check also the positivity conditions *) - if - not - (are_all_occurrences_positive tys uri indparamsno i 0 len - debrujinedte) - then - raise - (TypeCheckerFailure - (NotPositiveOccurrences (U.string_of_uri uri))) - ) cl ; - (i + 1) - ) itl 1 - in - () - -(* Main function to checks the correctness of a mutual *) -(* inductive block definition. *) -and check_mutual_inductive_defs uri = - function - Cic.InductiveDefinition (itl, params, indparamsno) -> - typecheck_mutual_inductive_defs uri (itl,params,indparamsno) - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions (UriManager.string_of_uri uri))) - -and type_of_mutual_inductive_defs uri i = - let module C = Cic in - let module R = CicReduction in - let module U = UriManager in - let cobj = - match CicEnvironment.is_type_checked ~trust:true uri with - CicEnvironment.CheckedObj cobj -> cobj - | CicEnvironment.UncheckedObj uobj -> - Logger.log (`Start_type_checking uri) ; - check_mutual_inductive_defs uri uobj ; - CicEnvironment.set_type_checking_info uri ; - Logger.log (`Type_checking_completed uri) ; - (match CicEnvironment.is_type_checked ~trust:false uri with - CicEnvironment.CheckedObj cobj -> cobj - | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError - ) - in - match cobj with - C.InductiveDefinition (dl,_,_) -> - let (_,_,arity,_) = List.nth dl i in - arity - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))) - -and type_of_mutual_inductive_constr uri i j = - let module C = Cic in - let module R = CicReduction in - let module U = UriManager in - let cobj = - match CicEnvironment.is_type_checked ~trust:true uri with - CicEnvironment.CheckedObj cobj -> cobj - | CicEnvironment.UncheckedObj uobj -> - Logger.log (`Start_type_checking uri) ; - check_mutual_inductive_defs uri uobj ; - CicEnvironment.set_type_checking_info uri ; - Logger.log (`Type_checking_completed uri) ; - (match CicEnvironment.is_type_checked ~trust:false uri with - CicEnvironment.CheckedObj cobj -> cobj - | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError - ) - in - match cobj with - C.InductiveDefinition (dl,_,_) -> - let (_,_,_,cl) = List.nth dl i in - let (_,ty) = List.nth cl (j-1) in - ty - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions (U.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 (TypeCheckerFailure (Impossible 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 (TypeCheckerFailure (Impossible 4)) (* due to type-checking *) - | C.Appl _ -> [] - | C.Const _ -> raise (TypeCheckerFailure (Impossible 5)) - | C.MutInd _ - | C.MutConstruct _ - | C.MutCase _ - | C.Fix _ - | C.CoFix _ -> - raise (TypeCheckerFailure (Impossible 6)) (* due to type-checking *) - -and get_new_safes 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 context c, R.whd 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 ((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) - | (_,_,_) -> - (* 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 (TypeCheckerFailure (Impossible 7)) - -and split_prods context n te = - let module C = Cic in - let module R = CicReduction in - match (n, R.whd context te) with - (0, _) -> context,te - | (n, C.Prod (name,so,ta)) when n > 0 -> - split_prods ((Some (name,(C.Decl so)))::context) (n - 1) ta - | (_, _) -> raise (TypeCheckerFailure (Impossible 8)) - -and eat_lambdas context n te = - let module C = Cic in - let module R = CicReduction in - match (n, R.whd context te) with - (0, _) -> (te, 0, context) - | (n, C.Lambda (name,so,ta)) when n > 0 -> - let (te, k, context') = - eat_lambdas ((Some (name,(C.Decl so)))::context) (n - 1) ta - in - (te, k + 1, context') - | (_, _) -> raise (TypeCheckerFailure (Impossible 9)) - -(*CSC: Tutto quello che segue e' l'intuzione di luca ;-) *) -and check_is_really_smaller_arg 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 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 n nn kl x safes te && - check_is_really_smaller_arg n nn kl x safes ty*) -(* | C.Prod (_,so,ta) -> - check_is_really_smaller_arg n nn kl x safes so && - check_is_really_smaller_arg (n+1) (nn+1) kl (x+1) - (List.map (fun x -> x + 1) safes) ta*) - | C.Prod _ -> raise (TypeCheckerFailure (Impossible 10)) - | C.Lambda (name,so,ta) -> - check_is_really_smaller_arg context n nn kl x safes so && - check_is_really_smaller_arg ((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,ta) -> - check_is_really_smaller_arg context n nn kl x safes so && - check_is_really_smaller_arg ((Some (name,(C.Def so)))::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 context n nn kl x safes he - | C.Appl [] -> raise (TypeCheckerFailure (Impossible 11)) - | C.Const _ - | C.MutInd _ -> raise (TypeCheckerFailure (Impossible 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 (tys,len,isinductive,paramsno,cl) = - match CicEnvironment.get_obj uri 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 tys paramsno ty))) cl - in - (tys,List.length tl,isinductive,paramsno,cl') - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))) - in - if not isinductive then - List.fold_right - (fun p i -> - i && check_is_really_smaller_arg context n nn kl x safes p) - pl true - else - List.fold_right - (fun (p,(_,c)) i -> - let rl' = - let debrujinedte = debrujin_constructor uri len c in - recursive_args tys 0 len debrujinedte - in - let (e,safes',n',nn',x',context') = - get_new_safes context p c rl' safes n nn x - in - i && - check_is_really_smaller_arg context' n' nn' kl x' safes' e - ) (List.combine pl cl) true - | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x -> - let (tys,len,isinductive,paramsno,cl) = - match CicEnvironment.get_obj uri 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 tys paramsno ty))) cl - in - (tys,List.length tl,isinductive,paramsno,cl') - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))) - in - if not isinductive then - List.fold_right - (fun p i -> - i && check_is_really_smaller_arg context n nn kl x safes p) - pl true - else - (*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 tys 0 len debrujinedte - in - let (e, safes',n',nn',x',context') = - get_new_safes context p c rl' safes n nn x - in - i && - check_is_really_smaller_arg context' n' nn' kl x' safes' e - ) (List.combine pl cl) true - | _ -> - List.fold_right - (fun p i -> - i && check_is_really_smaller_arg 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.map (fun (n,_,ty,_) -> Some (C.Name n,(C.Decl ty))) fl - and safes' = List.map (fun x -> x + len) safes in - List.fold_right - (fun (_,_,ty,bo) i -> - i && - check_is_really_smaller_arg (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.map (fun (n,ty,_) -> Some (C.Name n,(C.Decl ty))) fl - and safes' = List.map (fun x -> x + len) safes in - List.fold_right - (fun (_,ty,bo) i -> - i && - check_is_really_smaller_arg (tys@context) n_plus_len nn_plus_len kl - x_plus_len safes' bo - ) fl true - -and guarded_by_destructors 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 n -> - (match List.nth context (n-1) with - Some (_,C.Decl _) -> true - | Some (_,C.Def bo) -> guarded_by_destructors context n nn kl x safes bo - | None -> raise (TypeCheckerFailure RelToHiddenHypothesis) - ) - | C.Meta _ - | C.Sort _ - | C.Implicit -> true - | C.Cast (te,ty) -> - guarded_by_destructors context n nn kl x safes te && - guarded_by_destructors context n nn kl x safes ty - | C.Prod (name,so,ta) -> - guarded_by_destructors context n nn kl x safes so && - guarded_by_destructors ((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 context n nn kl x safes so && - guarded_by_destructors ((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,ta) -> - guarded_by_destructors context n nn kl x safes so && - guarded_by_destructors ((Some (name,(C.Def so)))::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 context n nn kl x safes param - ) tl true && - check_is_really_smaller_arg context n nn kl x safes (List.nth tl k) - | C.Appl tl -> - List.fold_right - (fun t i -> i && guarded_by_destructors 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 context n nn kl x safes t) - exp_named_subst true - | C.MutCase (uri,i,outtype,term,pl) -> - (match term with - C.Rel m when List.mem m safes || m = x -> - let (tys,len,isinductive,paramsno,cl) = - match CicEnvironment.get_obj uri 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 tys paramsno ty))) cl - in - (tys,List.length tl,isinductive,paramsno,cl') - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))) - in - if not isinductive then - guarded_by_destructors context n nn kl x safes outtype && - guarded_by_destructors 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 context n nn kl x safes p) - pl true - else - guarded_by_destructors context n nn kl x safes outtype && - (*CSC: manca ??? il controllo sul tipo di term? *) - List.fold_right - (fun (p,(_,c)) i -> - let rl' = - let debrujinedte = debrujin_constructor uri len c in - recursive_args tys 0 len debrujinedte - in - let (e,safes',n',nn',x',context') = - get_new_safes context p c rl' safes n nn x - in - i && - guarded_by_destructors context' n' nn' kl x' safes' e - ) (List.combine pl cl) true - | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x -> - let (tys,len,isinductive,paramsno,cl) = - match CicEnvironment.get_obj uri 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 tys paramsno ty))) cl - in - (tys,List.length tl,isinductive,paramsno,cl') - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))) - in - if not isinductive then - guarded_by_destructors context n nn kl x safes outtype && - guarded_by_destructors 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 context n nn kl x safes p) - pl true - else - guarded_by_destructors 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 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 tys 0 len debrujinedte - in - let (e, safes',n',nn',x',context') = - get_new_safes context p c rl' safes n nn x - in - i && - guarded_by_destructors context' n' nn' kl x' safes' e - ) (List.combine pl cl) true - | _ -> - guarded_by_destructors context n nn kl x safes outtype && - guarded_by_destructors 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 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.map (fun (n,_,ty,_) -> Some (C.Name n,(C.Decl ty))) fl - and safes' = List.map (fun x -> x + len) safes in - List.fold_right - (fun (_,_,ty,bo) i -> - i && guarded_by_destructors context n nn kl x_plus_len safes' ty && - guarded_by_destructors (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.map (fun (n,ty,_) -> Some (C.Name n,(C.Decl ty))) fl - and safes' = List.map (fun x -> x + len) safes in - List.fold_right - (fun (_,ty,bo) i -> - i && - guarded_by_destructors context n nn kl x_plus_len safes' ty && - guarded_by_destructors (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. *) -(*CSC: coInductiveTypeURI non cambia mai di ricorsione in ricorsione *) -and guarded_by_constructors 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 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 (TypeCheckerFailure (Impossible 17)) - | C.Lambda (name,so,de) -> - does_not_occur context n nn so && - guarded_by_constructors ((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 context n nn x) tl true - | C.Appl ((C.MutConstruct (uri,i,j,exp_named_subst))::tl) -> - let consty = - match CicEnvironment.get_cooked_obj ~trust:false uri 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 - (WrongUriToMutualInductiveDefinitions - (UriManager.string_of_uri uri))) - in - let rec analyse_branch context ty te = - match CicReduction.whd context ty with - C.Meta _ -> raise (TypeCheckerFailure (Impossible 34)) - | C.Rel _ - | C.Var _ - | C.Sort _ -> - does_not_occur context n nn te - | C.Implicit - | C.Cast _ -> - raise (TypeCheckerFailure (Impossible 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 (TypeCheckerFailure (Impossible 25))(* due to type-checking *) - | C.Appl ((C.MutInd (uri,_,_))::_) as ty - when uri == coInductiveTypeURI -> - guarded_by_constructors context n nn true te [] coInductiveTypeURI - | C.Appl ((C.MutInd (uri,_,_))::_) as ty -> - guarded_by_constructors context n nn true te tl coInductiveTypeURI - | C.Appl _ -> - does_not_occur context n nn te - | C.Const _ -> raise (TypeCheckerFailure (Impossible 26)) - | C.MutInd (uri,_,_) when uri == coInductiveTypeURI -> - guarded_by_constructors context n nn true te [] coInductiveTypeURI - | C.MutInd _ -> - does_not_occur context n nn te - | C.MutConstruct _ -> raise (TypeCheckerFailure (Impossible 27)) - (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *) - (*CSC: in head position. *) - | C.MutCase _ - | C.Fix _ - | C.CoFix _ -> - raise (TypeCheckerFailure (Impossible 28))(* due to type-checking *) - in - let rec analyse_instantiated_type context ty l = - match CicReduction.whd context ty with - C.Rel _ - | C.Var _ - | C.Meta _ - | C.Sort _ - | C.Implicit - | C.Cast _ -> - raise (TypeCheckerFailure (Impossible 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 (TypeCheckerFailure (Impossible 30))(* due to type-checking *) - | C.Appl _ -> - List.fold_left - (fun i x -> i && does_not_occur context n nn x) true l - | C.Const _ -> raise (TypeCheckerFailure (Impossible 31)) - | C.MutInd _ -> - List.fold_left - (fun i x -> i && does_not_occur context n nn x) true l - | C.MutConstruct _ -> raise (TypeCheckerFailure (Impossible 32)) - (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *) - (*CSC: in head position. *) - | C.MutCase _ - | C.Fix _ - | C.CoFix _ -> - raise (TypeCheckerFailure (Impossible 33))(* due to type-checking *) - in - let rec instantiate_type args consty = - function - [] -> true - | tlhe::tltl as l -> - let consty' = CicReduction.whd 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 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 (TypeCheckerFailure (Impossible 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 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.map (fun (n,ty,_) -> Some (C.Name n,(C.Decl ty))) fl in - List.fold_right - (fun (_,ty,bo) i -> - i && does_not_occur context n nn ty && - guarded_by_constructors (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 context n nn x) true tl && - does_not_occur context n nn out && - does_not_occur context n nn te && - List.fold_right - (fun x i -> - i && - guarded_by_constructors context n nn h x args coInductiveTypeURI - ) pl true - | C.Appl l -> - List.fold_right (fun x i -> i && does_not_occur 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 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 context n nn x) exp_named_subst true - | C.MutCase (_,_,out,te,pl) -> - does_not_occur context n nn out && - does_not_occur context n nn te && - List.fold_right - (fun x i -> - i && - guarded_by_constructors 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.map (fun (n,_,ty,_) -> Some (C.Name n,(C.Decl ty))) fl in - List.fold_right - (fun (_,_,ty,bo) i -> - i && does_not_occur context n nn ty && - does_not_occur (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.map (fun (n,ty,_) -> Some (C.Name n,(C.Decl ty))) fl in - List.fold_right - (fun (_,ty,bo) i -> - i && does_not_occur context n nn ty && - guarded_by_constructors (tys@context) n_plus_len nn_plus_len h bo - args coInductiveTypeURI - ) fl true - -and check_allowed_sort_elimination context uri i need_dummy ind arity1 arity2 = - let module C = Cic in - let module U = UriManager in - match (CicReduction.whd context arity1, CicReduction.whd context arity2) with - (C.Prod (_,so1,de1), C.Prod (_,so2,de2)) - when CicReduction.are_convertible context so1 so2 -> - check_allowed_sort_elimination context uri i need_dummy - (C.Appl [CicSubstitution.lift 1 ind ; C.Rel 1]) de1 de2 - | (C.Sort C.Prop, C.Sort C.Prop) when need_dummy -> true - | (C.Sort C.Prop, C.Sort C.Set) - | (C.Sort C.Prop, C.Sort C.Type) when need_dummy -> -(*CSC: WRONG. MISSING CONDITIONS ON THE ARGUMENTS OF THE CONSTRUTOR *) - (match CicEnvironment.get_obj uri with - C.InductiveDefinition (itl,_,_) -> - let (_,_,_,cl) = List.nth itl i in - (* is a singleton definition or the empty proposition? *) - List.length cl = 1 || List.length cl = 0 - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))) - ) - | (C.Sort C.Set, C.Sort C.Prop) when need_dummy -> true - | (C.Sort C.Set, C.Sort C.Set) when need_dummy -> true - | (C.Sort C.Set, C.Sort C.Type) when need_dummy -> - (match CicEnvironment.get_obj uri with - C.InductiveDefinition (itl,_,paramsno) -> - let tys = - List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl - in - let (_,_,_,cl) = List.nth itl i in - List.fold_right - (fun (_,x) i -> i && is_small tys paramsno x) cl true - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))) - ) - | (C.Sort C.Type, C.Sort _) when need_dummy -> true - | (C.Sort C.Prop, C.Prod (name,so,ta)) when not need_dummy -> - let res = CicReduction.are_convertible context so ind - in - res && - (match CicReduction.whd ((Some (name,(C.Decl so)))::context) ta with - C.Sort C.Prop -> true - | C.Sort C.Set -> - (match CicEnvironment.get_obj uri with - C.InductiveDefinition (itl,_,_) -> - let (_,_,_,cl) = List.nth itl i in - (* is a singleton definition? *) - List.length cl = 1 - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))) - ) - | _ -> false - ) - | (C.Sort C.Set, C.Prod (name,so,ta)) when not need_dummy -> - let res = CicReduction.are_convertible context so ind - in - res && - (match CicReduction.whd ((Some (name,(C.Decl so)))::context) ta with - C.Sort C.Prop - | C.Sort C.Set -> true - | C.Sort C.Type -> - (match CicEnvironment.get_obj uri with - C.InductiveDefinition (itl,_,paramsno) -> - let (_,_,_,cl) = List.nth itl i in - let tys = - List.map - (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl - in - List.fold_right - (fun (_,x) i -> i && is_small tys paramsno x) cl true - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))) - ) - | _ -> raise (TypeCheckerFailure (Impossible 19)) - ) - | (C.Sort C.Type, C.Prod (_,so,_)) when not need_dummy -> - CicReduction.are_convertible context so ind - | (_,_) -> false - -and type_of_branch context argsno need_dummy outtype term constype = - let module C = Cic in - let module R = CicReduction in - match R.whd 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 (C.Anonymous,so,type_of_branch - ((Some (name,(C.Decl so)))::context) argsno need_dummy - (CicSubstitution.lift 1 outtype) term' de) - | _ -> raise (TypeCheckerFailure (Impossible 20)) - -(* 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 metasenv context canonical_context l = - let module C = Cic in - let module R = CicReduction in - let module S = CicSubstitution in - let lifted_canonical_context = - let rec aux i = - function - [] -> [] - | (Some (n,C.Decl t))::tl -> - (Some (n,C.Decl (S.lift_meta l (S.lift i t))))::(aux (i+1) tl) - | (Some (n,C.Def t))::tl -> - (Some (n,C.Def (S.lift_meta l (S.lift i t))))::(aux (i+1) tl) - | None::tl -> None::(aux (i+1) tl) - in - aux 1 canonical_context - in - List.iter2 - (fun t ct -> - let res = - match (t,ct) with - _,None -> true - | Some t,Some (_,C.Def ct) -> - R.are_convertible context t ct - | Some t,Some (_,C.Decl ct) -> - R.are_convertible context (type_of_aux' metasenv context t) ct - | _, _ -> false - in - if not res then raise (TypeCheckerFailure MetasenvInconsistency) - ) l lifted_canonical_context - -(* type_of_aux' is just another name (with a different scope) for type_of_aux *) -and type_of_aux' metasenv context t = - let rec type_of_aux context = - let module C = Cic in - let module R = CicReduction in - let module S = CicSubstitution in - let module U = UriManager in - function - C.Rel n -> - (try - match List.nth context (n - 1) with - Some (_,C.Decl t) -> S.lift n t - | Some (_,C.Def bo) -> type_of_aux context (S.lift n bo) - | None -> raise (TypeCheckerFailure RelToHiddenHypothesis) - with - _ -> raise (TypeCheckerFailure (NotWellTyped "Not a close term")) - ) - | C.Var (uri,exp_named_subst) -> - incr fdebug ; - check_exp_named_subst context exp_named_subst ; - let ty = - CicSubstitution.subst_vars exp_named_subst (type_of_variable uri) - in - decr fdebug ; - ty - | C.Meta (n,l) -> - let (_,canonical_context,ty) = - List.find (function (m,_,_) -> n = m) metasenv - in - check_metasenv_consistency metasenv context canonical_context l; - CicSubstitution.lift_meta l ty - | C.Sort s -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *) - | C.Implicit -> raise (TypeCheckerFailure (Impossible 21)) - | C.Cast (te,ty) -> - let _ = type_of_aux context ty in - if R.are_convertible context (type_of_aux context te) ty then ty - else raise (TypeCheckerFailure (NotWellTyped "Cast")) - | C.Prod (name,s,t) -> - let sort1 = type_of_aux context s - and sort2 = type_of_aux ((Some (name,(C.Decl s)))::context) t in - sort_of_prod context (name,s) (sort1,sort2) - | C.Lambda (n,s,t) -> - let sort1 = type_of_aux context s - and type2 = type_of_aux ((Some (n,(C.Decl s)))::context) t in - let sort2 = type_of_aux ((Some (n,(C.Decl s)))::context) type2 in - (* only to check if the product is well-typed *) - let _ = sort_of_prod context (n,s) (sort1,sort2) in - C.Prod (n,s,type2) - | C.LetIn (n,s,t) -> - (* only to check if s is well-typed *) - let _ = type_of_aux context s in - (* The type of a LetIn is a LetIn. Extremely slow since the computed - LetIn is later reduced and maybe also re-checked. - (C.LetIn (n,s, type_of_aux ((Some (n,(C.Def s)))::context) t)) - *) - (* The type of the LetIn is reduced. Much faster than the previous - solution. Moreover the inferred type is probably very different - from the expected one. - (CicReduction.whd context - (C.LetIn (n,s, type_of_aux ((Some (n,(C.Def s)))::context) t))) - *) - (* One-step LetIn reduction. Even faster than the previous solution. - Moreover the inferred type is closer to the expected one. *) - (CicSubstitution.subst s - (type_of_aux ((Some (n,(C.Def s)))::context) t)) - | C.Appl (he::tl) when List.length tl > 0 -> - let hetype = type_of_aux context he - and tlbody_and_type = List.map (fun x -> (x, type_of_aux context x)) tl in - eat_prods context hetype tlbody_and_type - | C.Appl _ -> raise (TypeCheckerFailure (NotWellTyped "Appl: no arguments")) - | C.Const (uri,exp_named_subst) -> - incr fdebug ; - check_exp_named_subst context exp_named_subst ; - let cty = - CicSubstitution.subst_vars exp_named_subst (type_of_constant uri) - in - decr fdebug ; - cty - | C.MutInd (uri,i,exp_named_subst) -> - incr fdebug ; - check_exp_named_subst context exp_named_subst ; - let cty = - CicSubstitution.subst_vars exp_named_subst - (type_of_mutual_inductive_defs uri i) - in - decr fdebug ; - cty - | C.MutConstruct (uri,i,j,exp_named_subst) -> - check_exp_named_subst context exp_named_subst ; - let cty = - CicSubstitution.subst_vars exp_named_subst - (type_of_mutual_inductive_constr uri i j) - in - cty - | C.MutCase (uri,i,outtype,term,pl) -> - let outsort = type_of_aux context outtype in - let (need_dummy, k) = - let rec guess_args context t = - match CicReduction.whd context t with - C.Sort _ -> (true, 0) - | C.Prod (name, s, t) -> - let (b, n) = guess_args ((Some (name,(C.Decl s)))::context) t in - if n = 0 then - (* last prod before sort *) - match CicReduction.whd context s with -(*CSC: for _ see comment below about the missing named_exp_subst ?????????? *) - C.MutInd (uri',i',_) when U.eq uri' uri && i' = i -> - (false, 1) -(*CSC: for _ see comment below about the missing named_exp_subst ?????????? *) - | C.Appl ((C.MutInd (uri',i',_)) :: _) - when U.eq uri' uri && i' = i -> (false, 1) - | _ -> (true, 1) - else - (b, n + 1) - | _ -> - raise - (TypeCheckerFailure (NotWellTyped "MutCase: outtype ill-formed")) - in - (*CSC whd non serve dopo type_of_aux ? *) - let (b, k) = guess_args context outsort in - if not b then (b, k - 1) else (b, k) - in - let (parameters, arguments, exp_named_subst) = - match R.whd context (type_of_aux context term) with - (*CSC manca il caso dei CAST *) -(*CSC: ma servono i parametri (uri,i)? Se si', perche' non serve anche il *) -(*CSC: parametro exp_named_subst? Se no, perche' non li togliamo? *) -(*CSC: Hint: nella DTD servono per gli stylesheet. *) - C.MutInd (uri',i',exp_named_subst) as typ -> - if U.eq uri uri' && i = i' then ([],[],exp_named_subst) - else raise (TypeCheckerFailure - (NotWellTyped ("MutCase: the term is of type " ^ - CicPp.ppterm typ ^ - " instead of type " ^ (U.string_of_uri uri) ^ "#1/" ^ - string_of_int i ^ "{_}"))) - | C.Appl ((C.MutInd (uri',i',exp_named_subst) as typ):: tl) -> - if U.eq uri uri' && i = i' then - let params,args = - split tl (List.length tl - k) - in params,args,exp_named_subst - else raise (TypeCheckerFailure (NotWellTyped - ("MutCase: the term is of type " ^ - CicPp.ppterm typ ^ - " instead of type " ^ (U.string_of_uri uri) ^ "#1/" ^ - string_of_int i ^ "{_}"))) - | _ -> raise (TypeCheckerFailure - (NotWellTyped "MutCase: the term is not an inductive one")) - in - (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *) - let sort_of_ind_type = - if parameters = [] then - C.MutInd (uri,i,exp_named_subst) - else - C.Appl ((C.MutInd (uri,i,exp_named_subst))::parameters) - in - if not (check_allowed_sort_elimination context uri i need_dummy - sort_of_ind_type (type_of_aux context sort_of_ind_type) outsort) - then - raise - (TypeCheckerFailure - (NotWellTyped "MutCase: not allowed sort elimination")) ; - - (* let's check if the type of branches are right *) - let parsno = - match CicEnvironment.get_cooked_obj ~trust:false uri with - C.InductiveDefinition (_,_,parsno) -> parsno - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))) - in - let (_,branches_ok) = - List.fold_left - (fun (j,b) p -> - let cons = - if parameters = [] then - (C.MutConstruct (uri,i,j,exp_named_subst)) - else - (C.Appl (C.MutConstruct (uri,i,j,exp_named_subst)::parameters)) - in -(* - (j + 1, b && -*) - (j + 1, -let res = b && - R.are_convertible context (type_of_aux context p) - (type_of_branch context parsno need_dummy outtype cons - (type_of_aux context cons)) -in if not res then prerr_endline ("#### " ^ CicPp.ppterm (type_of_aux context p) ^ " <==> " ^ CicPp.ppterm (type_of_branch context parsno need_dummy outtype cons (type_of_aux context cons))) ; res - ) - ) (1,true) pl - in - if not branches_ok then - raise - (TypeCheckerFailure - (NotWellTyped "MutCase: wrong type of a branch")) ; - - if not need_dummy then - C.Appl ((outtype::arguments)@[term]) - else if arguments = [] then - outtype - else - C.Appl (outtype::arguments) - | C.Fix (i,fl) -> - let types_times_kl = - List.rev - (List.map - (fun (n,k,ty,_) -> - let _ = type_of_aux context ty in - (Some (C.Name n,(C.Decl ty)),k)) fl) - in - let (types,kl) = List.split types_times_kl in - let len = List.length types in - List.iter - (fun (name,x,ty,bo) -> - if - (R.are_convertible (types@context) (type_of_aux (types@context) bo) - (CicSubstitution.lift len ty)) - then - begin - let (m, eaten, context') = - eat_lambdas (types @ context) (x + 1) bo - in - (*let's control the guarded by destructors conditions D{f,k,x,M}*) - if - not - (guarded_by_destructors context' eaten (len + eaten) kl 1 [] m) - then - raise - (TypeCheckerFailure - (NotWellTyped "Fix: not guarded by destructors")) - end - else - raise (TypeCheckerFailure (NotWellTyped "Fix: ill-typed bodies")) - ) fl ; - - (*CSC: controlli mancanti solo su D{f,k,x,M} *) - let (_,_,ty,_) = List.nth fl i in - ty - | C.CoFix (i,fl) -> - let types = - List.rev - (List.map - (fun (n,ty,_) -> - let _ = type_of_aux context ty in Some (C.Name n,(C.Decl ty))) fl) - in - let len = List.length types in - List.iter - (fun (_,ty,bo) -> - if - (R.are_convertible (types @ context) - (type_of_aux (types @ context) bo) (CicSubstitution.lift len ty)) - then - begin - (* let's control that the returned type is coinductive *) - match returns_a_coinductive context ty with - None -> - raise - (TypeCheckerFailure - (NotWellTyped "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 (types @ context) 0 len false bo - [] uri) - then - raise - (TypeCheckerFailure - (NotWellTyped "CoFix: not guarded by constructors")) - end - else - raise - (TypeCheckerFailure - (NotWellTyped "CoFix: ill-typed bodies")) - ) fl ; - - let (_,ty,_) = List.nth fl i in - ty - - and check_exp_named_subst context = - let rec check_exp_named_subst_aux substs = - function - [] -> () - | ((uri,t) as subst)::tl -> - let typeofvar = - CicSubstitution.subst_vars substs (type_of_variable uri) in - (match CicEnvironment.get_cooked_obj ~trust:false uri with - Cic.Variable (_,Some bo,_,_) -> - raise - (TypeCheckerFailure - (NotWellTyped - "A variable with a body can not be explicit substituted")) - | Cic.Variable (_,None,_,_) -> () - | _ -> - raise - (TypeCheckerFailure - (WrongUriToVariable (UriManager.string_of_uri uri))) - ) ; - let typeoft = type_of_aux context t in - if CicReduction.are_convertible context typeoft typeofvar then - check_exp_named_subst_aux (substs@[subst]) tl - else - begin - CicReduction.fdebug := 0 ; - ignore (CicReduction.are_convertible context typeoft typeofvar) ; - fdebug := 0 ; - debug typeoft [typeofvar] ; - raise - (TypeCheckerFailure - (NotWellTyped "Wrong Explicit Named Substitution")) - end - in - check_exp_named_subst_aux [] - - and sort_of_prod context (name,s) (t1, t2) = - let module C = Cic in - let t1' = CicReduction.whd context t1 in - let t2' = CicReduction.whd ((Some (name,C.Decl s))::context) t2 in - match (t1', t2') with - (C.Sort s1, C.Sort s2) - when (s2 = C.Prop or s2 = C.Set) -> (* different from Coq manual!!! *) - C.Sort s2 - | (C.Sort s1, C.Sort s2) -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *) - | (_,_) -> - raise - (TypeCheckerFailure - (NotWellTyped - ("Prod: sort1= " ^ CicPp.ppterm t1' ^ " ; sort2= "^ CicPp.ppterm t2'))) - - and eat_prods context hetype = - (*CSC: siamo sicuri che le are_convertible non lavorino con termini non *) - (*CSC: cucinati *) - function - [] -> hetype - | (hete, hety)::tl -> - (match (CicReduction.whd context hetype) with - Cic.Prod (n,s,t) -> - if CicReduction.are_convertible context s hety then - (CicReduction.fdebug := -1 ; - eat_prods context (CicSubstitution.subst hete t) tl - ) - else - begin - CicReduction.fdebug := 0 ; - ignore (CicReduction.are_convertible context s hety) ; - fdebug := 0 ; - debug s [hety] ; - raise - (TypeCheckerFailure (NotWellTyped "Appl: wrong parameter-type")) - end - | _ -> raise (TypeCheckerFailure (NotWellTyped "Appl: wrong Prod-type")) - ) - - and returns_a_coinductive context ty = - let module C = Cic in - match CicReduction.whd context ty with - C.MutInd (uri,i,_) -> - (*CSC: definire una funzioncina per questo codice sempre replicato *) - (match CicEnvironment.get_cooked_obj ~trust:false uri with - C.InductiveDefinition (itl,_,_) -> - let (_,is_inductive,_,_) = List.nth itl i in - if is_inductive then None else (Some uri) - | _ -> - raise - (TypeCheckerFailure (WrongUriToMutualInductiveDefinitions - (UriManager.string_of_uri uri))) - ) - | C.Appl ((C.MutInd (uri,i,_))::_) -> - (match CicEnvironment.get_obj uri with - C.InductiveDefinition (itl,_,_) -> - let (_,is_inductive,_,_) = List.nth itl i in - if is_inductive then None else (Some uri) - | _ -> - raise - (TypeCheckerFailure - (WrongUriToMutualInductiveDefinitions - (UriManager.string_of_uri uri))) - ) - | C.Prod (n,so,de) -> - returns_a_coinductive ((Some (n,C.Decl so))::context) de - | _ -> None - - in -(*CSC -prerr_endline ("INIZIO TYPE_OF_AUX " ^ CicPp.ppterm t) ; flush stderr ; -let res = -*) - type_of_aux context t -(* -in prerr_endline "FINE TYPE_OF_AUX" ; flush stderr ; res -*) - -(* is a small constructor? *) -(*CSC: ottimizzare calcolando staticamente *) -and is_small context paramsno c = - let rec is_small_aux context c = - let module C = Cic in - match CicReduction.whd context c with - C.Prod (n,so,de) -> - (*CSC: [] is an empty metasenv. Is it correct? *) - let s = type_of_aux' [] context so in - (s = C.Sort C.Prop || s = C.Sort C.Set) && - is_small_aux ((Some (n,(C.Decl so)))::context) de - | _ -> true (*CSC: we trust the type-checker *) - in - let (context',dx) = split_prods context paramsno c in - is_small_aux context' dx - -and type_of t = -(*CSC -prerr_endline ("INIZIO TYPE_OF_AUX' " ^ CicPp.ppterm t) ; flush stderr ; -let res = -*) - type_of_aux' [] [] t -(*CSC -in prerr_endline "FINE TYPE_OF_AUX'" ; flush stderr ; res -*) -;; - -let typecheck uri = - let module C = Cic in - let module R = CicReduction in - let module U = UriManager in - match CicEnvironment.is_type_checked ~trust:false uri with - CicEnvironment.CheckedObj _ -> () - | CicEnvironment.UncheckedObj uobj -> - (* let's typecheck the uncooked object *) - Logger.log (`Start_type_checking uri) ; - (match uobj with - C.Constant (_,Some te,ty,_) -> - let _ = type_of ty in - if not (R.are_convertible [] (type_of te ) ty) then - raise - (TypeCheckerFailure - (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))) - | C.Constant (_,None,ty,_) -> - (* only to check that ty is well-typed *) - let _ = type_of ty in () - | C.CurrentProof (_,conjs,te,ty,_) -> - let _ = - List.fold_left - (fun metasenv ((_,context,ty) as conj) -> - ignore (type_of_aux' metasenv context ty) ; - metasenv @ [conj] - ) [] conjs - in - let _ = type_of_aux' conjs [] ty in - if not (R.are_convertible [] (type_of_aux' conjs [] te) ty) - then - raise - (TypeCheckerFailure - (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))) - | C.Variable (_,bo,ty,_) -> - (* only to check that ty is well-typed *) - let _ = type_of ty in - (match bo with - None -> () - | Some bo -> - if not (R.are_convertible [] (type_of bo) ty) then - raise - (TypeCheckerFailure - (NotWellTyped ("Variable" ^ (U.string_of_uri uri)))) - ) - | C.InductiveDefinition _ -> - check_mutual_inductive_defs uri uobj - ) ; - CicEnvironment.set_type_checking_info uri ; - Logger.log (`Type_checking_completed uri) -;;