+++ /dev/null
-(* 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)
-;;
projects / helm.git / blobdiff