- (* let's check if the types of the inductive constructors *)
- (* are well formed. *)
- (* In order not to use type_of_aux we put the types of the *)
- (* mutual inductive types at the head of the types of the *)
- (* constructors using Prods *)
- let len = List.length itl in
- let tys =
- List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl in
- let _,ugraph2 =
- List.fold_right
- (fun (_,_,_,cl) (i,ugraph) ->
- let ugraph'' =
- List.fold_left
- (fun ugraph (name,te) ->
- let debruijnedte = debruijn_constructor uri len te in
- let augmented_term =
- List.fold_right
- (fun (name,_,ty,_) i -> Cic.Prod (Cic.Name name, ty, i))
- itl debruijnedte
- in
- let _,ugraph' = type_of ~logger augmented_term ugraph in
- (* let's check also the positivity conditions *)
- if
- not
- (are_all_occurrences_positive tys uri indparamsno i 0 len
- debruijnedte)
- then
- begin
- prerr_endline (UriManager.string_of_uri uri);
- prerr_endline (string_of_int (List.length tys));
- raise
- (TypeCheckerFailure
- (lazy ("Non positive occurence in " ^ U.string_of_uri uri))) end
- else
- ugraph'
- ) ugraph cl in
- (i + 1),ugraph''
- ) itl (1,ugrap1)
- in
- ugraph2
-
-(* Main function to checks the correctness of a mutual *)
-(* inductive block definition. *)
-and check_mutual_inductive_defs uri obj ugraph =
- match obj with
- Cic.InductiveDefinition (itl, params, indparamsno, _) ->
- typecheck_mutual_inductive_defs uri (itl,params,indparamsno) ugraph
- | _ ->
- raise (TypeCheckerFailure (
- lazy ("Unknown mutual inductive definition:" ^
- UriManager.string_of_uri uri)))
-
-(* the boolean h means already protected *)
-(* args is the list of arguments the type of the constructor that may be *)
-(* found in head position must be applied to. *)
-and guarded_by_constructors ~subst context n nn h te args coInductiveTypeURI =
- let module C = Cic in
- (*CSC: There is a lot of code replication between the cases X and *)
- (*CSC: (C.Appl X tl). Maybe it will be better to define a function *)
- (*CSC: that maps X into (C.Appl X []) when X is not already a C.Appl *)
- match CicReduction.whd ~subst context te with
- C.Rel m when m > n && m <= nn -> h
- | C.Rel _ -> true
- | C.Meta _
- | C.Sort _
- | C.Implicit _
- | C.Cast _
- | C.Prod _
- | C.LetIn _ ->
- (* the term has just been type-checked *)
- raise (AssertFailure (lazy "17"))
- | C.Lambda (name,so,de) ->
- does_not_occur ~subst context n nn so &&
- guarded_by_constructors ~subst ((Some (name,(C.Decl so)))::context)
- (n + 1) (nn + 1) h de args coInductiveTypeURI
- | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
- h &&
- List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) tl true
- | C.Appl ((C.MutConstruct (uri,i,j,exp_named_subst))::tl) ->
- let consty =
- let obj,_ =
- try
- CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri
- with Not_found -> assert false
- in
- match obj with
- C.InductiveDefinition (itl,_,_,_) ->
- let (_,_,_,cl) = List.nth itl i in
- let (_,cons) = List.nth cl (j - 1) in
- CicSubstitution.subst_vars exp_named_subst cons
- | _ ->
- raise (TypeCheckerFailure
- (lazy ("Unknown mutual inductive definition:" ^ UriManager.string_of_uri uri)))
- in
- let rec analyse_branch context ty te =
- match CicReduction.whd ~subst context ty with
- C.Meta _ -> raise (AssertFailure (lazy "34"))
- | C.Rel _
- | C.Var _
- | C.Sort _ ->
- does_not_occur ~subst context n nn te
- | C.Implicit _
- | C.Cast _ ->
- raise (AssertFailure (lazy "24"))(* due to type-checking *)
- | C.Prod (name,so,de) ->
- analyse_branch ((Some (name,(C.Decl so)))::context) de te
- | C.Lambda _
- | C.LetIn _ ->
- raise (AssertFailure (lazy "25"))(* due to type-checking *)
- | C.Appl ((C.MutInd (uri,_,_))::_) when uri == coInductiveTypeURI ->
- guarded_by_constructors ~subst context n nn true te []
- coInductiveTypeURI
- | C.Appl ((C.MutInd (uri,_,_))::_) ->
- guarded_by_constructors ~subst context n nn true te tl
- coInductiveTypeURI
- | C.Appl _ ->
- does_not_occur ~subst context n nn te
- | C.Const _ -> raise (AssertFailure (lazy "26"))
- | C.MutInd (uri,_,_) when uri == coInductiveTypeURI ->
- guarded_by_constructors ~subst context n nn true te []
- coInductiveTypeURI
- | C.MutInd _ ->
- does_not_occur ~subst context n nn te
- | C.MutConstruct _ -> raise (AssertFailure (lazy "27"))
- (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
- (*CSC: in head position. *)
- | C.MutCase _
- | C.Fix _
- | C.CoFix _ ->
- raise (AssertFailure (lazy "28"))(* due to type-checking *)
- in
- let rec analyse_instantiated_type context ty l =
- match CicReduction.whd ~subst context ty with
- C.Rel _
- | C.Var _
- | C.Meta _
- | C.Sort _
- | C.Implicit _
- | C.Cast _ -> raise (AssertFailure (lazy "29"))(* due to type-checking *)
- | C.Prod (name,so,de) ->
- begin
- match l with
- [] -> true
- | he::tl ->
- analyse_branch context so he &&
- analyse_instantiated_type
- ((Some (name,(C.Decl so)))::context) de tl
- end
- | C.Lambda _
- | C.LetIn _ ->
- raise (AssertFailure (lazy "30"))(* due to type-checking *)
- | C.Appl _ ->
- List.fold_left
- (fun i x -> i && does_not_occur ~subst context n nn x) true l
- | C.Const _ -> raise (AssertFailure (lazy "31"))
- | C.MutInd _ ->
- List.fold_left
- (fun i x -> i && does_not_occur ~subst context n nn x) true l
- | C.MutConstruct _ -> raise (AssertFailure (lazy "32"))
- (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
- (*CSC: in head position. *)
- | C.MutCase _
- | C.Fix _
- | C.CoFix _ ->
- raise (AssertFailure (lazy "33"))(* due to type-checking *)
- in
- let rec instantiate_type args consty =
- function
- [] -> true
- | tlhe::tltl as l ->
- let consty' = CicReduction.whd ~subst context consty in
- match args with
- he::tl ->
- begin
- match consty' with
- C.Prod (_,_,de) ->
- let instantiated_de = CicSubstitution.subst he de in
- (*CSC: siamo sicuri che non sia troppo forte? *)
- does_not_occur ~subst context n nn tlhe &
- instantiate_type tl instantiated_de tltl
- | _ ->
- (*CSC:We do not consider backbones with a MutCase, a *)
- (*CSC:FixPoint, a CoFixPoint and so on in head position.*)
- raise (AssertFailure (lazy "23"))
- end
- | [] -> analyse_instantiated_type context consty' l
- (* These are all the other cases *)
- in
- instantiate_type args consty tl
- | C.Appl ((C.CoFix (_,fl))::tl) ->
- List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl &&
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + len
- (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
- and tys,_ =
- List.fold_left
- (fun (types,len) (n,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- in
- List.fold_right
- (fun (_,ty,bo) i ->
- i && does_not_occur ~subst context n nn ty &&
- guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len
- h bo args coInductiveTypeURI
- ) fl true
- | C.Appl ((C.MutCase (_,_,out,te,pl))::tl) ->
- List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl &&
- does_not_occur ~subst context n nn out &&
- does_not_occur ~subst context n nn te &&
- List.fold_right
- (fun x i ->
- i &&
- guarded_by_constructors ~subst context n nn h x args
- coInductiveTypeURI
- ) pl true
- | C.Appl l ->
- List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) l true
- | C.Var (_,exp_named_subst)
- | C.Const (_,exp_named_subst) ->
- List.fold_right
- (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
- | C.MutInd _ -> assert false
- | C.MutConstruct (_,_,_,exp_named_subst) ->
- List.fold_right
- (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
- | C.MutCase (_,_,out,te,pl) ->
- does_not_occur ~subst context n nn out &&
- does_not_occur ~subst context n nn te &&
- List.fold_right
- (fun x i ->
- i &&
- guarded_by_constructors ~subst context n nn h x args
- coInductiveTypeURI
- ) pl true
- | C.Fix (_,fl) ->
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + len
- (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
- and tys,_ =
- List.fold_left
- (fun (types,len) (n,_,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- in
- List.fold_right
- (fun (_,_,ty,bo) i ->
- i && does_not_occur ~subst context n nn ty &&
- does_not_occur ~subst (tys@context) n_plus_len nn_plus_len bo
- ) fl true
- | C.CoFix (_,fl) ->
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + len
- (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
- and tys,_ =
- List.fold_left
- (fun (types,len) (n,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- in
- List.fold_right
- (fun (_,ty,bo) i ->
- i && does_not_occur ~subst context n nn ty &&
- guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len
- h bo
- args coInductiveTypeURI
- ) fl true
-
-and type_of_branch ~subst context argsno need_dummy outtype term constype =
- let module C = Cic in
- let module R = CicReduction in
- match R.whd ~subst context constype with
- C.MutInd (_,_,_) ->
- if need_dummy then
- outtype
- else
- C.Appl [outtype ; term]
- | C.Appl (C.MutInd (_,_,_)::tl) ->
- let (_,arguments) = split tl argsno
- in
- if need_dummy && arguments = [] then
- outtype
- else
- C.Appl (outtype::arguments@(if need_dummy then [] else [term]))
- | C.Prod (name,so,de) ->
- let term' =
- match CicSubstitution.lift 1 term with
- C.Appl l -> C.Appl (l@[C.Rel 1])
- | t -> C.Appl [t ; C.Rel 1]
- in
- C.Prod (name,so,type_of_branch ~subst
- ((Some (name,(C.Decl so)))::context) argsno need_dummy
- (CicSubstitution.lift 1 outtype) term' de)
- | _ -> raise (AssertFailure (lazy "20"))