(* 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/.
*)
exception NotImplemented;;
exception Impossible of int;;
exception NotWellTyped of string;;
exception WrongUriToConstant of string;;
exception WrongUriToVariable of string;;
exception WrongUriToMutualInductiveDefinitions of string;;
exception ListTooShort;;
exception NotPositiveOccurrences of string;;
exception NotWellFormedTypeOfInductiveConstructor of string;;
exception WrongRequiredArgument of string;;
let log =
let module U = UriManager in
let indent = ref 0 in
function
`Start_type_checking uri ->
print_string (
(String.make !indent ' ') ^
"
" ^
"Type-Checking of " ^ (U.string_of_uri uri) ^ " started
\n"
) ;
flush stdout ;
incr indent
| `Type_checking_completed uri ->
decr indent ;
print_string (
(String.make !indent ' ') ^
"" ^
"Type-Checking of " ^ (U.string_of_uri uri) ^ " completed.
\n"
) ;
flush stdout
;;
let fdebug = ref 0;;
let debug t env =
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 (NotWellTyped ("\n" ^ List.fold_right debug_aux (t::env) ""))
(*print_endline ("\n" ^ List.fold_right debug_aux (t::env) "") ; 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 ListTooShort
;;
exception CicEnvironmentError;;
let rec cooked_type_of_constant uri cookingsno =
let module C = Cic in
let module R = CicReduction in
let module U = UriManager in
let cobj =
match CicEnvironment.is_type_checked uri cookingsno with
CicEnvironment.CheckedObj cobj -> cobj
| CicEnvironment.UncheckedObj uobj ->
log (`Start_type_checking uri) ;
(* let's typecheck the uncooked obj *)
(match uobj with
C.Definition (_,te,ty,_) ->
let _ = type_of ty in
if not (R.are_convertible (type_of te) ty) then
raise (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))
| C.Axiom (_,ty,_) ->
(* only to check that ty is well-typed *)
let _ = type_of ty in ()
| C.CurrentProof (_,_,te,ty) ->
let _ = type_of ty in
if not (R.are_convertible (type_of te) ty) then
raise (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))
| _ -> raise (WrongUriToConstant (U.string_of_uri uri))
) ;
CicEnvironment.set_type_checking_info uri ;
log (`Type_checking_completed uri) ;
match CicEnvironment.is_type_checked uri cookingsno with
CicEnvironment.CheckedObj cobj -> cobj
| CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
in
match cobj with
C.Definition (_,_,ty,_) -> ty
| C.Axiom (_,ty,_) -> ty
| C.CurrentProof (_,_,_,ty) -> ty
| _ -> raise (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 uri 0 with
CicEnvironment.CheckedObj (C.Variable (_,_,ty)) -> ty
| CicEnvironment.UncheckedObj (C.Variable (_,bo,ty)) ->
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 (NotWellTyped ("Variable " ^ (U.string_of_uri uri)))
) ;
CicEnvironment.set_type_checking_info uri ;
log (`Type_checking_completed uri) ;
ty
| _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
and does_not_occur 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 te with
C.Rel m when m > n && m <= nn -> false
| C.Rel _
| C.Var _
| C.Meta _
| C.Sort _
| C.Implicit -> true
| C.Cast (te,ty) -> does_not_occur n nn te && does_not_occur n nn ty
| C.Prod (_,so,dest) ->
does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
| C.Lambda (_,so,dest) ->
does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
| C.LetIn (_,so,dest) ->
does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
| C.Appl l ->
List.fold_right (fun x i -> i && does_not_occur n nn x) l true
| C.Const _
| C.Abst _
| C.MutInd _
| C.MutConstruct _ -> true
| C.MutCase (_,_,_,out,te,pl) ->
does_not_occur n nn out && does_not_occur n nn te &&
List.fold_right (fun x i -> i && does_not_occur 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
List.fold_right
(fun (_,_,ty,bo) i ->
i && does_not_occur n_plus_len nn_plus_len ty &&
does_not_occur 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
List.fold_right
(fun (_,ty,bo) i ->
i && does_not_occur n_plus_len nn_plus_len ty &&
does_not_occur 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 n nn uri te =
let module C = Cic in
(*CSC mettere in cicSubstitution *)
let rec subst_inductive_type_with_dummy_rel =
function
C.MutInd (uri',_,0) when UriManager.eq uri' uri ->
C.Rel 0 (* dummy rel *)
| C.Appl ((C.MutInd (uri',_,0))::tl) when UriManager.eq uri' uri ->
C.Rel 0 (* dummy rel *)
| C.Cast (te,ty) -> subst_inductive_type_with_dummy_rel te
| C.Prod (name,so,ta) ->
C.Prod (name, subst_inductive_type_with_dummy_rel so,
subst_inductive_type_with_dummy_rel ta)
| C.Lambda (name,so,ta) ->
C.Lambda (name, subst_inductive_type_with_dummy_rel so,
subst_inductive_type_with_dummy_rel ta)
| C.Appl tl ->
C.Appl (List.map subst_inductive_type_with_dummy_rel tl)
| C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
C.MutCase (uri,cookingsno,i,
subst_inductive_type_with_dummy_rel outtype,
subst_inductive_type_with_dummy_rel term,
List.map subst_inductive_type_with_dummy_rel pl)
| C.Fix (i,fl) ->
C.Fix (i,List.map (fun (name,i,ty,bo) -> (name,i,
subst_inductive_type_with_dummy_rel ty,
subst_inductive_type_with_dummy_rel bo)) fl)
| C.CoFix (i,fl) ->
C.CoFix (i,List.map (fun (name,ty,bo) -> (name,
subst_inductive_type_with_dummy_rel ty,
subst_inductive_type_with_dummy_rel bo)) fl)
| t -> t
in
match CicReduction.whd 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.Anonimous,source,dest) ->
strictly_positive n nn (subst_inductive_type_with_dummy_rel source) &&
weakly_positive (n + 1) (nn + 1) uri dest
| C.Prod (name,source,dest) when does_not_occur 0 n dest ->
(* dummy abstraction, so we behave as in the anonimous case *)
strictly_positive n nn (subst_inductive_type_with_dummy_rel source) &&
weakly_positive (n + 1) (nn + 1) uri dest
| C.Prod (_,source,dest) ->
does_not_occur n nn (subst_inductive_type_with_dummy_rel source) &&
weakly_positive (n + 1) (nn + 1) uri dest
| _ -> raise (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 (Impossible 1)
and strictly_positive n nn te =
let module C = Cic in
let module U = UriManager in
match CicReduction.whd te with
C.Rel _ -> true
| C.Cast (te,ty) ->
(*CSC: bisogna controllare ty????*)
strictly_positive n nn te
| C.Prod (_,so,ta) ->
does_not_occur n nn so &&
strictly_positive (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 n nn x) tl true
| C.Appl ((C.MutInd (uri,_,i))::tl) ->
let (ok,paramsno,cl) =
match CicEnvironment.get_obj uri with
C.InductiveDefinition (tl,_,paramsno) ->
let (_,_,_,cl) = List.nth tl i in
(List.length tl = 1, paramsno, cl)
| _ -> raise(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 te) cl
in
ok &&
List.fold_right
(fun x i -> i && does_not_occur n nn x)
arguments true &&
(*CSC: MEGAPATCH3 (sara' quella giusta?)*)
List.fold_right
(fun x i ->
i &&
weakly_positive (n+1) (nn+1) uri x
) cl' true
| t -> does_not_occur n nn t
(*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
and are_all_occurrences_positive uri indparamsno i n nn te =
let module C = Cic in
match CicReduction.whd 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 x with
C.Rel m when m = n - (indparamsno - k) -> k - 1
| _ -> raise (WrongRequiredArgument (UriManager.string_of_uri uri))
) indparamsno tl
in
if last = 0 then
List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
else
raise (WrongRequiredArgument (UriManager.string_of_uri uri))
| C.Rel m when m = i ->
if indparamsno = 0 then
true
else
raise (WrongRequiredArgument (UriManager.string_of_uri uri))
| C.Prod (C.Anonimous,source,dest) ->
strictly_positive n nn source &&
are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
| C.Prod (name,source,dest) when does_not_occur 0 n dest ->
(* dummy abstraction, so we behave as in the anonimous case *)
strictly_positive n nn source &&
are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
| C.Prod (_,source,dest) ->
does_not_occur n nn source &&
are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
| _ -> raise (NotWellFormedTypeOfInductiveConstructor (UriManager.string_of_uri uri))
(*CSC: cambiare il nome, torna unit! *)
and cooked_mutual_inductive_defs uri =
let module U = UriManager in
function
Cic.InductiveDefinition (itl, _, indparamsno) ->
(* 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 *)
(*CSC: piccola??? inefficienza *)
let len = List.length itl in
let _ =
List.fold_right
(fun (_,_,_,cl) i ->
List.iter
(fun (name,te,r) ->
let augmented_term =
List.fold_right
(fun (name,_,ty,_) i -> Cic.Prod (Cic.Name name, ty, i))
itl te
in
let _ = type_of augmented_term in
(* let's check also the positivity conditions *)
if not (are_all_occurrences_positive uri indparamsno i 0 len te)
then
raise (NotPositiveOccurrences (U.string_of_uri uri))
else
match !r with
Some _ -> raise (Impossible 2)
| None -> r := Some (recursive_args 0 len te)
) cl ;
(i + 1)
) itl 1
in
()
| _ ->
raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
and cooked_type_of_mutual_inductive_defs uri cookingsno i =
let module C = Cic in
let module R = CicReduction in
let module U = UriManager in
let cobj =
match CicEnvironment.is_type_checked uri cookingsno with
CicEnvironment.CheckedObj cobj -> cobj
| CicEnvironment.UncheckedObj uobj ->
log (`Start_type_checking uri) ;
cooked_mutual_inductive_defs uri uobj ;
CicEnvironment.set_type_checking_info uri ;
log (`Type_checking_completed uri) ;
(match CicEnvironment.is_type_checked uri cookingsno 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 (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
and cooked_type_of_mutual_inductive_constr uri cookingsno i j =
let module C = Cic in
let module R = CicReduction in
let module U = UriManager in
let cobj =
match CicEnvironment.is_type_checked uri cookingsno with
CicEnvironment.CheckedObj cobj -> cobj
| CicEnvironment.UncheckedObj uobj ->
log (`Start_type_checking uri) ;
cooked_mutual_inductive_defs uri uobj ;
CicEnvironment.set_type_checking_info uri ;
log (`Type_checking_completed uri) ;
(match CicEnvironment.is_type_checked uri cookingsno 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 (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
and recursive_args n nn te =
let module C = Cic in
match CicReduction.whd te with
C.Rel _ -> []
| C.Var _
| C.Meta _
| C.Sort _
| C.Implicit
| C.Cast _ (*CSC ??? *) -> raise (Impossible 3) (* due to type-checking *)
| C.Prod (_,so,de) ->
(not (does_not_occur n nn so))::(recursive_args (n+1) (nn + 1) de)
| C.Lambda _
| C.LetIn _ -> raise (Impossible 4) (* due to type-checking *)
| C.Appl _ -> []
| C.Const _
| C.Abst _ -> raise (Impossible 5)
| C.MutInd _
| C.MutConstruct _
| C.MutCase _
| C.Fix _
| C.CoFix _ -> raise (Impossible 6) (* due to type-checking *)
and get_new_safes 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 c, R.whd p, rl) with
(C.Prod (_,_,ta1), C.Lambda (_,_,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 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)
| (_,_,_) ->
(* 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 (Impossible 7)
and split_prods n te =
let module C = Cic in
let module R = CicReduction in
match (n, R.whd te) with
(0, _) -> [],te
| (n, C.Prod (_,so,ta)) when n > 0 ->
let (l1,l2) = split_prods (n - 1) ta in
(so::l1,l2)
| (_, _) -> raise (Impossible 8)
and eat_lambdas n te =
let module C = Cic in
let module R = CicReduction in
match (n, R.whd te) with
(0, _) -> (te, 0)
| (n, C.Lambda (_,_,ta)) when n > 0 ->
let (te, k) = eat_lambdas (n - 1) ta in
(te, k + 1)
| (_, _) -> raise (Impossible 9)
(*CSC: Tutto quello che segue e' l'intuzione di luca ;-) *)
and check_is_really_smaller_arg 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 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 (Impossible 10)
| C.Lambda (_,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.LetIn (_,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.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 n nn kl x safes he
| C.Appl [] -> raise (Impossible 11)
| C.Const _
| C.Abst _
| C.MutInd _ -> raise (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 (isinductive,paramsno,cl) =
match CicEnvironment.get_obj uri with
C.InductiveDefinition (tl,_,paramsno) ->
let (_,isinductive,_,cl) = List.nth tl i in
let cl' =
List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
in
(isinductive,paramsno,cl')
| _ ->
raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
in
if not isinductive then
List.fold_right
(fun p i -> i && check_is_really_smaller_arg n nn kl x safes p)
pl true
else
List.fold_right
(fun (p,(_,c,rl)) i ->
let rl' =
match !rl with
Some rl' ->
let (_,rl'') = split rl' paramsno in
rl''
| None -> raise (Impossible 13)
in
let (e,safes',n',nn',x') =
get_new_safes p c rl' safes n nn x
in
i &&
check_is_really_smaller_arg 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 (isinductive,paramsno,cl) =
match CicEnvironment.get_obj uri with
C.InductiveDefinition (tl,_,paramsno) ->
let (_,isinductive,_,cl) = List.nth tl i in
let cl' =
List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
in
(isinductive,paramsno,cl')
| _ ->
raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
in
if not isinductive then
List.fold_right
(fun p i -> i && check_is_really_smaller_arg 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,rl)) i ->
let rl' =
match !rl with
Some rl' ->
let (_,rl'') = split rl' paramsno in
rl''
| None -> raise (Impossible 14)
in
let (e, safes',n',nn',x') =
get_new_safes p c rl' safes n nn x
in
i &&
check_is_really_smaller_arg n' nn' kl x' safes' e
) (List.combine pl cl) true
| _ ->
List.fold_right
(fun p i -> i && check_is_really_smaller_arg 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 safes' = List.map (fun x -> x + len) safes in
List.fold_right
(fun (_,_,ty,bo) i ->
i &&
check_is_really_smaller_arg 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 safes' = List.map (fun x -> x + len) safes in
List.fold_right
(fun (_,ty,bo) i ->
i &&
check_is_really_smaller_arg n_plus_len nn_plus_len kl x_plus_len
safes' bo
) fl true
and guarded_by_destructors 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 _
| C.Var _
| C.Meta _
| C.Sort _
| C.Implicit -> true
| C.Cast (te,ty) ->
guarded_by_destructors n nn kl x safes te &&
guarded_by_destructors n nn kl x safes ty
| C.Prod (_,so,ta) ->
guarded_by_destructors n nn kl x safes so &&
guarded_by_destructors (n+1) (nn+1) kl (x+1)
(List.map (fun x -> x + 1) safes) ta
| C.Lambda (_,so,ta) ->
guarded_by_destructors n nn kl x safes so &&
guarded_by_destructors (n+1) (nn+1) kl (x+1)
(List.map (fun x -> x + 1) safes) ta
| C.LetIn (_,so,ta) ->
guarded_by_destructors n nn kl x safes so &&
guarded_by_destructors (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 n nn kl x safes param
) tl true &&
check_is_really_smaller_arg n nn kl x safes (List.nth tl k)
| C.Appl tl ->
List.fold_right (fun t i -> i && guarded_by_destructors n nn kl x safes t)
tl true
| C.Const _
| C.Abst _
| C.MutInd _
| C.MutConstruct _ -> true
| C.MutCase (uri,_,i,outtype,term,pl) ->
(match term with
C.Rel m when List.mem m safes || m = x ->
let (isinductive,paramsno,cl) =
match CicEnvironment.get_obj uri with
C.InductiveDefinition (tl,_,paramsno) ->
let (_,isinductive,_,cl) = List.nth tl i in
let cl' =
List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
in
(isinductive,paramsno,cl')
| _ ->
raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
in
if not isinductive then
guarded_by_destructors n nn kl x safes outtype &&
guarded_by_destructors n nn kl x safes term &&
(*CSC: manca ??? il controllo sul tipo di term? *)
List.fold_right
(fun p i -> i && guarded_by_destructors n nn kl x safes p)
pl true
else
guarded_by_destructors n nn kl x safes outtype &&
(*CSC: manca ??? il controllo sul tipo di term? *)
List.fold_right
(fun (p,(_,c,rl)) i ->
let rl' =
match !rl with
Some rl' ->
let (_,rl'') = split rl' paramsno in
rl''
| None -> raise (Impossible 15)
in
let (e,safes',n',nn',x') =
get_new_safes p c rl' safes n nn x
in
i &&
guarded_by_destructors 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 (isinductive,paramsno,cl) =
match CicEnvironment.get_obj uri with
C.InductiveDefinition (tl,_,paramsno) ->
let (_,isinductive,_,cl) = List.nth tl i in
let cl' =
List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
in
(isinductive,paramsno,cl')
| _ ->
raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
in
if not isinductive then
guarded_by_destructors n nn kl x safes outtype &&
guarded_by_destructors n nn kl x safes term &&
(*CSC: manca ??? il controllo sul tipo di term? *)
List.fold_right
(fun p i -> i && guarded_by_destructors n nn kl x safes p)
pl true
else
guarded_by_destructors n nn kl x safes outtype &&
(*CSC: manca ??? il controllo sul tipo di term? *)
List.fold_right
(fun t i -> i && guarded_by_destructors n nn kl x safes t)
tl true &&
List.fold_right
(fun (p,(_,c,rl)) i ->
let rl' =
match !rl with
Some rl' ->
let (_,rl'') = split rl' paramsno in
rl''
| None -> raise (Impossible 16)
in
let (e, safes',n',nn',x') =
get_new_safes p c rl' safes n nn x
in
i &&
guarded_by_destructors n' nn' kl x' safes' e
) (List.combine pl cl) true
| _ ->
guarded_by_destructors n nn kl x safes outtype &&
guarded_by_destructors n nn kl x safes term &&
(*CSC: manca ??? il controllo sul tipo di term? *)
List.fold_right
(fun p i -> i && guarded_by_destructors 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 safes' = List.map (fun x -> x + len) safes in
List.fold_right
(fun (_,_,ty,bo) i ->
i && guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
safes' ty &&
guarded_by_destructors 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 safes' = List.map (fun x -> x + len) safes in
List.fold_right
(fun (_,ty,bo) i ->
i && guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
safes' ty &&
guarded_by_destructors 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 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 te with
C.Rel m when m > n && m <= nn -> h
| C.Rel _
| C.Var _ -> true
| C.Meta _
| C.Sort _
| C.Implicit
| C.Cast _
| C.Prod _
| C.LetIn _ ->
raise (Impossible 17) (* the term has just been type-checked *)
| C.Lambda (_,so,de) ->
does_not_occur n nn so &&
guarded_by_constructors (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 n nn x) tl true
| C.Appl ((C.MutConstruct (uri,cookingsno,i,j))::tl) ->
let consty =
match CicEnvironment.get_cooked_obj uri cookingsno with
C.InductiveDefinition (itl,_,_) ->
let (_,_,_,cl) = List.nth itl i in
let (_,cons,_) = List.nth cl (j - 1) in cons
| _ ->
raise (WrongUriToMutualInductiveDefinitions
(UriManager.string_of_uri uri))
in
let rec analyse_branch ty te =
match CicReduction.whd ty with
C.Meta _ -> raise (Impossible 34)
| C.Rel _
| C.Var _
| C.Sort _ ->
does_not_occur n nn te
| C.Implicit
| C.Cast _ -> raise (Impossible 24) (* due to type-checking *)
| C.Prod (_,_,de) ->
analyse_branch de te
| C.Lambda _
| C.LetIn _ -> raise (Impossible 25) (* due to type-checking *)
| C.Appl ((C.MutInd (uri,_,_))::tl) as ty
when uri == coInductiveTypeURI ->
guarded_by_constructors n nn true te [] coInductiveTypeURI
| C.Appl ((C.MutInd (uri,_,_))::tl) as ty ->
guarded_by_constructors n nn true te tl coInductiveTypeURI
| C.Appl _ ->
does_not_occur n nn te
| C.Const _
| C.Abst _ -> raise (Impossible 26)
| C.MutInd (uri,_,_) when uri == coInductiveTypeURI ->
guarded_by_constructors n nn true te [] coInductiveTypeURI
| C.MutInd _ ->
does_not_occur n nn te
| C.MutConstruct _ -> raise (Impossible 27)
(*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
(*CSC: in head position. *)
| C.MutCase _
| C.Fix _
| C.CoFix _ -> raise (Impossible 28) (* due to type-checking *)
in
let rec analyse_instantiated_type ty l =
match CicReduction.whd ty with
C.Rel _
| C.Var _
| C.Meta _
| C.Sort _
| C.Implicit
| C.Cast _ -> raise (Impossible 29) (* due to type-checking *)
| C.Prod (_,so,de) ->
begin
match l with
[] -> true
| he::tl ->
analyse_branch so he &&
analyse_instantiated_type de tl
end
| C.Lambda _
| C.LetIn _ -> raise (Impossible 30) (* due to type-checking *)
| C.Appl _ ->
List.fold_left (fun i x -> i && does_not_occur n nn x) true l
| C.Const _
| C.Abst _ -> raise (Impossible 31)
| C.MutInd _ ->
List.fold_left (fun i x -> i && does_not_occur n nn x) true l
| C.MutConstruct _ -> raise (Impossible 32)
(*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
(*CSC: in head position. *)
| C.MutCase _
| C.Fix _
| C.CoFix _ -> raise (Impossible 33) (* due to type-checking *)
in
let rec instantiate_type args consty =
function
[] -> true
| tlhe::tltl as l ->
let consty' = CicReduction.whd 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 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 (Impossible 23)
end
| [] -> analyse_instantiated_type 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 n nn x) true tl &&
let len = List.length fl in
let n_plus_len = n + len
and nn_plus_len = nn + len in
List.fold_right
(fun (_,ty,bo) i ->
i && does_not_occur n_plus_len nn_plus_len ty &&
guarded_by_constructors 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 n nn x) true tl &&
does_not_occur n nn out &&
does_not_occur n nn te &&
List.fold_right
(fun x i ->
i &&
guarded_by_constructors n nn h x args coInductiveTypeURI
) pl true
| C.Appl l ->
List.fold_right (fun x i -> i && does_not_occur n nn x) l true
| C.Const _ -> true
| C.Abst _
| C.MutInd _ -> assert false
| C.MutConstruct _ -> true
| C.MutCase (_,_,_,out,te,pl) ->
does_not_occur n nn out &&
does_not_occur n nn te &&
List.fold_right
(fun x i ->
i &&
guarded_by_constructors 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 in
List.fold_right
(fun (_,_,ty,bo) i ->
i && does_not_occur n_plus_len nn_plus_len ty &&
does_not_occur 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 in
List.fold_right
(fun (_,ty,bo) i ->
i && does_not_occur n_plus_len nn_plus_len ty &&
guarded_by_constructors n_plus_len nn_plus_len h bo args
coInductiveTypeURI
) fl true
and check_allowed_sort_elimination uri i need_dummy ind arity1 arity2 =
let module C = Cic in
let module U = UriManager in
match (CicReduction.whd arity1, CicReduction.whd arity2) with
(C.Prod (_,so1,de1), C.Prod (_,so2,de2))
when CicReduction.are_convertible so1 so2 ->
check_allowed_sort_elimination 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) when need_dummy ->
(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 (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 (_,_,_,cl) = List.nth itl i in
List.fold_right (fun (_,x,_) i -> i && is_small paramsno x) cl true
| _ ->
raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
)
| (C.Sort C.Type, C.Sort _) when need_dummy -> true
| (C.Sort C.Prop, C.Prod (_,so,ta)) when not need_dummy ->
let res = CicReduction.are_convertible so ind
in
res &&
(match CicReduction.whd 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 (WrongUriToMutualInductiveDefinitions
(U.string_of_uri uri))
)
| _ -> false
)
| (C.Sort C.Set, C.Prod (_,so,ta)) when not need_dummy ->
let res = CicReduction.are_convertible so ind
in
res &&
(match CicReduction.whd 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
List.fold_right
(fun (_,x,_) i -> i && is_small paramsno x) cl true
| _ ->
raise (WrongUriToMutualInductiveDefinitions
(U.string_of_uri uri))
)
| _ -> raise (Impossible 19)
)
| (C.Sort C.Type, C.Prod (_,so,_)) when not need_dummy ->
CicReduction.are_convertible so ind
| (_,_) -> false
and type_of_branch argsno need_dummy outtype term constype =
let module C = Cic in
let module R = CicReduction in
match R.whd 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) ->
C.Prod (C.Name "pippo",so,type_of_branch argsno need_dummy
(CicSubstitution.lift 1 outtype)
(C.Appl [CicSubstitution.lift 1 term ; C.Rel 1]) de)
| _ -> raise (Impossible 20)
(* type_of_aux' is just another name (with a different scope) for type_of_aux *)
and type_of_aux' env t =
let rec type_of_aux env =
let module C = Cic in
let module R = CicReduction in
let module S = CicSubstitution in
let module U = UriManager in
function
C.Rel n ->
let t =
try
List.nth env (n - 1)
with
_ -> raise (NotWellTyped "Not a close term")
in
S.lift n t
| C.Var uri ->
incr fdebug ;
let ty = type_of_variable uri in
decr fdebug ;
ty
| C.Meta n -> raise NotImplemented
| C.Sort s -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
| C.Implicit -> raise (Impossible 21)
| C.Cast (te,ty) ->
let _ = type_of ty in
if R.are_convertible (type_of_aux env te) ty then ty
else raise (NotWellTyped "Cast")
| C.Prod (_,s,t) ->
let sort1 = type_of_aux env s
and sort2 = type_of_aux (s::env) t in
sort_of_prod (sort1,sort2)
| C.Lambda (n,s,t) ->
let sort1 = type_of_aux env s
and type2 = type_of_aux (s::env) t in
let sort2 = type_of_aux (s::env) type2 in
(* only to check if the product is well-typed *)
let _ = sort_of_prod (sort1,sort2) in
C.Prod (n,s,type2)
| C.LetIn (n,s,t) ->
let t' = CicSubstitution.subst s t in
type_of_aux env t'
| C.Appl (he::tl) when List.length tl > 0 ->
let hetype = type_of_aux env he
and tlbody_and_type = List.map (fun x -> (x, type_of_aux env x)) tl in
eat_prods hetype tlbody_and_type
| C.Appl _ -> raise (NotWellTyped "Appl: no arguments")
| C.Const (uri,cookingsno) ->
incr fdebug ;
let cty = cooked_type_of_constant uri cookingsno in
decr fdebug ;
cty
| C.Abst _ -> raise (Impossible 22)
| C.MutInd (uri,cookingsno,i) ->
incr fdebug ;
let cty = cooked_type_of_mutual_inductive_defs uri cookingsno i in
decr fdebug ;
cty
| C.MutConstruct (uri,cookingsno,i,j) ->
let cty = cooked_type_of_mutual_inductive_constr uri cookingsno i j
in
cty
| C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
let outsort = type_of_aux env outtype in
let (need_dummy, k) =
let rec guess_args t =
match CicReduction.whd t with
C.Sort _ -> (true, 0)
| C.Prod (_, s, t) ->
let (b, n) = guess_args t in
if n = 0 then
(* last prod before sort *)
match CicReduction.whd s with
(*CSC vedi nota delirante su cookingsno in cicReduction.ml *)
C.MutInd (uri',_,i') when U.eq uri' uri && i' = i -> (false, 1)
| C.Appl ((C.MutInd (uri',_,i')) :: _)
when U.eq uri' uri && i' = i -> (false, 1)
| _ -> (true, 1)
else
(b, n + 1)
| _ -> raise (NotWellTyped "MutCase: outtype ill-formed")
in
(*CSC whd non serve dopo type_of_aux ? *)
let (b, k) = guess_args outsort in
if not b then (b, k - 1) else (b, k)
in
let (parameters, arguments) =
match R.whd (type_of_aux env term) with
(*CSC manca il caso dei CAST *)
C.MutInd (uri',_,i') ->
(*CSC vedi nota delirante sui cookingsno in cicReduction.ml*)
if U.eq uri uri' && i = i' then ([],[])
else raise (NotWellTyped ("MutCase: the term is of type " ^
(U.string_of_uri uri') ^ "," ^ string_of_int i' ^
" instead of type " ^ (U.string_of_uri uri') ^ "," ^
string_of_int i))
| C.Appl (C.MutInd (uri',_,i') :: tl) ->
if U.eq uri uri' && i = i' then split tl (List.length tl - k)
else raise (NotWellTyped ("MutCase: the term is of type " ^
(U.string_of_uri uri') ^ "," ^ string_of_int i' ^
" instead of type " ^ (U.string_of_uri uri) ^ "," ^
string_of_int i))
| _ -> raise (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,cookingsno,i)
else
C.Appl ((C.MutInd (uri,cookingsno,i))::parameters)
in
if not (check_allowed_sort_elimination uri i need_dummy
sort_of_ind_type (type_of_aux env sort_of_ind_type) outsort)
then
raise (NotWellTyped "MutCase: not allowed sort elimination") ;
(* let's check if the type of branches are right *)
let (cl,parsno) =
match CicEnvironment.get_cooked_obj uri cookingsno with
C.InductiveDefinition (tl,_,parsno) ->
let (_,_,_,cl) = List.nth tl i in (cl,parsno)
| _ ->
raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
in
let (_,branches_ok) =
List.fold_left
(fun (j,b) (p,(_,c,_)) ->
let cons =
if parameters = [] then
(C.MutConstruct (uri,cookingsno,i,j))
else
(C.Appl (C.MutConstruct (uri,cookingsno,i,j)::parameters))
in
(j + 1, b &&
R.are_convertible (type_of_aux env p)
(type_of_branch parsno need_dummy outtype cons
(type_of_aux env cons))
)
) (1,true) (List.combine pl cl)
in
if not branches_ok then
raise (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 (_,k,ty,_) -> let _ = type_of_aux env ty in (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 (type_of_aux (types @ env) bo)
(CicSubstitution.lift len ty))
then
begin
let (m, eaten) = eat_lambdas (x + 1) bo in
(*let's control the guarded by destructors conditions D{f,k,x,M}*)
if not (guarded_by_destructors eaten (len + eaten) kl 1 [] m) then
raise (NotWellTyped "Fix: not guarded by destructors")
end
else
raise (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 (_,ty,_) -> let _ = type_of_aux env ty in ty) fl)
in
let len = List.length types in
List.iter
(fun (_,ty,bo) ->
if (R.are_convertible (type_of_aux (types @ env) bo)
(CicSubstitution.lift len ty))
then
begin
(* let's control that the returned type is coinductive *)
match returns_a_coinductive ty with
None ->
raise(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 0 len false bo [] uri) then
raise (NotWellTyped "CoFix: not guarded by constructors")
end
else
raise (NotWellTyped "CoFix: ill-typed bodies")
) fl ;
let (_,ty,_) = List.nth fl i in
ty
and sort_of_prod (t1, t2) =
let module C = Cic in
let t1' = CicReduction.whd t1 in
let t2' = CicReduction.whd 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
(NotWellTyped
("Prod: sort1= " ^ CicPp.ppterm t1' ^ " ; sort2= " ^ CicPp.ppterm t2'))
and eat_prods hetype =
(*CSC: siamo sicuri che le are_convertible non lavorino con termini non *)
(*CSC: cucinati *)
function
[] -> hetype
| (hete, hety)::tl ->
(match (CicReduction.whd hetype) with
Cic.Prod (n,s,t) ->
if CicReduction.are_convertible s hety then
(CicReduction.fdebug := -1 ;
eat_prods (CicSubstitution.subst hete t) tl
)
else
begin
CicReduction.fdebug := 0 ;
ignore (CicReduction.are_convertible s hety) ;
fdebug := 0 ;
debug s [hety] ;
raise (NotWellTyped "Appl: wrong parameter-type")
end
| _ -> raise (NotWellTyped "Appl: wrong Prod-type")
)
and returns_a_coinductive ty =
let module C = Cic in
match CicReduction.whd ty with
C.MutInd (uri,cookingsno,i) ->
(*CSC: definire una funzioncina per questo codice sempre replicato *)
(match CicEnvironment.get_cooked_obj uri cookingsno with
C.InductiveDefinition (itl,_,_) ->
let (_,is_inductive,_,cl) = List.nth itl i in
if is_inductive then None else (Some uri)
| _ ->
raise (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 (WrongUriToMutualInductiveDefinitions
(UriManager.string_of_uri uri))
)
| C.Prod (_,_,de) -> returns_a_coinductive de
| _ -> None
in
type_of_aux env t
(* is a small constructor? *)
(*CSC: ottimizzare calcolando staticamente *)
and is_small paramsno c =
let rec is_small_aux env c =
let module C = Cic in
match CicReduction.whd c with
C.Prod (_,so,de) ->
let s = type_of_aux' env so in
(s = C.Sort C.Prop || s = C.Sort C.Set) &&
is_small_aux (so::env) de
| _ -> true (*CSC: we trust the type-checker *)
in
let (sx,dx) = split_prods paramsno c in
is_small_aux (List.rev sx) dx
and type_of t =
type_of_aux' [] t
;;
let typecheck uri =
let module C = Cic in
let module R = CicReduction in
let module U = UriManager in
match CicEnvironment.is_type_checked uri 0 with
CicEnvironment.CheckedObj _ -> ()
| CicEnvironment.UncheckedObj uobj ->
(* let's typecheck the uncooked object *)
log (`Start_type_checking uri) ;
(match uobj with
C.Definition (_,te,ty,_) ->
let _ = type_of ty in
if not (R.are_convertible (type_of te ) ty) then
raise (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))
| C.Axiom (_,ty,_) ->
(* only to check that ty is well-typed *)
let _ = type_of ty in ()
| C.CurrentProof (_,_,te,ty) ->
(*CSC [] wrong *)
let _ = type_of ty in
debug (type_of te) [] ;
if not (R.are_convertible (type_of te) ty) then
raise (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 (NotWellTyped ("Variable" ^ (U.string_of_uri uri)))
)
| C.InductiveDefinition _ ->
cooked_mutual_inductive_defs uri uobj
) ;
CicEnvironment.set_type_checking_info uri ;
log (`Type_checking_completed uri)
;;