exception TypeCheckerFailure of string Lazy.t
exception AssertFailure of string Lazy.t
+let shift_k e (c,rf,x,safes) =
+ e::c,List.map (fun (k,v) -> k+1,v) rf,x+1,List.map ((+)1) safes
+;;
+
(* $Id: cicTypeChecker.ml 8213 2008-03-13 18:48:26Z sacerdot $ *)
(*
-let debrujin_constructor ?(cb=fun _ _ -> ()) uri number_of_types =
- let rec aux k t =
- let module C = Cic in
- let res =
- match t with
- C.Rel n as t when n <= k -> t
- | C.Rel _ ->
- raise (TypeCheckerFailure (lazy "unbound variable found in constructor type"))
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
- in
- C.Var (uri,exp_named_subst')
- | C.Meta (i,l) ->
- let l' = List.map (function None -> None | Some t -> Some (aux k t)) l in
- C.Meta (i,l')
- | C.Sort _
- | C.Implicit _ as t -> t
- | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty)
- | C.Prod (n,s,t) -> C.Prod (n, aux k s, aux (k+1) t)
- | C.Lambda (n,s,t) -> C.Lambda (n, aux k s, aux (k+1) t)
- | C.LetIn (n,s,ty,t) -> C.LetIn (n, aux k s, aux k ty, aux (k+1) t)
- | C.Appl l -> C.Appl (List.map (aux k) l)
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
- in
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri',tyno,exp_named_subst) when UriManager.eq uri uri' ->
- if exp_named_subst != [] then
- raise (TypeCheckerFailure
- (lazy ("non-empty explicit named substitution is applied to "^
- "a mutual inductive type which is being defined"))) ;
- C.Rel (k + number_of_types - tyno) ;
- | C.MutInd (uri',tyno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
- in
- C.MutInd (uri',tyno,exp_named_subst')
- | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
- in
- C.MutConstruct (uri,tyno,consno,exp_named_subst')
- | C.MutCase (sp,i,outty,t,pl) ->
- C.MutCase (sp, i, aux k outty, aux k t,
- List.map (aux k) pl)
- | C.Fix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, i, ty, bo) -> (name, i, aux k ty, aux (k+len) bo))
- fl
- in
- C.Fix (i, liftedfl)
- | C.CoFix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, ty, bo) -> (name, aux k ty, aux (k+len) bo))
- fl
- in
- C.CoFix (i, liftedfl)
- in
- cb t res;
- res
- in
- aux 0
-;;
-
exception CicEnvironmentError;;
(*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
let ugraph'' =
List.fold_left
(fun ugraph (name,te) ->
- let debrujinedte = debrujin_constructor uri len te in
+ 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 debrujinedte
+ 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
- debrujinedte)
+ debruijnedte)
then
begin
prerr_endline (UriManager.string_of_uri uri);
lazy ("Unknown mutual inductive definition:" ^
UriManager.string_of_uri uri)))
-and recursive_args context n nn te =
- let module C = Cic in
- match CicReduction.whd context te with
- C.Rel _ -> []
- | C.Var _
- | C.Meta _
- | C.Sort _
- | C.Implicit _
- | C.Cast _ (*CSC ??? *) ->
- raise (AssertFailure (lazy "3")) (* due to type-checking *)
- | C.Prod (name,so,de) ->
- (not (does_not_occur context n nn so)) ::
- (recursive_args ((Some (name,(C.Decl so)))::context) (n+1) (nn + 1) de)
- | C.Lambda _
- | C.LetIn _ ->
- raise (AssertFailure (lazy "4")) (* due to type-checking *)
- | C.Appl _ -> []
- | C.Const _ -> raise (AssertFailure (lazy "5"))
- | C.MutInd _
- | C.MutConstruct _
- | C.MutCase _
- | C.Fix _
- | C.CoFix _ -> raise (AssertFailure (lazy "6")) (* due to type-checking *)
-
-and get_new_safes ~subst context p c rl safes n nn x =
- let module C = Cic in
- let module U = UriManager in
- let module R = CicReduction in
- match (R.whd ~subst context c, R.whd ~subst context p, rl) with
- (C.Prod (_,so,ta1), C.Lambda (name,_,ta2), b::tl) ->
- (* we are sure that the two sources are convertible because we *)
- (* have just checked this. So let's go along ... *)
- let safes' =
- List.map (fun x -> x + 1) safes
- in
- let safes'' =
- if b then 1::safes' else safes'
- in
- get_new_safes ~subst ((Some (name,(C.Decl so)))::context)
- ta2 ta1 tl safes'' (n+1) (nn+1) (x+1)
- | (C.Prod _, (C.MutConstruct _ as e), _)
- | (C.Prod _, (C.Rel _ as e), _)
- | (C.MutInd _, e, [])
- | (C.Appl _, e, []) -> (e,safes,n,nn,x,context)
- | (c,p,l) ->
- (* CSC: If the next exception is raised, it just means that *)
- (* CSC: the proof-assistant allows to use very strange things *)
- (* CSC: as a branch of a case whose type is a Prod. In *)
- (* CSC: particular, this means that a new (C.Prod, x,_) case *)
- (* CSC: must be considered in this match. (e.g. x = MutCase) *)
- raise
- (AssertFailure (lazy
- (Printf.sprintf "Get New Safes: c=%s ; p=%s"
- (CicPp.ppterm c) (CicPp.ppterm p))))
-
-and split_prods ~subst context n te =
- let module C = Cic in
- let module R = CicReduction in
- match (n, R.whd ~subst context te) with
- (0, _) -> context,te
- | (n, C.Prod (name,so,ta)) when n > 0 ->
- split_prods ~subst ((Some (name,(C.Decl so)))::context) (n - 1) ta
- | (_, _) -> raise (AssertFailure (lazy "8"))
-
-and eat_lambdas ~subst context n te =
- let module C = Cic in
- let module R = CicReduction in
- match (n, R.whd ~subst context te) with
- (0, _) -> (te, 0, context)
- | (n, C.Lambda (name,so,ta)) when n > 0 ->
- let (te, k, context') =
- eat_lambdas ~subst ((Some (name,(C.Decl so)))::context) (n - 1) ta
- in
- (te, k + 1, context')
- | (n, te) ->
- raise (AssertFailure (lazy (sprintf "9 (%d, %s)" n (CicPp.ppterm te))))
-
-(*CSC: Tutto quello che segue e' l'intuzione di luca ;-) *)
-and check_is_really_smaller_arg ~subst context n nn kl x safes te =
- (*CSC: forse la whd si puo' fare solo quando serve veramente. *)
- (*CSC: cfr guarded_by_destructors *)
- let module C = Cic in
- let module U = UriManager in
- match CicReduction.whd ~subst context te with
- C.Rel m when List.mem m safes -> true
- | C.Rel _ -> false
- | C.Var _
- | C.Meta _
- | C.Sort _
- | C.Implicit _
- | C.Cast _
-(* | C.Cast (te,ty) ->
- check_is_really_smaller_arg ~subst n nn kl x safes te &&
- check_is_really_smaller_arg ~subst n nn kl x safes ty*)
-(* | C.Prod (_,so,ta) ->
- check_is_really_smaller_arg ~subst n nn kl x safes so &&
- check_is_really_smaller_arg ~subst (n+1) (nn+1) kl (x+1)
- (List.map (fun x -> x + 1) safes) ta*)
- | C.Prod _ -> raise (AssertFailure (lazy "10"))
- | C.Lambda (name,so,ta) ->
- check_is_really_smaller_arg ~subst context n nn kl x safes so &&
- check_is_really_smaller_arg ~subst ((Some (name,(C.Decl so)))::context)
- (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
- | C.LetIn (name,so,ty,ta) ->
- check_is_really_smaller_arg ~subst context n nn kl x safes so &&
- check_is_really_smaller_arg ~subst context n nn kl x safes ty &&
- check_is_really_smaller_arg ~subst ((Some (name,(C.Def (so,ty))))::context)
- (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
- | C.Appl (he::_) ->
- (*CSC: sulla coda ci vogliono dei controlli? secondo noi no, ma *)
- (*CSC: solo perche' non abbiamo trovato controesempi *)
- check_is_really_smaller_arg ~subst context n nn kl x safes he
- | C.Appl [] -> raise (AssertFailure (lazy "11"))
- | C.Const _
- | C.MutInd _ -> raise (AssertFailure (lazy "12"))
- | C.MutConstruct _ -> false
- | C.MutCase (uri,i,outtype,term,pl) ->
- (match term with
- C.Rel m when List.mem m safes || m = x ->
- let (lefts_and_tys,len,isinductive,paramsno,cl) =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
- match o with
- C.InductiveDefinition (tl,_,paramsno,_) ->
- let tys =
- List.map
- (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) tl
- in
- let (_,isinductive,_,cl) = List.nth tl i in
- let cl' =
- List.map
- (fun (id,ty) ->
- (id, snd (split_prods ~subst tys paramsno ty))) cl in
- let lefts =
- match tl with
- [] -> assert false
- | (_,_,ty,_)::_ ->
- fst (split_prods ~subst [] paramsno ty)
- in
- (tys@lefts,List.length tl,isinductive,paramsno,cl')
- | _ ->
- raise (TypeCheckerFailure
- (lazy ("Unknown mutual inductive definition:" ^
- UriManager.string_of_uri uri)))
- in
- if not isinductive then
- List.fold_right
- (fun p i ->
- i && check_is_really_smaller_arg ~subst context n nn kl x safes p)
- pl true
- else
- let pl_and_cl =
- try
- List.combine pl cl
- with
- Invalid_argument _ ->
- raise (TypeCheckerFailure (lazy "not enough patterns"))
- in
- (*CSC: supponiamo come prima che nessun controllo sia necessario*)
- (*CSC: sugli argomenti di una applicazione *)
- List.fold_right
- (fun (p,(_,c)) i ->
- let rl' =
- let debrujinedte = debrujin_constructor uri len c in
- recursive_args lefts_and_tys 0 len debrujinedte
- in
- let (e,safes',n',nn',x',context') =
- get_new_safes ~subst context p c rl' safes n nn x
- in
- i &&
- check_is_really_smaller_arg ~subst context' n' nn' kl x' safes' e
- ) pl_and_cl true
- | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
- let (lefts_and_tys,len,isinductive,paramsno,cl) =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
- match o with
- C.InductiveDefinition (tl,_,paramsno,_) ->
- let (_,isinductive,_,cl) = List.nth tl i in
- let tys =
- List.map (fun (n,_,ty,_) ->
- Some(Cic.Name n,(Cic.Decl ty))) tl
- in
- let cl' =
- List.map
- (fun (id,ty) ->
- (id, snd (split_prods ~subst tys paramsno ty))) cl in
- let lefts =
- match tl with
- [] -> assert false
- | (_,_,ty,_)::_ ->
- fst (split_prods ~subst [] paramsno ty)
- in
- (tys@lefts,List.length tl,isinductive,paramsno,cl')
- | _ ->
- raise (TypeCheckerFailure
- (lazy ("Unknown mutual inductive definition:" ^
- UriManager.string_of_uri uri)))
- in
- if not isinductive then
- List.fold_right
- (fun p i ->
- i && check_is_really_smaller_arg ~subst context n nn kl x safes p)
- pl true
- else
- let pl_and_cl =
- try
- List.combine pl cl
- with
- Invalid_argument _ ->
- raise (TypeCheckerFailure (lazy "not enough patterns"))
- in
- (*CSC: supponiamo come prima che nessun controllo sia necessario*)
- (*CSC: sugli argomenti di una applicazione *)
- List.fold_right
- (fun (p,(_,c)) i ->
- let rl' =
- let debrujinedte = debrujin_constructor uri len c in
- recursive_args lefts_and_tys 0 len debrujinedte
- in
- let (e,safes',n',nn',x',context') =
- get_new_safes ~subst context p c rl' safes n nn x
- in
- i &&
- check_is_really_smaller_arg ~subst context' n' nn' kl x' safes' e
- ) pl_and_cl true
- | _ ->
- List.fold_right
- (fun p i ->
- i && check_is_really_smaller_arg ~subst context n nn kl x safes p
- ) pl true
- )
- | C.Fix (_, fl) ->
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + len
- and x_plus_len = x + len
- and tys,_ =
- List.fold_left
- (fun (types,len) (n,_,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- and safes' = List.map (fun x -> x + len) safes in
- List.fold_right
- (fun (_,_,ty,bo) i ->
- i &&
- check_is_really_smaller_arg ~subst (tys@context) n_plus_len nn_plus_len kl
- x_plus_len safes' bo
- ) fl true
- | C.CoFix (_, fl) ->
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + len
- and x_plus_len = x + len
- and tys,_ =
- List.fold_left
- (fun (types,len) (n,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- and safes' = List.map (fun x -> x + len) safes in
- List.fold_right
- (fun (_,ty,bo) i ->
- i &&
- check_is_really_smaller_arg ~subst (tys@context) n_plus_len nn_plus_len kl
- x_plus_len safes' bo
- ) fl true
-
-and guarded_by_destructors ~subst context n nn kl x safes =
- let module C = Cic in
- let module U = UriManager in
- function
- C.Rel m when m > n && m <= nn -> false
- | C.Rel m ->
- (match List.nth context (n-1) with
- Some (_,C.Decl _) -> true
- | Some (_,C.Def (bo,_)) ->
- guarded_by_destructors ~subst context m nn kl x safes
- (CicSubstitution.lift m bo)
- | None -> raise (TypeCheckerFailure (lazy "Reference to deleted hypothesis"))
- )
- | C.Meta _
- | C.Sort _
- | C.Implicit _ -> true
- | C.Cast (te,ty) ->
- guarded_by_destructors ~subst context n nn kl x safes te &&
- guarded_by_destructors ~subst context n nn kl x safes ty
- | C.Prod (name,so,ta) ->
- guarded_by_destructors ~subst context n nn kl x safes so &&
- guarded_by_destructors ~subst ((Some (name,(C.Decl so)))::context)
- (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
- | C.Lambda (name,so,ta) ->
- guarded_by_destructors ~subst context n nn kl x safes so &&
- guarded_by_destructors ~subst ((Some (name,(C.Decl so)))::context)
- (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
- | C.LetIn (name,so,ty,ta) ->
- guarded_by_destructors ~subst context n nn kl x safes so &&
- guarded_by_destructors ~subst context n nn kl x safes ty &&
- guarded_by_destructors ~subst ((Some (name,(C.Def (so,ty))))::context)
- (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
- | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
- let k = List.nth kl (m - n - 1) in
- if not (List.length tl > k) then false
- else
- List.fold_right
- (fun param i ->
- i && guarded_by_destructors ~subst context n nn kl x safes param
- ) tl true &&
- check_is_really_smaller_arg ~subst context n nn kl x safes (List.nth tl k)
- | C.Appl tl ->
- List.fold_right
- (fun t i -> i && guarded_by_destructors ~subst context n nn kl x safes t)
- tl true
- | C.Var (_,exp_named_subst)
- | C.Const (_,exp_named_subst)
- | C.MutInd (_,_,exp_named_subst)
- | C.MutConstruct (_,_,_,exp_named_subst) ->
- List.fold_right
- (fun (_,t) i -> i && guarded_by_destructors ~subst context n nn kl x safes t)
- exp_named_subst true
- | C.MutCase (uri,i,outtype,term,pl) ->
- (match CicReduction.whd ~subst context term with
- C.Rel m when List.mem m safes || m = x ->
- let (lefts_and_tys,len,isinductive,paramsno,cl) =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
- match o with
- C.InductiveDefinition (tl,_,paramsno,_) ->
- let len = List.length tl in
- let (_,isinductive,_,cl) = List.nth tl i in
- let tys =
- List.map (fun (n,_,ty,_) ->
- Some(Cic.Name n,(Cic.Decl ty))) tl
- in
- let cl' =
- List.map
- (fun (id,ty) ->
- let debrujinedty = debrujin_constructor uri len ty in
- (id, snd (split_prods ~subst tys paramsno ty),
- snd (split_prods ~subst tys paramsno debrujinedty)
- )) cl in
- let lefts =
- match tl with
- [] -> assert false
- | (_,_,ty,_)::_ ->
- fst (split_prods ~subst [] paramsno ty)
- in
- (tys@lefts,len,isinductive,paramsno,cl')
- | _ ->
- raise (TypeCheckerFailure
- (lazy ("Unknown mutual inductive definition:" ^
- UriManager.string_of_uri uri)))
- in
- if not isinductive then
- guarded_by_destructors ~subst context n nn kl x safes outtype &&
- guarded_by_destructors ~subst context n nn kl x safes term &&
- (*CSC: manca ??? il controllo sul tipo di term? *)
- List.fold_right
- (fun p i ->
- i && guarded_by_destructors ~subst context n nn kl x safes p)
- pl true
- else
- let pl_and_cl =
- try
- List.combine pl cl
- with
- Invalid_argument _ ->
- raise (TypeCheckerFailure (lazy "not enough patterns"))
- in
- guarded_by_destructors ~subst context n nn kl x safes outtype &&
- (*CSC: manca ??? il controllo sul tipo di term? *)
- List.fold_right
- (fun (p,(_,c,brujinedc)) i ->
- let rl' = recursive_args lefts_and_tys 0 len brujinedc in
- let (e,safes',n',nn',x',context') =
- get_new_safes ~subst context p c rl' safes n nn x
- in
- i &&
- guarded_by_destructors ~subst context' n' nn' kl x' safes' e
- ) pl_and_cl true
- | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
- let (lefts_and_tys,len,isinductive,paramsno,cl) =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
- match o with
- C.InductiveDefinition (tl,_,paramsno,_) ->
- let (_,isinductive,_,cl) = List.nth tl i in
- let tys =
- List.map
- (fun (n,_,ty,_) -> Some(Cic.Name n,(Cic.Decl ty))) tl
- in
- let cl' =
- List.map
- (fun (id,ty) ->
- (id, snd (split_prods ~subst tys paramsno ty))) cl in
- let lefts =
- match tl with
- [] -> assert false
- | (_,_,ty,_)::_ ->
- fst (split_prods ~subst [] paramsno ty)
- in
- (tys@lefts,List.length tl,isinductive,paramsno,cl')
- | _ ->
- raise (TypeCheckerFailure
- (lazy ("Unknown mutual inductive definition:" ^
- UriManager.string_of_uri uri)))
- in
- if not isinductive then
- guarded_by_destructors ~subst context n nn kl x safes outtype &&
- guarded_by_destructors ~subst context n nn kl x safes term &&
- (*CSC: manca ??? il controllo sul tipo di term? *)
- List.fold_right
- (fun p i ->
- i && guarded_by_destructors ~subst context n nn kl x safes p)
- pl true
- else
- let pl_and_cl =
- try
- List.combine pl cl
- with
- Invalid_argument _ ->
- raise (TypeCheckerFailure (lazy "not enough patterns"))
- in
- guarded_by_destructors ~subst context n nn kl x safes outtype &&
- (*CSC: manca ??? il controllo sul tipo di term? *)
- List.fold_right
- (fun t i ->
- i && guarded_by_destructors ~subst context n nn kl x safes t)
- tl true &&
- List.fold_right
- (fun (p,(_,c)) i ->
- let rl' =
- let debrujinedte = debrujin_constructor uri len c in
- recursive_args lefts_and_tys 0 len debrujinedte
- in
- let (e, safes',n',nn',x',context') =
- get_new_safes ~subst context p c rl' safes n nn x
- in
- i &&
- guarded_by_destructors ~subst context' n' nn' kl x' safes' e
- ) pl_and_cl true
- | _ ->
- guarded_by_destructors ~subst context n nn kl x safes outtype &&
- guarded_by_destructors ~subst context n nn kl x safes term &&
- (*CSC: manca ??? il controllo sul tipo di term? *)
- List.fold_right
- (fun p i -> i && guarded_by_destructors ~subst context n nn kl x safes p)
- pl true
- )
- | C.Fix (_, fl) ->
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + len
- and x_plus_len = x + len
- and tys,_ =
- List.fold_left
- (fun (types,len) (n,_,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- and safes' = List.map (fun x -> x + len) safes in
- List.fold_right
- (fun (_,_,ty,bo) i ->
- i && guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
- guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
- x_plus_len safes' bo
- ) fl true
- | C.CoFix (_, fl) ->
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + len
- and x_plus_len = x + len
- and tys,_ =
- List.fold_left
- (fun (types,len) (n,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- and safes' = List.map (fun x -> x + len) safes in
- List.fold_right
- (fun (_,ty,bo) i ->
- i &&
- guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
- guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
- x_plus_len safes' bo
- ) fl true
-
(* the boolean h means already protected *)
(* args is the list of arguments the type of the constructor that may be *)
(* found in head position must be applied to. *)
| _ -> None
in
- type_of_aux ~logger context t ugraph
-
-;;
-
-(** wrappers which instantiate fresh loggers *)
-
-(* check_allowed_sort_elimination uri i s1 s2
- This function is used outside the kernel to determine in advance whether
- a MutCase will be allowed or not.
- [uri,i] is the type of the term to match
- [s1] is the sort of the term to eliminate (i.e. the head of the arity
- of the inductive type [uri,i])
- [s2] is the sort of the goal (i.e. the head of the type of the outtype
- of the MutCase) *)
-let check_allowed_sort_elimination uri i s1 s2 =
- fst (check_allowed_sort_elimination ~subst:[] ~metasenv:[]
- ~logger:(new CicLogger.logger) [] uri i true
- (Cic.Implicit None) (* never used *) (Cic.Sort s1) (Cic.Sort s2)
- CicUniv.empty_ugraph)
+ type_of_aux ~logger context t ugraph
+
+;;
+
+(** wrappers which instantiate fresh loggers *)
+
+(* check_allowed_sort_elimination uri i s1 s2
+ This function is used outside the kernel to determine in advance whether
+ a MutCase will be allowed or not.
+ [uri,i] is the type of the term to match
+ [s1] is the sort of the term to eliminate (i.e. the head of the arity
+ of the inductive type [uri,i])
+ [s2] is the sort of the goal (i.e. the head of the type of the outtype
+ of the MutCase) *)
+let check_allowed_sort_elimination uri i s1 s2 =
+ fst (check_allowed_sort_elimination ~subst:[] ~metasenv:[]
+ ~logger:(new CicLogger.logger) [] uri i true
+ (Cic.Implicit None) (* never used *) (Cic.Sort s1) (Cic.Sort s2)
+ CicUniv.empty_ugraph)
+;;
+
+Deannotate.type_of_aux' := fun context t -> fst (type_of_aux' [] context t CicUniv.oblivion_ugraph);;
+
+*)
+
+module C = NCic
+module R = NCicReduction
+module Ref = NReference
+module S = NCicSubstitution
+module U = NCicUtils
+module E = NCicEnvironment
+
+let rec split_prods ~subst context n te =
+ match (n, R.whd ~subst context te) with
+ | (0, _) -> context,te
+ | (n, C.Prod (name,so,ta)) when n > 0 ->
+ split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
+ | (_, _) -> raise (AssertFailure (lazy "split_prods"))
+;;
+
+let debruijn_constructor ?(cb=fun _ _ -> ()) uri number_of_types t = assert false
+(*
+ let rec aux k t =
+ let module C = Cic in
+ let res =
+ match t with
+ C.Rel n as t when n <= k -> t
+ | C.Rel _ ->
+ raise (TypeCheckerFailure (lazy "unbound variable found in constructor type"))
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.Var (uri,exp_named_subst')
+ | C.Meta (i,l) ->
+ let l' = List.map (function None -> None | Some t -> Some (aux k t)) l in
+ C.Meta (i,l')
+ | C.Sort _
+ | C.Implicit _ as t -> t
+ | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty)
+ | C.Prod (n,s,t) -> C.Prod (n, aux k s, aux (k+1) t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, aux k s, aux (k+1) t)
+ | C.LetIn (n,s,ty,t) -> C.LetIn (n, aux k s, aux k ty, aux (k+1) t)
+ | C.Appl l -> C.Appl (List.map (aux k) l)
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.Const (uri,exp_named_subst')
+ | C.MutInd (uri',tyno,exp_named_subst) when UriManager.eq uri uri' ->
+ if exp_named_subst != [] then
+ raise (TypeCheckerFailure
+ (lazy ("non-empty explicit named substitution is applied to "^
+ "a mutual inductive type which is being defined"))) ;
+ C.Rel (k + number_of_types - tyno) ;
+ | C.MutInd (uri',tyno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.MutInd (uri',tyno,exp_named_subst')
+ | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.MutConstruct (uri,tyno,consno,exp_named_subst')
+ | C.MutCase (sp,i,outty,t,pl) ->
+ C.MutCase (sp, i, aux k outty, aux k t,
+ List.map (aux k) pl)
+ | C.Fix (i, fl) ->
+ let len = List.length fl in
+ let liftedfl =
+ List.map
+ (fun (name, i, ty, bo) -> (name, i, aux k ty, aux (k+len) bo))
+ fl
+ in
+ C.Fix (i, liftedfl)
+ | C.CoFix (i, fl) ->
+ let len = List.length fl in
+ let liftedfl =
+ List.map
+ (fun (name, ty, bo) -> (name, aux k ty, aux (k+len) bo))
+ fl
+ in
+ C.CoFix (i, liftedfl)
+ in
+ cb t res;
+ res
+ in
+ aux 0*)
;;
-Deannotate.type_of_aux' := fun context t -> fst (type_of_aux' [] context t CicUniv.oblivion_ugraph);;
-
-*)
-
-module C = NCic
-module R = NCicReduction
-module Ref = NReference
-module S = NCicSubstitution
-module U = NCicUtils
-module E = NCicEnvironment
-
-let rec split_prods ~subst context n te =
- match (n, R.whd ~subst context te) with
- | (0, _) -> context,te
- | (n, C.Prod (name,so,ta)) when n > 0 ->
- split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
- | (_, _) -> raise (AssertFailure (lazy "split_prods"))
-;;
let sort_of_prod ~subst context (name,s) (t1, t2) =
let t1 = R.whd ~subst context t1 in
aux ty_he args_with_ty
;;
+let fix_lefts_in_constrs ~subst paramsno tyl i =
+ let len = List.length tyl in
+ let _,_,arity,cl = List.nth tyl i in
+ let tys = List.map (fun (_,n,ty,_) -> n,C.Decl ty) tyl in
+ let cl' =
+ List.map
+ (fun (_,id,ty) ->
+ let debruijnedty = debruijn_constructor ref len ty in
+ id, snd (split_prods ~subst tys paramsno ty),
+ snd (split_prods ~subst tys paramsno debruijnedty))
+ cl
+ in
+ let lefts = fst (split_prods ~subst [] paramsno arity) in
+ tys@lefts, len, cl'
+;;
+
exception DoesOccur;;
let does_not_occur ~subst context n nn t =
with DoesOccur -> false
;;
+exception NotGuarded;;
+
let rec typeof ~subst ~metasenv context term =
let rec typeof_aux context = function
| C.Rel n ->
typeof_aux context term
and check_mutual_inductive_defs _ = assert false
-and eat_lambdas ~subst _ _ _ = assert false
+
+and eat_lambdas ~subst context n te =
+ match (n, R.whd ~subst context te) with
+ | (0, _) -> (te, context)
+ | (n, C.Lambda (name,so,ta)) when n > 0 ->
+ eat_lambdas ~subst ((name,(C.Decl so))::context) (n - 1) ta
+ | (n, te) ->
+ raise (AssertFailure
+ (lazy (Printf.sprintf "9 (%d, %s)" n (NCicPp.ppterm te))))
+
+and guarded_by_destructors ~subst context recfuns t =
+ let recursor f k t = NCicUtils.fold shift_k k (fun k () -> f k) () t in
+ let rec aux (context, recfuns, x, safes as k) = function
+ | C.Rel m when List.mem_assoc m recfuns -> raise NotGuarded
+ | C.Rel m ->
+ (match List.nth context (m-1) with
+ | _,C.Decl _ -> ()
+ | _,C.Def (bo,_) -> aux (context, recfuns, x, safes) (S.lift m bo))
+ | C.Meta _ -> ()
+ | C.Appl ((C.Rel m)::tl) when List.mem_assoc m recfuns ->
+ let rec_no = List.assoc m recfuns in
+ if not (List.length tl > rec_no) then raise NotGuarded
+ else
+ let rec_arg = List.nth tl rec_no in
+ aux k rec_arg;
+ List.iter (aux k) tl
+ | C.Match (ref,outtype,term,pl) as t ->
+ (match R.whd ~subst context term with
+ | C.Rel m | C.Appl (C.Rel m :: _ ) as t when List.mem m safes || m = x ->
+ let isinductive, paramsno, tl, _, i = E.get_checked_indtys ref in
+ if not isinductive then recursor aux k t
+ else
+ let lefts_and_tys,len,cl = fix_lefts_in_constrs ~subst paramsno tl i in
+ let args = match t with C.Appl (_::tl) -> tl | _ -> [] in
+ aux k outtype;
+ List.iter (aux k) args;
+ List.iter2
+ (fun p (_,c,bruijnedc) ->
+ let rl = recursive_args ~subst lefts_and_tys 0 len bruijnedc in
+ let p, k = get_new_safes ~subst k p rl in
+ aux k p)
+ pl cl
+ | _ -> recursor aux k t)
+ | t -> recursor aux k t
+ in
+ try aux (context, recfuns, 1, []) t;true
+ with NotGuarded -> false
+
+(*
+ | C.Fix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,_,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,_,ty,bo) i ->
+ i && guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
+ guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+ | C.CoFix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,ty,bo) i ->
+ i &&
+ guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
+ guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+*)
+
and guarded_by_constructors ~subst _ _ _ _ _ _ _ = assert false
-and guarded_by_destructors ~subst _ _ _ _ _ _ _ = assert false
+
+and recursive_args ~subst context n nn te =
+ match R.whd context te with
+ | C.Rel _ -> []
+ | C.Prod (name,so,de) ->
+ (not (does_not_occur ~subst context n nn so)) ::
+ (recursive_args ~subst ((name,(C.Decl so))::context) (n+1) (nn + 1) de)
+ | _ -> raise (AssertFailure (lazy ("recursive_args")))
+
+and get_new_safes ~subst (context, recfuns, x, safes as k) p rl =
+ match R.whd ~subst context p, rl with
+ | C.Lambda (name,so,ta), b::tl ->
+ let safes = (if b then [0] else []) @ safes in
+ get_new_safes ~subst
+ (shift_k (name,(C.Decl so)) (context, recfuns, x, safes)) ta tl
+ | C.Meta _ as e, _ | e, [] -> e, k
+ | _ -> raise (AssertFailure (lazy "Ill formed pattern"))
+
+and split_prods ~subst context n te =
+ match n, R.whd ~subst context te with
+ | 0, _ -> context,te
+ | n, C.Prod (name,so,ta) when n > 0 ->
+ split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
+ | _ -> raise (AssertFailure (lazy "split_prods"))
+
+(*CSC: Tutto quello che segue e' l'intuzione di luca ;-) *)
+and check_is_really_smaller_arg ~subst context n nn kl x safes te =
+assert false (*
+ (*CSC: forse la whd si puo' fare solo quando serve veramente. *)
+ (*CSC: cfr guarded_by_destructors *)
+ let module C = Cic in
+ let module U = UriManager in
+ match CicReduction.whd ~subst context te with
+ C.Rel m when List.mem m safes -> true
+ | C.Rel _ -> false
+ | C.Var _
+ | C.Meta _
+ | C.Sort _
+ | C.Implicit _
+ | C.Cast _
+(* | C.Cast (te,ty) ->
+ check_is_really_smaller_arg ~subst n nn kl x safes te &&
+ check_is_really_smaller_arg ~subst n nn kl x safes ty*)
+(* | C.Prod (_,so,ta) ->
+ check_is_really_smaller_arg ~subst n nn kl x safes so &&
+ check_is_really_smaller_arg ~subst (n+1) (nn+1) kl (x+1)
+ (List.map (fun x -> x + 1) safes) ta*)
+ | C.Prod _ -> raise (AssertFailure (lazy "10"))
+ | C.Lambda (name,so,ta) ->
+ check_is_really_smaller_arg ~subst context n nn kl x safes so &&
+ check_is_really_smaller_arg ~subst ((Some (name,(C.Decl so)))::context)
+ (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
+ | C.LetIn (name,so,ty,ta) ->
+ check_is_really_smaller_arg ~subst context n nn kl x safes so &&
+ check_is_really_smaller_arg ~subst context n nn kl x safes ty &&
+ check_is_really_smaller_arg ~subst ((Some (name,(C.Def (so,ty))))::context)
+ (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta
+ | C.Appl (he::_) ->
+ (*CSC: sulla coda ci vogliono dei controlli? secondo noi no, ma *)
+ (*CSC: solo perche' non abbiamo trovato controesempi *)
+ check_is_really_smaller_arg ~subst context n nn kl x safes he
+ | C.Appl [] -> raise (AssertFailure (lazy "11"))
+ | C.Const _
+ | C.MutInd _ -> raise (AssertFailure (lazy "12"))
+ | C.MutConstruct _ -> false
+ | C.MutCase (uri,i,outtype,term,pl) ->
+ (match term with
+ C.Rel m when List.mem m safes || m = x ->
+ let (lefts_and_tys,len,isinductive,paramsno,cl) =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tl,_,paramsno,_) ->
+ let tys =
+ List.map
+ (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) tl
+ in
+ let (_,isinductive,_,cl) = List.nth tl i in
+ let cl' =
+ List.map
+ (fun (id,ty) ->
+ (id, snd (split_prods ~subst tys paramsno ty))) cl in
+ let lefts =
+ match tl with
+ [] -> assert false
+ | (_,_,ty,_)::_ ->
+ fst (split_prods ~subst [] paramsno ty)
+ in
+ (tys@lefts,List.length tl,isinductive,paramsno,cl')
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ in
+ if not isinductive then
+ List.fold_right
+ (fun p i ->
+ i && check_is_really_smaller_arg ~subst context n nn kl x safes p)
+ pl true
+ else
+ let pl_and_cl =
+ try
+ List.combine pl cl
+ with
+ Invalid_argument _ ->
+ raise (TypeCheckerFailure (lazy "not enough patterns"))
+ in
+ (*CSC: supponiamo come prima che nessun controllo sia necessario*)
+ (*CSC: sugli argomenti di una applicazione *)
+ List.fold_right
+ (fun (p,(_,c)) i ->
+ let rl' =
+ let debruijnedte = debruijn_constructor uri len c in
+ recursive_args lefts_and_tys 0 len debruijnedte
+ in
+ let (e,safes',n',nn',x',context') =
+ get_new_safes ~subst context p c rl' safes n nn x
+ in
+ i &&
+ check_is_really_smaller_arg ~subst context' n' nn' kl x' safes' e
+ ) pl_and_cl true
+ | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
+ let (lefts_and_tys,len,isinductive,paramsno,cl) =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tl,_,paramsno,_) ->
+ let (_,isinductive,_,cl) = List.nth tl i in
+ let tys =
+ List.map (fun (n,_,ty,_) ->
+ Some(Cic.Name n,(Cic.Decl ty))) tl
+ in
+ let cl' =
+ List.map
+ (fun (id,ty) ->
+ (id, snd (split_prods ~subst tys paramsno ty))) cl in
+ let lefts =
+ match tl with
+ [] -> assert false
+ | (_,_,ty,_)::_ ->
+ fst (split_prods ~subst [] paramsno ty)
+ in
+ (tys@lefts,List.length tl,isinductive,paramsno,cl')
+ | _ ->
+ raise (TypeCheckerFailure
+ (lazy ("Unknown mutual inductive definition:" ^
+ UriManager.string_of_uri uri)))
+ in
+ if not isinductive then
+ List.fold_right
+ (fun p i ->
+ i && check_is_really_smaller_arg ~subst context n nn kl x safes p)
+ pl true
+ else
+ let pl_and_cl =
+ try
+ List.combine pl cl
+ with
+ Invalid_argument _ ->
+ raise (TypeCheckerFailure (lazy "not enough patterns"))
+ in
+ (*CSC: supponiamo come prima che nessun controllo sia necessario*)
+ (*CSC: sugli argomenti di una applicazione *)
+ List.fold_right
+ (fun (p,(_,c)) i ->
+ let rl' =
+ let debruijnedte = debruijn_constructor uri len c in
+ recursive_args lefts_and_tys 0 len debruijnedte
+ in
+ let (e,safes',n',nn',x',context') =
+ get_new_safes ~subst context p c rl' safes n nn x
+ in
+ i &&
+ check_is_really_smaller_arg ~subst context' n' nn' kl x' safes' e
+ ) pl_and_cl true
+ | _ ->
+ List.fold_right
+ (fun p i ->
+ i && check_is_really_smaller_arg ~subst context n nn kl x safes p
+ ) pl true
+ )
+ | C.Fix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,_,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,_,ty,bo) i ->
+ i &&
+ check_is_really_smaller_arg ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+ | C.CoFix (_, fl) ->
+ let len = List.length fl in
+ let n_plus_len = n + len
+ and nn_plus_len = nn + len
+ and x_plus_len = x + len
+ and tys,_ =
+ List.fold_left
+ (fun (types,len) (n,ty,_) ->
+ (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+ len+1)
+ ) ([],0) fl
+ and safes' = List.map (fun x -> x + len) safes in
+ List.fold_right
+ (fun (_,ty,bo) i ->
+ i &&
+ check_is_really_smaller_arg ~subst (tys@context) n_plus_len nn_plus_len kl
+ x_plus_len safes' bo
+ ) fl true
+ *)
+
and returns_a_coinductive ~subst _ _ = assert false
and type_of_constant ref = assert false (* USARE typecheck_obj0 *)
| C.Fixpoint (inductive,fl,_) ->
let types,kl,len =
List.fold_left
- (fun (types,kl,len) (_,n,k,ty,_) ->
+ (fun (types,kl,len) (_,name,k,ty,_) ->
let _ = typeof ~subst ~metasenv [] ty in
- ((n,(C.Decl (S.lift len ty)))::types, k::kl,len+1)
+ ((name,(C.Decl (S.lift len ty)))::types, k::kl,len+1)
) ([],[],0) fl
in
List.iter (fun (_,name,x,ty,bo) ->
then raise (TypeCheckerFailure (lazy ("(Co)Fix: ill-typed bodies")))
else
if inductive then begin
- let m, eaten, context =
- eat_lambdas ~subst types (x + 1) bo
+ let m, context = eat_lambdas ~subst types (x + 1) bo in
+ (* guarded by destructors conditions D{f,k,x,M} *)
+ let rec enum_from k =
+ function [] -> [] | v::tl -> (k,v)::enum_from (k+1) tl
in
- (* guarded by destructors conditions D{f,k,x,M} *)
- if not (guarded_by_destructors ~subst context eaten
- (len + eaten) kl 1 [] m)
- then
+ if not (guarded_by_destructors
+ ~subst context (enum_from (x+1) kl) m) then
raise(TypeCheckerFailure(lazy("Fix: not guarded by destructors")))
end else
match returns_a_coinductive ~subst [] ty with
projects / helm.git / commitdiff