(**** DELIFT ****)
-(* the delift function takes in input an ordered list of integers [n1,...,nk]
- and a term t, and relocates rel(nk) to k. Typically, the list of integers
- is a parameter of a metavariable occurrence. *)
+(* the delift function takes in input an ordered list of optional terms *)
+(* [t1,...,tn] and a term t, and substitutes every tk = Some (rel(nk)) with *)
+(* rel(k). Typically, the list of optional terms is the explicit substitution *)
+(* that is applied to a metavariable occurrence and the result of the delift *)
+(* function is a term the implicit variable can be substituted with to make *)
+(* the term [t] unifiable with the metavariable occurrence. *)
+(* In general, the problem is undecidable if we consider equivalence in place *)
+(* of alpha convertibility. Our implementation, though, is even weaker than *)
+(* alpha convertibility, since it replace the term [tk] if and only if [tk] *)
+(* is a Rel (missing all the other cases). Does this matter in practice? *)
exception NotInTheList;;
aux 1
;;
+(*CSC: this restriction function is utterly wrong, since it does not check *)
+(*CSC: that the variable that is going to be restricted does not occur free *)
+(*CSC: in a part of the sequent that is not going to be restricted. *)
+(*CSC: In particular, the whole approach is wrong; if restriction can fail *)
+(*CSC: (as indeed it is the case), we can not collect all the restrictions *)
+(*CSC: and restrict everything at the end ;-( *)
let restrict to_be_restricted =
let rec erase i n =
function
- [] -> []
- | _::tl when List.mem (n,i) to_be_restricted ->
- None::(erase (i+1) n tl)
+ [] -> []
+ | _::tl when List.mem (n,i) to_be_restricted ->
+ None::(erase (i+1) n tl)
| he::tl -> he::(erase (i+1) n tl) in
let rec aux =
function
- [] -> []
- | (n,context,t)::tl -> (n,erase 1 n context,t)::(aux tl) in
+ [] -> []
+ | (n,context,t)::tl -> (n,erase 1 n context,t)::(aux tl) in
aux
;;
+(*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
let delift context metasenv l t =
let module S = CicSubstitution in
let to_be_restricted = ref [] in
if m <=k then
C.Rel m (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
(*CSC: deliftato la regola per il LetIn *)
+ (*CSC: FALSO! La regola per il LetIn non lo fa *)
else
- (match List.nth context (m-k-1) with
- Some (_,C.Def t) -> deliftaux k (S.lift m t)
- | Some (_,C.Decl t) ->
- (* It may augment to_be_restricted *)
- ignore (deliftaux k (S.lift m t)) ;
+ (match List.nth context (m-k-1) with
+ Some (_,C.Def (t,_)) ->
+ (*CSC: Hmmm. This bit of reduction is not in the spirit of *)
+ (*CSC: first order unification. Does it help or does it harm? *)
+ deliftaux k (S.lift m t)
+ | Some (_,C.Decl t) ->
+ (*CSC: The following check seems to be wrong! *)
+ (*CSC: B:Set |- ?2 : Set *)
+ (*CSC: A:Set ; x:?2[A/B] |- ?1[x/A] =?= x *)
+ (*CSC: Why should I restrict ?2 over B? The instantiation *)
+ (*CSC: ?1 := A is perfectly reasonable and well-typed. *)
+ (*CSC: Thus I comment out the following two lines that *)
+ (*CSC: are the incriminated ones. *)
+ (*(* It may augment to_be_restricted *)
+ ignore (deliftaux k (S.lift m t)) ;*)
+ (*CSC: end of bug commented out *)
C.Rel ((position (m-k) l) + k)
- | None -> raise RelToHiddenHypothesis)
+ | None -> raise RelToHiddenHypothesis)
| C.Var (uri,exp_named_subst) ->
let exp_named_subst' =
List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
in
C.CoFix (i, liftedfl)
in
- let res = deliftaux 0 t in
+ let res =
+ try
+ deliftaux 0 t
+ with
+ NotInTheList ->
+ (* This is the case where we fail even first order unification. *)
+ (* The reason is that our delift function is weaker than first *)
+ (* order (in the sense of alpha-conversion). See comment above *)
+ (* related to the delift function. *)
+prerr_endline "!!!!!!!!!!! First Order UnificationFailed, but maybe it could have been successful even in a first order setting (no conversion, only alpha convertibility)! Please, implement a better delift function !!!!!!!!!!!!!!!!" ;
+ raise UnificationFailed
+ in
res, restrict !to_be_restricted metasenv
;;
(* First possibility: restriction *)
(* Second possibility: unification *)
(* Third possibility: convertibility *)
- R.are_convertible context t1' t2'
+ R.are_convertible context t1' t2'
) true ln lm
in
if ok then subst,metasenv else raise UnificationFailed
| (C.Meta (n,l), t)
| (t, C.Meta (n,l)) ->
let subst',metasenv' =
- try
- let oldt = (List.assoc n subst) in
- let lifted_oldt = S.lift_meta l oldt in
- fo_unif_subst subst context metasenv lifted_oldt t
- with Not_found ->
- let t',metasenv' = delift context metasenv l t in
- (n, t')::subst, metasenv'
+ try
+ let oldt = (List.assoc n subst) in
+ let lifted_oldt = S.lift_meta l oldt in
+ fo_unif_subst subst context metasenv lifted_oldt t
+ with Not_found ->
+ let t',metasenv' = delift context metasenv l t in
+ (n, t')::subst, metasenv'
in
- let (_,_,meta_type) =
- List.find (function (m,_,_) -> m=n) metasenv' in
- let tyt = CicTypeChecker.type_of_aux' metasenv' context t in
- fo_unif_subst subst' context metasenv' (S.lift_meta l meta_type) tyt
+ let (_,_,meta_type) =
+ List.find (function (m,_,_) -> m=n) metasenv' in
+ let tyt = CicTypeChecker.type_of_aux' metasenv' context t in
+ fo_unif_subst subst' context metasenv' (S.lift_meta l meta_type) tyt
| (C.Var (uri1,exp_named_subst1),C.Var (uri2,exp_named_subst2))
| (C.Const (uri1,exp_named_subst1),C.Const (uri2,exp_named_subst2)) ->
if UriManager.eq uri1 uri2 then
raise UnificationFailed
| (C.Rel _, _)
| (_, C.Rel _)
- | (C.Var _, _)
- | (_, C.Var _)
| (C.Sort _ ,_)
| (_, C.Sort _)
| (C.Implicit, _)
in
fo_unif_l subst' metasenv' (l1,l2)
in
- fo_unif_l subst metasenv (lr1, lr2)
+ fo_unif_l subst metasenv (lr1, lr2)
| (C.Const _, _)
| (_, C.Const _)
| (C.MutInd _, _)
let subst', metasenv' =
fo_unif_subst subst context metasenv outt1 outt2 in
let subst'',metasenv'' =
- fo_unif_subst subst' context metasenv' t1 t2 in
+ fo_unif_subst subst' context metasenv' t1 t2 in
List.fold_left2
- (function (subst,metasenv) ->
+ (function (subst,metasenv) ->
fo_unif_subst subst context metasenv
) (subst'',metasenv'') pl1 pl2
| (C.Fix _, _)
" <==> " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst2))) ; raise e
;;
-(*CSC: ???????????????
-(* m is the index of a metavariable to restrict, k is nesting depth
-of the occurrence m, and l is its relocation list. canonical_context
-is the context of the metavariable we are instantiating - containing
-m - Only rel in the domain of canonical_context are accessible.
-This function takes in input a metasenv and gives back a metasenv.
-A rel(j) in the canonical context of m, is rel(List.nth l j) for the
-instance of m under consideration, that is rel (List.nth l j) - k
-in canonical_context. *)
-
-let restrict canonical_context m k l =
- let rec erase i =
- function
- [] -> []
- | None::tl -> None::(erase (i+1) tl)
- | he::tl ->
- let i' = (List.nth l (i-1)) in
- if i' <= k
- then he::(erase (i+1) tl) (* local variable *)
- else
- let acc =
- (try List.nth canonical_context (i'-k-1)
- with Failure _ -> None) in
- if acc = None
- then None::(erase (i+1) tl)
- else he::(erase (i+1) tl) in
- let rec aux =
- function
- [] -> []
- | (n,context,t)::tl when n=m -> (n,erase 1 context,t)::tl
- | hd::tl -> hd::(aux tl)
- in
- aux
-;;
-
-
-let check_accessibility metasenv i =
- let module C = Cic in
- let module S = CicSubstitution in
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=i) metasenv in
- List.map
- (function t ->
- let =
- delift canonical_context metasenv ? t
- ) canonical_context
-CSCSCS
-
-
-
- let rec aux metasenv k =
- function
- C.Rel i ->
- if i <= k then
- metasenv
- else
- (try
- match List.nth canonical_context (i-k-1) with
- Some (_,C.Decl t)
- | Some (_,C.Def t) -> aux metasenv k (S.lift i t)
- | None -> raise RelToHiddenHypothesis
- with
- Failure _ -> raise OpenTerm
- )
- | C.Var _ -> metasenv
- | C.Meta (i,l) -> restrict canonical_context i k l metasenv
- | C.Sort _ -> metasenv
- | C.Implicit -> metasenv
- | C.Cast (te,ty) ->
- let metasenv' = aux metasenv k te in
- aux metasenv' k ty
- | C.Prod (_,s,t)
- | C.Lambda (_,s,t)
- | C.LetIn (_,s,t) ->
- let metasenv' = aux metasenv k s in
- aux metasenv' (k+1) t
- | C.Appl l ->
- List.fold_left
- (function metasenv -> aux metasenv k) metasenv l
- | C.Const _
- | C.MutInd _
- | C.MutConstruct _ -> metasenv
- | C.MutCase (_,_,_,outty,t,pl) ->
- let metasenv' = aux metasenv k outty in
- let metasenv'' = aux metasenv' k t in
- List.fold_left
- (function metasenv -> aux metasenv k) metasenv'' pl
- | C.Fix (i, fl) ->
- let len = List.length fl in
- List.fold_left
- (fun metasenv f ->
- let (_,_,ty,bo) = f in
- let metasenv' = aux metasenv k ty in
- aux metasenv' (k+len) bo
- ) metasenv fl
- | C.CoFix (i, fl) ->
- let len = List.length fl in
- List.fold_left
- (fun metasenv f ->
- let (_,ty,bo) = f in
- let metasenv' = aux metasenv k ty in
- aux metasenv' (k+len) bo
- ) metasenv fl
- in aux metasenv 0
-;;
-*)
-
-
let unwind metasenv subst unwinded t =
let unwinded = ref unwinded in
let frozen = ref [] in
C.Rel _ as t -> t,metasenv
| C.Var _ as t -> t,metasenv
| C.Meta (i,l) ->
- (try
+ (try
S.lift_meta l (List.assoc i !unwinded), metasenv
with Not_found ->
if List.mem i !frozen then raise OccurCheck
else
let saved_frozen = !frozen in
- frozen := i::!frozen ;
+ frozen := i::!frozen ;
let res =
try
- let t = List.assoc i subst in
+ let t = List.assoc i subst in
let t',metasenv' = um_aux metasenv t in
- let _,metasenv'' =
+ let _,metasenv'' =
let (_,canonical_context,_) =
List.find (function (m,_,_) -> m=i) metasenv
in
(* not constrained variable, i.e. free in subst*)
let l',metasenv' =
List.fold_right
- (fun t (tl,metasenv) ->
+ (fun t (tl,metasenv) ->
match t with
None -> None::tl,metasenv
| Some t ->
- let t',metasenv' = um_aux metasenv t in
- (Some t')::tl, metasenv'
- ) l ([],metasenv)
+ let t',metasenv' = um_aux metasenv t in
+ (Some t')::tl, metasenv'
+ ) l ([],metasenv)
in
C.Meta (i,l'), metasenv'
in
| C.Appl (he::tl) ->
let tl',metasenv' =
List.fold_right
- (fun t (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- t'::tl, metasenv'
- ) tl ([],metasenv)
+ (fun t (tl,metasenv) ->
+ let t',metasenv' = um_aux metasenv t in
+ t'::tl, metasenv'
+ ) tl ([],metasenv)
in
begin
match um_aux metasenv' he with
| C.Const (uri,exp_named_subst) ->
let exp_named_subst', metasenv' =
List.fold_right
- (fun (uri,t) (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- (uri,t')::tl, metasenv'
- ) exp_named_subst ([],metasenv)
+ (fun (uri,t) (tl,metasenv) ->
+ let t',metasenv' = um_aux metasenv t in
+ (uri,t')::tl, metasenv'
+ ) exp_named_subst ([],metasenv)
in
C.Const (uri,exp_named_subst'),metasenv'
| C.MutInd (uri,typeno,exp_named_subst) ->
let exp_named_subst', metasenv' =
List.fold_right
- (fun (uri,t) (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- (uri,t')::tl, metasenv'
- ) exp_named_subst ([],metasenv)
+ (fun (uri,t) (tl,metasenv) ->
+ let t',metasenv' = um_aux metasenv t in
+ (uri,t')::tl, metasenv'
+ ) exp_named_subst ([],metasenv)
in
C.MutInd (uri,typeno,exp_named_subst'),metasenv'
| C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
let exp_named_subst', metasenv' =
List.fold_right
- (fun (uri,t) (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- (uri,t')::tl, metasenv'
- ) exp_named_subst ([],metasenv)
+ (fun (uri,t) (tl,metasenv) ->
+ let t',metasenv' = um_aux metasenv t in
+ (uri,t')::tl, metasenv'
+ ) exp_named_subst ([],metasenv)
in
C.MutConstruct (uri,typeno,consno,exp_named_subst'),metasenv'
| C.MutCase (sp,i,outty,t,pl) ->
let t',metasenv'' = um_aux metasenv' t in
let pl',metasenv''' =
List.fold_right
- (fun p (pl,metasenv) ->
- let p',metasenv' = um_aux metasenv p in
- p'::pl, metasenv'
- ) pl ([],metasenv'')
+ (fun p (pl,metasenv) ->
+ let p',metasenv' = um_aux metasenv p in
+ p'::pl, metasenv'
+ ) pl ([],metasenv'')
in
C.MutCase (sp, i, outty', t', pl'),metasenv'''
| C.Fix (i, fl) ->
let liftedfl,metasenv' =
List.fold_right
(fun (name, i, ty, bo) (fl,metasenv) ->
- let ty',metasenv' = um_aux metasenv ty in
- let bo',metasenv'' = um_aux metasenv' bo in
- (name, i, ty', bo')::fl,metasenv''
- ) fl ([],metasenv)
+ let ty',metasenv' = um_aux metasenv ty in
+ let bo',metasenv'' = um_aux metasenv' bo in
+ (name, i, ty', bo')::fl,metasenv''
+ ) fl ([],metasenv)
in
C.Fix (i, liftedfl),metasenv'
| C.CoFix (i, fl) ->
let liftedfl,metasenv' =
List.fold_right
(fun (name, ty, bo) (fl,metasenv) ->
- let ty',metasenv' = um_aux metasenv ty in
- let bo',metasenv'' = um_aux metasenv' bo in
- (name, ty', bo')::fl,metasenv''
- ) fl ([],metasenv)
+ let ty',metasenv' = um_aux metasenv ty in
+ let bo',metasenv'' = um_aux metasenv' bo in
+ (name, ty', bo')::fl,metasenv''
+ ) fl ([],metasenv)
in
C.CoFix (i, liftedfl),metasenv'
in
(* during the unwinding the eta-expansions are undone. *)
let apply_subst_reducing subst meta_to_reduce t =
+ (* andrea: che senso ha questo ref ?? *)
let unwinded = ref subst in
let rec um_aux =
let module C = Cic in
(* a new metasenv in which some hypothesis in the contexts of the *)
(* metavariables may have been restricted. *)
let fo_unif metasenv context t1 t2 =
-prerr_endline "INIZIO FASE 1" ; flush stderr ;
let subst_to_unwind,metasenv' = fo_unif_subst [] context metasenv t1 t2 in
-prerr_endline "FINE FASE 1" ; flush stderr ;
-let res =
unwind_subst metasenv' subst_to_unwind
-in
-prerr_endline "FINE FASE 2" ; flush stderr ; res
;;
projects / helm.git / blobdiff