+exception RelToHiddenHypothesis;;
+
+let alpha_equivalence =
+ let module C = Cic in
+ let rec aux t t' =
+ if t = t' then true
+ else
+ match t,t' with
+ C.Var (uri1,exp_named_subst1), C.Var (uri2,exp_named_subst2) ->
+ UriManager.eq uri1 uri2 &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.Cast (te,ty), C.Cast (te',ty') ->
+ aux te te' && aux ty ty'
+ | C.Prod (_,s,t), C.Prod (_,s',t') ->
+ aux s s' && aux t t'
+ | C.Lambda (_,s,t), C.Lambda (_,s',t') ->
+ aux s s' && aux t t'
+ | C.LetIn (_,s,t), C.LetIn(_,s',t') ->
+ aux s s' && aux t t'
+ | C.Appl l, C.Appl l' ->
+ (try
+ List.fold_left2
+ (fun b t1 t2 -> b && aux t1 t2) true l l'
+ with
+ Invalid_argument _ -> false)
+ | C.Const (uri,exp_named_subst1), C.Const (uri',exp_named_subst2) ->
+ UriManager.eq uri uri' &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.MutInd (uri,i,exp_named_subst1), C.MutInd (uri',i',exp_named_subst2) ->
+ UriManager.eq uri uri' && i = i' &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.MutConstruct (uri,i,j,exp_named_subst1),
+ C.MutConstruct (uri',i',j',exp_named_subst2) ->
+ UriManager.eq uri uri' && i = i' && j = j' &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.MutCase (sp,i,outt,t,pl), C.MutCase (sp',i',outt',t',pl') ->
+ UriManager.eq sp sp' && i = i' &&
+ aux outt outt' && aux t t' &&
+ (try
+ List.fold_left2
+ (fun b t1 t2 -> b && aux t1 t2) true pl pl'
+ with
+ Invalid_argument _ -> false)
+ | C.Fix (i,fl), C.Fix (i',fl') ->
+ i = i' &&
+ (try
+ List.fold_left2
+ (fun b (_,i,ty,bo) (_,i',ty',bo') ->
+ b && i = i' && aux ty ty' && aux bo bo'
+ ) true fl fl'
+ with
+ Invalid_argument _ -> false)
+ | C.CoFix (i,fl), C.CoFix (i',fl') ->
+ i = i' &&
+ (try
+ List.fold_left2
+ (fun b (_,ty,bo) (_,ty',bo') ->
+ b && aux ty ty' && aux bo bo'
+ ) true fl fl'
+ with
+ Invalid_argument _ -> false)
+ | _,_ -> false (* we already know that t != t' *)
+ and aux_exp_named_subst exp_named_subst1 exp_named_subst2 =
+ try
+ List.fold_left2
+ (fun b (uri1,t1) (uri2,t2) ->
+ b && UriManager.eq uri1 uri2 && aux t1 t2
+ ) true exp_named_subst1 exp_named_subst2
+ with
+ Invalid_argument _ -> false
+ in
+ aux
+;;