+(* syntactic_equality up to the *)
+(* distinction between fake dependent products *)
+(* and non-dependent products, alfa-conversion *)
+let alpha_equivalence =
+ 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,ty,t), C.LetIn(_,s',ty',t') ->
+ aux s s' && aux ty ty' && aux t t'
+ | C.Appl l, C.Appl l' when List.length l = List.length 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)
+ | C.Meta (i, subst), C.Meta (i', subst') ->
+ i = i' &&
+ (try
+ List.fold_left2
+ (fun b xt xt' -> match xt,xt' with
+ | Some t, Some t' -> b && aux t t'
+ | _ -> b
+ ) true subst subst'
+ with
+ Invalid_argument _ -> false)
+ | C.Appl [t], t' | t, C.Appl [t'] -> assert false
+(* FG: are we _really_ sure of these?
+ | C.Sort (C.Type u), C.Sort (C.Type u') -> u = u'
+ | C.Implicit a, C.Implicit a' -> a = a'
+ we insert an unused variable below to genarate a warning at compile time
+*)
+ | _,_ -> 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
+
+let is_sober t =
+ let rec sober_term g = function
+ | C.Rel _
+ | C.Sort _
+ | C.Implicit _ -> g
+ | C.Const (_, xnss)
+ | C.Var (_, xnss)
+ | C.MutConstruct (_, _, _, xnss)
+ | C.MutInd (_, _, xnss) -> sober_xnss g xnss
+ | C.Meta (_, xss) -> sober_xss g xss
+ | C.Lambda (_, v, t)
+ | C.Prod (_, v, t)
+ | C.Cast (t, v) -> sober_term (sober_term g t) v
+ | C.LetIn (_, v, ty, t) -> sober_term
+ (sober_term (sober_term g t) ty) v
+ | C.Appl []
+ | C.Appl [_] -> fun b -> false
+ | C.Appl ts -> sober_terms g ts
+ | C.MutCase (_, _, t, v, ts) ->
+ sober_terms (sober_term (sober_term g t) v) ts
+ | C.Fix (_, ifs) -> sober_ifs g ifs
+ | C.CoFix (_, cifs) -> sober_cifs g cifs
+ and sober_terms g = List.fold_left sober_term g
+ and sober_xnss g =
+ let map g (_, t) = sober_term g t in
+ List.fold_left map g
+ and sober_xss g =
+ let map g = function
+ | None -> g
+ | Some t -> sober_term g t
+ in
+ List.fold_left map g
+ and sober_ifs g =
+ let map g (_, _, t, v) = sober_term (sober_term g t) v in
+ List.fold_left map g
+ and sober_cifs g =
+ let map g (_, t, v) = sober_term (sober_term g t) v in
+ List.fold_left map g
+ in
+ sober_term (fun b -> b) t true