- | `Lam(b,nf) -> `Lam (b, aux (l+1) nf)
+ | `Lam(b,nf,g) -> `Lam (b, aux (l+1) nf, List.map (aux (l+1)) g)
| `I((x,ar),args) ->
(if x < n then [] else [(x-n,ar)]) @
List.concat (List.map (aux n) (Listx.to_list args))
| `I((x,ar),args) ->
(if x < n then [] else [(x-n,ar)]) @
List.concat (List.map (aux n) (Listx.to_list args))
| `Match(t,_,liftno,bs,args) ->
aux n (t :> nf) @
List.concat (List.map (fun (_,t) -> aux (n-liftno) t) !bs) @
| `Match(t,_,liftno,bs,args) ->
aux n (t :> nf) @
List.concat (List.map (fun (_,t) -> aux (n-liftno) t) !bs) @
| `Match(t,_,liftno,bs,args) ->
| `Match(t,_,liftno,bs,args) ->
List.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) m args
| `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) (Pure.V v) args
and t_of_nf =
function
| #i_num_var as x -> t_of_i_num_var x
List.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) m args
| `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) (Pure.V v) args
and t_of_nf =
function
| #i_num_var as x -> t_of_i_num_var x
else "`" ^ string_of_int (n-lev) in
let rec string_of_term_w_pars lev l = function
| `Var(n,ar) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "")
else "`" ^ string_of_int (n-lev) in
let rec string_of_term_w_pars lev l = function
| `Var(n,ar) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "")
| `Lam _ as t -> "(" ^ string_of_term_no_pars_lam lev l t ^ ")"
| `Match(t,(v,ar),bs_lift,bs,args) ->
(* assert (bs_lift = lev); *)
| `Lam _ as t -> "(" ^ string_of_term_no_pars_lam lev l t ^ ")"
| `Match(t,(v,ar),bs_lift,bs,args) ->
(* assert (bs_lift = lev); *)
" with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (t :> nf)) !bs) ^ "] " ^
String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")"
and string_of_term_no_pars_app lev l = function
| `I((n,ar), args) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") ^ " " ^ String.concat " " (List.map (string_of_term_w_pars lev l) (Listx.to_list args :> nf list))
| #nf as t -> string_of_term_w_pars lev l t
and string_of_term_no_pars_lam lev l = function
" with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (t :> nf)) !bs) ^ "] " ^
String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")"
and string_of_term_no_pars_app lev l = function
| `I((n,ar), args) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") ^ " " ^ String.concat " " (List.map (string_of_term_w_pars lev l) (Listx.to_list args :> nf list))
| #nf as t -> string_of_term_w_pars lev l t
and string_of_term_no_pars_lam lev l = function
- | `Lam(_,t) -> "λ" ^ boundvar lev ^ ". " ^ (string_of_term_no_pars_lam (lev+1) l t)
+ | `Lam(_,t,g) -> "λ" ^ boundvar lev ^ ". " ^ (string_of_term_no_pars_lam (lev+1) l t)
+ ^ (if g = [] then "" else String.concat ", " ("" :: List.map (string_of_term_no_pars (lev+1) l) g))
| _ as t -> string_of_term_no_pars lev l t
and string_of_term_no_pars lev l = function
| `Lam _ as t -> string_of_term_no_pars_lam lev l t
| #nf as t -> string_of_term_no_pars_app lev l t
| _ as t -> string_of_term_no_pars lev l t
and string_of_term_no_pars lev l = function
| `Lam _ as t -> string_of_term_no_pars_lam lev l t
| #nf as t -> string_of_term_no_pars_app lev l t
(* FIXME because onlt variables should be in branches of matches, one day *)
| `Var(n,_) -> `Var(n,arity)
| `N _ as t -> t
(* FIXME because onlt variables should be in branches of matches, one day *)
| `Var(n,_) -> `Var(n,arity)
| `N _ as t -> t
-| `Lam(false, t) -> `Lam(false, set_arity arity t)
+| `Lam(false, t, []) -> `Lam(false, set_arity arity t, [])
| `Match(t,(n,_),bs_lift,bs,args) -> `Match(t,(n,arity),bs_lift,bs,args)
| `I _ | `Lam _ -> assert false
| `Match(t,(n,_),bs_lift,bs,args) -> `Match(t,(n,arity),bs_lift,bs,args)
| `I _ | `Lam _ -> assert false
match h with
`I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
| `Var v -> `I(v, Listx.Nil arg)
match h with
`I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
| `Var v -> `I(v, Listx.Nil arg)
| `Match(t,v,lift,bs,args) -> `Match(t,v,lift,bs,List.append args [arg])
| `N _ -> assert false (* Numbers cannot be applied *)
(*in let l = ["v0";"v1";"v2"] in
| `Match(t,v,lift,bs,args) -> `Match(t,v,lift,bs,List.append args [arg])
| `N _ -> assert false (* Numbers cannot be applied *)
(*in let l = ["v0";"v1";"v2"] in
and subst truelam delift_by_one what (with_what : nf) (where : nf) =
let rec aux_propagate_arity ar = function
and subst truelam delift_by_one what (with_what : nf) (where : nf) =
let rec aux_propagate_arity ar = function
- | `Lam(false, t) when not delift_by_one -> `Lam(false, aux_propagate_arity ar t)
+ | `Lam(false,t,g) when not delift_by_one -> assert (g = []); `Lam(false,aux_propagate_arity ar t,[])
| `Match(`I(v,args),(x,_),liftno,bs,args') when not delift_by_one ->
`Match(`I(v,args),(x,ar),liftno,bs,args')
| `Var(i,oldar) -> `Var(i, if truelam then (assert (oldar = min_int); ar) else oldar)
| `Match(`I(v,args),(x,_),liftno,bs,args') when not delift_by_one ->
`Match(`I(v,args),(x,ar),liftno,bs,args')
| `Var(i,oldar) -> `Var(i, if truelam then (assert (oldar = min_int); ar) else oldar)
| `N _ as x -> x
| `Match(t,v,bs_lift,bs,args) ->
let bs_lift = bs_lift + if delift_by_one then -1 else 0 in
| `N _ as x -> x
| `Match(t,v,bs_lift,bs,args) ->
let bs_lift = bs_lift + if delift_by_one then -1 else 0 in
- (* let l' = l - bs_lift in *)
- (* let with_what' = lift l' (with_what :> nf) in *)
+ (* Warning! It now applies again the substitution in branches of matches.
+ But careful, it does it many times, for every occurrence of
+ the match. This is okay because what does not occur in with_what. *)
+ let l' = l - bs_lift in
+ let with_what' = lift l' (with_what :> nf) in
(* The following line should be the identity when delift_by_one = true because we
are assuming the ts to not contain lambda-bound variables. *)
(* The following line should be the identity when delift_by_one = true because we
are assuming the ts to not contain lambda-bound variables. *)
- | `Lam(b, nf) -> `Lam(b, aux (l+1) nf)
+ | `Lam(b, nf, g) -> `Lam(b, aux (l+1) nf, List.map (aux (l+1)) g)
(*in let ll = ["v0";"v1";"v2"] in
prerr_endline ("subst l:" ^ string_of_int l ^ " delift_by_one:" ^ string_of_bool delift_by_one ^ " what:" ^ (List.nth ll what) ^ " with_what:" ^ print ~l:ll with_what ^ " where:" ^ print ~l:ll iii ^ " res:" ^ print ~l:ll res); res*)
in
(*in let ll = ["v0";"v1";"v2"] in
prerr_endline ("subst l:" ^ string_of_int l ^ " delift_by_one:" ^ string_of_bool delift_by_one ^ " what:" ^ (List.nth ll what) ^ " with_what:" ^ print ~l:ll with_what ^ " where:" ^ print ~l:ll iii ^ " res:" ^ print ~l:ll res); res*)
in
- | `Lam(_,t1), `Lam(_,t2) -> aux t1 t2
- | `Lam(_,t1), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
- | t2, `Lam(_,t1) -> aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
+ | `Lam(_,t1,_), `Lam(_,t2,_) -> aux t1 t2
+ | `Lam(_,t1,_), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
+ | t2, `Lam(_,t1,_) -> aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
| `N n1, `N n2 -> compare n1 n2
| `Match(u,_,bs_lift,bs,args), `Match(u',_,bs_lift',bs',args') ->
let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in
| `N n1, `N n2 -> compare n1 n2
| `Match(u,_,bs_lift,bs,args), `Match(u',_,bs_lift',bs',args') ->
let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in
| `Match(u,ar,liftno,bs,args) ->
eta_subterm sub (u :> nf)
|| List.exists (fun (_, t) -> eta_subterm sub (lift liftno t)) !bs
| `Match(u,ar,liftno,bs,args) ->
eta_subterm sub (u :> nf)
|| List.exists (fun (_, t) -> eta_subterm sub (lift liftno t)) !bs
| `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l args)) (aux_tms l (List.map snd !bs))
| `N _ -> None
and aux_tms l =
| `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l args)) (aux_tms l (List.map snd !bs))
| `N _ -> None
and aux_tms l =
| `Match(u,orig,liftno,bs,args) -> Util.concat_map (aux l) args
| `I((n,_), args) -> if n = var + l then [Listx.last args] else []
| `N _
| `Match(u,orig,liftno,bs,args) -> Util.concat_map (aux l) args
| `I((n,_), args) -> if n = var + l then [Listx.last args] else []
| `N _
let arity = match max_arity_tms (m-n) tms with None -> -666 | Some x -> x in
arity :: (aux (n-1) tms)
in fun tms -> List.rev (aux m tms)
let arity = match max_arity_tms (m-n) tms with None -> -666 | Some x -> x in
arity :: (aux (n-1) tms)
in fun tms -> List.rev (aux m tms)