| `N _ -> None
| `Match _ -> assert false
+let arity_of_hd =
+function
+ `I ((_,a),_)
+| `Var(_,a) -> a
+| _ -> 0 (* FIXME? *)
+
let lift m (t : nf) =
let aux_var l (n, ar) = (if n < l then n else n+m), ar in
let rec aux_i_num_var l =
(************ Pretty-printing ************************************)
-let rec print ?(l=[]) =
- function
- `Var(n,_) -> print_name l n
- | `N n -> string_of_int n
- | `Match(t,_,bs_lift,bs,args) ->
- "([" ^ print ~l (t :> nf) ^
- " ? " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ print ~l (lift bs_lift t)) !bs) ^ "] " ^
- String.concat " " (List.map (print ~l) args) ^ ")"
- | `I((n,_),args) -> "(" ^ print_name l n ^ " " ^ String.concat " " (Listx.to_list (Listx.map (print ~l) args)) ^ ")"
- | `Lam(_,nf) ->
- let name = string_of_var (List.length l) in
- "λ" ^ name ^ "." ^ print ~l:(name::l) (nf : nf)
-;;
-
let rec string_of_term l =
let rec string_of_term_w_pars l = function
- | `Var(n,_) -> print_name l n
+ | `Var(n,ar) -> print_name l n ^ ":" ^ string_of_int ar
| `N n -> string_of_int n
| `I _ as t -> "(" ^ string_of_term_no_pars_app l (t :> nf) ^ ")"
| `Lam _ as t -> "(" ^ string_of_term_no_pars_lam l t ^ ")"
" with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (lift bs_lift t)) !bs) ^ "] " ^
String.concat " " (List.map (string_of_term l) args) ^ ")"
and string_of_term_no_pars_app l = function
- | `I((n,_), args) -> print_name l n ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args))
+ | `I((n,ar), args) -> print_name l n ^ ":" ^ string_of_int ar ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args))
| #nf as t -> string_of_term_w_pars l t
and string_of_term_no_pars_lam l = function
| `Lam(_,t) -> let name = string_of_var (List.length l) in
prerr_endline (print (t :> nf));
assert false (* algorithm failed *)
+let set_arity arity = function
+| `Var(n,_) -> `Var(n,arity)
+| `Lam(false, `N _)
+| `Lam(false, `Lam _) as t -> t
+| `Lam(false, `Match(t,(n,ar),bs_lift,bs,args)) -> `Lam(false, `Match(t,(n,arity),bs_lift,bs,args))
+| _ -> assert false
+
let rec mk_app (h : nf) (arg : nf) =
(*let res =*)
match h with
and mk_appx h args = Listx.fold_left mk_app h args
-and mk_match t ar bs_lift bs args =
+and mk_match t (n,ar) bs_lift bs args =
(*prerr_endline ("MK_MATCH: ([" ^ print t ^ "] " ^ String.concat " " (Listx.to_list (Listx.map (fun (n,t) -> string_of_int n ^ " => " ^ print t) bs)) ^ ") " ^ String.concat " " (List.map print args));*)
match t with
`N m ->
(try
let h = List.assoc m !bs in
+ let h = set_arity (ar-1) h in
let h = lift bs_lift h in
mk_appl h args
with Not_found ->
- `Match (t,ar,bs_lift,bs,args))
- | `I _ | `Var _ | `Match _ -> `Match(t,ar,bs_lift,bs,args)
+ `Match (t,(n,ar),bs_lift,bs,args))
+ | `I _ | `Var _ | `Match _ -> `Match(t,(n,ar),bs_lift,bs,args)
and subst delift_by_one what (with_what : nf) (where : nf) =
+ let aux_propagate_arity ar = function
+ | `Lam(false,`Match(`I(v,args),(x,_),liftno,bs,args')) ->
+ `Lam(false,`Match(`I(v,args),(x,ar),liftno,bs,args'))
+ | _ as t -> t in
let rec aux_i_num_var l =
function
`I((n,ar),args) ->
if n = what + l then
- mk_appx (lift l with_what) (Listx.map (aux l) args)
+ mk_appx (lift l (aux_propagate_arity ar with_what)) (Listx.map (aux l) args)
else
`I (((if delift_by_one && n >= l then n-1 else n), ar), Listx.map (aux l) args)
| `Var(n,ar) ->
if n = what + l then
- lift l with_what
+ lift l (aux_propagate_arity ar with_what)
else
`Var((if delift_by_one && n >= l then n-1 else n), ar)
| `N _ as x -> x
(************ Parsing ************************************)
let parse' strs =
+ let fix_arity = function
+ | `I((n,_),args) -> `I((n,Listx.length args),args)
+ | _ -> assert false in
let rec aux = function
| Parser.Lam t -> `Lam (true, aux t)
- | Parser.App (t1, t2) -> mk_app (aux t1) (aux t2)
- | Parser.Var v -> `Var(v,-666)
- in let (tms, free) = Parser.parse_many strs
- in (List.map aux tms, free)
+ | Parser.App (t1, t2) -> fix_arity (mk_app (aux t1) (aux t2))
+ | Parser.Var v -> `Var(v,0) in
+ let (tms, free) = Parser.parse_many strs in
+ List.map aux tms, free
;;
(************** Algorithm(s) ************************)
;;
let eta_subterm (#nf as x) (#nf as y) = eta_subterm x y;;
+
+
+let max_arity_tms n =
+ let aux_var l (m,a) = if n + l = m then a else -1 in
+ let rec aux l = function
+ | `Var v -> aux_var l v
+ | `I(v,tms) -> max (aux_var l v) (aux_tms l (Listx.to_list tms))
+ | `Lam(_,t) -> aux (l+1) t
+ | `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l args)) (aux_tms l (List.map snd !bs))
+ | `N _ -> -1
+ and aux_tms l =
+ List.fold_left (fun acc t -> Pervasives.max acc (aux l t)) ~-1 in
+ fun tms -> aux_tms 0 (tms :> nf list)
+;;
+
+let get_first_args var =
+let rec aux l = function
+| `Lam(_,t) -> aux (l+1) t
+| `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 _
+| `Var _ -> []
+in aux 0
+;;
+
+let compute_arities m =
+ let rec aux n tms =
+ if n = 0
+ then []
+ else
+ let tms = Util.filter_map (function `Lam(_,t) -> Some t | _ -> None ) tms in
+ let arity = max 0 (max_arity_tms (m-n) tms) in (* FIXME: 0 or -1 ??? *)
+ arity :: (aux (n-1) tms)
+ in fun tms -> List.rev (aux m tms)
+;;
+
+let compute_arities var special_k all_tms =
+ let tms = List.fold_left (fun acc t -> acc @ (get_first_args var t)) [] all_tms in
+ compute_arities special_k tms
+;;