| `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 =
| n when n > 0 -> `Lam (false, lift 1 (make_lams t (n-1)))
| _ -> assert false
-let free_vars =
+let free_vars' =
let rec aux n = function
`N _ -> []
- | `Var(x,_) -> if x < n then [] else [x-n]
- | `I((x,_),args) ->
- (if x < n then [] else [x-n]) @
+ | `Var(x,ar) -> if x < n then [] else [(x-n,ar)]
+ | `I((x,ar),args) ->
+ (if x < n then [] else [(x-n,ar)]) @
List.concat (List.map (aux n) (Listx.to_list args))
| `Lam(_,t) -> aux (n+1) t
| `Match(t,_,liftno,bs,args) ->
List.concat (List.map (aux n) args)
in aux 0
;;
+let free_vars = (List.map fst) ++ free_vars';;
module ToScott =
struct
(************ 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 ^ ")"
- | `Match(t,_,bs_lift,bs,args) ->
- "(match " ^ string_of_term_no_pars l (t :> nf) ^
+ | `Match(t,(v,ar),bs_lift,bs,args) ->
+ "[match("^ string_of_var v ^":"^ string_of_int ar ^") " ^ string_of_term_no_pars l (t :> nf) ^
" 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 rec set_arity arity = function
+| `Var(n,_) -> `Var(n,arity)
+| `N _ as t -> 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
+
+let minus1 n = if n = min_int then n else n - 1;;
+
let rec mk_app (h : nf) (arg : nf) =
(*let res =*)
match h with
`I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
| `Var v -> `I(v, Listx.Nil arg)
- | `Lam(_,nf) -> subst true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
+ | `Lam(truelam,nf) -> subst truelam true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
| `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 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 (minus1 ar) 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)
-
-and subst delift_by_one what (with_what : nf) (where : nf) =
+ `Match (t,(n,ar),bs_lift,bs,args))
+ | `I _ | `Var _ | `Match _ -> `Match(t,(n,ar),bs_lift,bs,args)
+
+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)
+ | `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)
+ | _ 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
let with_what' = lift l' with_what 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. *)
- bs := List.map (fun (n,t) -> n,subst false what with_what' t) !bs ;
+ bs := List.map (fun (n,t) -> n,subst truelam false what with_what' t) !bs ;
mk_match (cast_to_i_num_var (aux_i_num_var l t)) v bs_lift bs (List.map (aux l) args)
and aux l(*lift*) =
(*function iii -> let res = match iii with*)
(************ Parsing ************************************)
let parse' strs =
+ let fix_arity = function
+ | `I((n,_),args) -> `I((n,1+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,1) 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 max a b = match a, b with
+ | None, None -> None
+ | None, Some x
+ | Some x, None -> Some x
+ | Some x, Some y -> Some (Pervasives.max x y) in
+ let aux_var l (m,a) = if n + l = m then Some a else None 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 _ -> None
+ and aux_tms l =
+ List.fold_left (fun acc t -> Pervasives.max acc (aux l t)) None 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 = 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 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
+;;
projects / fireball-separation.git / blobdiff