open Util.Vars
open Pure
+(* debug options *)
+let debug_display_arities = false;;
+
(************ Syntax ************************************)
(* Normal forms*)
and i =
| I of int * nf listx
;;*)
-type 'nf i_var_ = [ `I of int * 'nf Listx.listx | `Var of int ]
+type var = int * (* arity of variable*) int;;
+type 'nf i_var_ = [ `I of var * 'nf Listx.listx | `Var of var ]
type 'nf i_n_var_ = [ `N of int | 'nf i_var_ ]
type 'nf i_num_var_ = [
| 'nf i_n_var_
- | `Match of 'nf i_num_var_ * (* arity of branches *) int * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list
+ | `Match of 'nf i_num_var_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list
]
-type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * (* arity of variable*) int * 'nf nf_ | 'nf i_num_var_ ]
+type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ | 'nf i_num_var_ ]
type nf = nf nf_
type i_var = nf i_var_;;
type i_n_var = nf i_n_var_;;
let hd_of_i_var =
function
- `I (v,_)
- | `Var v -> v
+ `I ((v,_),_)
+ | `Var (v,_) -> v
let hd_of =
function
- `I (v,_)
- | `Var v -> Some v
+ `I ((v,_),_)
+ | `Var(v,_) -> Some v
| `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 =
function
- `I(n,args) -> (`I((if n < l then n else n+m),Listx.map (aux l) args) : i_num_var)
- | `Var n -> `Var (if n < l then n else n+m)
+ `I(v,args) -> `I(aux_var l v, Listx.map (aux l) args)
+ | `Var v -> `Var(aux_var l v)
| `N _ as x -> x
- | `Match(t,ar,lift,bs,args) ->
- `Match(aux_i_num_var l t, ar,lift + m, bs, List.map (aux l) args)
+ | `Match(t,v,lift,bs,args) ->
+ `Match(aux_i_num_var l t, v, lift + m, bs, List.map (aux l) args)
and aux l =
function
#i_num_var as x -> (aux_i_num_var l x :> nf)
- | `Lam(b,ar,nf) -> `Lam (b,ar,aux (l+1) nf)
+ | `Lam(b,nf) -> `Lam (b, aux (l+1) nf)
in
(aux 0 t : nf)
;;
let rec make_lams t =
function
0 -> t
- | n when n > 0 -> `Lam (false,-666,lift 1 (make_lams t (n-1)))
+ | 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
+ | `Lam(_,t) -> aux (n+1) t
| `Match(t,_,liftno,bs,args) ->
aux n (t :> nf) @
List.concat (List.map (fun (_,t) -> aux (n-liftno) t) !bs) @
List.concat (List.map (aux n) args)
in aux 0
;;
+let free_vars = (List.map fst) ++ free_vars';;
module ToScott =
struct
let rec t_of_i_num_var =
function
| `N n -> Scott.mk_n n
- | `Var v -> Pure.V v
+ | `Var(v,_) -> Pure.V v
| `Match(t,_,liftno,bs,args) ->
let bs = List.map (fun (n,t) -> n, t_of_nf (lift liftno t)) !bs in
let t = t_of_i_num_var t in
let m = Scott.mk_match t bs in
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
+ | `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
- | `Lam(b,_,f) -> Pure.L (t_of_nf f)
+ | `Lam(b,f) -> Pure.L (t_of_nf f)
end
(************ 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 = fun _ -> "";; *)
-let rec string_of_term l =
- let rec string_of_term_w_pars l = function
- | `Var n -> print_name l n
+let rec string_of_term =
+ let boundvar x = "v" ^ string_of_int x in
+ let varname lev l n =
+ if n < lev then boundvar (lev-n-1)
+ else if n < List.length l then List.nth l (n-lev)
+ 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 "")
| `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) ^
- " 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))
- | #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
- "λ" ^ name ^ ". " ^ (string_of_term_no_pars_lam (name::l) t)
- | _ as t -> string_of_term_no_pars l t
- and string_of_term_no_pars l : nf -> string = function
- | `Lam _ as t -> string_of_term_no_pars_lam l t
- | #nf as t -> string_of_term_no_pars_app l t
- in string_of_term_no_pars l
+ | `I _ as t -> "(" ^ string_of_term_no_pars_app lev l t ^ ")"
+ | `Lam _ as t -> "(" ^ string_of_term_no_pars_lam lev l t ^ ")"
+ | `Match(t,(v,ar),bs_lift,bs,args) ->
+ (* assert (bs_lift = lev); *)
+ "(["^ varname 0 l v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",match " ^ string_of_term_no_pars lev l (t :> nf) ^
+ " 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)
+ | _ 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
+ in string_of_term_no_pars 0
;;
let print ?(l=[]) = string_of_term l;;
prerr_endline (print (t :> nf));
assert false (* algorithm failed *)
+let rec set_arity arity = function
+(* 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)
+| `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(n,args) -> `I(n,Listx.append (Listx.Nil arg) args)
- | `Var n -> `I(n, Listx.Nil arg)
- | `Lam(_,_,nf) -> subst true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
- | `Match(t,ar,lift,bs,args) -> `Match(t,ar,lift,bs,List.append args [arg])
+ `I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
+ | `Var v -> `I(v, Listx.Nil arg)
+ | `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
prerr_endline ("mk_app h:" ^ print ~l h ^ " arg:" ^ print ~l:l arg ^ " res:" ^ print ~l:l res); res*)
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,args) ->
+ `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), Listx.map (aux l) args)
- | `Var n ->
+ `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)
+ `Var((if delift_by_one && n >= l then n-1 else n), ar)
| `N _ as x -> x
- | `Match(t,ar,bs_lift,bs,args) ->
+ | `Match(t,v,bs_lift,bs,args) ->
let bs_lift = bs_lift + if delift_by_one then -1 else 0 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 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. *)
- bs := List.map (fun (n,t) -> n,subst false what with_what' t) !bs ;
- mk_match (cast_to_i_num_var (aux_i_num_var l t)) ar bs_lift bs (List.map (aux l) args)
+ bs := List.map (fun (n,t) -> n,subst truelam false what with_what' t) !bs ;
+ let body = cast_to_i_num_var (aux_i_num_var l t) in
+ mk_match body v bs_lift bs (List.map (aux l) (args :> nf list))
and aux l(*lift*) =
(*function iii -> let res = match iii with*)
function
| #i_num_var as x -> aux_i_num_var l x
- | `Lam(b,ar,nf) -> `Lam(b,ar,aux (l+1) nf)
+ | `Lam(b, nf) -> `Lam(b, aux (l+1) nf)
(*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
aux 0 where
;;
-(************ Parsing ************************************)
-
-let parse' strs =
- let rec aux = function
- | Parser.Lam t -> `Lam (true,-666,aux t)
- | Parser.App (t1, t2) -> mk_app (aux t1) (aux t2)
- | Parser.Var v -> `Var v
- in let (tms, free) = Parser.parse_many strs
- in (List.map aux tms, free)
-;;
-
(************** Algorithm(s) ************************)
let eta_compare x y =
| _, [] -> 1
| x::xs, y::ys -> clex aux (lex aux) (x,xs) (y,ys) in
let rec aux t1 t2 = match t1, t2 with
- | `Var n , `Var m -> compare n m
- | `I(n1, l1), `I(n2, l2) ->
+ | `Var(n,_) , `Var(m,_) -> compare n m
+ | `I((n1,_), l1), `I((n2,_), l2) ->
clex compare (lex aux) (n1, Listx.to_list l1) (n2, Listx.to_list l2)
| `Lam _, `N _ -> -1
| `N _, `Lam _ -> 1
- | `Lam(_,_,t1), `Lam(_,_,t2) -> aux t1 t2
- | `Lam(_,_,t1), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var 0))
- | t2, `Lam(_,_,t1) -> aux t1 (mk_app (lift 1 t2) (`Var 0))
+ | `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
let rec eta_subterm sub t =
if eta_eq sub t then true else
match t with
- | `Lam(_,_,t') -> eta_subterm (lift 1 sub) t'
+ | `Lam(_,t') -> eta_subterm (lift 1 sub) t'
| `Match(u,ar,liftno,bs,args) ->
eta_subterm sub (u :> nf)
|| List.exists (fun (_, t) -> eta_subterm sub (lift liftno t)) !bs
- || List.exists (eta_subterm sub) args
- | `I(v, args) -> List.exists (eta_subterm sub) (Listx.to_list args) || (match sub with
- | `Var v' -> v = v'
- | `I(v', args') -> v = v'
+ || List.exists (eta_subterm sub) (args :> nf list)
+ | `I((v,_), args) -> List.exists (eta_subterm sub) ((Listx.to_list args) :> nf list) || (match sub with
+ | `Var(v',_) -> v = v'
+ | `I((v',_), args') -> v = v'
&& Listx.length args' < Listx.length args
&& List.for_all (fun (x,y) -> eta_eq x y) (List.combine (Util.take (Listx.length args') (Listx.to_list args)) (Listx.to_list args'))
| _ -> false
;;
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 -> 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