open Util.Vars
open Pure
+(* debug options *)
+let debug_display_arities = false;;
+
(************ Syntax ************************************)
(* Normal forms*)
| I of int * nf listx
;;*)
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_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list
+type 'nf_nob i_var_ = [ `I of var * 'nf_nob Listx.listx | `Var of var ]
+type 'nf_nob i_n_var_ = [ `N of int | 'nf_nob i_var_ ]
+type ('nf_nob,'nf) i_num_var_ = [
+ | 'nf_nob i_n_var_
+ | `Match of ('nf_nob,'nf) i_num_var_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf_nob list
]
-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_;;
-type i_num_var = nf i_num_var_;;
+type 'nf nf_nob_ = [ `Lam of (* was_unpacked *) bool * 'nf | `Pacman | ('nf nf_nob_,'nf) i_num_var_ ]
+type nf = [ nf nf_nob_ | `Bottom ]
+type nf_nob = nf nf_nob_
+type i_var = nf_nob i_var_;;
+type i_n_var = nf_nob i_n_var_;;
+type i_num_var = (nf_nob,nf) i_num_var_;;
let hd_of_i_var =
function
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(v,args) -> `I(aux_var l v, Listx.map (aux l) args)
+ `I(v,args) -> `I(aux_var l v, Listx.map (aux_nob l) args)
| `Var v -> `Var(aux_var l v)
| `N _ as x -> x
| `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 =
+ `Match(aux_i_num_var l t, v, lift + m, bs, List.map (aux_nob l) args)
+ and aux_nob l =
function
- #i_num_var as x -> (aux_i_num_var l x :> nf)
+ #i_num_var as x -> (aux_i_num_var l x :> nf_nob)
| `Lam(b,nf) -> `Lam (b, aux (l+1) nf)
+ | `Pacman -> `Pacman
+ and aux l =
+ function
+ #nf_nob as x -> (aux_nob l x :> nf)
+ | `Bottom -> `Bottom
in
(aux 0 t : nf)
;;
| 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]) @
- List.concat (List.map (aux n) (Listx.to_list args))
+ | `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 :> nf list))
| `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)
+ List.concat (List.map (aux n) (args :> nf list))
+ | `Bottom | `Pacman -> []
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
- | `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
-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)
-
+let rec scott_of_nf = function
+ | `N n -> Scott.mk_n n
+ | `Var(v,_) -> Pure.V v
+ | `Match(t,_,liftno,bs,args) ->
+ let bs = List.map (fun (n,t) -> n, scott_of_nf (lift liftno (t :> nf))) !bs in
+ let t = scott_of_nf (t :> nf) in
+ let m = Scott.mk_match t bs in
+ List.fold_left (fun acc t -> Pure.A(acc,scott_of_nf t)) m (args :> nf list)
+ | `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,scott_of_nf t)) (Pure.V v) (args :> nf Listx.listx)
+ | `Lam(_,t) -> Pure.L (scott_of_nf t)
+ | `Bottom -> Pure.B
+ | `Pacman -> let f x = Pure.A (x,x) in f (Pure.L (Pure.L (f (Pure.V 0))))
end
(************ Pretty-printing ************************************)
-let rec string_of_term l =
- let rec string_of_term_w_pars l = function
- | `Var(n,ar) -> print_name l n ^ ":" ^ string_of_int ar
+(* let rec string_of_term l = fun _ -> "";; *)
+
+let rec string_of_term l =
+ let rec string_of_term_w_pars l = function
+ | `Var(n,ar) -> print_name 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) ^ ")"
+ | `I _ as t -> "(" ^ string_of_term_no_pars_app l t ^ ")"
+ | `Lam(_,`Bottom) -> "BOMB"
| `Lam _ as t -> "(" ^ string_of_term_no_pars_lam l t ^ ")"
| `Match(t,(v,ar),bs_lift,bs,args) ->
- "[match("^print_name l 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,ar), args) -> print_name l n ^ ":" ^ string_of_int ar ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args))
+ "["^ string_of_var v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",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 :> nf))) !bs) ^ "] " ^
+ String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")"
+ | `Bottom -> "BOT"
+ | `Pacman -> "PAC"
+ and string_of_term_no_pars_app l = function
+ | `I((n,ar), args) -> print_name l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args :> nf list))
| #nf as t -> string_of_term_w_pars l t
and string_of_term_no_pars_lam l = function
+ | `Lam(_,`Bottom) -> "BOMB"
| `Lam(_,t) -> let name = string_of_var (List.length l) in
- "λ" ^ name ^ ". " ^ (string_of_term_no_pars_lam (name::l) t)
+ "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
+ and string_of_term_no_pars l = 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
;;
let print ?(l=[]) = string_of_term l;;
-let string_of_nf t = string_of_term [] (t:>nf);;
+let string_of_nf t = string_of_term [] (t :> nf);;
(************ Hereditary substitutions ************************************)
prerr_endline (print (t :> nf));
assert false (* algorithm failed *)
-let set_arity arity = function
+let rec set_arity arity = function
| `Var(n,_) -> `Var(n,arity)
-| `Lam(false, `N _)
-| `Lam(false, `Lam _) as t -> t
-| `Lam(false, `Match(t,(n,_),bs_lift,bs,args)) -> `Lam(false, `Match(t,(n,arity),bs_lift,bs,args))
-| _ -> assert false
+| `N _ | `Bottom | `Pacman 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(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 *)
+ match arg with
+ | `Bottom -> `Bottom
+ | #nf_nob as arg ->
+ match h with
+ | `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])
+ | `Bottom | `Pacman as t -> t
+ | `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_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 ->
+ let m =
+ match t with
+ `N m as t ->
(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
+ h
with Not_found ->
- `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 aux_propagate_arity ar = function
- | `Lam(false,`Match(`I(v,args),(x,_),liftno,bs,args')) when not delift_by_one ->
- `Lam(false,`Match(`I(v,args),(x,ar),liftno,bs,args'))
+ `Match (t,(n,ar),bs_lift,bs,[]))
+ (* We are assuming that the econding of matches is s.t.:
+ - match PAC.. --> PAC
+ - match BOT.. --> BOT *)
+ | `Bottom -> `Bottom
+ | `Pacman -> `Pacman
+ | `Lam _ -> assert false
+ | `I _ | `Var _ | `Match _ as t -> `Match(t,(n,ar),bs_lift,bs,[]) in
+ mk_appl m args
+
+and subst truelam delift_by_one what (with_what : nf(*_nob*)) (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 (aux_propagate_arity ar with_what)) (Listx.map (aux l) args)
+ let args = Listx.map (aux l) (args :> nf Listx.listx) in
+ mk_appx (lift l (aux_propagate_arity ar (with_what :> nf))) args
else
- `I (((if delift_by_one && n >= l then n-1 else n), ar), Listx.map (aux l) args)
+ mk_appl (`Var ((if delift_by_one && n >= l then n-1 else n), ar)) (List.map (aux l) (Listx.to_list (args :> nf Listx.listx)))
| `Var(n,ar) ->
if n = what + l then
- lift l (aux_propagate_arity ar with_what)
+ lift l (aux_propagate_arity ar (with_what :> nf))
else
`Var((if delift_by_one && n >= l then n-1 else n), ar)
| `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 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 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)
+ let body = 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, nf) -> `Lam(b, aux (l+1) nf)
+ | `Bottom -> `Bottom
+ | `Pacman -> `Pacman
(*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
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) -> fix_arity (mk_app (aux t1) (aux t2))
- | Parser.Var v -> `Var(v,1) in
+ | `I((n,_),args) -> `I((n,1+Listx.length args),args)
+ | _ -> assert false in
let (tms, free) = Parser.parse_many strs in
- List.map aux tms, free
+ (* Replace pacmans and bottoms *)
+ let n_bot = try Util.index_of "BOT" free with Not_found -> min_int in
+ let n_pac = try Util.index_of "PAC" free with Not_found -> min_int in
+ let n_bomb = try Util.index_of "BOMB" free with Not_found -> min_int in
+ let fix lev v =
+ if v = lev + n_bot then `Bottom
+ else if v = lev + n_pac then `Pacman
+ else if v = lev + n_bomb then `Lam(true, `Bottom)
+ else `Var(v,1) in (* 1 by default when variable not applied *)
+ (* Fix arity *)
+ let rec aux lev = function
+ | Parser.Lam t -> `Lam (true, aux (lev+1) t)
+ | Parser.App (t1, t2) -> fix_arity (mk_app (aux lev t1) (aux lev t2))
+ | Parser.Var v -> fix lev v in
+ List.map (aux 0) tms, free
;;
(************** Algorithm(s) ************************)
let rec aux t1 t2 = match t1, t2 with
| `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)
+ clex compare (lex aux) (n1, (Listx.to_list l1 :> nf list)) (n2, (Listx.to_list l2 :> nf list))
+ | `Bottom, `Bottom
+ | `Pacman, `Pacman -> 0
| `Lam _, `N _ -> -1
| `N _, `Lam _ -> 1
+ | `Bottom, `Lam _
+ | `Lam _, `Bottom -> assert false (* TO BE UNDERSTOOD *)
| `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)))
| `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 bs' = List.sort (fun (n,_) (m,_) -> compare n m) !bs' in
- clex aux (clex (lex (clex compare aux)) (lex aux)) ((u :> nf), (bs, args)) ((u' :> nf), (bs', args'))
+ clex aux (clex (lex (clex compare aux)) (lex aux)) ((u :> nf), (bs, (args :> nf list))) ((u' :> nf), (bs', (args' :> nf list)))
| `Match _, _ -> -1
| _, `Match _ -> 1
| `N _, _ -> -1
| _, `N _ -> 1
| `I _, _ -> -1
| _, `I _ -> 1
+ | `Bottom, _ -> -1
+ | _, `Bottom -> 1
+ | `Pacman, _ -> -1
+ | _, `Pacman -> 1
in aux x y
;;
if eta_eq sub t then true else
match t with
| `Lam(_,t') -> eta_subterm (lift 1 sub) t'
+ | `Bottom
+ | `Pacman -> false
| `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
+ || 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'))
+ && List.for_all (fun (x,y) -> eta_eq x y) (List.combine (Util.take (Listx.length args') (Listx.to_list args :> nf list)) (Listx.to_list args' :> nf list))
| _ -> false
)
| `N _ | `Var _ -> 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
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))
+ | `I(v,tms) -> max (aux_var l v) (aux_tms l (Listx.to_list tms :> nf list))
| `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
+ | `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l (args :> nf list))) (aux_tms l (List.map snd !bs))
+ | `N _ | `Bottom | `Pacman -> None
and aux_tms l =
- List.fold_left (fun acc t -> Pervasives.max acc (aux l t)) None in
+ 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