Removed old .ar files

diff --git a/ocaml/num.ml.ar b/ocaml/num.ml.ar
deleted file mode 100644 (file)
index 6a11731..0000000
--- a/ocaml/num.ml.ar
+++ /dev/null
@@ -1,294 +0,0 @@
-open Util
-open Util.Vars
-open Pure
-
-(************ Syntax ************************************)
-
-(* Normal forms*)
-
-(* Var n = n-th De Bruijn index, 0-based *)
-
-(*type nf =
-  | Lam of nf
-  | Var of int
-  | i
-and i =
-  | I of int * nf listx
-;;*)
-type 'nf i_var_ = [ `I of int * int * 'nf Listx.listx | `Var of int * int ]
-type 'nf i_n_var_ = [ `N of int | 'nf i_var_ ]
-type 'nf i_num_var_ = [
-  | 'nf i_n_var_
-  | `Match of int * 'nf i_num_var_ * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf 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_;;
-
-let hd_of_i_var =
- function
-   `I (_,v,_)
- | `Var (_,v) -> v
-
-let hd_of =
- function
-   `I (_,v,_)
- | `Var (_,v) -> Some v
- | `N _ -> None
- | `Match _ -> assert false
-
-let lift m (t : nf) =
- let rec aux_i_num_var l =
-  function
-    `I(ar,n,args) -> (`I(ar,(if n < l then n else n+m),Listx.map (aux l) args) : i_num_var)
-   | `Var (ar,n) -> `Var (ar, if n < l then n else n+m)
-   | `N _ as x -> x
-   | `Match(ar,t,lift,bs,args) ->
-      `Match(ar,aux_i_num_var l t, 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,nf) -> `Lam (b,aux (l+1) nf)
- in
-  (aux 0 t : nf)
-;;
-
-(* put t under n lambdas, lifting t accordingtly *)
-let rec make_lams t =
- function
-   0 -> t
- | n when n > 0 -> `Lam (false,lift 1 (make_lams t (n-1)))
- | _ -> assert false
-
-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))
-  | `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
-;;
-
-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)
-
-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 =
- let rec string_of_term_w_pars l = function
-  | `Var (_,n) -> print_name l n
-  | `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
-;;
-
-let print ?(l=[]) = string_of_term l;;
-let string_of_nf t = string_of_term [] (t:>nf);;
-
-(************ Hereditary substitutions ************************************)
-
-let cast_to_i_var =
- function
-    #i_var as y -> (y : i_var)
-  | t ->
-    prerr_endline (print (t :> nf));
-    assert false (* algorithm failed *)
-
-let cast_to_i_n_var =
- function
-    #i_n_var as y -> (y : i_n_var)
-  | t ->
-    prerr_endline (print (t :> nf));
-    assert false (* algorithm failed *)
-
-let cast_to_i_num_var =
- function
-    #i_num_var as y -> (y : i_num_var)
-  | t ->
-    prerr_endline (print (t :> nf));
-    assert false (* algorithm failed *)
-
-let rec mk_app (h : nf) (arg : nf) =
-(*let res =*)
- match h with
-    `I(ar,n,args) -> `I(ar,n,Listx.append (Listx.Nil arg) args)
-  | `Var (ar,n) -> `I(ar,n, Listx.Nil arg)
-  | `Lam(_,nf) -> subst true 0 arg (nf : nf)
-  | `Match(ar,t,lift,bs,args) -> `Match(ar,t,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_appl h args =
- (*prerr_endline ("MK_APPL: " ^ print h ^ " " ^ String.concat " " (List.map print args));*)
- List.fold_left mk_app h args
-
-and mk_appx h args = Listx.fold_left mk_app h args
-
-and mk_match ar t 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 = lift bs_lift h in
-        mk_appl h args
-       with Not_found ->
-        `Match (ar,t,bs_lift,bs,args))
-  | `I _ | `Var _ | `Match _ -> `Match(ar,t,bs_lift,bs,args)
-
-and subst delift_by_one what (with_what : nf) (where : nf) =
- let rec aux_i_num_var l =
-  function
-     `I(ar,n,args) ->
-       if n = what + l then
-        mk_appx (lift l with_what) (Listx.map (aux l) args)
-       else
-        `I (ar,(if delift_by_one && n >= l then n-1 else n), Listx.map (aux l) args)
-   | `Var (ar,n) ->
-       if n = what + l then
-        lift l with_what
-       else
-        `Var (ar,if delift_by_one && n >= l then n-1 else n)
-   | `N _ as x -> x
-   | `Match(ar,t,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
-       (* 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 ar (cast_to_i_num_var (aux_i_num_var l t)) bs_lift bs (List.map (aux l) args)
- 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)
-(*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,aux t)
-  | Parser.App (t1, t2) -> mk_app (aux t1) (aux t2)
-  | Parser.Var v -> `Var (-1,v)
-  in let (tms, free) = Parser.parse_many strs
-  in (List.map aux tms, free)
-;;
-
-(************** Algorithm(s) ************************)
-
-let eta_compare x y =
- (* let clex a b = let diff = ? a b in if diff = 0 then cont () else 0 in *)
- let clex aux1 aux2 (a1,a2) (b1,b2) =
-  let diff = aux1 a1 b1 in if diff = 0 then aux2 a2 b2 else diff in
- let rec lex aux l1 l2 =
-  match l1,l2 with
- | [], [] -> 0
- | [], _ -> -1
- | _, [] -> 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) ->
-    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 (-1,0)))
-  | t2, `Lam(_,t1) ->   aux t1 (mk_app (lift 1 t2) (`Var (-1,0)))
-  | `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 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'))
-  | `Match _, _ -> -1
-  | _, `Match _ -> 1
-  | `N _, _ -> -1
-  | _, `N _ -> 1
-  | `I _, _ -> -1
-  | _, `I _ -> 1
-  in aux x y
-;;
-
-let eta_eq (#nf as x) (#nf as y) = 0 = eta_compare x y ;;
-
-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'
-  | `Match(_,u,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'
-    && 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
-   )
-  | `N _ | `Var _ -> false
-;;
-
-let eta_subterm (#nf as x) (#nf as y) = eta_subterm x y;;