--- /dev/null
+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 * 'nf Listx.listx | `Var of int ]
+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_ * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list
+]
+type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ | `Bomb | `Pacman | '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 _ | `Bomb -> assert false
+
+let lift m (t : nf) =
+ 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)
+ | `N _ as x -> x
+ | `Match(t,lift,bs,args) ->
+ `Match(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)
+ | `Bomb -> `Bomb
+ | `Pacman -> `Pacman
+ 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)
+ | `Bomb | `Pacman -> []
+ 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)
+ | `Bomb -> let f x = Pure.A (x,x) in f (Pure.L (f (Pure.V 0)))
+ | `Pacman -> let f x = Pure.A (x,x) in f (Pure.L (Pure.L (f (Pure.V 0))))
+
+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) ^ ")"
+ | `Bomb -> "TNT"
+ | `Pacman -> "PAC"
+ 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 rec print ?(l=[]) = string_of_term l;;
+
+(************ 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(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)
+ | `Match(t,lift,bs,args) -> `Match(t,lift,bs,List.append args [arg])
+ | `N _ -> assert false (* Numbers cannot be applied *)
+ | `Bomb | `Pacman -> failwith "mk_app su bomba o pacman"
+(*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 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 (t,bs_lift,bs,args))
+ | `I _ | `Var _ | `Match _ -> `Match(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(n,args) ->
+ if n = what + l then
+ mk_appx (lift l 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 ->
+ if n = what + l then
+ lift l with_what
+ else
+ `Var (if delift_by_one && n >= l then n-1 else n)
+ | `N _ as x -> x
+ | `Match(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 (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)
+ | `Bomb -> `Bomb
+ | `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
+ 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 v
+ in let (tms, free) = Parser.parse_many strs
+ in (List.map aux tms, free)
+;;
+
+(************** Algorithm(s) ************************)
+
+let eta_eq x y =
+ let rec aux = function
+ | `Var n , `Var m -> n = m
+ | `I(n1, l1), `I(n2, l2) ->
+ n1 = n2 && Listx.length l1 = Listx.length l2 &&
+ List.for_all aux (List.combine (Listx.to_list l1) (Listx.to_list l2))
+ | `Lam(_,t1), `Lam(_,t2) -> aux (t1,t2)
+ | `Lam(_,t1), t2
+ | t2, `Lam(_,t1) -> aux( t1, (mk_app (lift 1 t2) (`Var 0)) )
+ | `N n1, `N n2 -> n1 = n2
+ | `Match(u,bs_lift,bs,args), `Match(u',bs_lift',bs',args') ->
+ aux ((u :> nf), (u' :> nf)) && List.length !bs = List.length !bs' &&
+ let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in
+ let bs' = List.sort (fun (n,_) (m,_) -> compare n m) !bs' in
+ List.for_all (fun ((n,t),(n',t')) -> n = n' && aux (t, t')) (List.combine bs bs') && List.length args = List.length args' &&
+ List.for_all aux (List.combine args args')
+ | _ -> false
+ in aux (x, y)
+;;
+
+let eta_compare x y =
+ if eta_eq x y then 0 else compare x y
+;;
+
+let eta_eq (#nf as x) (#nf as y) = eta_eq 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 _ | `Bomb | `Pacman -> false
+;;
+
+let eta_subterm (#nf as x) (#nf as y) = eta_subterm x y;;
projects / fireball-separation.git / blobdiff