For Scott's encoding, two.
*)
let num_more_args = 2;;
+let _very_verbose = false;;
+
+let verbose s =
+ if _very_verbose then prerr_endline s
+;;
let convergent_dummy = `N ~-1;
; sigma: (int * nf) list (* the computed substitution *)
; deltas: (int * nf) list ref list (* collection of all branches *)
; initialSpecialK: int
+ ; label : string
+ ; var_names : string list (* names of the original free variables *)
};;
let all_terms p =
let problem_measure p = sum_arities p;;
let string_of_measure = string_of_int;;
-let print_problem label ({freshno; div; conv; ps; deltas} as p) =
+let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
Console.print_hline ();
prerr_string ("\n(* DISPLAY PROBLEM (" ^ label ^ ") - ");
let nl = "\n" in
let failwithProblem p reason =
- print_endline (print_problem "FAIL" p);
+ print_endline (string_of_problem "FAIL" p);
failwith reason
;;
let simple_expand_match ps =
let rec aux level = function
- | #i_num_var as t -> aux_i_num_var level t
+ | #i_num_var as t -> (aux_i_num_var level t :> nf)
| `Lam(b,t) -> `Lam(b,aux (level+1) t)
and aux_i_num_var level = function
| `Match(u,v,bs_lift,bs,args) as torig ->
- let u = aux_i_num_var level u in
+ let (u : i_num_var) = aux_i_num_var level u in
bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
(try
(match u with
| #i_n_var as u ->
- let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
- in let t = mk_match (`N i) v bs_lift bs args in
+ let i = index_of ~eq:eta_eq (lift (-level) u) (ps :> nf list) in (* can raise Not_found *)
+ let t = cast_to_i_num_var (mk_match (`N i) v bs_lift bs (args :> nf list)) in
if t <> torig then
- aux level (t :> nf)
- else raise Not_found
+ aux_i_num_var level t
+ else raise Not_found
| _ -> raise Not_found)
with Not_found ->
- `Match(cast_to_i_num_var u,v,bs_lift,bs,List.map (aux level) args))
- | `I(v,args) -> `I(v,Listx.map (aux level) args)
+ cast_to_i_num_var (mk_appl (`Match(u,v,bs_lift,bs,[])) (List.map (aux level) args)))
+ | `I(v,args) -> cast_to_i_num_var (mk_appl (`Var v) (List.map (aux level) (Listx.to_list args)))
| `N _ | `Var _ as t -> t
in aux_i_num_var 0
;;
;;
let rec super_simplify_ps ps =
+ fixpoint (List.map (fun x -> cast_to_i_n_var (simple_expand_match ps (x :> i_num_var))))
+;;
+
+let rec super_simplify_ps_with_match ps =
fixpoint (List.map (cast_to_i_num_var ++ (simple_expand_match ps)))
;;
let super_simplify ({div; ps; conv} as p) =
- let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
- let conv = super_simplify_ps ps (p.conv :> i_num_var list) in
+ let ps = super_simplify_ps p.ps p.ps in
+ let conv = super_simplify_ps ps p.conv in
let div = option_map (fun div ->
- let divs = super_simplify_ps p.ps ([div] :> i_num_var list) in
+ let divs = super_simplify_ps p.ps ([div] :> i_n_var list) in
List.hd divs) div in
- {p with div=option_map cast_to_i_var div; ps=List.map cast_to_i_n_var ps; conv=List.map cast_to_i_n_var conv}
+ {p with div=option_map cast_to_i_var div; ps; conv}
exception ExpandedToLambda;;
| `N i -> acc_new_ps,i
| _ ->
let ps = List.map (fun t -> cast_to_i_num_var (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
- let super_simplified_ps = super_simplify_ps ps ps in
+ let super_simplified_ps = super_simplify_ps_with_match ps ps in
(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
);
let p = {p with sigma = sigma@[x,inst]} in
let p = super_simplify p in
- prerr_endline (print_problem "instantiate" p);
+ prerr_endline (string_of_problem "instantiate" p);
p
;;
let arity_of arities k =
let _,pos,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
+ let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | `N _ -> assert false in
arity + if pos = -1 then - 1 else 0
;;
let old_conv = p.conv in
let p = { p with ps; conv } in
if l <> [] || old_conv <> conv
- then prerr_endline (print_problem "eat" p);
+ then prerr_endline (string_of_problem "eat" p);
if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
`Finished p
else
with
Not_found ->
let arity_of_x = max_arity_tms x (all_terms p) in
- assert (Util.option_get arity_of_x > 0);
+ assert (Util.option_get arity_of_x > 0);
x in
(* Instantiate in decreasing order of compute_special_k
1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
else ([],Pure.V n,[]))::e
in aux 0
;;
+(* ************************************************************************** *)
+
+type result = [
+ | `Separable of (int * Num.nf) list
+ | `Unseparable of string
+]
+
+let check p =
+ (* check if there are duplicates in p.ps *)
+ (* FIXME what about initial fragments? *)
+ if (let rec f = function
+ | [] -> false
+ | hd::tl -> List.exists (eta_eq hd) tl || f tl in
+ f p.ps)
+ then Some "ps contains duplicate entries"
+ (* check if div occurs somewhere in ps@conv *)
+ else match p.div with
+ | None -> None
+ | Some div ->
+ if (List.exists (eta_subterm div) (p.ps@p.conv))
+ then Some "div occurs as subterm in ps or conv"
+ else None
+;;
-prerr_endline "########## main ##########";;
-
-(* Commands:
- v ==> v := \a. a k1 .. kn \^m.0
- + ==> v := \^k. numero for every v such that ...
- * ==> tries v as long as possible and then +v as long as possible
-*)
-let main problems =
- let rec aux ({ps} as p) n l =
- if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then begin
- p
- end else
- let _ = prerr_endline (print_problem "main" p) in
- let x,l =
- match l with
- | cmd::l -> cmd,l
- | [] -> read_line (),[] in
- let cmd =
- if x = "+" then
- `DoneWith
- else if x = "*" then
- `Auto
- else
- `Step x in
- match cmd with
- | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
- | `Step x ->
- let x = var_of_string x in
- aux (instantiate p x n) n l
- | `Auto -> aux (auto p n) n l
- in
- List.iter
- (fun (p,n,cmds) ->
- Console.print_hline();
- bomb := `Var (-1,-666);
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline ("------- <DONE> ------\n ");
- (* prerr_endline (print_problem "Original problem" p); *)
- prerr_endline "---------------------";
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- prerr_endline (" BOMB == " ^ print ~l !bomb);
- prerr_endline "---------------------";
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
-(*
- prerr_endline "----------------------";
- let ps =
- List.fold_left (fun ps (x,inst) ->
- (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
- (* In this non-recursive version, the intermediate states may containt Matchs *)
- List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
- (p.ps :> i_num_var list) sigma in
- prerr_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
- List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
-*)
- prerr_endline "---------<OPT>----------";
- let sigma = optimize_numerals p_finale in (* optimize numerals *)
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
- prerr_endline "---------<PURE>---------";
- let div = option_map (fun div -> ToScott.t_of_nf (div :> nf)) p.div in
- let conv = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.conv in
- let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
- let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
- (*let ps_ok = List.fold_left (fun ps (x,inst) ->
- List.map (Pure.subst false x inst) ps) ps sigma in*)
- let e = env_of_sigma freshno sigma true in
- let e' = env_of_sigma freshno sigma false in
-
-(*
- prerr_endline "---------<PPP>---------";
-let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
-in
- prerr_endline (print_e e);
- List.iter (fun (t,t_ok) ->
- prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
- (*assert (Pure.unwind (e,t,[]) = t_ok)*)
- ) (List.combine ps ps_ok);
-*)
- prerr_endline "--------<REDUCE>---------";
- (function Some div ->
- print_endline (Pure.print div);
- let t = Pure.mwhd (e',div,[]) in
- prerr_endline ("*:: " ^ (Pure.print t));
- prerr_endline (print !bomb);
- assert (t = ToScott.t_of_nf (!bomb:>nf))
- | None -> ()) div;
- List.iter (fun n ->
- prerr_endline ("_::: " ^ (Pure.print n));
- let t = Pure.mwhd (e,n,[]) in
- prerr_endline ("_:: " ^ (Pure.print t))
- ) conv ;
- List.iteri (fun i n ->
- prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));
- let t = Pure.mwhd (e,n,[]) in
- prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
- assert (t = Scott.mk_n i)
- ) ps ;
- prerr_endline "-------- </DONE> --------"
- ) problems
-
-(********************** problems *******************)
+let solve p =
+ prerr_endline (string_of_problem "main" p);
+ match check p with
+ | Some s -> `Unseparable s
+ | None ->
+ bomb := `Var(-1,-666);
+ Console.print_hline();
+ let p_finale = auto p p.initialSpecialK in
+ let freshno,sigma = p_finale.freshno, p_finale.sigma in
+ prerr_endline ("------- <DONE> ------ measure=. \n ");
+ let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
+ List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
+
+ prerr_endline "---------<OPT>----------";
+ let sigma = optimize_numerals p_finale in (* optimize numerals *)
+ let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
+ List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
+
+ prerr_endline "---------<PURE>---------";
+ let t_of_nf t = ToScott.t_of_nf (t :> nf) in
+ let div = option_map t_of_nf p.div in
+ let conv = List.map t_of_nf p.conv in
+ let ps = List.map t_of_nf p.ps in
+
+ let sigma' = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
+ let e' = env_of_sigma freshno sigma' false (* FIXME shoudl_explode *) in
+
+ prerr_endline "--------<REDUCE>---------";
+ let pure_bomb = ToScott.t_of_nf (!bomb) in (* Pure.B *)
+ (function Some div ->
+ print_endline (Pure.print div);
+ let t = Pure.mwhd (e',div,[]) in
+ prerr_endline ("*:: " ^ (Pure.print t));
+ assert (t = pure_bomb)
+ | None -> ()) div;
+ List.iter (fun n ->
+ verbose ("_::: " ^ (Pure.print n));
+ let t = Pure.mwhd (e',n,[]) in
+ verbose ("_:: " ^ (Pure.print t));
+ assert (t <> pure_bomb)
+ ) conv ;
+ List.iteri (fun i n ->
+ verbose ((string_of_int i) ^ "::: " ^ (Pure.print n));
+ let t = Pure.mwhd (e',n,[]) in
+ verbose ((string_of_int i) ^ ":: " ^ (Pure.print t));
+ assert (t = Scott.mk_n i)
+ ) ps ;
+ prerr_endline "-------- </DONE> --------";
+ `Separable p_finale.sigma
+;;
let zero = `Var(0,0);;
let append_zero =
function
| `I _
- | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
- | _ -> assert false
+ | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
+ | `N _ -> raise (Parser.ParsingError " numbers in ps")
;;
-type t = problem * int * string list;;
+let tmp (label, div, conv, nums, var_names) =
+ (* DA SPOSTARE NEI TEST: *)
+ let ps = List.map append_zero nums in (* crea lista applicando zeri o dummies *)
+ let ps = sort_uniq ~compare:eta_compare (ps :> nf list) in
+ let ps = List.map (cast_to_i_n_var) ps in
-let magic_conv ~div ~conv ~nums cmds =
- let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
- let all_tms, var_names = parse' all_tms in
- let div, (tms, conv) = match div with
- | None -> None, list_cut (List.length nums, all_tms)
- | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
-
- if match div with None -> false | Some div -> List.exists (eta_subterm div) (tms@conv)
- then (
- prerr_endline "--- TEST SKIPPED ---";
- {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0}, 0, []
- ) else
- let tms = sort_uniq ~compare:eta_compare tms in
- let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
- (* casts *)
- let div = option_map cast_to_i_var div in
- let conv = Util.filter_map (function #i_n_var as t -> Some (cast_to_i_n_var t) | _ -> None) conv in
- let tms = List.map cast_to_i_n_var tms in
-
- let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
- let freshno = List.length var_names in
- let deltas =
- let dummy = `Var (max_int / 2, -666) in
- [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
-
- {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k}, special_k, cmds
+ (* TODO: *)
+ (* replace div with bottom in problem??? *)
+ let special_k =
+ let all_tms = (match div with None -> [] | Some div -> [(div :> i_n_var)]) @ nums @ conv in
+ compute_special_k (Listx.from_list (all_tms :> nf list)) in (* compute initial special K *)
+ let freshno = List.length var_names in
+ let deltas =
+ let dummy = `Var (max_int / 2, -666) in
+ [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
+ {freshno; div; conv; ps; sigma=[]; deltas; initialSpecialK=special_k; var_names; label}
;;
-let magic strings cmds = magic_conv None [] strings cmds;;
+let problem_of ~div ~conv ~nums =
+ let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
+ let all_tms, var_names = Parser.parse' all_tms in
+ let div, (ps, conv) = match div with
+ | None -> None, list_cut (List.length nums, all_tms)
+ | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
+
+ let div =
+ match div with
+ | None -> None
+ | Some (`I _ as t) -> Some t
+ | _ -> raise (Parser.ParsingError "div is not an inert or BOT in the initial problem") in
+ let conv = Util.filter_map (
+ function
+ | #i_n_var as t -> Some t
+ | `Lam _ -> None
+ | _ -> raise (Parser.ParsingError "A term in conv is not i_n_var")
+ ) conv in
+ let ps = List.map (
+ function
+ | #i_n_var as y -> y
+ | _ -> raise (Parser.ParsingError "A term in num is not i_n_var")
+ ) ps in
+ tmp("missing label", div, conv, ps, var_names)
+;;
projects / fireball-separation.git / blobdiff