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);;
exception Pacman
exception Bottom
exception Backtrack of string
+exception Fail of string
let first bound p var f =
let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
try
f p i
with Backtrack s ->
-prerr_endline ("!!BACKTRACK!! " ^ s);
+prerr_endline (">>>>>> BACKTRACK (reason: " ^ s ^") measure=$ ");
List.iter (fun (r,l) -> r := l) (List.combine p.deltas (List.hd p.trail)) ;
prerr_endline("Now trying var="^string_of_var var^" i="^string_of_int i);
aux (i+1)
let simple_expand_match ps =
let rec aux_nob 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)
| `Pacman as t -> t
and aux level = function
| #nf_nob as t -> aux_nob level 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 :> nf list) 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 ->
- mk_appl (`Match(cast_to_i_num_var u,v,bs_lift,bs,[])) (List.map (aux_nob level) args))
- | `I(v,args) -> mk_appl (`Var v) (List.map (aux_nob level) (Listx.to_list args))
+ cast_to_i_num_var (mk_appl (`Match(u,v,bs_lift,bs,[])) (List.map (aux_nob level) args)))
+ | `I(v,args) -> cast_to_i_num_var (mk_appl (`Var v) (List.map (aux_nob 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}
-let cast_to_ps =
+let cast_to_ps_with_match =
function
#i_num_var as y -> (y : i_num_var)
- | `Bottom | `Pacman -> raise (Backtrack "foo")
+ | `Bottom | `Pacman -> raise (Backtrack "BOT/PAC in ps")
| t ->
prerr_endline (print (t :> nf));
assert false (* algorithm failed *)
function
| None -> freshno, None, acc_new_ps
| Some t ->
+ let t = subst false false x inst (t :> nf) in
try
- let t = subst false false x inst (t :> nf) in
let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
- freshno,Some(cast_to_i_var new_t),acc_new_ps
- with Bottom -> freshno, None, acc_new_ps
- | Pacman -> raise (Backtrack "Pacman in div")
+ (* backtrack if it is a number or a variable *)
+ match new_t with
+ | `N _ -> raise (Backtrack "div=`N")
+ | `Var _
+ | `I _ as new_t -> freshno, Some(new_t), acc_new_ps
+ with
+ | Bottom -> freshno, None, acc_new_ps
+ | Pacman -> raise (Backtrack "div=PAC")
and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
match t with
match u with
| `N i -> acc_new_ps,i
| _ ->
- let ps = List.map (fun t -> cast_to_ps (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
- let super_simplified_ps = super_simplify_ps ps ps in
+ let ps = List.map (fun t -> cast_to_ps_with_match (subst false false x inst (t:> nf))) (acc_ps@acc_new_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;*)
- match index_of_opt ~eq:eta_eq super_simplified_ps u with
+ match index_of_opt ~eq:eta_eq super_simplified_ps (u :> i_num_var) with
Some i -> acc_new_ps, i
| None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
in
| `Pacman -> raise Pacman
| #i_n_var as x ->
let x = simple_expand_match (acc_ps@acc_new_ps) x in
- freshno,cast_to_i_num_var x,acc_new_ps in
+ freshno,cast_to_i_n_var x,acc_new_ps in
- let freshno,old_ps,new_ps = aux_ps (freshno,[],[]) (ps :> i_num_var list) in
- let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
+ let freshno,old_ps,new_ps = aux_ps (freshno,[],[]) ps in
+ let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) conv in
let freshno,div,new_ps = aux_div old_ps (freshno,new_ps) (div :> i_num_var option) in
let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
else
`Continue p
+
+let safe_arity_of_var p x =
+ (* Compute the minimum number of arguments when x is in head
+ position at p.div or p.ps *)
+ let aux = function
+ | `Var(y,_) -> if x = y then 0 else max_int
+ | `I((y,_),args) -> if x = y then Listx.length args else max_int
+ | _ -> max_int in
+ let tms = ((match p.div with None -> [] | Some t -> [(t :> i_n_var)]) @ p.ps) in
+ List.fold_left (fun acc t -> Pervasives.min acc (aux t)) max_int tms
+;;
+
let instantiate p x perm n =
- let arity_of_x = max_arity_tms x (all_terms p) in
- (if arity_of_x = None then failwithProblem p "step on var non occurring in problem");
- let arity_of_x = Util.option_get(arity_of_x) in
- (if arity_of_x = min_int then failwithProblem p "step on fake variable");
- (if arity_of_x <= 0 then failwithProblem p "step on var of non-positive arity");
- (if perm < 1 || perm > arity_of_x then
- failwithProblem p ("Tried to permutate variable "^ string_of_var x ^" beyond its max arity"));
let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in
let arities = Array.to_list (Array.make (n+1) min_int) in
let p,vars = make_fresh_vars p arities in
prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
x
with
- Not_found -> x in
+ Not_found ->
+ let arity_of_x = max_arity_tms x (all_terms p) in
+ 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
let x =
if special_k < n then
prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
- x,arity_of_x,special_k
+ let safe_arity_of_x = safe_arity_of_var p x in
+ x, min arity_of_x safe_arity_of_x, special_k
let rec auto_eat (n,p) =
prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
in aux 0
;;
-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 (string_of_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 -> assert false
- (* let x = var_of_string x in
- aux (instantiate p x 1 n) n l *)
- | `Auto -> aux (auto p n) n l
- in
- List.iter
- (fun (p,n,cmds) ->
- Console.print_hline();
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline ("------- <DONE> ------\n ");
- (* prerr_endline (string_of_problem "Original problem" p); *)
- prerr_endline "---------------------";
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- prerr_endline "---------------------";
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
+let solve p =
+ if List.for_all (function `N _ -> true | _ -> false) p.ps && p.div = None
+ then (prerr_endline "Initial problem is already completed, nothing to do")
+ else (
+ Console.print_hline();
+ prerr_endline (string_of_problem "main" p);
+ let p_finale =
+ try
+ auto p p.initialSpecialK
+ with Backtrack _ -> raise (Fail "Unsolvable problem, apparently") in
+ let freshno,sigma = p_finale.freshno, p_finale.sigma in
+ prerr_endline ("------- <DONE> ------ measure=. \n ");
+ (* prerr_endline (string_of_problem "Original problem" p); *)
+ (* prerr_endline "---------------------"; *)
+ let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
+ (* 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 (string_of_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 "----------------------";
+ 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 (string_of_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>---------";
+ 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;
- let div = option_map (fun div -> ToScott.scott_of_nf (div :> nf)) p.div in
- let conv = List.map (fun t -> ToScott.scott_of_nf (t :> nf)) p.conv in
- let ps = List.map (fun t -> ToScott.scott_of_nf (t :> nf)) p.ps in
+ prerr_endline "---------<PURE>---------";
+ let scott_of_nf t = ToScott.scott_of_nf (t :> nf) in
+ let div = option_map scott_of_nf p.div in
+ let conv = List.map scott_of_nf p.conv in
+ let ps = List.map scott_of_nf p.ps in
- let sigma' = List.map (fun (x,inst) -> x, ToScott.scott_of_nf inst) sigma in
- let e' = env_of_sigma freshno sigma' in
+ let sigma' = List.map (fun (x,inst) -> x, ToScott.scott_of_nf inst) sigma in
+ let e' = env_of_sigma freshno sigma' in
(*
-
prerr_endline "---------<PPP>---------";
+ prerr_endline "---------<PPP>---------";
let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) 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 (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));
- assert (t = Pure.B)
- | None -> ()) div;
- List.iter (fun n ->
- prerr_endline ("_::: " ^ (Pure.print n));
- let t = Pure.mwhd (e',n,[]) in
- prerr_endline ("_:: " ^ (Pure.print t));
- assert (t <> Pure.B)
- ) 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
+ prerr_endline "--------<REDUCE>---------";
+ (function Some div ->
+ print_endline (Pure.print div);
+ let t = Pure.mwhd (e',div,[]) in
+ prerr_endline ("*:: " ^ (Pure.print t));
+ assert (t = Pure.B)
+ | None -> ()) div;
+ List.iter (fun n ->
+ verbose ("_::: " ^ (Pure.print n));
+ let t = Pure.mwhd (e',n,[]) in
+ verbose ("_:: " ^ (Pure.print t));
+ assert (t <> Pure.B)
+ ) 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> --------"
+ )
+;;
(********************** problems *******************)
| _ -> assert false
;;
-type t = problem * int * string list;;
-
-let magic_conv ~div ~conv ~nums 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 = parse' all_tms in
let div, (tms, conv) = match div with
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; trail=[]}, 0, []
+ {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0; trail=[]}
) 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 div =
+ match div with
+ | None | Some `Bottom -> None
+ | Some (`I _ as t) -> Some t
+ | _ -> raise (Fail "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 (Fail "A term in conv is not i_n_var")
+ ) conv in
+ let tms = List.map (
+ function
+ | #i_n_var as y -> y
+ | _ -> raise (Fail "A term in num is not 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 dummy = `Var (max_int / 2, -666) in
[ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
let trail = [] in
- {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k; trail}, special_k, cmds
+ {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k; trail}
;;
-let magic strings cmds = magic_conv None [] strings cmds;;
+let should_fail f =
+ try
+ solve (f ());
+ failwith "The problem should have failed"
+ with Fail _ ->
+ prerr_endline "The problem failed, as expected"
+;;
projects / fireball-separation.git / blobdiff