let bomb = ref(`Var(-1,-666));;
+(*
+ The number of arguments which can applied to numbers
+ safely, depending on the encoding of numbers.
+ For Scott's encoding, two.
+*)
+let num_more_args = 2;;
+
type problem =
{ freshno: int
; div: i_var option (* None = bomb *)
let sum_arities p =
let rec aux = function
| `N _ -> 0
- | `Var(_,ar) -> if ar = min_int then 0 else (assert (ar >= 0); ar)
+ | `Var(_,ar) -> if ar = min_int then 0 else max 0 ar (*assert (ar >= 0); ar*)
| `Lam(_,t) -> aux t
| `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args)
- | `Match(u,v,_,_,args) -> (*aux (u :> nf) +*) aux (`Var v) + aux_many args
+ | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int then 0 else ar - 1) + aux_many args
and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
aux_many (all_terms p :> nf list)
;;
| `Var(_,ar) -> if ar = min_int then 1 else 0
| `Lam(_,t) -> aux t
| `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args)
- | `Match(u,v,_,_,args) -> (*aux (u :> nf) +*) aux (`Var v) + aux_many args
+ | `Match(u,v,_,_,args) -> aux (u :> nf) + aux (`Var v) + aux_many args
and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
aux_many (all_terms p :> nf list)
;;
if List.exists (fun (j,_) -> i=j) !bs then
freshno
else
- let freshno,v = freshno+1, `Var (freshno+1, snd orig - 1) in (* make_fresh_var freshno in *)
+ let freshno,v = freshno+1, `Var (freshno+1, -666) in (* make_fresh_var freshno in *)
bs := !bs @ [i, v] ;
freshno in
(*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
let p = {p with freshno; div; conv; ps} in
( (* check if double substituting a variable *)
if List.exists (fun (x',_) -> x = x') sigma
- then failwithProblem p "Variable replaced twice"
+ then failwithProblem p ("Variable "^ string_of_var x ^"replaced twice")
);
let p = {p with sigma = sigma@[x,inst]} in
let p = super_simplify p in
(match t with
`N _ -> List.iter (dangerous arities showstoppers) args
| `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
- | `Var(x,_) -> dangerous_inert arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
- | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
+ | `Var(x,_) -> dangerous_inert arities showstoppers x args num_more_args
+ | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) num_more_args
)
| `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
(match t with
`N _ -> concat_map (dangerous_conv arities showstoppers) args
| `Match _ as t -> dangerous_conv arities showstoppers t @ concat_map (dangerous_conv arities showstoppers) args
- | `Var(x,_) -> dangerous_inert_conv arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
- | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
+ | `Var(x,_) -> dangerous_inert_conv arities showstoppers x [] args 2
+ | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args') args 2
)
- | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) 0
+ | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) [] 0
-and dangerous_inert_conv arities showstoppers k args more_args =
- concat_map (dangerous_conv arities showstoppers) args @
- if List.mem k showstoppers then k :: concat_map free_vars args else
+and dangerous_inert_conv arities showstoppers k args match_args more_args =
+ let all_args = args @ match_args in
+ let dangerous_args = concat_map (dangerous_conv arities showstoppers) all_args in
+ if dangerous_args = [] then (
+ if List.mem k showstoppers then k :: concat_map free_vars all_args else
try
let arity = arity_of arities k in
- prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var k ^ " listlenargs=" ^ (string_of_int (List.length args)) );
- if List.length args + more_args > arity then k :: concat_map free_vars args else []
+prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var k ^ " listlenargs=" ^ (string_of_int (List.length args)) ^ " more_args=" ^ string_of_int more_args);
+ if more_args > 0 (* match argument*) && List.length args = arity then []
+ else if List.length all_args + more_args > arity then k :: concat_map free_vars all_args else []
with
Not_found -> []
+ ) else k :: concat_map free_vars all_args
(* inefficient algorithm *)
let rec edible arities div ps conv showstoppers =
let dangerous_conv =
List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
- prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
- List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
+prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
+List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
+
let showstoppers' = showstoppers @ List.concat dangerous_conv in
let showstoppers' = sort_uniq (match div with
| None -> showstoppers'
else
`Continue p
-let instantiate p x n =
+let instantiate p x perm n =
(if hd_of_i_var (cast_to_i_var !bomb) = x
then failwithProblem p ("BOMB (" ^ string_of_nf !bomb ^ ") cannot be instantiated!"));
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");
- (if Util.option_get(arity_of_x) = min_int then failwithProblem p "step on fake variable");
- (if Util.option_get(arity_of_x) <= 0 then failwithProblem p "step on var of non-positive arity");
+ 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
- (* AC: Once upon a time, it was:
- let arities = Num.compute_arities x (n+1) (all_terms p :> nf list) in *)
- (* let arities = Array.to_list (Array.make (n+1) 0) in *)
let arities = Array.to_list (Array.make (n+1) min_int) in
let p,vars = make_fresh_vars p arities in
let args = Listx.from_list (vars :> nf list) in
let bs = ref [] in
+ (* other_vars are the variables which are delayed and re-applied to the match *)
+ let other_vars = Array.mapi (fun n () -> `Var(n+1,min_int)) (Array.make (perm-1) ()) in
+ let other_vars = Array.to_list other_vars in
(* 666, since it will be replaced anyway during subst: *)
- let inst = `Lam(false,`Match(`I((0,n+2),Listx.map (lift 1) args),(x,666),1,bs,[])) in
+ let inst = `Match(`I((0,min_int),Listx.map (lift perm) args),(x,-666),perm,bs,other_vars) in
+ (* Add a number of 'perm' leading lambdas *)
+ let inst = Array.fold_left (fun t () -> `Lam(false, t)) inst (Array.make perm ()) in
let p = {p with deltas=bs::p.deltas} in
subst_in_problem x inst p
;;
let compute_special_k tms =
- let rec aux k (t: nf) = Pervasives.max k (match t with
- | `Lam(b,t) -> aux (k + if b then 1 else 0) t
- | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
- | `Match(t, _, liftno, bs, args) ->
- List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
- | `N _ -> 0
- | `Var _ -> 0
- ) in Listx.max (Listx.map (aux 0) tms)
+ let rec aux k (t: nf) = Pervasives.max k (match t with
+ | `Lam(b,t) -> aux (k + if b then 1 else 0) t
+ | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
+ | `Match(t, _, liftno, bs, args) ->
+ List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
+ | `N _
+ | `Var _ -> 0
+ ) in Listx.max (Listx.map (aux 0) tms)
;;
let auto_instantiate (n,p) =
- let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
+ let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
let x =
match showstoppers_step, showstoppers_eat with
- | [], y::_ ->
- prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
- | [], [] ->
+ | [], y::_ ->
+ prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
+ | [], [] ->
let heads =
- (* Choose only variables still alive (with arity >= 0) *)
+ (* Choose only variables still alive (with arity > 0) *)
List.sort compare (filter_map (
fun t -> match t with `Var _ -> None | x -> if arity_of_hd x <= 0 then None else hd_of x
) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
(match heads with
- [] -> assert false
- | x::_ ->
- prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
- x)
+ | [] ->
+ (try
+ fst (List.find (((<) 0) ++ snd) (concat_map free_vars' (p.conv :> nf list)))
+ with
+ Not_found -> assert false)
+ | x::_ ->
+ prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
+ x)
| x::_, _ ->
prerr_endline ("INSTANTIATING " ^ string_of_var x);
x in
(* Strategy that decreases the special_k to 0 first (round robin)
1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
-let x =
- try
- match hd_of (List.find (fun t ->
- compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t >= 0
- ) (all_terms p)) with
- None -> assert false
+ let x =
+ try
+ match
+ hd_of (List.find (fun t ->
+ compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
+ ) (all_terms p))
+ with
+ | None -> assert false
| Some x ->
prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
x
- with
- Not_found -> x
-in
+ with
+ Not_found -> 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 =
compute_special_k (Listx.from_list (all_terms p :> nf list) )in
if special_k < n then
prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
- let p = instantiate p x special_k in
+ let p = instantiate p x 1 special_k in
special_k,p
let m = problem_measure p in
let (n,p') = auto_instantiate (n,p) in
match eat p' with
- `Finished p -> p
+ | `Finished p -> p
| `Continue p ->
prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
- let m' = problem_measure p in
- let delta = compare m m' in
- print_endline ("compare " ^ string_of_measure m' ^ " " ^ string_of_measure m ^ "= " ^ string_of_int delta);
+ let delta = problem_measure p - m in
(* let delta = m - problem_measure p' in *)
- if delta <= 0 then (
- failwith
- (* prerr_endline *)
- ("Measure did not decrease (delta=" ^ string_of_int delta ^ ")"))
- else prerr_endline ("$ Measure decreased by " ^ string_of_int delta);
+ if delta >= 0
+ then
+ (failwith
+ ("Measure did not decrease (+=" ^ string_of_int delta ^ ")"))
+ else prerr_endline ("$ Measure decreased of " ^ string_of_int delta);
auto_eat (n,p)
;;
let auto p n =
prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
match eat p with
- `Finished p -> p
+ | `Finished p -> p
| `Continue p -> auto_eat (n,p)
;;
| `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
+ aux (instantiate p x 1 n) n l
| `Auto -> aux (auto p n) n l
in
List.iter