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 *)
; ps: i_n_var list (* the n-th inert must become n *)
; sigma: (int * nf) list (* the computed substitution *)
; deltas: (int * nf) list ref list (* collection of all branches *)
- }
-
-
-(* let heads = Util.sort_uniq (List.map hd_of_i_var p.ps) in
-for all head
- List.map (fun (_, bs) -> List.map (fun (x,_) -> List.nth p.ps x) !bs) p.deltas *)
-
-(* let ($) f x = f x;; *)
-
-(* let subterms tms freshno =
- let apply_var =
- let no = ref freshno in
- function t -> incr no; mk_app t (`Var !no) in
- let applicative hd args = snd (
- List.fold_left (fun (hd, acc) t -> let hd = mk_app hd t in hd, hd::acc) (hd, []) args) in
- let rec aux t = match t with
- | `Var _ -> []
- | `I(v,ts) ->
- (* applicative (`Var v) (Listx.to_list ts) @ *)
- Util.concat_map aux (Listx.to_list ts) @ List.map apply_var (Listx.to_list ts)
- | `Lam(_,_,t) -> aux (lift ~-1 t)
- | `Match(u,_,bs_lift,bs,args) ->
- aux (u :> nf) @
- (* applicative (`Match(u,bs_lift,bs,[])) args @ *)
- Util.concat_map aux args @ List.map apply_var args
- (* @ Util.concat_map (aux ++ (lift bs_lift) ++ snd) !bs *)
- | `N _ -> []
- in let tms' = (* Util.sort_uniq ~compare:eta_compare*) (Util.concat_map aux tms) in
- tms @ tms'
- (* List.map (fun (t, v) -> match t with `N _ -> t | _ -> mk_app t v) (List.combine tms (List.mapi (fun i _ -> `Var(freshno+i)) tms)) *)
-;; *)
+ ; initialSpecialK: int
+};;
let all_terms p =
-(match p.div with None -> [] | Some t -> [(t :> i_n_var)])
-@ p.conv
-@ p.ps
+ (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
+ @ p.conv
+ @ p.ps
+;;
+
+let sum_arities p =
+ let rec aux = function
+ | `N _ -> 0
+ | `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,(_,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)
+ ;;
+
+let count_fakevars p =
+ let rec aux = function
+ | `N _ -> 0
+ | `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
+ and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
+ aux_many (all_terms p :> nf list)
;;
-let problem_measure p = 0 ;;
+(* let problem_measure p = count_fakevars p, sum_arities p;;
+let string_of_measure (a,b) = "(fakevars="^string_of_int a^",sum_arities="^string_of_int b^")" *)
+
+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) =
Console.print_hline ();
let nl = "\n| " in
let deltas = String.concat nl (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- nl ^ "measure="^string_of_int(problem_measure p)^" freshno = " ^ string_of_int freshno
+ nl ^ "measure="^string_of_measure(problem_measure p)^" freshno = " ^ string_of_int freshno
^ nl ^ "\b> DISCRIMINATING SETS (deltas)"
^ nl ^ deltas ^ (if deltas = "" then "" else nl)
^ "\b> DIVERGENT" ^ nl
let make_fresh_vars p arities =
List.fold_right
- (* fold_left vs. fold_right hides/shows the bug in problem q7 *)
(fun arity (p, vars) -> let p, var = make_fresh_var p arity in p, var::vars)
arities
(p, [])
;;
let simple_expand_match ps =
- let rec aux level = function
+ let rec aux level = function
| #i_num_var as t -> aux_i_num_var level t
| `Lam(b,t) -> `Lam(b,aux (level+1) t)
- and aux_i_num_var level = function
+ 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
bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
`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)
| `N _ | `Var _ as t -> t
-in aux_i_num_var 0;;
+ in aux_i_num_var 0
+;;
let fixpoint f =
let rec aux x = let x' = f x in if x <> x' then aux x' else x in aux
| [] -> acc
| t::todo_ps ->
(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- let t = subst false x inst (t :> nf) in
+ let t = subst false false x inst (t :> nf) in
(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
let freshno,new_t,acc_new_ps =
expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
| t::todo_conv ->
(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
(* try *)
- let t = subst false x inst (t :> nf) in
+ let t = subst false false x inst (t :> nf) in
(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
let freshno,new_t,acc_new_ps =
expand_match (freshno,ps,acc_new_ps) t
function
| None -> freshno, None, acc_new_ps
| Some t ->
- let t = subst false x inst (t :> nf) in
+ 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
match u with
| `N i -> acc_new_ps,i
| _ ->
- let ps = List.map (fun t -> cast_to_i_num_var (subst false x inst (t:> nf))) (acc_ps@acc_new_ps) in
+ 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
(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
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'
(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 < 0 then failwithProblem p "step on a var of negative arity");
- (* AC: FIXME compute arities correctly below! *)
- let arities = Array.to_list (Array.make (n+1) 0) 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 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 p,zero = make_fresh_var p in *)
- (* let zero = Listx.Nil zero in *)
- (* let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in *)
let args = Listx.from_list (vars :> nf list) in
let bs = ref [] in
- let inst = `Lam(false,`Match(`I((0,0),Listx.map (lift 1) args),(x,arity_of_x),1,bs,[])) in
+ (* 666, since it will be replaced anyway during subst: *)
+ let inst = `Lam(false,`Match(`I((0,min_int),Listx.map (lift 1) args),(x,-666),1,bs,[])) 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) *)
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
+ 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)
+(* 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 =
special_k,p
-let rec auto_eat (n,({ps} as p)) =
+let rec auto_eat (n,p) =
prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
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 delta = m - problem_measure p' in
- if delta <= 0 then (
- (* failwithProblem p' *)
- prerr_endline
- ("Measure did not decrease (delta=" ^ string_of_int delta ^ ")"))
- else prerr_endline ("$ Measure decreased by " ^ string_of_int delta);
+ let delta = problem_measure p - m in
+ (* let delta = m - problem_measure p' in *)
+ 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)
;;
(********************** problems *******************)
-let zero = `Var(0,-1);;
+let zero = `Var(0,0);;
let append_zero =
function
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=[]}, 0, []
+ {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 *)
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}, special_k, cmds
+ {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k}, special_k, cmds
;;
let magic strings cmds = magic_conv None [] strings cmds;;