open Pure
open Num
-let bomb = ref(`Var ~-1);;
+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;;
+let _very_verbose = false;;
+
+let verbose s =
+ if _very_verbose then prerr_endline s
+;;
+
+let convergent_dummy = `N ~-1;
type problem =
{ freshno: int
; 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
+ ; label : string
+ ; var_names : string list (* names of the original free variables *)
+};;
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 problem_measure p = 0 ;;
+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 = 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) =
+let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
Console.print_hline ();
- prerr_endline ("\n||||| Displaying problem: " ^ label ^ " |||||");
- 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
+ prerr_string ("\n(* DISPLAY PROBLEM (" ^ label ^ ") - ");
+ 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 ^ "\b> DISCRIMINATING SETS (deltas)"
- ^ nl ^ deltas ^ (if deltas = "" then "" else nl)
- ^ "\b> DIVERGENT" ^ nl
- ^ "*: " ^ (match div with None -> "*" | Some div -> print ~l (div :> nf)) ^ "\n| "
- ^ "\b> CONVERGENT" ^ nl
- ^ String.concat "\n| " (List.map (fun t -> "_: " ^ (if t = `N (-1) then "_" else print ~l (t :> nf))) conv) ^
- (if conv = [] then "" else "\n| ")
- ^ "\b> NUMERIC" ^ nl
- ^ String.concat "\n| " (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
- ^ nl
+ "measure="^string_of_measure(problem_measure p) (* ^ " freshno = " ^ string_of_int freshno*)
+ ^ nl ^ " Discriminating sets (deltas):"
+ ^ nl ^ " " ^ deltas ^ (if deltas = " " then "" else nl) ^ "*)"
+ ^"(* DIVERGENT *)" ^ nl
+ ^" "^ (match div with None -> "None" | Some div -> "(Some\""^ print ~l (div :> nf) ^"\")") ^ nl
+ ^" (* CONVERGENT *) [" ^ nl ^ " "
+ ^ String.concat "\n " (List.map (fun t -> "(* _ *) " ^ (if t = convergent_dummy then "" else "\""^ print ~l (t :> nf) ^"\";")) conv) ^
+ (if conv = [] then "" else nl)
+ ^ "] (* NUMERIC *) [" ^ nl ^ " "
+ ^ String.concat "\n " (List.mapi (fun i t -> " (* "^ string_of_int i ^" *) \"" ^ print ~l (t :> nf) ^ "\";") ps)
+ ^ nl ^ "] [\"*\"];;" ^ nl
;;
let failwithProblem p reason =
- print_endline (print_problem "FAIL" p);
+ print_endline (string_of_problem "FAIL" p);
failwith reason
;;
-let make_fresh_var p =
+let make_fresh_var p arity =
let freshno = p.freshno + 1 in
- {p with freshno}, `Var freshno
+ {p with freshno}, `Var(freshno,arity)
;;
-let make_fresh_vars p m =
- Array.fold_left
- (* fold_left vs. fold_right hides/shows the bug in problem q7 *)
- (fun (p, vars) _ -> let p, var = make_fresh_var p in p, var::vars)
+let make_fresh_vars p arities =
+ List.fold_right
+ (fun arity (p, vars) -> let p, var = make_fresh_var p arity in p, var::vars)
+ arities
(p, [])
- (Array.make m ())
;;
let simple_expand_match ps =
- let rec aux level = function
- | #i_num_var as t -> aux_i_num_var level t
- | `Lam(b,ar,t) -> `Lam(b,ar,aux (level+1) t)
- and aux_i_num_var level = function
- | `Match(u,ar,bs_lift,bs,args) as torig ->
- let u = aux_i_num_var level u in
+ let rec aux level = function
+ | #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 : 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) ar 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,ar,bs_lift,bs,List.map (aux level) args))
- | `I(k,args) -> `I(k,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;;
+ 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
;;
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;;
| [] -> 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)::todo_ps,acc_new_ps) t
+ expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
in
aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
| 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
and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
match t with
- | `Match(u',ar,bs_lift,bs,args) ->
+ | `Match(u',orig,bs_lift,bs,args) ->
let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
let acc_new_ps,i =
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 super_simplified_ps = super_simplify_ps ps 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_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;*)
if List.exists (fun (j,_) -> i=j) !bs then
freshno
else
- let freshno,v = freshno+1, `Var (freshno+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 t = mk_match (`N i) ar bs_lift bs args in
+ let t = mk_match (`N i) orig bs_lift bs args in
(*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
expand_match (freshno,acc_ps,acc_new_ps) t
| `Lam _ -> raise ExpandedToLambda
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
- 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
;;
(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
+ | `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
and dangerous_inert arities showstoppers k args more_args =
List.iter (dangerous arities showstoppers) args ;
(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'
let showstoppers_eat =
let heads_and_arities =
List.sort (fun (k,_) (h,_) -> compare k h)
- (filter_map (function `Var k -> Some (k,0) | `I(k,args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
+ (filter_map (function `Var(k,_) -> Some (k,0) | `I((k,_),args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
let rec multiple_arities =
function
[]
then p
else
let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
- let p, bomb' = make_fresh_var p in
- (if !bomb <> `Var (-1) then
+ let p, bomb' = make_fresh_var p (-666) in
+ (if !bomb <> `Var (-1,-666) then
failwithProblem p
("Bomb was duplicated! It was " ^ string_of_nf !bomb ^
", tried to change it to " ^ string_of_nf bomb'));
let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
t)
with Not_found -> match hd_of t with
- | None -> assert (t = `N ~-1); t
+ | None -> assert (t = convergent_dummy); t
| Some h ->
prerr_endline ("FREEZING " ^ string_of_var h);
- `N ~-1 (* convergent dummy*)
+ convergent_dummy
) (List.combine showstoppers_conv p.conv) in
List.iter
(fun bs ->
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
`Continue p
let instantiate p x n =
- (if `Var x = !bomb
+ (if hd_of_i_var (cast_to_i_var !bomb) = x
then failwithProblem p ("BOMB (" ^ string_of_nf !bomb ^ ") cannot be instantiated!"));
- let p,vars = make_fresh_vars p n 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 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 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
- let arity1 = (*assert false; -666*) 0 in
- let arity2 = (*assert false; -666*) 0 in
- let inst = `Lam(false,arity1,`Match(`I(0,Listx.map (lift 1) args),arity2,1,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
- | [], [] ->
- let heads = List.sort compare (filter_map (fun t -> match t with `Var _ -> None | x -> hd_of x) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
+ | [], 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
+ ) ((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) (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 ->
+ 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 =
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)
;;
| `N n -> `N (List.nth perm n)
| `I _ -> assert false
| `Var _ as t -> t
- | `Lam(v,ar,t) -> `Lam(v, ar, aux t)
+ | `Lam(v,t) -> `Lam(v, aux t)
| `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
in List.map (fun (n,t) -> (n,aux t))
in
e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
with
Not_found ->
- if should_explode && `Var n = !bomb
+ if should_explode && n = hd_of_i_var (cast_to_i_var !bomb)
then ([], (let f t = Pure.A(t,t) in f (Pure.L (f (Pure.V 0)))), [])
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 ##########";;
+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
+;;
-(* 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);
- 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 zero = `Var 0;;
+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=[]}, 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 = List.map cast_to_i_n_var 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) in
- [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
-
- {freshno; div; conv; ps; sigma=[] ; deltas}, 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