open Pure
open Num
-let bomb = ref(`Var(-1,-666));;
-
(*
The number of arguments which can applied to numbers
safely, depending on the encoding of numbers.
; trail: discriminating_set list list
};;
+(* exceptions *)
+exception Pacman
+exception Bottom
+exception Backtrack of string
+
+let first bound p var f =
+ let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
+ let rec aux i =
+ if i > bound then
+ raise (Backtrack ("no more alternatives for " ^ string_of_var var))
+ else
+ try(try
+ f p i
+ with Pacman | Bottom -> raise (Backtrack "Pacman/Bottom"))
+ with Backtrack s ->
+prerr_endline ("!!BACKTRACK!! " ^ s);
+ 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)
+ in
+ aux 1
+
+
let all_terms p =
(match p.div with None -> [] | Some t -> [(t :> i_n_var)])
@ p.conv
let sum_arities p =
let rec aux = function
- | `N _ -> 0
+ | `N _ | `Bottom | `Pacman -> 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
+ | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args :> nf list)
+ | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int then 0 else ar - 1) + aux_many (args :> nf list)
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_measure(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 = `N (-1) 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 simple_expand_match ps =
- let rec aux level = function
+ let rec aux_nob level = function
| #i_num_var as t -> aux_i_num_var level t
| `Lam(b,t) -> `Lam(b,aux (level+1) t)
+ | `Pacman as t -> t
+ and aux level = function
+ | `Bottom as t -> t
+ | #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
(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
+ in let t = mk_match (`N i) v bs_lift bs (args :> nf list) in
if t <> torig then
aux level (t :> nf)
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)
+ 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))
| `N _ | `Var _ as t -> t
in aux_i_num_var 0
;;
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}
-exception ExpandedToLambda;;
+let cast_to_ps =
+ function
+ #i_num_var as y -> (y : i_num_var)
+ | `Bottom | `Pacman -> raise (Backtrack "foo")
+ | t ->
+ prerr_endline (print (t :> nf));
+ assert false (* algorithm failed *)
let subst_in_problem x inst ({freshno; div; conv; ps; sigma} as p) =
let len_ps = List.length ps in
(*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
- let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
+ let rec aux_ps ((freshno,acc_ps,acc_new_ps) as acc) =
function
| [] -> acc
| t::todo_ps ->
let freshno,new_t,acc_new_ps =
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
+ aux_ps (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
(* cut&paste from aux above *)
- and aux' ps ((freshno,acc_conv,acc_new_ps) as acc) =
+ and aux_conv ps ((freshno,acc_conv,acc_new_ps) as acc) =
function
| [] -> acc
| t::todo_conv ->
-(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- (* try *)
- let t = subst false false x inst (t :> nf) in
+ (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
+ let t = try
+ subst false false x inst (t :> nf)
+ with Pacman -> `N(-1) in (* DUMMY CONVERGENT *)
(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
- let freshno,new_t,acc_new_ps =
- expand_match (freshno,ps,acc_new_ps) t
- in
- aux' ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
- (* with ExpandedToLambda -> aux' ps (freshno,acc_conv@[`N(-1)],acc_new_ps) todo_conv *)
+ let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
+ aux_conv ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
(* cut&paste from aux' above *)
- and aux'' ps (freshno,acc_new_ps) =
+ and aux_div ps (freshno,acc_new_ps) =
function
| None -> freshno, None, acc_new_ps
| Some t ->
- 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 new_t,acc_new_ps
+ 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
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_i_num_var (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
+ 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
(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
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) orig bs_lift bs args in
+ let t = mk_match (`N i) orig bs_lift bs (args :> nf list) 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
+ | `Lam _ -> assert false (* algorithm invariant/loose typing *)
+ | `Bottom -> raise Bottom
+ | `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
- let freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
- let freshno,conv,new_ps = aux' old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
- let freshno,div,new_ps = aux'' old_ps (freshno,new_ps) (div :> i_num_var option) in
- let div = option_map cast_to_i_var div 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,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
let conv = List.map cast_to_i_n_var conv in
(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
);
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
;;
function
`N _
| `Var _
- | `Lam _ -> ()
+ | `Lam _
+ | `Pacman -> ()
| `Match(t,_,liftno,bs,args) ->
(* CSC: XXX partial dependency on the encoding *)
(match t with
function
`N _
| `Var _
- | `Lam _ -> []
+ | `Lam _
+ | `Pacman -> []
| `Match(t,_,liftno,bs,args) ->
(* CSC: XXX partial dependency on the encoding *)
(match t with
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
+ let all_args = (all_args :> nf list) in
if dangerous_args = [] then (
if List.mem k showstoppers then k :: concat_map free_vars all_args else
try
None -> aux showstoppers xs
| Some h ->
try
- dangerous arities showstoppers (x : i_n_var :> nf) ;
+ dangerous arities showstoppers (x : i_n_var :> nf_nob) ;
aux showstoppers xs
with
Dangerous ->
in
let showstoppers = sort_uniq (aux showstoppers ps) in
let dangerous_conv =
- List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
+ List.map (dangerous_conv arities showstoppers) conv 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;
let heads = List.sort compare (filter_map hd_of ps) in
let arities = precompute_edible_data p (uniq heads) in
let showstoppers, showstoppers_conv =
- edible arities p.div ps p.conv showstoppers in
+ edible arities p.div ps (p.conv :> nf_nob list) showstoppers in
let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
let p =
List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
then p
else
let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
- 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'));
- bomb := bomb';
- prerr_endline ("Just created bomb var: " ^ string_of_nf !bomb);
let x = hd_of_i_var div in
- let inst = make_lams !bomb n in
- prerr_endline ("# INST (div): " ^ string_of_var x ^ " := " ^ string_of_nf inst);
- let p = {p with div=None} in
- (* subst_in_problem (hd_of_i_var div) inst p in *)
- {p with sigma=p.sigma@[x,inst]} in
- let dangerous_conv = showstoppers_conv in
+ let inst = make_lams `Bottom n in
+ subst_in_problem x inst p in
+ let dangerous_conv = showstoppers_conv in
let _ = 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; in
let conv =
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 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");
let arity_of_x = Util.option_get(arity_of_x) in
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
- let args = Listx.from_list (vars :> nf list) in
+ (* manual lifting of vars by perm in next line *)
+ let vars = List.map (function `Var (n,ar) -> `Var (n+perm,ar)) vars in
+ let args = Listx.from_list vars 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 = `Match(`I((0,min_int),Listx.map (lift perm) args),(x,-666),perm,bs,other_vars) in
+ let inst = `Match(`I((0,min_int),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
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)
+ | `I(n, tms) -> Listx.max (Listx.map (aux 0) (tms :> nf Listx.listx))
| `Match(t, _, liftno, bs, args) ->
- List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
+ List.fold_left max 0 (List.map (aux 0) ((t :> nf)::(args :> nf list)@List.map snd !bs))
| `N _
+ | `Bottom
+ | `Pacman
| `Var _ -> 0
) in Listx.max (Listx.map (aux 0) tms)
;;
let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
x,arity_of_x,special_k
-exception Backtrack
-
-let first bound p var f =
- let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
- let rec aux i =
- if i > bound then
- (prerr_endline (">>>>>>>>>>>>>>>>>> BACKTRACKING ON "^ string_of_var var ^" J="^ string_of_int i ^" <<<<<<<<<<<<<<<<<<");
- raise Backtrack)
- else
- try
- f p i
- with
- Backtrack ->
- List.iter (fun (r,l) -> r := l) (List.combine p.deltas (List.hd p.trail)) ;
- aux (i+1)
- in
- aux 1
-
let rec auto_eat (n,p) =
prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
let m = problem_measure p in
let replace_in_sigma perm =
let rec aux = function
| `N n -> `N (List.nth perm n)
+ | `Pacman
| `I _ -> assert false
| `Var _ as t -> 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
+ | `Bottom as t -> t
in List.map (fun (n,t) -> (n,aux t))
in
let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
replace_in_sigma (List.rev perm) p.sigma
;;
-let env_of_sigma freshno sigma should_explode =
+let env_of_sigma freshno sigma =
let rec aux n =
if n > freshno then
[]
(try
e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
with
- Not_found ->
- 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
+ Not_found -> ([],Pure.V n,[]))::e
in aux 0
;;
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 _ = prerr_endline (string_of_problem "main" p) in
let x,l =
match l with
| cmd::l -> cmd,l
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 (string_of_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;
(*
(* 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});
+ 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 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
+
+ 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
+
+ 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>---------";
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))
+ assert (t = Pure.B)
| None -> ()) div;
List.iter (fun n ->
prerr_endline ("_::: " ^ (Pure.print n));
- let t = Pure.mwhd (e,n,[]) in
+ 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
+ let t = Pure.mwhd (e',n,[]) in
prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
assert (t = Scott.mk_n i)
) ps ;
projects / fireball-separation.git / blobdiff