+open Util
+open Util.Vars
+open Pure
+open Num
+
+let bomb = ref(`Var ~-1);;
+
+type problem =
+ { freshno: int
+ ; div: i_var option (* None = bomb *)
+ ; conv: i_n_var list (* the inerts that must converge *)
+ ; 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 *)
+ ; steps: int (* how many steps the algorithm made until now *)
+ }
+
+
+(* 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)) *)
+;;
+
+let all_terms p =
+(match p.div with None -> [] | Some t -> [(t :> i_n_var)])
+@ p.conv
+@ p.ps
+;;
+
+let problem_measure p =
+ let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
+ let open Listx in
+ (* aux |t1;t2| e' numero di step per portare la diff in testa
+ INVARIANTE: t1 <eta> t2
+ *)
+ let rec aux t1 t2 =
+ match t1, t2 with
+ | `I(v1,nfs1), `I(v2,nfs2) ->
+ if v1 <> v2
+ then 0 else 1 + find_first_diff (to_list nfs1, to_list nfs2)
+ | `Match (t1,bs_lift,bs,args), `Match (t2,bs_lift',bs',args') ->
+ if bs != bs' then 0 (* TODO *)
+ else if eta_eq (t1 :> nf) (t2 :> nf) then 1 + find_first_diff (args, args') else aux (t1 :> nf) (t2 :> nf) (* TODO *)
+ | `Match _, _
+ | _, `Match _ -> 0 (* FIXME!!! *)
+ | `Lam(_,t1), `Lam(_,t2) -> aux t1 t2
+ | _ -> 0
+ and find_first_diff = function
+ | [], [] -> assert false
+ | [], t::_
+ | t::_, [] -> 1
+ | t1::ts1, t2::ts2 ->
+ if eta_eq (t1 :> nf) (t2 :> nf) then 1 + find_first_diff (ts1, ts2) else aux t1 t2
+ (* no. di step da fare per separare t1 e t2 *)
+ in let diff t1 t2 = (
+ let res = if eta_eq t1 t2 then 0 else aux t1 t2 in
+ if res <> 0 then prerr_endline ("diff (" ^ print ~l t1 ^ ") (" ^ print ~l t2 ^ ") = " ^ string_of_int res);
+ res
+ )
+ (* aux calcola la somma delle differenze tra i termini in una lista (quadratico) *)
+ in let rec sum = function
+ | [] -> 0
+ | x::xs -> List.fold_right ((+) ++ (diff (x :> nf))) (xs :> nf list) (sum xs)
+ in let subterms = subterms ((all_terms p) :> nf list) p.freshno
+ (* let subterms = sort_uniq ~compare:eta_compare subterms in *)
+ in let a = sum subterms
+ in let b = List.fold_right (fun bs -> (+) (sum (List.map ((List.nth p.ps) ++ fst) !bs))) p.deltas 0
+ in let _ = prerr_endline ("Computed measure: " ^ string_of_int a ^ "," ^ string_of_int b)
+ in a + b
+;;
+
+let print_problem label ({freshno; div; conv; ps; deltas; steps} 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
+ let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
+ nl ^ string_of_int steps ^ " steps left; 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
+;;
+
+
+let failwithProblem p reason =
+ print_endline (print_problem "FAIL" p);
+ failwith reason
+;;
+
+let make_fresh_var p =
+ let freshno = p.freshno + 1 in
+ {p with freshno}, `Var freshno
+;;
+
+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)
+ (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,t) -> `Lam(b, aux (level+1) t)
+ and aux_i_num_var level = function
+ | `Match(u,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;
+ (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) bs_lift bs args 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,bs_lift,bs,List.map (aux level) args))
+ | `I(k,args) -> `I(k,Listx.map (aux level) args)
+ | `N _ | `Var _ as t -> t
+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 (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 div = option_map (fun div ->
+ let divs = super_simplify_ps p.ps ([div] :> i_num_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}
+
+exception ExpandedToLambda;;
+
+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) =
+ function
+ | [] -> acc
+ | t::todo_ps ->
+(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
+ let t = subst 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
+ in
+ aux (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) =
+ function
+ | [] -> acc
+ | t::todo_conv ->
+(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
+ (* try *)
+ let t = subst 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
+ 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 *)
+
+ (* cut&paste from aux' above *)
+ and aux'' ps (freshno,acc_new_ps) =
+ function
+ | None -> freshno, None, acc_new_ps
+ | Some t ->
+ let t = subst 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
+
+ and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
+ match t with
+ | `Match(u',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
+(*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
+ Some i -> acc_new_ps, i
+ | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
+ in
+ let freshno=
+ 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 *)
+ 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) 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
+ | #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 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
+prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
+ 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"
+ );
+ let p = {p with sigma = sigma@[x,inst]} in
+ let p = super_simplify p in
+ prerr_endline (print_problem "instantiate" p);
+ p
+;;
+
+exception Dangerous
+
+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
+ arity + if pos = -1 then - 1 else 0
+;;
+
+let rec dangerous arities showstoppers =
+ function
+ `N _
+ | `Var _
+ | `Lam _ -> ()
+ | `Match(t,liftno,bs,args) ->
+ (* CSC: XXX partial dependency on the encoding *)
+ (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 *)
+ )
+ | `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 ;
+ if List.mem k showstoppers then raise Dangerous else
+ try
+ let arity = arity_of arities k in
+ if List.length args + more_args > arity then raise Dangerous else ()
+ with
+ Not_found -> ()
+
+(* cut & paste from above *)
+let rec dangerous_conv arities showstoppers =
+ function
+ `N _
+ | `Var _
+ | `Lam _ -> []
+ | `Match(t,liftno,bs,args) ->
+ (* CSC: XXX partial dependency on the encoding *)
+ (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 *)
+ )
+ | `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
+ 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 []
+ with
+ Not_found -> []
+
+(* inefficient algorithm *)
+let rec edible arities div ps conv showstoppers =
+ let rec aux showstoppers =
+ function
+ [] -> showstoppers
+ | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
+ (* se la testa di x e' uno show-stopper *)
+ let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
+ (* aggiungi tutte le variabili libere di x *)
+ if List.length showstoppers <> List.length new_showstoppers then
+ aux new_showstoppers ps
+ else
+ aux showstoppers xs
+ | x::xs ->
+ match hd_of x with
+ None -> aux showstoppers xs
+ | Some h ->
+ try
+ dangerous arities showstoppers (x : i_n_var :> nf) ;
+ aux showstoppers xs
+ with
+ Dangerous ->
+ aux (sort_uniq (h::showstoppers)) ps
+ in
+ let showstoppers = sort_uniq (aux showstoppers ps) in
+ 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;
+ let showstoppers' = showstoppers @ List.concat dangerous_conv in
+ let showstoppers' = sort_uniq (match div with
+ | None -> showstoppers'
+ | Some div ->
+ if List.exists ((=) (hd_of_i_var div)) showstoppers'
+ then showstoppers' @ free_vars (div :> nf) else showstoppers') in
+ if showstoppers <> showstoppers' then edible arities div ps conv showstoppers' else showstoppers', dangerous_conv
+;;
+
+let precompute_edible_data {ps; div} xs =
+ (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @
+ List.map (fun hd ->
+ let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in
+ hd, i, tm
+ ) xs
+;;
+
+let critical_showstoppers p =
+ let p = super_simplify p in
+ let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
+ let showstoppers_step =
+ concat_map (fun bs ->
+ let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
+ let heads = List.sort compare (hd_of_div @ filter_map hd_of heads) in
+ snd (split_duplicates heads)
+ ) p.deltas @
+ if List.exists (fun t -> [hd_of t] = List.map (fun x -> Some x) hd_of_div) p.conv
+ then hd_of_div else [] in
+ let showstoppers_step = sort_uniq showstoppers_step in
+ 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
+ let rec multiple_arities =
+ function
+ []
+ | [_] -> []
+ | (x,i)::(y,j)::tl when x = y && i <> j ->
+ x::multiple_arities tl
+ | _::tl -> multiple_arities tl in
+ multiple_arities heads_and_arities in
+
+ let showstoppers_eat = sort_uniq showstoppers_eat in
+ let showstoppers_eat = List.filter
+ (fun x -> not (List.mem x showstoppers_step))
+ showstoppers_eat in
+ List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
+ List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
+ p, showstoppers_step, showstoppers_eat
+ ;;
+
+let eat p =
+ let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
+ let showstoppers = showstoppers_step @ showstoppers_eat in
+ 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
+ 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
+ let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
+ let v = `N(pos) in
+ let inst = make_lams v n in
+(let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
+prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
+ { p with sigma = p.sigma @ [x,inst] }
+ ) p l in
+ (* to avoid applied numbers in safe positions that
+ trigger assert failures subst_in_problem x inst p*)
+ let ps =
+ List.map (fun t ->
+ try
+ let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
+ `N j
+ with Not_found -> t
+ ) ps in
+ let p = match p.div with
+ | None -> p
+ | Some div ->
+ if List.mem (hd_of_i_var div) showstoppers
+ 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
+ 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 _ = 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 =
+ List.map (function s,t ->
+ try
+ if s <> [] then t else (
+ (match t with | `Var _ -> raise Not_found | _ -> ());
+ 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
+ | Some h ->
+ prerr_endline ("FREEZING " ^ string_of_var h);
+ `N ~-1 (* convergent dummy*)
+ ) (List.combine showstoppers_conv p.conv) in
+ List.iter
+ (fun bs ->
+ bs :=
+ List.map
+ (fun (n,t as res) ->
+ match List.nth ps n with
+ `N m -> m,t
+ | _ -> res
+ ) !bs
+ ) p.deltas ;
+ 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);
+ 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
+ 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 bs = ref [] in
+ let inst = `Lam(false,`Match(`I(0,Listx.map (lift 1) args),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 auto_instantiate (n,p) =
+ 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
+ (match heads with
+ [] -> 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) (all_terms p)) with
+ None -> assert false
+ | Some x ->
+ prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
+ x
+ 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 =
+ try
+ (match hd_of (snd (List.hd (List.sort (fun c1 c2 -> - compare (fst c1) (fst c2)) (filter_map (function `I _ as t -> Some (compute_special_k (Listx.Nil (t :> nf)),t) | _ -> None) (all_terms p))))) with
+ None -> assert false
+ | Some x ->
+ prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
+ x)
+ with
+ Not_found -> x
+in*)
+ let special_k =
+ 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
+ special_k,p
+
+
+let rec auto_eat (n,({ps} as 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
+ | `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 p' = {p' with steps=(p'.steps - 1)} in
+ (if p'.steps < 0 then prerr_endline ">>>>>>>>>> STEPS ARE OVER <<<<<<<<<"
+ (*failwithProblem p' "steps are over. sorry."*) );
+ auto_eat (n,p)
+;;
+
+let auto p n =
+ prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
+ match eat p with
+ `Finished p -> p
+ | `Continue p -> auto_eat (n,p)
+;;
+
+(*
+0 = snd
+
+ x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
+1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
+2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
+3 x b y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 (\u. u h1 h2 0) 3 b 0 (\u. u h1 (\w.h3) 0)
+4 x b c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c
+5 x (b e) 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0
+6 y y 6 y y 6 y y 6 y y 6 y y 6 h1 h1 h2 0 h2 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
+
+ l2 _ = l3
+b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
+1 k 1 k 1 k
+2 h3 2 h3 2 h3
+3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
+4 l2 0 c 4 l3 c 4 c j 0
+5 e l1 l2 0 0 5 f 5 f
+6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
+*)
+
+(*
+ x n = n 0 ?
+x a (b (a c)) a 0 = 1 ? (b (a c)) 8
+x a (b d') a 0 = 1 ? (b d') 7
+x b (a c) b 0 = 1 ? (a c) 4
+x b (a c') b 0 = 1 ? (a c') 5
+
+c = 2
+c' = 3
+a 2 = 4 (* a c *)
+a 3 = 5 (* a c' *)
+d' = 6
+b 6 = 7 (* b d' *)
+b 4 = 8 (* b (a c) *)
+b 0 = 1
+a 0 = 1
+*)
+
+(************** Tests ************************)
+
+let optimize_numerals p =
+ let replace_in_sigma perm =
+ let rec aux = function
+ | `N n -> `N (List.nth perm n)
+ | `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
+ 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
+ let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
+ let max = List.fold_left max 0 (concat_map snd deltas') in
+ let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
+ let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
+ (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
+ let neww = List.fold_left Pervasives.max 0 (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs) in
+ let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
+ (neww::perm, maxs)
+ ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
+ replace_in_sigma (List.rev perm) p.sigma
+;;
+
+let env_of_sigma freshno sigma should_explode =
+ let rec aux n =
+ if n > freshno then
+ []
+ else
+ let e = aux (n+1) in
+ (try
+ e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
+ with
+ Not_found ->
+ if should_explode && `Var n = !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
+;;
+
+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 (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 " ^ (string_of_int (p.steps - p_finale.steps)) ^ " steps of "^ (string_of_int p.steps) ^".");
+ (* 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 append_zero =
+ function
+ | `I _
+ | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
+ | _ -> assert false
+;;
+
+let bounds_on_steps all_tms =
+ let rec aux = function
+ | `I(k,args) -> Listx.fold_left (fun acc t -> 1 + acc + (aux t)) 0 args
+ | `Var _ -> 1
+ | `Lam (_, t) -> 1 + aux t
+ | _ -> assert false
+ in List.fold_right ((+) ++ aux) all_tms 0
+;;
+
+type t = problem * int * string list;;
+
+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 steps = bounds_on_steps 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=[]; steps=(-1)}, 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; steps}, special_k, cmds
+;;
+
+let magic strings cmds = magic_conv None [] strings cmds;;