LIB = unix.cmxa str.cmxa
UTILS = parser.cmx console.cmx listx.cmx util.cmx pure.cmx num.cmx
-all: a.out test.out test34.out
+all: a.out test4.out
+ # test.out
-a.out: $(UTILS) lambda3.cmx lambda4.cmx problems.cmx
+a.out: $(UTILS) lambda4.cmx problems.cmx
$(OCAMLC) -o a.out $(LIB) $^
-test.out: $(UTILS) lambda3.cmx test1.ml
- $(OCAMLC) -o test.out $(LIB) $^
-
-test34.out: $(UTILS) lambda3.cmx lambda4.cmx test.ml
- $(OCAMLC) -o test34.out $(LIB) $^
+# test.out: $(UTILS) lambda3.cmx test1.ml
+# $(OCAMLC) -o test.out $(LIB) $^
+#
+test4.out: $(UTILS) lambda4.cmx test.ml
+ $(OCAMLC) -o test4.out $(LIB) $^
%.cmi: %.mli
$(OCAMLC) -c $<
+++ /dev/null
-open Util
-open Util.Vars
-open Pure
-open Num
-
-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 print_problem {freshno; ps; deltas} =
- let deltas = String.concat "\n" (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
- deltas ^ (if deltas = "" then "" else "\n") ^
- String.concat "\n" (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
-;;
-
-let make_fresh_var freshno =
- freshno+1, freshno+1
-
-let make_fresh_vars p m =
- let rec aux =
- function
- 0 -> p.freshno,[]
- | n when n > 0 ->
- let freshno,vars = aux (n-1) in
- let freshno,v = make_fresh_var freshno in
- freshno,`Var v::vars
- | _ -> assert false in
- let freshno,vars = aux m in
- {p with freshno}, vars
-
-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 rec super_simplify_ps ps it =
- let it' = List.map (fun t -> cast_to_i_num_var (simple_expand_match ps t)) (it :> i_num_var list) in
- if it <> it' then super_simplify_ps ps it' else it'
-
-let super_simplify ({ps} as p) =
- let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
- {p with ps=List.map cast_to_i_n_var ps}
-
-let subst_in_problem x inst ({freshno; 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
-
- 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 = make_fresh_var freshno in
- bs := !bs @ [i, `Var 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 _ ->
- (* the cast will fail *)
- (* freshno,(cast_to_i_n_var t),acc_new_ps *)
- assert false
- | #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 ps = List.map cast_to_i_n_var (old_ps @ new_ps) 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; ps; sigma = sigma@[x,inst]} in
- let p = super_simplify p in
-prerr_endline (print_problem p); p
-
-exception Dangerous
-
-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 _,_,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
- if List.length args + more_args > arity then raise Dangerous else ()
- with
- Not_found -> ()
-
-(* inefficient algorithm *)
-let edible arities showstoppers ps =
- 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
- aux showstoppers ps
-
-let precompute_edible_data {ps} xs =
- List.map (fun x ->
- let y = List.find (fun y -> hd_of y = Some x) ps in
- x, index_of ~eq:eta_eq y ps, y) xs
-;;
-
-let critical_showstoppers p =
- let p = super_simplify p in
- let showstoppers_step =
- List.concat (List.map (fun bs ->
- let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
- let heads = List.sort compare (filter_map hd_of heads) in
- snd (split_duplicates heads)
- ) p.deltas) 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 = edible arities showstoppers ps 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)) ->
- 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));
- (* CSC: XXX to avoid applied numbers in safe positions that
- trigger assert failures subst_in_problem x inst p*)
- { p with sigma = p.sigma @ [x,inst] }
- ) p l in
- 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
- 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 p = { p with ps } in
- if l <> [] then prerr_endline (print_problem p);
- if List.for_all (function `N _ -> true | _ -> false) ps then
- `Finished p
- else
- `Continue p
-
-let instantiate p x n =
- let p,vars = make_fresh_vars p n in
- let freshno,zero = make_fresh_var p.freshno in
- let p = {p with freshno} in
- let zero = Listx.Nil (`Var 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 ({ps} as 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) 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) ps) 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) ps)))) 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 (p.ps :> 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 problem_measure {ps} =
- (* let rec term_size_i_n_var =
- function
- | `I(v,nfs) ->
- (Listx.length nfs) *
- (List.fold_right (fun (a,b) c -> 10 + ((a+1) * term_size b) + c) (List.mapi (fun x y -> (x,y)) (Listx.to_list nfs)) 0)
- | `Var _ -> 1
- | `N _ -> 0
- and term_size =
- function
- | #i_n_var as t -> term_size_i_n_var t
- | `Match(t,lift,bs,args) -> 1 + (term_size (t :> nf)) + 1 + (List.fold_right ((+) ++ term_size) args 0)
- | `Lam(b,t) -> (if b then 0 else 1) + term_size t
- (* in List.fold_right ((+) ++ term_size_i_n_var) ps 0;; *)
- in ... *)
- 0
-
-let rec auto_eat (n,({ps} as p)) =
- match eat p with
- `Finished p -> p
- | `Continue p ->
- let p' = auto_instantiate (n,p) in
- let m' = problem_measure (snd p') in
- let delta = m' - problem_measure p in
- (if delta >= 0
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after inst) delta=" ^ string_of_int delta));
- let p'' = auto_eat p' in
- (if m' <= problem_measure p''
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after eat) $$$"));
- p''
-;;
-
-let auto p n =
- prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
- 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 _ | `Var _ -> assert false
- | `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 = Listx.max (Listx.from_list (
- List.concat (List.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 = Listx.max (Listx.from_list (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
-;;
-
-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 then begin
- assert (l = []);
- p
- end else
- let _ = prerr_endline (print_problem 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) ->
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline "------- <DONE> ------";
- prerr_endline (print_problem p);
- prerr_endline "---------------------";
- 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 "----------------------";
- 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 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 =
- let rec aux n =
- if n > freshno then
- []
- else
- let e = aux (n+1) in
- (try
- e,Pure.lift (-n-1) (let t = (snd (List.find (fun (i,_) -> i = n) sigma)) in prerr_endline (string_of_var n ^ " := " ^ Pure.print t); t),[]
- with
- Not_found -> [],Pure.V n,[])::e
- in
- aux 0 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>---------";
- 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
-;;
-
-type t = problem * int * string list;;
-
-let magic strings cmds =
- let tms, _ = parse' strings in (* *)
- let tms = sort_uniq ~compare:eta_compare tms in
- let special_k = compute_special_k (Listx.from_list tms) in (* compute special K *)
- let fv = sort_uniq (List.concat (List.map free_vars tms)) in (* free variables *)
- let tms = List.map cast_to_i_n_var tms in (* cast nf list -> i_n_var list *)
- let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
- (*let _ = prerr_endline ("Free vars: " ^ String.concat ", " (List.map string_of_var fv)) in*)
- let freshno = Listx.max (Listx.from_list fv) in
- let dummy = `Var (max_int / 2) in
- let deltas = [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
- {freshno; ps; sigma=[] ; deltas}, special_k, cmds
-;;
-
-let magic_conv ~div:_ ~conv:_ ~nums:_ _ = assert false;;
+++ /dev/null
-open Util
-open Util.Vars
-open Pure
-open Num
-
-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 print_problem {freshno; ps; deltas} =
- let deltas = String.concat "\n" (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
- deltas ^ (if deltas = "" then "" else "\n") ^
- String.concat "\n" (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
-;;
-
-let make_fresh_var freshno =
- freshno+1, freshno+1
-
-let make_fresh_vars p m =
- let rec aux =
- function
- 0 -> p.freshno,[]
- | n when n > 0 ->
- let freshno,vars = aux (n-1) in
- let freshno,v = make_fresh_var freshno in
- freshno,`Var (0,v)::vars
- | _ -> assert false in
- let freshno,vars = aux m in
- {p with freshno}, vars
-
-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(ar,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 ar (`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(ar,cast_to_i_num_var u,bs_lift,bs,List.map (aux level) args))
- | `I(ar,k,args) -> `I(ar,k,Listx.map (aux level) args)
- | `N _ | `Var _ as t -> t
-in aux_i_num_var 0;;
-
-let rec super_simplify_ps ps it =
- let it' = List.map (fun t -> cast_to_i_num_var (simple_expand_match ps t)) (it :> i_num_var list) in
- if it <> it' then super_simplify_ps ps it' else it'
-
-let super_simplify ({ps} as p) =
- let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
- {p with ps=List.map cast_to_i_n_var ps}
-
-let subst_in_problem x inst ({freshno; 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(-1,max_int/3)::todo_ps,acc_new_ps) t
- in
- aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
-
- and expand_match ((freshno,acc_ps, acc_new_ps) as acc) t =
- match t with
- | `Match(ar,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 = make_fresh_var freshno in
- bs := !bs @ [i, `Var (ar - 1,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 ar (`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 _ ->
- (* the cast will fail *)
- (* freshno,(cast_to_i_n_var t),acc_new_ps *)
- assert false
- | #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 ps = List.map cast_to_i_n_var (old_ps @ new_ps) 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; ps; sigma = sigma@[x,inst]} in
- let p = super_simplify p in
-prerr_endline (print_problem p); p
-
-exception Dangerous
-
-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 _,_,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,_,args) -> Listx.length args | _ -> assert false in
- if List.length args + more_args > arity then raise Dangerous else ()
- with
- Not_found -> ()
-
-(* inefficient algorithm *)
-let edible arities showstoppers ps =
- 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
- aux showstoppers ps
-
-let precompute_edible_data {ps} xs =
- List.map (fun x ->
- let y = List.find (fun y -> hd_of y = Some x) ps in
- x, index_of ~eq:eta_eq y ps, y) xs
-;;
-
-let critical_showstoppers p =
- let p = super_simplify p in
- let showstoppers_step =
- List.concat (List.map (fun bs ->
- let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
- let heads = List.sort compare (filter_map hd_of heads) in
- snd (split_duplicates heads)
- ) p.deltas) 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 = edible arities showstoppers ps 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)) ->
- 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));
- (* CSC: XXX to avoid applied numbers in safe positions that
- trigger assert failures subst_in_problem x inst p*)
- { p with sigma = p.sigma @ [x,inst] }
- ) p l in
- 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
- 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 p = { p with ps } in
- if l <> [] then prerr_endline (print_problem p);
- if List.for_all (function `N _ -> true | _ -> false) ps then
- `Finished p
- else
- `Continue p
-
-let instantiate p x n =
- let p,vars = make_fresh_vars p n in
- let freshno,zero = make_fresh_var p.freshno in
- let p = {p with freshno} in
- let zero = Listx.Nil (`Var (0,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(-1,`I(-1,0,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 ({ps} as 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) 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) ps) 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) ps)))) 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 (p.ps :> 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 problem_measure {ps} =
- (* let rec term_size_i_n_var =
- function
- | `I(v,nfs) ->
- (Listx.length nfs) *
- (List.fold_right (fun (a,b) c -> 10 + ((a+1) * term_size b) + c) (List.mapi (fun x y -> (x,y)) (Listx.to_list nfs)) 0)
- | `Var _ -> 1
- | `N _ -> 0
- and term_size =
- function
- | #i_n_var as t -> term_size_i_n_var t
- | `Match(t,lift,bs,args) -> 1 + (term_size (t :> nf)) + 1 + (List.fold_right ((+) ++ term_size) args 0)
- | `Lam(b,t) -> (if b then 0 else 1) + term_size t
- (* in List.fold_right ((+) ++ term_size_i_n_var) ps 0;; *)
- in ... *)
- 0
-
-let rec auto_eat (n,({ps} as p)) =
- match eat p with
- `Finished p -> p
- | `Continue p ->
- let p' = auto_instantiate (n,p) in
- let m' = problem_measure (snd p') in
- let delta = m' - problem_measure p in
- (if delta >= 0
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after inst) delta=" ^ string_of_int delta));
- let p'' = auto_eat p' in
- (if m' <= problem_measure p''
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after eat) $$$"));
- p''
-;;
-
-let auto p n =
- prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
- 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 _ | `Var _ -> assert false
- | `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 = Listx.max (Listx.from_list (
- List.concat (List.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 = Listx.max (Listx.from_list (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
-;;
-
-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 then begin
- assert (l = []);
- p
- end else
- let _ = prerr_endline (print_problem 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) ->
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline "------- <DONE> ------";
- prerr_endline (print_problem p);
- prerr_endline "---------------------";
- 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 "----------------------";
- 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 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 =
- let rec aux n =
- if n > freshno then
- []
- else
- let e = aux (n+1) in
- (try
- e,Pure.lift (-n-1) (let t = (snd (List.find (fun (i,_) -> i = n) sigma)) in prerr_endline (string_of_var n ^ " := " ^ Pure.print t); t),[]
- with
- Not_found -> [],Pure.V n,[])::e
- in
- aux 0 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>---------";
- 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 (0,0);;
-
-let append_zero =
- function
- | `I _
- | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
- | _ -> assert false
-;;
-
-type t = problem * int * string list;;
-
-let magic strings cmds =
- let tms, _ = parse' strings in (* *)
- let tms = sort_uniq ~compare:eta_compare tms in
- let special_k = compute_special_k (Listx.from_list tms) in (* compute special K *)
- let fv = sort_uniq (List.concat (List.map free_vars tms)) in (* free variables *)
- let tms = List.map cast_to_i_n_var tms in (* cast nf list -> i_n_var list *)
- let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
- (*let _ = prerr_endline ("Free vars: " ^ String.concat ", " (List.map string_of_var fv)) in*)
- let freshno = Listx.max (Listx.from_list fv) in
- let dummy = `Var (-1,max_int / 2) in
- let deltas = [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
- {freshno; ps; sigma=[] ; deltas}, special_k, cmds
-;;
-
-let magic_conv ~div:_ ~conv:_ ~nums:_ _ = assert false;;
+++ /dev/null
-include Discriminator.Discriminator\r
; 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 *)
}
| `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) ->
+ | `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
@ 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 problem_measure p = 0 ;;
-let print_problem label ({freshno; div; conv; ps; deltas; steps} as p) =
+let print_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
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 ^ "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
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)
+ | `Lam(b,ar,t) -> `Lam(b,ar,aux (level+1) t)
and aux_i_num_var level = function
- | `Match(u,bs_lift,bs,args) as torig ->
+ | `Match(u,ar,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
+ in let t = mk_match (`N i) ar 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))
+ `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)
| `N _ | `Var _ as t -> t
in aux_i_num_var 0;;
and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
match t with
- | `Match(u',bs_lift,bs,args) ->
+ | `Match(u',ar,bs_lift,bs,args) ->
let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
let acc_new_ps,i =
match u with
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
+ let t = mk_match (`N i) ar 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
`N _
| `Var _
| `Lam _ -> ()
- | `Match(t,liftno,bs,args) ->
+ | `Match(t,_,liftno,bs,args) ->
(* CSC: XXX partial dependency on the encoding *)
(match t with
`N _ -> List.iter (dangerous arities showstoppers) args
`N _
| `Var _
| `Lam _ -> []
- | `Match(t,liftno,bs,args) ->
+ | `Match(t,_,liftno,bs,args) ->
(* CSC: XXX partial dependency on the encoding *)
(match t with
`N _ -> concat_map (dangerous_conv arities showstoppers) args
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 arity1 = (assert false; -666) in
+ let arity2 = (assert false; -666) in
+ let inst = `Lam(false,arity1,`Match(`I(0,Listx.map (lift 1) args),arity2,1,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
+ | `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) ->
+ | `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
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)
;;
| `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
+ | `Lam(v,ar,t) -> `Lam(v, ar, 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
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 ("------- <DONE> ------\n ");
(* prerr_endline (print_problem "Original problem" p); *)
prerr_endline "---------------------";
let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
| _ -> 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, []
+ {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 *)
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
+ {freshno; div; conv; ps; sigma=[] ; deltas}, special_k, cmds
;;
let magic strings cmds = magic_conv None [] strings cmds;;
let use_lambda3 = Array.length Sys.argv = 1;;
-let discriminator =
- if use_lambda3 then (module Lambda3 : Discriminator.Discriminator) else (module Lambda4);;
+let discriminator = ( module Lambda4 : Discriminator.Discriminator );;
module Pippo = (val discriminator);;
open Pippo;;
let three = Array.length Sys.argv = 1;;
let discriminator =
- if three
- then (module Lambda3 : Discriminator.Discriminator)
- else (module Lambda4);;
+ (* if three *)
+ (* then (module Lambda3 : Discriminator.Discriminator) *)
+ (* else *)
+ (module Lambda4 : Discriminator.Discriminator);;
module Pippo = (val discriminator);;
open Pippo;;
if n > 0 then repeat f (n-1)
;;
-let call_main3 tms =
+(* let call_main3 tms =
let _ = (
List.iter prerr_endline tms; prerr_newline ();
) in Lambda3.main [Lambda3.magic tms ["*"]]
-;;
+;; *)
let call_main4 div convs nums =
let _ = (
(match div with Some div -> prerr_endline ("DIV: " ^ div) | None -> ());
(* let open Parser in *)
- if three then repeat (fun _ ->
+ (* if three then repeat (fun _ ->
let tms = test3 complex vars in
call_main3 tms
) num
- else repeat (fun _ ->
+ else *)
+ repeat (fun _ ->
let div, (conv, nums) = test4 complex vars in
call_main4 (Some div) conv nums
) num
projects / fireball-separation.git / commitdiff