+(* 0: 7 4 0.312 3 5 7
+ 1: 29 6 0.549 3 8 16 24 29
+ 2: 120 10 25.525 3 8 19 39 66 95 113 119 120
+ 3: > 327 >9 3 8 19 39 75 134 208 274
+ 4: > 657 >9 3 8 19 39 75 139 245
+ 5: > 526 >8 3 8 19 39 75 139 245
+ 6: > 529 >8
+ 7: > 529 >8
+ 8: > 529 >8
+
+(CMM?)+ | (MM?C)+
+
+cCw = Cw
+-Cw = MCw
+cMw = CMw
+-MMw = -w
+-MCw = MMCw
+iw = w
+
+
+ s <= s' s <= s' s <= s' s <= s'
+=========== =========== ============ ==========
+ ws <= Cws' Cs <= Cs' CMs' <= Ms Ms' <= MCs
+
+ s <= s' s <= s'
+=========== ============
+ s <= MMs' Ms' <= Ms
+
+*)
+
type t = M | I | C
type w = t list
type eqclass = w list
]
;;
+let inject =
+ let cache = Hashtbl.create 5393 in
+ function w ->
+ try
+ Hashtbl.find cache w
+ with
+ Not_found ->
+ let rec aux acc =
+ function
+ [] -> acc
+ | he::tl -> aux (4 * acc + (match he with I -> 1 | C -> 2 | M -> 3)) tl
+ in
+ let res = 0, aux 0 w, w in
+ Hashtbl.add cache w res;
+ res
+;;
+
+module VL =
+ struct
+ type t = eqclass
+ let compare = compare
+ let hash = Hashtbl.hash
+ let equal = (=)
+ end
+
+module GL = Graph.Imperative.Digraph.Concrete(VL);;
+
let swap = function Le -> Ge | Ge -> Le;;
let rec new_dir dir =
;;
let string_of_w w =
- String.concat ""
- (List.map (function I -> "i" | C -> "c" | M -> "-") w)
+ let s =
+ String.concat ""
+ (List.map (function I -> "i" | C -> "c" | M -> "-") w)
+ in
+ if s = "" then "." else s
;;
+let string_of_w' w =
+ let s =
+ String.concat ""
+ (List.map (function I -> "i" | C -> "c" | M -> "m") w)
+ in
+ if s = "" then "E" else s
+;;
+
+let string_of_eqclass l = String.concat "=" (List.map string_of_w l);;
+
+let name_of_eqclass l = String.concat "_" (List.map string_of_w' l);;
+
exception NoMatch;;
let (@@) l1 ll2 = List.map (function l2 -> l1 @ l2) ll2;;
function
[],w -> w
| x::lhs,x'::w when x = x' -> aux (lhs,w)
- | _,_ -> raise NoMatch
- in
- rhs @@ apply_rules (aux (lhs,w),new_dir dir lhs)
+ | _,_ -> raise NoMatch in
+ let w' = aux (lhs,w) in
+ if List.length rhs < List.length lhs then rhs @@ [w']
+ else rhs @@ apply_rules (aux (lhs,w),new_dir dir lhs)
and apply_rules (w,_ as w_and_dir) =
if w = [] then [[]]
else
(List.map
(function w ->
List.map (fun x -> x@w)
- (if List.length (List.filter (fun w -> w = M) w) >= 2 then
- [[I];[C];[]]
+ (if List.length (List.filter (fun w -> w = M) w) >= 5 then
+ [[I];[C]]
else
- [[I];[C];[M];[]])
+ [[I];[C];[M]])
) l))
;;
print_newline ();
;;
-let normalize (l : w list) =
+let normalize canonical (l : w list) =
print_endline (string_of_int (List.length l) ^ " nodes to be normalized");
- let rels =
- List.flatten
- (mapi (fun x -> apply_rules (x,Le) @ apply_rules (x,Ge)) l) in
- let arcs =
- List.rev (List.rev_map
- (function (x,rel,y) -> match rel with Le -> x,y | Ge -> y,x) rels) in
- let res = uniq arcs in
- res
+ let rec aux all l =
+ let rels =
+ List.flatten
+ (mapi (fun x -> apply_rules (x,Le) @ apply_rules (x,Ge)) l) in
+ let arcs =
+ mapi
+ (function (x,rel,y) ->
+ let x = canonical x(*(inject x)*) in
+ let y = canonical y(*(inject y)*) in
+ match rel with Le -> x,y | Ge -> y,x) rels in
+ let res = uniq arcs in
+ let nodes = uniq (l @ List.map (fun (_,_,n) -> n) rels) in
+ let new_nodes = List.filter (fun n -> not (List.mem n all)) nodes in
+ let new_nodes = List.filter (function n -> [n] = canonical n) new_nodes in
+ if new_nodes = [] then
+ res
+ else
+ uniq (res @ aux nodes new_nodes)
+ in
+ aux l l
;;
-let visualize describe graph =
- let module G =
+let visualize graph =
+ let module GL =
struct
- include Graph.Pack.Digraph;;
+ include GL;;
let edge_attributes _ = []
let default_edge_attributes _ = []
let get_subgraph _ = None
- let vertex_attributes v = [`Label (describe (Graph.Pack.Digraph.V.label v))]
- let vertex_name v = "v" ^ string_of_int (Graph.Pack.Digraph.V.label v)
+ let vertex_attributes v = [`Label (string_of_eqclass (GL.V.label v))]
+ let vertex_name v = name_of_eqclass (GL.V.label v)
let default_vertex_attributes _ = []
let graph_attributes _ = []
end in
- let module D = Graph.Graphviz.Dot(G) in
+ let module D = Graph.Graphviz.Dot(GL) in
let ch = open_out "/tmp/comb.dot" in
D.output_graph ch graph;
close_out ch;
(*Unix.system ("ggv /tmp/red.ps");*)
;;
-let mk_vertex_and_dsc_vertex =
- function () ->
- let cache1 = Hashtbl.create 5393 in
- let cache2 = Hashtbl.create 5393 in
- (function w ->
- try
- Hashtbl.find cache1 w
- with
- Not_found ->
- let n =
- let rec aux acc =
- function
- [] -> acc
- | he::tl -> aux (acc * 4 + (match he with I -> 1 | C -> 2 | M -> 3)) tl
- in
- aux 0 w
- in
- let v = Graph.Pack.Digraph.V.create n in
- Hashtbl.add cache1 w v;
- Hashtbl.add cache2 v w;
- v),
- (Hashtbl.find cache2)
-;;
-
-let mk_vertex2 =
- function () ->
- let cache1 = Hashtbl.create 5393 in
- function n ->
- try
- Hashtbl.find cache1 n
- with
- Not_found ->
- let v = Graph.Pack.Digraph.V.create n in
- Hashtbl.add cache1 n v;
- v
-;;
-
-let string_compare s1 s2 =
- let c = compare (String.length s1) (String.length s2) in
- if c = 0 then String.compare s1 s2 else c
-;;
-
-let normalize_and_describe norm mk_vertex dsc_vertex =
- let cache = Hashtbl.create 5393 in
- let canonicals = Hashtbl.create 5393 in
- let descriptions = Hashtbl.create 5393 in
- (function n ->
- let v = mk_vertex n in
- let normalized = norm v in
- let dsc = dsc_vertex v in
- if not (List.mem dsc (Hashtbl.find_all cache normalized)) then
- Hashtbl.add cache normalized dsc;
- normalized),
- (function () ->
- let vertexes = uniq (Hashtbl.fold (fun k _ l -> k::l) cache []) in
- let xx =
- mapi
- (fun v ->
- v,
- List.sort string_compare
- (List.map string_of_w (Hashtbl.find_all cache v))
- ) vertexes in
- iteri (function (_,w::_) -> Hashtbl.add canonicals w () | _ -> ()) xx;
- let is_not_redundant s =
- let len = String.length s in
- if len <= 1 then true
- else
- let w = String.sub s 1 (len - 1) in
- try Hashtbl.find canonicals w; true with Not_found -> false
- in
- iteri
- (function (v,x) ->
- Hashtbl.add descriptions v
- (let s = String.concat "=" (List.filter is_not_redundant x) in
- if s = "" then "." else s)) xx),
- Hashtbl.find descriptions
+let w_compare s1 s2 =
+ let c = compare (List.length s1) (List.length s2) in
+ if c = 0 then compare s1 s2 else c
;;
-let classify arcs =
- print_endline (string_of_int (List.length arcs) ^ " arcs to be classified");
- let mk_vertex,dsc_vertex = mk_vertex_and_dsc_vertex () in
- let graph = Graph.Pack.Digraph.create () in
- iteri
- (fun (x,y) ->
- Graph.Pack.Digraph.add_edge graph (mk_vertex x) (mk_vertex y)) arcs;
- print_endline ("<scc>");
- let classes,norm = Graph.Pack.Digraph.Components.scc graph in
- print_endline (string_of_int classes ^ " classes");
- print_endline ("-----");
- norm,mk_vertex,dsc_vertex,arcs
-;;
+exception Found of GL.V.t;;
-let analyze (norm,mk_vertex,dsc_vertex,arcs) =
- print_endline ("building class graph (" ^ string_of_int (List.length arcs) ^ ")");
- let normalize,finish,describe =
- normalize_and_describe norm mk_vertex dsc_vertex in
- let arcs =
- uniq (mapi (fun (x,y) -> normalize x,normalize y) arcs) in
- let cgraph = Graph.Pack.Digraph.create () in
- let mk_vertex2 = mk_vertex2 () in
- List.iter
- (function (x,y) ->
- if x <> y then
- Graph.Pack.Digraph.add_edge cgraph (mk_vertex2 x) (mk_vertex2 y)) arcs;
- print_endline "finish";
- finish ();
- print_endline "visualize";
- visualize describe cgraph;
- print_endline ("/////");
-;;
+let rec iter n cgraph (canonical: w -> GL.V.t) =
+ print_endline ("STEP " ^ string_of_int n);
+ let nodes = GL.fold_vertex (fun n l -> n::l) cgraph [] in
+ let nodes = step (List.map List.hd nodes) in
+(*let nodes = [[C;M];[C;M;C;M];[C;M;C;M;C;M];[C;M;C;M;C;M;C;M];[C;M;C;M;C;M;C;M;C;M]] in*)
+(*let nodes = [[C;I;C;I;C;I]] in*)
+ (*let nodes = step (List.concat nodes) in*)
+(*List.iter (fun x -> prerr_endline ("#@ " ^ string_of_w x)) nodes;*)
+ let arcs = normalize canonical nodes in
+ iteri (fun (x,y) -> if x <> y then GL.add_edge cgraph x y) arcs;
+(*List.iter (fun (x,y) -> prerr_endline (string_of_eqclass x ^ " -> " ^ string_of_eqclass y)) arcs;*)
-let rec iter n l =
- let pkg = classify (normalize l) in
- if n > 0 then
- iter (n - 1) (step l)
- else
- analyze pkg
+ print_endline ("<scc>");
+ let classes,norm =
+ let module SCC = Graph.Components.Make(GL) in SCC.scc cgraph in
+ let xxx =
+ let module SCC = Graph.Components.Make(GL) in SCC.scc_array cgraph in
+ print_endline ("</scc>");
+ let get_canonical n =
+ try List.sort w_compare (List.concat (xxx.(norm n)))
+ with Not_found -> n
+ in
+ let nodes = GL.fold_vertex (fun n l -> n::l) cgraph [] in
+ print_endline "get_canonical";
+ let nodes = mapi (fun n -> n,get_canonical n) nodes in
+ print_endline "/get_canonical";
+ print_endline ("collapse " ^ string_of_int (List.length nodes));
+ iteri
+ (function (n,n') ->
+ let succ = GL.succ cgraph n in
+ let pred = GL.pred cgraph n in
+ GL.remove_vertex cgraph n;
+ let add_edge s t = if s <> t then GL.add_edge cgraph s t in
+ List.iter (fun s -> add_edge n' (get_canonical s)) succ;
+ List.iter (fun p -> add_edge (get_canonical p) n') pred)
+ nodes;
+ print_endline (string_of_int classes ^ " classes");
+ print_endline ("-----");
+ print_endline "visualize";
+ visualize cgraph;
+ print_endline ("/////");
+ GL.iter_vertex (fun l -> print_endline ("?" ^ string_of_eqclass l)) cgraph;
+ let canonical =
+ function (*_,_,*)w ->
+ try
+ GL.iter_vertex (fun l -> if List.mem w l then raise (Found l)) cgraph;
+ [w]
+ with
+ Found l -> l in
+ if n > 0 then
+ iter (n - 1) cgraph canonical
+ else
+ ()
in
- iter 10 [[]]
+ let cgraph = GL.create () in
+ GL.add_vertex cgraph [[]];
+ iter 9 cgraph (fun w(*(_,_,w)*) -> [w])
;;
projects / helm.git / blobdiff