src/Pure/General/graph.ML
author berghofe
Thu, 21 Aug 2003 16:18:43 +0200
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permissions -rw-r--r--
Added function strong_conn for computing the strongly connected components of the graph.
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(*  Title:      Pure/General/graph.ML
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    ID:         $Id$
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    Author:     Markus Wenzel, TU Muenchen
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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Directed graphs.
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*)
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signature GRAPH =
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sig
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  type key
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  type 'a T
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  exception UNDEF of key
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  exception DUP of key
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  exception DUPS of key list
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  val empty: 'a T
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  val keys: 'a T -> key list
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  val map_nodes: ('a -> 'b) -> 'a T -> 'b T
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  val get_node: 'a T -> key -> 'a
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  val map_node: key -> ('a -> 'a) -> 'a T -> 'a T
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  val imm_preds: 'a T -> key -> key list
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  val imm_succs: 'a T -> key -> key list
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  val all_preds: 'a T -> key list -> key list
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  val all_succs: 'a T -> key list -> key list
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  val strong_conn: 'a T -> key list list
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  val find_paths: 'a T -> key * key -> key list list
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  val new_node: key * 'a -> 'a T -> 'a T
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  val del_nodes: key list -> 'a T -> 'a T
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  val edges: 'a T -> (key * key) list
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  val add_edge: key * key -> 'a T -> 'a T
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  val del_edge: key * key -> 'a T -> 'a T
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  exception CYCLES of key list list
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  val add_edge_acyclic: key * key -> 'a T -> 'a T
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  val add_deps_acyclic: key * key list -> 'a T -> 'a T
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  val merge_acyclic: ('a * 'a -> bool) -> 'a T * 'a T -> 'a T
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  val merge: ('a * 'a -> bool) -> 'a T * 'a T -> 'a T
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end;
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functor GraphFun(Key: KEY): GRAPH =
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struct
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(* keys *)
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type key = Key.key;
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val eq_key = equal EQUAL o Key.ord;
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infix mem_key;
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val op mem_key = gen_mem eq_key;
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infix ins_key;
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val op ins_key = gen_ins eq_key;
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infix del_key;
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fun xs del_key x = if x mem_key xs then gen_rem eq_key (xs, x) else xs;
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infix del_keys;
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val op del_keys = foldl (op del_key);
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(* tables and sets of keys *)
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structure Table = TableFun(Key);
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type keys = unit Table.table;
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val empty_keys = Table.empty: keys;
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infix mem_keys;
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fun x mem_keys tab = is_some (Table.lookup (tab: keys, x));
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infix ins_keys;
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fun x ins_keys tab = if x mem_keys tab then tab else Table.update ((x, ()), tab);
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(* graphs *)
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datatype 'a T = Graph of ('a * (key list * key list)) Table.table;
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exception UNDEF of key;
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exception DUP = Table.DUP;
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exception DUPS = Table.DUPS;
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val empty = Graph Table.empty;
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fun keys (Graph tab) = Table.keys tab;
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fun get_entry (Graph tab) x =
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  (case Table.lookup (tab, x) of
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    Some entry => entry
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  | None => raise UNDEF x);
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fun map_entry x f (G as Graph tab) = Graph (Table.update ((x, f (get_entry G x)), tab));
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(* nodes *)
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fun map_nodes f (Graph tab) = Graph (Table.map (fn (i, ps) => (f i, ps)) tab);
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fun get_node G = #1 o get_entry G;
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fun map_node x f = map_entry x (fn (i, ps) => (f i, ps));
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(* reachability *)
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(*nodes reachable from xs -- topologically sorted for acyclic graphs*)
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fun reachable next xs =
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  let
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    fun reach ((R, rs), x) =
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      if x mem_keys R then (R, rs)
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      else apsnd (cons x) (reachs ((x ins_keys R, rs), next x))
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    and reachs R_xs = foldl reach R_xs;
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  in foldl_map (reach o apfst (rpair [])) (empty_keys, xs) end;
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(*immediate*)
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fun imm_preds G = #1 o #2 o get_entry G;
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fun imm_succs G = #2 o #2 o get_entry G;
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(*transitive*)
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fun all_preds G = flat o snd o reachable (imm_preds G);
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fun all_succs G = flat o snd o reachable (imm_succs G);
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(* strongly connected components; see: David King and John Launchbury, *)
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(* "Structuring Depth First Search Algorithms in Haskell"              *)
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fun strong_conn G = filter_out null (snd (reachable (imm_preds G)
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  (flat (rev (snd (reachable (imm_succs G) (keys G)))))));
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(* paths *)
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fun find_paths G (x, y) =
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  let
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    val (X, _) = reachable (imm_succs G) [x];
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    fun paths ps p =
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      if not (null ps) andalso eq_key (p, x) then [p :: ps]
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      else if p mem_keys X andalso not (p mem_key ps)
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      then flat (map (paths (p :: ps)) (imm_preds G p))
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      else [];
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  in paths [] y end;
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(* nodes *)
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exception DUPLICATE of key;
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fun new_node (x, info) (Graph tab) =
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  Graph (Table.update_new ((x, (info, ([], []))), tab));
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fun del_nodes xs (Graph tab) =
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  let
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    fun del (x, (i, (preds, succs))) =
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      if x mem_key xs then None
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      else Some (x, (i, (preds del_keys xs, succs del_keys xs)));
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  in Graph (Table.make (mapfilter del (Table.dest tab))) end;
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(* edges *)
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fun edges (Graph tab) =
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  flat (map (fn (x, (_, (_, succs))) => (map (pair x) succs)) (Table.dest tab));
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fun add_edge (x, y) =
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  map_entry x (fn (i, (preds, succs)) => (i, (preds, y ins_key succs))) o
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   map_entry y (fn (i, (preds, succs)) => (i, (x ins_key preds, succs)));
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fun del_edge (x, y) =
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  map_entry x (fn (i, (preds, succs)) => (i, (preds, succs del_key y))) o
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   map_entry y (fn (i, (preds, succs)) => (i, (preds del_key x, succs)));
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exception CYCLES of key list list;
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fun add_edge_acyclic (x, y) G =
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  if y mem_key imm_succs G x then G
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  else
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    (case find_paths G (y, x) of
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      [] => add_edge (x, y) G
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    | cycles => raise CYCLES (map (cons x) cycles));
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fun add_deps_acyclic (y, xs) G =
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  foldl (fn (H, x) => add_edge_acyclic (x, y) H) (G, xs);
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(* merge_acyclic *)
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fun gen_merge add eq (Graph tab1, G2 as Graph tab2) =
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  foldl (fn (G, xy) => add xy G)
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    (Graph (Table.merge (fn ((i1, _), (i2, _)) => eq (i1, i2)) (tab1, tab2)), edges G2);
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fun merge_acyclic eq p = gen_merge add_edge_acyclic eq p;
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fun merge eq p = gen_merge add_edge eq p;
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end;
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(*graphs indexed by strings*)
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structure Graph = GraphFun(type key = string val ord = string_ord);