--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/General/graph.scala Thu Feb 23 14:17:51 2012 +0100
@@ -0,0 +1,200 @@
+/* Title: Pure/General/graph.scala
+ Module: PIDE
+ Author: Makarius
+
+Directed graphs.
+*/
+
+package isabelle
+
+
+import scala.annotation.tailrec
+
+
+object Graph
+{
+ class Duplicate[Key](x: Key) extends Exception
+ class Undefined[Key](x: Key) extends Exception
+ class Cycles[Key](cycles: List[List[Key]]) extends Exception
+
+ def empty[Key, A]: Graph[Key, A] = new Graph[Key, A](Map.empty)
+}
+
+
+class Graph[Key, A] private(rep: Map[Key, (A, (Set[Key], Set[Key]))])
+ extends Iterable[(Key, (A, (Set[Key], Set[Key])))]
+{
+ type Keys = Set[Key]
+ type Entry = (A, (Keys, Keys))
+
+ def iterator: Iterator[(Key, Entry)] = rep.iterator
+
+ def is_empty: Boolean = rep.isEmpty
+
+ def keys: Set[Key] = rep.keySet.toSet
+
+ def dest: List[(Key, List[Key])] =
+ (for ((x, (_, (_, succs))) <- iterator) yield (x, succs.toList)).toList
+
+
+ /* entries */
+
+ private def get_entry(x: Key): Entry =
+ rep.get(x) match {
+ case Some(entry) => entry
+ case None => throw new Graph.Undefined(x)
+ }
+
+ private def map_entry(x: Key, f: Entry => Entry): Graph[Key, A] =
+ new Graph[Key, A](rep + (x -> f(get_entry(x))))
+
+
+ /* nodes */
+
+ def map_nodes[B](f: A => B): Graph[Key, B] =
+ new Graph[Key, B](rep mapValues { case (i, ps) => (f(i), ps) })
+
+ def get_node(x: Key): A = get_entry(x)._1
+
+ def map_node(x: Key, f: A => A): Graph[Key, A] =
+ map_entry(x, { case (i, ps) => (f(i), ps) })
+
+
+ /* reachability */
+
+ /*nodes reachable from xs -- topologically sorted for acyclic graphs*/
+ def reachable(next: Key => Keys, xs: List[Key]): (List[List[Key]], Keys) =
+ {
+ def reach(reached: (List[Key], Keys), x: Key): (List[Key], Keys) =
+ {
+ val (rs, r_set) = reached
+ if (r_set(x)) reached
+ else {
+ val (rs1, r_set1) = ((rs, r_set + x) /: next(x))(reach)
+ (x :: rs1, r_set1)
+ }
+ }
+ def reachs(reached: (List[List[Key]], Keys), x: Key): (List[List[Key]], Keys) =
+ {
+ val (rss, r_set) = reached
+ val (rs, r_set1) = reach((Nil, r_set), x)
+ (rs :: rss, r_set1)
+ }
+ ((List.empty[List[Key]], Set.empty[Key]) /: xs)(reachs)
+ }
+
+ /*immediate*/
+ def imm_preds(x: Key): Keys = get_entry(x)._2._1
+ def imm_succs(x: Key): Keys = get_entry(x)._2._2
+
+ /*transitive*/
+ def all_preds(xs: List[Key]): List[Key] = reachable(imm_preds, xs)._1.flatten
+ def all_succs(xs: List[Key]): List[Key] = reachable(imm_succs, xs)._1.flatten
+
+
+ /* minimal and maximal elements */
+
+ def minimals: List[Key] =
+ (List.empty[Key] /: rep) {
+ case (ms, (m, (_, (preds, _)))) => if (preds.isEmpty) m :: ms else ms }
+
+ def maximals: List[Key] =
+ (List.empty[Key] /: rep) {
+ case (ms, (m, (_, (_, succs)))) => if (succs.isEmpty) m :: ms else ms }
+
+ def is_minimal(x: Key): Boolean = imm_preds(x).isEmpty
+ def is_maximal(x: Key): Boolean = imm_succs(x).isEmpty
+
+
+ /* nodes */
+
+ def new_node(x: Key, info: A): Graph[Key, A] =
+ {
+ if (rep.isDefinedAt(x)) throw new Graph.Duplicate(x)
+ else new Graph[Key, A](rep + (x -> (info, (Set.empty, Set.empty))))
+ }
+
+ def del_nodes(xs: List[Key]): Graph[Key, A] =
+ {
+ xs.foreach(get_entry)
+ new Graph[Key, A](
+ (rep -- xs) mapValues { case (i, (preds, succs)) => (i, (preds -- xs, succs -- xs)) })
+ }
+
+ private def del_adjacent(fst: Boolean, x: Key)(map: Map[Key, Entry], y: Key): Map[Key, Entry] =
+ map.get(y) match {
+ case None => map
+ case Some((i, (preds, succs))) =>
+ map + (y -> (i, if (fst) (preds - x, succs) else (preds, succs - x)))
+ }
+
+ def del_node(x: Key): Graph[Key, A] =
+ {
+ val (preds, succs) = get_entry(x)._2
+ new Graph[Key, A](
+ (((rep - x) /: preds)(del_adjacent(false, x)) /: succs)(del_adjacent(true, x)))
+ }
+
+
+ /* edges */
+
+ def is_edge(x: Key, y: Key): Boolean =
+ try { imm_succs(x)(y) }
+ catch { case _: Graph.Undefined[_] => false }
+
+ def add_edge(x: Key, y: Key): Graph[Key, A] =
+ if (is_edge(x, y)) this
+ else
+ map_entry(y, { case (i, (preds, succs)) => (i, (preds + x, succs)) }).
+ map_entry(x, { case (i, (preds, succs)) => (i, (preds, succs + y)) })
+
+ def del_edge(x: Key, y: Key): Graph[Key, A] =
+ if (is_edge(x, y))
+ map_entry(y, { case (i, (preds, succs)) => (i, (preds - x, succs)) }).
+ map_entry(x, { case (i, (preds, succs)) => (i, (preds, succs - y)) })
+ else this
+
+
+ /* irreducible paths -- Hasse diagram */
+
+ def irreducible_preds(x_set: Set[Key], path: List[Key], z: Key): List[Key] =
+ {
+ def red(x: Key)(x1: Key) = is_edge(x, x1) && x1 != z
+ @tailrec def irreds(xs0: List[Key], xs1: List[Key]): List[Key] =
+ xs0 match {
+ case Nil => xs1
+ case x :: xs =>
+ if (!(x_set(x)) || x == z || path.contains(x) ||
+ xs.exists(red(x)) || xs1.exists(red(x)))
+ irreds(xs, xs1)
+ else irreds(xs, x :: xs1)
+ }
+ irreds(imm_preds(z).toList, Nil)
+ }
+
+ def irreducible_paths(x: Key, y: Key): List[List[Key]] =
+ {
+ val (_, x_set) = reachable(imm_succs, List(x))
+ def paths(path: List[Key])(ps: List[List[Key]], z: Key): List[List[Key]] =
+ if (x == z) (z :: path) :: ps
+ else (ps /: irreducible_preds(x_set, path, z))(paths(z :: path))
+ if ((x == y) && !is_edge(x, x)) List(Nil) else paths(Nil)(Nil, y)
+ }
+
+
+ /* maintain acyclic graphs */
+
+ def add_edge_acyclic(x: Key, y: Key): Graph[Key, A] =
+ if (is_edge(x, y)) this
+ else {
+ irreducible_paths(y, x) match {
+ case Nil => add_edge(x, y)
+ case cycles => throw new Graph.Cycles(cycles.map(x :: _))
+ }
+ }
+
+ def add_deps_cyclic(y: Key, xs: List[Key]): Graph[Key, A] =
+ (this /: xs)(_.add_edge_acyclic(_, y))
+
+ def topological_order: List[Key] = all_succs(minimals)
+}