src/Pure/PIDE/markup_tree.scala

strengthened and renamed lemma antisym_converse and added lemma antisymp_on_conversep

/*  Title:      Pure/PIDE/markup_tree.scala
    Author:     Fabian Immler, TU Munich
    Author:     Makarius

Markup trees over nested / non-overlapping text ranges.
*/

package isabelle


import scala.collection.immutable.SortedMap
import scala.collection.mutable
import scala.annotation.tailrec


object Markup_Tree {
  /* construct trees */

  val empty: Markup_Tree = new Markup_Tree(Branches.empty)

  def merge(trees: List[Markup_Tree], range: Text.Range, elements: Markup.Elements): Markup_Tree =
    trees.foldLeft(empty)(_.merge(_, range, elements))

  def merge_disjoint(trees: List[Markup_Tree]): Markup_Tree =
    trees match {
      case Nil => empty
      case head :: tail =>
        new Markup_Tree(
          tail.foldLeft(head.branches) {
            case (branches, tree) =>
              tree.branches.foldLeft(branches) {
                case (bs, (r, entry)) =>
                  require(!bs.isDefinedAt(r), "cannot merge markup trees")
                  bs + (r -> entry)
              }
          })
    }


  /* tree building blocks */

  object Entry {
    def apply(markup: Text.Markup, subtree: Markup_Tree): Entry =
      Entry(markup.range, List(markup.info), subtree)
  }

  sealed case class Entry(
    range: Text.Range,
    rev_markup: List[XML.Elem],
    subtree: Markup_Tree
  ) {
    def markup: List[XML.Elem] = rev_markup.reverse

    def filter_markup(elements: Markup.Elements): List[XML.Elem] = {
      var result: List[XML.Elem] = Nil
      for (elem <- rev_markup if elements(elem.name))
        result ::= elem
      result
    }

    def + (markup: Text.Markup): Entry = copy(rev_markup = markup.info :: rev_markup)
    def \ (markup: Text.Markup): Entry = copy(subtree = subtree + markup)
  }

  object Branches {
    type T = SortedMap[Text.Range, Entry]
    val empty: T = SortedMap.empty(Text.Range.Ordering)
  }


  /* XML representation */

  @tailrec private def strip_elems(
      elems: List[XML.Elem], body: XML.Body): (List[XML.Elem], XML.Body) =
    body match {
      case List(XML.Wrapped_Elem(markup1, body1, body2)) =>
        strip_elems(XML.Elem(markup1, body1) :: elems, body2)
      case List(XML.Elem(markup1, body1)) =>
        strip_elems(XML.Elem(markup1, Nil) :: elems, body1)
      case _ => (elems, body)
    }

  private def make_trees(
    acc: (Int, List[Markup_Tree]),
    tree: XML.Tree
  ): (Int, List[Markup_Tree]) = {
    val (offset, markup_trees) = acc

    strip_elems(Nil, List(tree)) match {
      case (Nil, body) =>
        (offset + XML.text_length(body), markup_trees)

      case (elems, body) =>
        val (end_offset, subtrees) =
           body.foldLeft((offset, List.empty[Markup_Tree]))(make_trees)
        if (offset == end_offset) acc
        else {
          val range = Text.Range(offset, end_offset)
          val entry = Entry(range, elems, merge_disjoint(subtrees))
          (end_offset, new Markup_Tree(Branches.empty, entry) :: markup_trees)
        }
    }
  }

  def from_XML(body: XML.Body): Markup_Tree =
    merge_disjoint(body.foldLeft((0, List.empty[Markup_Tree]))(make_trees)._2)
}


final class Markup_Tree private(val branches: Markup_Tree.Branches.T) {
  import Markup_Tree._

  private def this(branches: Markup_Tree.Branches.T, entry: Markup_Tree.Entry) =
    this(branches + (entry.range -> entry))

  private def overlapping(range: Text.Range): Branches.T =
    if (branches.isEmpty ||
        (range.contains(branches.firstKey.start) && branches.lastKey.stop <= range.stop))
      branches
    else {
      val start = Text.Range(range.start)
      val stop = Text.Range(range.stop)
      val bs = branches.range(start, stop)
      branches.get(stop) match {
        case Some(end) if range overlaps end.range => bs + (end.range -> end)
        case _ => bs
      }
    }

  def restrict(range: Text.Range): Markup_Tree =
    new Markup_Tree(overlapping(range))

  def is_empty: Boolean = branches.isEmpty

  def + (new_markup: Text.Markup): Markup_Tree = {
    val new_range = new_markup.range

    branches.get(new_range) match {
      case None => new Markup_Tree(branches, Entry(new_markup, empty))
      case Some(entry) =>
        if (entry.range == new_range)
          new Markup_Tree(branches, entry + new_markup)
        else if (entry.range.contains(new_range))
          new Markup_Tree(branches, entry \ new_markup)
        else if (new_range.contains(branches.head._1) && new_range.contains(branches.last._1))
          new Markup_Tree(Branches.empty, Entry(new_markup, this))
        else {
          val body = overlapping(new_range)
          if (body.forall(e => new_range.contains(e._1)))
            new Markup_Tree(branches -- body.keys, Entry(new_markup, new Markup_Tree(body)))
          else {
            Output.warning("Ignored overlapping markup information: " + new_markup + "\n" +
              body.filter(e => !new_range.contains(e._1)).values.mkString("\n"))
            this
          }
        }
    }
  }

  def merge(other: Markup_Tree, root_range: Text.Range, elements: Markup.Elements): Markup_Tree = {
    def merge_trees(tree1: Markup_Tree, tree2: Markup_Tree): Markup_Tree =
      tree2.branches.foldLeft(tree1) {
        case (tree, (range, entry)) =>
          if (!range.overlaps(root_range)) tree
          else {
            entry.filter_markup(elements).foldLeft(merge_trees(tree, entry.subtree)) {
              case (t, elem) => t + Text.Info(range, elem)
            }
          }
      }

    if (this eq other) this
    else {
      val tree1 = this.restrict(root_range)
      val tree2 = other.restrict(root_range)
      if (tree1.is_empty) tree2
      else merge_trees(tree1, tree2)
    }
  }

  def cumulate[A](
    root_range: Text.Range,
    root_info: A,
    elements: Markup.Elements,
    result: (A, Text.Markup) => Option[A]
  ): List[Text.Info[A]] = {
    def results(x: A, entry: Entry): Option[A] = {
      var y = x
      var changed = false
      for {
        elem <- entry.filter_markup(elements)
        y1 <- result(y, Text.Info(entry.range, elem))
      } { y = y1; changed = true }
      if (changed) Some(y) else None
    }

    def traverse(
      last: Text.Offset,
      stack: List[(Text.Info[A], List[(Text.Range, Entry)])]
    ): List[Text.Info[A]] = {
      stack match {
        case (parent, (range, entry) :: more) :: rest =>
          val subrange = range.restrict(root_range)
          val subtree = entry.subtree.overlapping(subrange).toList
          val start = subrange.start

          results(parent.info, entry) match {
            case Some(res) =>
              val next = Text.Info(subrange, res)
              val nexts = traverse(start, (next, subtree) :: (parent, more) :: rest)
              if (last < start) parent.restrict(Text.Range(last, start)) :: nexts
              else nexts
            case None => traverse(last, (parent, subtree ::: more) :: rest)
          }

        case (parent, Nil) :: rest =>
          val stop = parent.range.stop
          val nexts = traverse(stop, rest)
          if (last < stop) parent.restrict(Text.Range(last, stop)) :: nexts
          else nexts

        case Nil =>
          val stop = root_range.stop
          if (last < stop) List(Text.Info(Text.Range(last, stop), root_info))
          else Nil
      }
    }
    traverse(root_range.start,
      List((Text.Info(root_range, root_info), overlapping(root_range).toList)))
  }

  def to_XML(root_range: Text.Range, text: CharSequence, elements: Markup.Elements): XML.Body = {
    def make_text(start: Text.Offset, stop: Text.Offset): XML.Body =
      if (start == stop) Nil
      else List(XML.Text(text.subSequence(start, stop).toString))

    def make_elems(rev_markups: List[XML.Elem], body: XML.Body): XML.Body =
      rev_markups.foldLeft(body) {
        case (b, elem) =>
          if (!elements(elem.name)) b
          else if (elem.body.isEmpty) List(XML.Elem(elem.markup, b))
          else List(XML.Wrapped_Elem(elem.markup, elem.body, b))
      }

    def make_body(
      elem_range: Text.Range,
      elem_markup: List[XML.Elem],
      entries: Branches.T
    ) : XML.Body = {
      val body = new mutable.ListBuffer[XML.Tree]
      var last = elem_range.start
      for ((range, entry) <- entries) {
        val subrange = range.restrict(elem_range)
        body ++= make_text(last, subrange.start)
        body ++= make_body(subrange, entry.rev_markup, entry.subtree.overlapping(subrange))
        last = subrange.stop
      }
      body ++= make_text(last, elem_range.stop)
      make_elems(elem_markup, body.toList)
    }
    make_body(root_range, Nil, overlapping(root_range))
  }

  override def toString: String =
    branches.toList.map(_._2) match {
      case Nil => "Empty"
      case list => list.mkString("Tree(", ",", ")")
    }
}