src/HOL/Induct/Tree.thy
author kleing
Mon Jun 21 10:25:57 2004 +0200 (2004-06-21)
changeset 14981 e73f8140af78
parent 12171 dc87f33db447
child 16078 e1364521a250
permissions -rw-r--r--
Merged in license change from Isabelle2004
     1 (*  Title:      HOL/Induct/Tree.thy
     2     ID:         $Id$
     3     Author:     Stefan Berghofer,  TU Muenchen
     4 *)
     5 
     6 header {* Infinitely branching trees *}
     7 
     8 theory Tree = Main:
     9 
    10 datatype 'a tree =
    11     Atom 'a
    12   | Branch "nat => 'a tree"
    13 
    14 consts
    15   map_tree :: "('a => 'b) => 'a tree => 'b tree"
    16 primrec
    17   "map_tree f (Atom a) = Atom (f a)"
    18   "map_tree f (Branch ts) = Branch (\<lambda>x. map_tree f (ts x))"
    19 
    20 lemma tree_map_compose: "map_tree g (map_tree f t) = map_tree (g \<circ> f) t"
    21   by (induct t) simp_all
    22 
    23 consts
    24   exists_tree :: "('a => bool) => 'a tree => bool"
    25 primrec
    26   "exists_tree P (Atom a) = P a"
    27   "exists_tree P (Branch ts) = (\<exists>x. exists_tree P (ts x))"
    28 
    29 lemma exists_map:
    30   "(!!x. P x ==> Q (f x)) ==>
    31     exists_tree P ts ==> exists_tree Q (map_tree f ts)"
    32   by (induct ts) auto
    33 
    34 end