src/HOL/Induct/Tree.thy
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7017:e4e64a0b0b6b 7018:ae18bb3075c3
       
     1 (*  Title:      HOL/Induct/Tree.thy
       
     2     ID:         $Id$
       
     3     Author:     Stefan Berghofer,  TU Muenchen
       
     4     Copyright   1999  TU Muenchen
       
     5 
       
     6 Infinitely branching trees
       
     7 *)
       
     8 
       
     9 Tree = Main +
       
    10 
       
    11 datatype 'a tree = Atom 'a | Branch "nat => 'a tree"
       
    12 
       
    13 consts
       
    14   map_tree :: "('a => 'b) => 'a tree => 'b tree"
       
    15 
       
    16 primrec
       
    17   "map_tree f (Atom a) = Atom (f a)"
       
    18   "map_tree f (Branch ts) = Branch (%x. map_tree f (ts x))"
       
    19 
       
    20 consts
       
    21   exists_tree :: "('a => bool) => 'a tree => bool"
       
    22 
       
    23 primrec
       
    24   "exists_tree P (Atom a) = P a"
       
    25   "exists_tree P (Branch ts) = (? x. exists_tree P (ts x))"
       
    26 
       
    27 end