Infinitely branching trees.
(* Title: HOL/ex/Acc.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 University of Cambridge
Inductive definition of acc(r)
See Ch. Paulin-Mohring, Inductive Definitions in the System Coq.
Research Report 92-49, LIP, ENS Lyon. Dec 1992.
*)
Acc = WF + Inductive +
constdefs
pred :: "['b, ('a * 'b)set] => 'a set" (*Set of predecessors*)
"pred x r == {y. (y,x):r}"
consts
acc :: "('a * 'a)set => 'a set" (*Accessible part*)
inductive "acc(r)"
intrs
pred "pred a r: Pow(acc(r)) ==> a: acc(r)"
monos Pow_mono
syntax termi :: "('a * 'a)set => 'a set"
translations "termi r" == "acc(r^-1)"
end