src/HOL/Trancl.thy
author paulson
Tue, 16 Jul 1996 15:49:46 +0200
changeset 1868 836950047d85
parent 1642 21db0cf9a1a4
child 1916 43521f79f016
permissions -rw-r--r--
Put in minimal simpset to avoid excessive simplification, just as in revision 1.9 of HOL/indrule.ML

(*  Title:      HOL/Trancl.thy
    ID:         $Id$
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1992  University of Cambridge

Relfexive and Transitive closure of a relation

rtrancl is reflexive/transitive closure;
trancl  is transitive closure
reflcl  is reflexive closure
*)

Trancl = Lfp + Relation + 

constdefs
  rtrancl :: "('a * 'a)set => ('a * 'a)set"   ("(_^*)" [100] 100)
  "r^*  ==  lfp(%s. id Un (r O s))"

  trancl  :: "('a * 'a)set => ('a * 'a)set"   ("(_^+)" [100] 100)
  "r^+  ==  r O rtrancl(r)"

syntax
  reflcl  :: "('a*'a)set => ('a*'a)set"       ("(_^=)" [100] 100)

translations
  "r^=" == "r Un id"

end