# Theory MuCalculus

Up to index of Isabelle/HOLCF/IOA/Modelcheck

theory MuCalculus
imports Main
begin

    (*  Title:      HOL/Modelcheck/MuCalculus.thy
        ID:         $Id: MuCalculus.thy,v 1.4 2005/09/06 14:24:54 wenzelm Exp $
        Author:     Olaf Mueller, Jan Philipps, Robert Sandner
        Copyright   1997  TU Muenchen
    *)

    theory MuCalculus
    imports Main
    begin

    types
     'a pred = "'a=>bool"

    constdefs
      Charfun :: "'a set => 'a pred"
      "Charfun == (% A.% x. x:A)"

      monoP  :: "('a pred => 'a pred) => bool"
      "monoP f == mono(Collect o f o Charfun)"

      mu :: "('a pred => 'a pred) => 'a pred"    (binder "Mu " 10)
      "mu f == Charfun(lfp(Collect o f o Charfun))"

      nu :: "('a pred => 'a pred) => 'a pred"    (binder "Nu " 10)
      "nu f == Charfun(gfp(Collect o f o Charfun))"

    ML {* use_legacy_bindings (the_context ()) *}

    end