Theory MuCalculus

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theory MuCalculus
imports Main

(*  Title:      HOL/Modelcheck/MuCalculus.thy
Author: Olaf Mueller, Jan Philipps, Robert Sandner
Copyright 1997 TU Muenchen
*)


theory MuCalculus
imports Main
begin


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


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


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


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


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


end