Theory Discrete_Cpo

(*  Title:      HOL/HOLCF/Discrete_Cpo.thy
    Author:     Tobias Nipkow
*)

section ‹Discrete cpo types›

theory Discrete_Cpo
  imports Cont
begin

datatype 'a discr = Discr "'a :: type"

subsection ‹Discrete cpo class instance›

instantiation discr :: (type) discrete_cpo
begin

definition "((⊑) :: 'a discr ⇒ 'a discr ⇒ bool) = (=)"

instance
  by standard (simp add: below_discr_def)

end


subsection ‹\emph{undiscr}›

definition undiscr :: "('a::type)discr ⇒ 'a"
  where "undiscr x = (case x of Discr y ⇒ y)"

lemma undiscr_Discr [simp]: "undiscr (Discr x) = x"
  by (simp add: undiscr_def)

lemma Discr_undiscr [simp]: "Discr (undiscr y) = y"
  by (induct y) simp

end