(* Title: HOL/HOLCF/Discrete.thy
Author: Tobias Nipkow
*)
section \<open>Discrete cpo types\<close>
theory Discrete
imports Cont
begin
datatype 'a discr = Discr "'a :: type"
subsection \<open>Discrete cpo class instance\<close>
instantiation discr :: (type) discrete_cpo
begin
definition "((\<sqsubseteq>) :: 'a discr \<Rightarrow> 'a discr \<Rightarrow> bool) = (=)"
instance
by standard (simp add: below_discr_def)
end
subsection \<open>\emph{undiscr}\<close>
definition undiscr :: "('a::type)discr \<Rightarrow> 'a"
where "undiscr x = (case x of Discr y \<Rightarrow> 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