(* Title: HOL/HOLCF/Discrete.thy
Author: Tobias Nipkow
*)
header {* Discrete cpo types *}
theory Discrete
imports Cont
begin
datatype 'a discr = Discr "'a :: type"
subsection {* Discrete cpo class instance *}
instantiation discr :: (type) discrete_cpo
begin
definition
"(op \<sqsubseteq> :: 'a discr \<Rightarrow> 'a discr \<Rightarrow> bool) = (op =)"
instance
by default (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