src/HOL/HOLCF/Discrete.thy

+(*  Title:      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