--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Doc/Tutorial/Misc/Option2.thy Tue Aug 28 18:57:32 2012 +0200
@@ -0,0 +1,33 @@
+(*<*)
+theory Option2 imports Main begin
+hide_const None Some
+hide_type option
+(*>*)
+
+text{*\indexbold{*option (type)}\indexbold{*None (constant)}%
+\indexbold{*Some (constant)}
+Our final datatype is very simple but still eminently useful:
+*}
+
+datatype 'a option = None | Some 'a;
+
+text{*\noindent
+Frequently one needs to add a distinguished element to some existing type.
+For example, type @{text"t option"} can model the result of a computation that
+may either terminate with an error (represented by @{const None}) or return
+some value @{term v} (represented by @{term"Some v"}).
+Similarly, @{typ nat} extended with $\infty$ can be modeled by type
+@{typ"nat option"}. In both cases one could define a new datatype with
+customized constructors like @{term Error} and @{term Infinity},
+but it is often simpler to use @{text option}. For an application see
+\S\ref{sec:Trie}.
+*}
+(*<*)
+(*
+definition infplus :: "nat option \<Rightarrow> nat option \<Rightarrow> nat option" where
+"infplus x y \<equiv> case x of None \<Rightarrow> None
+ | Some m \<Rightarrow> (case y of None \<Rightarrow> None | Some n \<Rightarrow> Some(m+n))"
+
+*)
+end
+(*>*)