doc-src/TutorialI/Misc/Option2.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/TutorialI/Misc/Option2.thy	Fri Dec 01 13:47:37 2000 +0100
@@ -0,0 +1,33 @@
+(*<*)
+theory Option2 = Main:
+hide const None Some
+hide type option
+(*>*)
+
+text{*\indexbold{*option}\indexbold{*None}\indexbold{*Some}
+Our final datatype is very simple but still eminently useful:
+*}
+
+datatype 'a option = None | Some 'a;
+
+text{*\noindent
+Frequently one needs to add a distiguished 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 @{term 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}.
+*}
+(*<*)
+(*
+constdefs
+ infplus :: "nat option \<Rightarrow> nat option \<Rightarrow> nat option"
+"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
+(*>*)