doc-src/TutorialI/Misc/document/Option2.tex

renamed HOL + - * etc. to HOL.plus HOL.minus HOL.times etc.

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\indexbold{*option (type)}\indexbold{*None (constant)}%
\indexbold{*Some (constant)}
Our final datatype is very simple but still eminently useful:%
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\ {\isacharprime}a\ option\ {\isacharequal}\ None\ {\isacharbar}\ Some\ {\isacharprime}a%
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\noindent
Frequently one needs to add a distinguished element to some existing type.
For example, type \isa{t\ option} can model the result of a computation that
may either terminate with an error (represented by \isa{None}) or return
some value \isa{v} (represented by \isa{Some\ v}).
Similarly, \isa{nat} extended with $\infty$ can be modeled by type
\isa{nat\ option}. In both cases one could define a new datatype with
customized constructors like \isa{Error} and \isa{Infinity},
but it is often simpler to use \isa{option}. For an application see
\S\ref{sec:Trie}.%
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