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\title{Functional Data Structures}
\author{Tobias Nipkow}
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\begin{abstract}
A collection of verified functional data structures. The emphasis is on
conciseness of algorithms and succinctness of proofs, more in the style
of a textbook than a library of efficient algorithms.
\end{abstract}
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\section{Bibliographic Notes}
\paragraph{Red-black trees}
The insert function follows Okasaki \cite{Okasaki}, the delete function
Kahrs \cite{Kahrs-html,Kahrs-JFP01}.
\paragraph{2-3 trees}
The function definitions are based on the teaching material by
Turbak~\cite{Turbak230}.
\paragraph{1-2 brother trees}
They were invented by Ottmann and Six~\cite{OttmannS76,OttmannW-CJ80}.
The functional version is due to Hinze~\cite{Hinze-bro12}.
\paragraph{Splay trees}
They were invented by Sleator and Tarjan \cite{SleatorT-JACM85}.
Our formalisation follows Schoenmakers \cite{Schoenmakers-IPL93}.
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