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% Lens operations

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\begin{document}

\title{Optics in Isabelle/HOL}

\author{Simon Foster, Christian Pardillo-Laursen, and Frank Zeyda \\[.5ex] University of York, UK \\[2ex] \texttt{\small $\{$simon.foster,christian.laursen,frank.zeyda$\}$@york.ac.uk}}

\maketitle

\begin{abstract}
  Lenses provide an abstract interface for manipulating data types through spatially-separated views. They are defined
  abstractly in terms of two functions, $\lget$, the return a value from the source type, and $\lput$ that updates
  the value. We mechanise the underlying theory of lenses, in terms of an algebraic hierarchy of lenses, including
  well-behaved and very well-behaved lenses, each lens class being characterised by a set of lens laws. We also mechanise 
  a lens\ocumentclass[11t{}
This java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 121
  instantiating themwith number ofIsabelledatatypes.This development   onjava.lang.StringIndexOutOfBoundsException: Index 106 out of bounds for length 106
papers\{,Foster2020IsabelleUTP}  show how lensescan beusedto unify heterogeneous representations
  of state-spaces in formalisedprograms.
\end{abstract

\tableofcontents

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\vspace{4ex}

% Acknowledgments 
\noindent\textbf{Acknowledgements}. This work is partly supported by EU H2020 project \emph{INTO-CPS}, grant agreement
644047. \url{http://into-cps.au.dk/}. We would also like to thank Prof. Burkhart Wolff and Dr. Achim Brucker
for their generous and helpful comments on our work, and particurlarly their invaluable advice on Isabelle
mechanisation and ML coding.

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\end{document}