\part{Overview of HOL~4}

\frame[plain]{\partpage}

\begin{frame}
\frametitle{Overview of HOL 4}

\begin{itemize}
\item in this course we discussed the basics of HOL 4
\item you were encouraged to learn more on your own in exercises
\item there is a lot more to learn even after the end of the course
\begin{itemize}
\item many more libraries
\item proof tools
\item existing formalisations
\item ...
\end{itemize}
\item to really use HOL well, you should continue learning
\item to help getting started, a short overview is presented here
\end{itemize}
\end{frame}


\begin{frame}
\frametitle{HOL Bare Source Directories}

The following source directories are the very basis of HOL. They
are required to build \hol{hol.bare}.

\begin{itemize}
\item \hol{src/portableML} -- common stuff for PolyML and MoscowML
\item \hol{src/prekernel}
\item \hol{src/0} -- Standard Kernel
\item \hol{src/logging-kernel} -- Logging Kernel
\item \hol{src/experimental-kernel} -- Experimental Kernel
\item \hol{src/postkernel}
\item \hol{src/opentheory}
\item \hol{src/parse}
\item \hol{src/bool}
\item \hol{src/1}
\item \hol{src/proofman}
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{HOL Basic Directories I}

On top of \texttt{hol.bare}, there are many basic theories and tools. These
are all required for building the main \texttt{hol} executable.

\begin{itemize}
\item \hol{src/compute} -- fast ground term rewriting
\item \hol{src/HolSat} -- SAT solver interfaces
\item \hol{src/taut} -- propositional proofs using \texttt{HolSat}
\item \hol{src/marker} -- marking terms
\item \hol{src/q} -- parsing support 
\item \hol{src/combin} -- combinators
\item \hol{src/lite} -- some simple lib with various stuff
\item \hol{src/refute} -- refutation prover, normal forms 
\item \hol{src/metis} -- first order resolution prover
\item \hol{src/meson} -- first order model elimination prover
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{HOL Basic Directories II}

\begin{itemize}
\item \hol{src/simp} -- simplifier
\item \hol{src/holyhammer} -- tool for finding Metis proofs
\item \hol{src/tactictoe} -- machine learning tool for finding proofs
\item \hol{src/IndDef} -- (co)inductive relation definitions
\item \hol{src/basicProof} -- library containing proof tools
\item \hol{src/relation} -- relations and order theory
\item \hol{src/one} -- unit type theory
\item \hol{src/pair} -- tuples
\item \hol{src/sum} -- sum types
\item \hol{src/tfl} -- defining terminating functions
\item \hol{src/option} -- option types
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{HOL Basic Directories III}

\begin{itemize}
\item \hol{src/num} -- numbers and arithmetic
\item \hol{src/pred\_set} -- predicate sets
\item \hol{src/datatype} -- Datatype package
\item \hol{src/list} -- list theories
\item \hol{src/monad} -- monads
\item \hol{src/quantHeuristics} -- instantiating quantifiers
\item \hol{src/unwind} -- lib for unwinding structural hardware definitions
\item \hol{src/pattern\_matches} -- pattern matches alternative
\item \hol{src/bossLib} -- main HOL lib loaded at start
\end{itemize}
\bigskip

\hol{bossLib} is one central library. It loads all basic theories and libraries and
provides convenient wrappers for the most common tools.
\end{frame}


\begin{frame}
\frametitle{HOL More Theories I}

Besides the basic libraries and theories that are required and loaded by \ml{hol}, there
are many more developements in HOL's source directory.

\begin{itemize}
\item \hol{src/sort} -- sorting lists
\item \hol{src/string} -- strings
\item \hol{src/TeX} -- exporting LaTeX code
\item \hol{src/res\_quan} -- restricted quantifiers
\item \hol{src/quotient} -- quotient type package
\item \hol{src/finite\_map} -- finite map theory
\item \hol{src/bag} -- bags \aka multisets
\item \hol{src/n-bit} -- machine words
\end{itemize}
\end{frame}


\begin{frame}
\frametitle{HOL More Theories II}

\begin{itemize}
\item \hol{src/ring} -- reasoning about rings
\item \hol{src/integer} -- integers
\item \hol{src/llists} -- lazy lists
\item \hol{src/path} -- finite and infinite paths through a transition system
\item \hol{src/patricia} -- efficient finite map implementations using trees
\item \hol{src/emit} -- emitting SML and OCaml code
\item \hol{src/search} -- traversal of graphs that may contain cycles
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{HOL More Theories III}

\begin{itemize}
\item \hol{src/rational} -- rational numbers
\item \hol{src/real} -- real numbers
\item \hol{src/complex} -- comples numbers
\item \hol{src/HolQbf} -- quantified boolean formulas
\item \hol{src/HolSmt} -- support for external SMT solvers
\item \hol{src/float} -- IEEE floating point numbers
\item \hol{src/floating-point} -- new version of IEEE floating point numbers
\item \hol{src/probability} -- some propability theory
\item \hol{src/temporal} -- shallow embedding of temporal logic
\item \ldots
\end{itemize}
\end{frame}


\begin{frame}
\frametitle{HOL Selected Examples I}

The directory examples hosts many theories and libraries as well. There is not
always a clear distinction between an example and a development in \ml{src}. However, 
in general examples are more specialised and often larger. They are not required to
follow HOL's coding style as much as developments in \ml{src}.
\bigskip

\begin{itemize}
\item \hol{examples/balanced\_bst} -- finite maps via balanced trees
\item \hol{examples/unification} -- (nominal) unification
\item \hol{examples/Crypto} -- various block ciphers
\item \hol{examples/elliptic} -- elliptic curve cryptography
\item \hol{examples/formal-languages} -- regular and context free formal languages
\item \hol{examples/computability} -- basic computability theory
\end{itemize}
\end{frame}



\begin{frame}
\frametitle{HOL Selected Examples II}
\begin{itemize}
\item \hol{examples/set-theory} -- axiomatic formalisation of set theory
\item \hol{examples/lambda} -- lambda calculus
\item \hol{examples/acl2} -- connection to ACL2 prover
\item \hol{examples/theorem-prover} -- soundness proof of Milawa prover
\item \hol{examples/PSL} -- formalisation of PSL
\item \hol{examples/HolBdd} -- Binary Decision Diagrams
\item \hol{examples/HolCheck} -- basic model checker
\item \hol{examples/temporal\_deep} -- deep embedding of temporal logics and automata
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{HOL Selected Examples III}
\begin{itemize}
\item \hol{examples/pgcl} formalisation of pGCL (the Probabilistic Guarded Command Language)
\item \hol{examples/dev} -- some hardware compilation
\item \hol{examples/STE} -- symbolic trajectory evalutation
\item \hol{examples/separationLogic} -- formalisation of separation logic
\item \hol{examples/ARM} -- formalisation of ARM architecture
\item \hol{examples/l3-machine-code} -- l3 language
\item \hol{examples/machine-code} -- compilers and decompilers to machine-code
\item \ldots
\end{itemize}
\end{frame}


\begin{frame}
\frametitle{Concluding Remarks}
\begin{itemize}
\item some useful tools are a bit hidden in the HOL sources
\item moreover there are developments outside the main HOL 4 sources
\begin{itemize}
\item CakeML \emph{\url{https://cakeml.org}}
\end{itemize}
\item keep in touch with community to continue learning about HOL 4
\begin{itemize}
\item mailing-list \ml{hol-info}
\item GitHub \emph{\url{https://github.com/HOL-Theorem-Prover/HOL}}
\item \emph{\url{https://hol-theorem-prover.org}}
\end{itemize}
\item if you continue using HOL, please consider sharing your work with the community
\end{itemize}
\end{frame}

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