\chapter{Isabelle/HOL Tools and Packages}
\section{Primitive types}
\indexisarcmd{typedecl}\indexisarcmd{typedef}
\begin{matharray}{rcl}
\isarcmd{typedecl} & : & \isartrans{theory}{theory} \\
\isarcmd{typedef} & : & \isartrans{theory}{proof(prove)} \\
\end{matharray}
\begin{rail}
'typedecl' typespec infix? comment?
;
'typedef' parname? typespec infix? \\ '=' term comment?
;
\end{rail}
\begin{description}
\item [$\isarkeyword{typedecl}~(\vec\alpha)t$] is similar to the original
$\isarkeyword{typedecl}$ of Isabelle/Pure (see \S\ref{sec:types-pure}), but
also declares type arity $t :: (term, \dots, term) term$, making $t$ an
actual HOL type constructor.
\item [$\isarkeyword{typedef}~(\vec\alpha)t = A$] sets up a goal stating
non-emptiness of the set $A$. After finishing the proof, the theory will be
augmented by a Gordon/HOL-style type definitions. See \cite{isabelle-HOL}
for more information. Note that user-level work usually does not directly
refer to the HOL $\isarkeyword{typedef}$ primitive, but uses more advanced
packages such as $\isarkeyword{record}$ (\S\ref{sec:record}) or
$\isarkeyword{datatype}$ (\S\ref{sec:datatype}).
\end{description}
\section{Records}\label{sec:record}
%FIXME record_split method
\indexisarcmd{record}
\begin{matharray}{rcl}
\isarcmd{record} & : & \isartrans{theory}{theory} \\
\end{matharray}
\begin{rail}
'record' typespec '=' (type '+')? (field +)
;
field: name '::' type comment?
;
\end{rail}
\begin{description}
\item [$\isarkeyword{record}~(\vec\alpha)t = \tau + \vec c :: \vec\sigma$]
defines extensible record type $(\vec\alpha)t$, derived from the optional
parent record $\tau$ by adding new field components $\vec c :: \vec\sigma$.
See \cite{isabelle-HOL,NaraschewskiW-TPHOLs98} for more information only
simply-typed records.
\end{description}
\section{Datatypes}\label{sec:datatype}
\indexisarcmd{datatype}\indexisarcmd{rep_datatype}
\begin{matharray}{rcl}
\isarcmd{datatype} & : & \isartrans{theory}{theory} \\
\isarcmd{rep_datatype} & : & \isartrans{theory}{theory} \\
\end{matharray}
\railalias{repdatatype}{rep\_datatype}
\railterm{repdatatype}
\begin{rail}
'datatype' (parname? typespec infix? \\ '=' (cons + '|') + 'and')
;
repdatatype (name * ) \\ 'distinct' thmrefs 'inject' thmrefs 'induction' thmrefs
;
cons: name (type * ) mixfix? comment?
;
\end{rail}
\begin{description}
\item [$\isarkeyword{datatype}$] FIXME
\item [$\isarkeyword{rep_datatype}$] FIXME
\end{description}
\section{Recursive functions}
\indexisarcmd{primrec}\indexisarcmd{recdef}
\begin{matharray}{rcl}
\isarcmd{primrec} & : & \isartrans{theory}{theory} \\
\isarcmd{recdef} & : & \isartrans{theory}{theory} \\
%FIXME
% \isarcmd{defer_recdef} & : & \isartrans{theory}{theory} \\
\end{matharray}
\begin{rail}
'primrec' parname? (thmdecl? prop comment? + )
;
'recdef' name term (term comment? +) \\ ('congs' thmrefs)? ('simpset' name)?
;
\end{rail}
\begin{description}
\item [$\isarkeyword{primrec}$] FIXME
\item [$\isarkeyword{recdef}$] FIXME
\end{description}
\section{(Co)Inductive sets}
\indexisarcmd{inductive}\indexisarcmd{coinductive}\indexisarcmd{inductive\_cases}
\begin{matharray}{rcl}
\isarcmd{inductive} & : & \isartrans{theory}{theory} \\
\isarcmd{coinductive} & : & \isartrans{theory}{theory} \\
\isarcmd{inductive_cases} & : & \isartrans{theory}{theory} \\
\end{matharray}
\railalias{condefs}{con\_defs}
\railalias{indcases}{inductive\_cases}
\railterm{condefs,indcases}
\begin{rail}
('inductive' | 'coinductive') (term comment? +) \\
'intrs' attributes? (thmdecl? prop comment? +) \\
'monos' thmrefs comment? \\ condefs thmrefs comment?
;
indcases thmdef? nameref ':' \\ (prop +) comment?
;
\end{rail}
\begin{description}
\item [$\isarkeyword{inductive}$ and $\isarkeyword{coinductive}$] FIXME
\item [$\isarkeyword{inductive_cases}$] FIXME
\end{description}
\section{Proof by induction}
%FIXME induct proof method
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