7046
|
1 |
|
7141
|
2 |
\chapter{Isabelle/HOL Tools and Packages}
|
7135
|
3 |
|
|
4 |
\section{Primitive types}
|
|
5 |
|
7141
|
6 |
\indexisarcmd{typedecl}\indexisarcmd{typedef}
|
|
7 |
\begin{matharray}{rcl}
|
|
8 |
\isarcmd{typedecl} & : & \isartrans{theory}{theory} \\
|
|
9 |
\isarcmd{typedef} & : & \isartrans{theory}{proof(prove)} \\
|
|
10 |
\end{matharray}
|
|
11 |
|
|
12 |
\begin{rail}
|
|
13 |
'typedecl' typespec infix? comment?
|
|
14 |
;
|
|
15 |
'typedef' parname? typespec infix? \\ '=' term comment?
|
|
16 |
;
|
|
17 |
\end{rail}
|
|
18 |
|
|
19 |
\begin{description}
|
|
20 |
\item [$\isarkeyword{typedecl}~(\vec\alpha)t$] is similar to the original
|
|
21 |
$\isarkeyword{typedecl}$ of Isabelle/Pure (see \S\ref{sec:types-pure}), but
|
|
22 |
also declares type arity $t :: (term, \dots, term) term$, making $t$ an
|
|
23 |
actual HOL type constructor.
|
|
24 |
\item [$\isarkeyword{typedef}~(\vec\alpha)t = A$] sets up a goal stating
|
|
25 |
non-emptiness of the set $A$. After finishing the proof, the theory will be
|
|
26 |
augmented by a Gordon/HOL-style type definitions. See \cite{isabelle-HOL}
|
|
27 |
for more information. Note that user-level work usually does not directly
|
|
28 |
refer to the HOL $\isarkeyword{typedef}$ primitive, but uses more advanced
|
|
29 |
packages such as $\isarkeyword{record}$ (\S\ref{sec:record}) or
|
|
30 |
$\isarkeyword{datatype}$ (\S\ref{sec:datatype}).
|
|
31 |
\end{description}
|
|
32 |
|
|
33 |
|
|
34 |
\section{Records}\label{sec:record}
|
|
35 |
|
|
36 |
%FIXME record_split method
|
|
37 |
\indexisarcmd{record}
|
|
38 |
\begin{matharray}{rcl}
|
|
39 |
\isarcmd{record} & : & \isartrans{theory}{theory} \\
|
|
40 |
\end{matharray}
|
|
41 |
|
|
42 |
\begin{rail}
|
|
43 |
'record' typespec '=' (type '+')? (field +)
|
|
44 |
;
|
7135
|
45 |
|
7141
|
46 |
field: name '::' type comment?
|
|
47 |
;
|
|
48 |
\end{rail}
|
|
49 |
|
|
50 |
\begin{description}
|
|
51 |
\item [$\isarkeyword{record}~(\vec\alpha)t = \tau + \vec c :: \vec\sigma$]
|
|
52 |
defines extensible record type $(\vec\alpha)t$, derived from the optional
|
|
53 |
parent record $\tau$ by adding new field components $\vec c :: \vec\sigma$.
|
|
54 |
See \cite{isabelle-HOL,NaraschewskiW-TPHOLs98} for more information only
|
|
55 |
simply-typed records.
|
|
56 |
\end{description}
|
|
57 |
|
|
58 |
|
|
59 |
\section{Datatypes}\label{sec:datatype}
|
|
60 |
|
|
61 |
\indexisarcmd{datatype}\indexisarcmd{rep_datatype}
|
|
62 |
\begin{matharray}{rcl}
|
|
63 |
\isarcmd{datatype} & : & \isartrans{theory}{theory} \\
|
|
64 |
\isarcmd{rep_datatype} & : & \isartrans{theory}{theory} \\
|
|
65 |
\end{matharray}
|
|
66 |
|
|
67 |
\railalias{repdatatype}{rep\_datatype}
|
|
68 |
\railterm{repdatatype}
|
|
69 |
|
|
70 |
\begin{rail}
|
|
71 |
'datatype' (parname? typespec infix? \\ '=' (cons + '|') + 'and')
|
|
72 |
;
|
|
73 |
repdatatype (name * ) \\ 'distinct' thmrefs 'inject' thmrefs 'induction' thmrefs
|
|
74 |
;
|
|
75 |
|
|
76 |
cons: name (type * ) mixfix? comment?
|
|
77 |
;
|
|
78 |
\end{rail}
|
|
79 |
|
|
80 |
\begin{description}
|
|
81 |
\item [$\isarkeyword{datatype}$] FIXME
|
|
82 |
\item [$\isarkeyword{rep_datatype}$] FIXME
|
|
83 |
\end{description}
|
|
84 |
|
7135
|
85 |
|
|
86 |
\section{Recursive functions}
|
|
87 |
|
7141
|
88 |
\indexisarcmd{primrec}\indexisarcmd{recdef}
|
|
89 |
\begin{matharray}{rcl}
|
|
90 |
\isarcmd{primrec} & : & \isartrans{theory}{theory} \\
|
|
91 |
\isarcmd{recdef} & : & \isartrans{theory}{theory} \\
|
|
92 |
%FIXME
|
|
93 |
% \isarcmd{defer_recdef} & : & \isartrans{theory}{theory} \\
|
|
94 |
\end{matharray}
|
|
95 |
|
|
96 |
\begin{rail}
|
|
97 |
'primrec' parname? (thmdecl? prop comment? + )
|
|
98 |
;
|
|
99 |
'recdef' name term (term comment? +) \\ ('congs' thmrefs)? ('simpset' name)?
|
|
100 |
;
|
|
101 |
\end{rail}
|
|
102 |
|
|
103 |
\begin{description}
|
|
104 |
\item [$\isarkeyword{primrec}$] FIXME
|
|
105 |
\item [$\isarkeyword{recdef}$] FIXME
|
|
106 |
\end{description}
|
|
107 |
|
|
108 |
|
7135
|
109 |
\section{(Co)Inductive sets}
|
|
110 |
|
7141
|
111 |
\indexisarcmd{inductive}\indexisarcmd{coinductive}\indexisarcmd{inductive\_cases}
|
|
112 |
\begin{matharray}{rcl}
|
|
113 |
\isarcmd{inductive} & : & \isartrans{theory}{theory} \\
|
|
114 |
\isarcmd{coinductive} & : & \isartrans{theory}{theory} \\
|
|
115 |
\isarcmd{inductive_cases} & : & \isartrans{theory}{theory} \\
|
|
116 |
\end{matharray}
|
|
117 |
|
|
118 |
\railalias{condefs}{con\_defs}
|
|
119 |
\railalias{indcases}{inductive\_cases}
|
|
120 |
\railterm{condefs,indcases}
|
|
121 |
|
|
122 |
\begin{rail}
|
|
123 |
('inductive' | 'coinductive') (term comment? +) \\
|
|
124 |
'intrs' attributes? (thmdecl? prop comment? +) \\
|
|
125 |
'monos' thmrefs comment? \\ condefs thmrefs comment?
|
|
126 |
;
|
|
127 |
indcases thmdef? nameref ':' \\ (prop +) comment?
|
|
128 |
;
|
|
129 |
\end{rail}
|
|
130 |
|
|
131 |
\begin{description}
|
|
132 |
\item [$\isarkeyword{inductive}$ and $\isarkeyword{coinductive}$] FIXME
|
|
133 |
\item [$\isarkeyword{inductive_cases}$] FIXME
|
|
134 |
\end{description}
|
|
135 |
|
|
136 |
|
|
137 |
\section{Proof by induction}
|
|
138 |
|
|
139 |
%FIXME induct proof method
|
|
140 |
|
7046
|
141 |
|
|
142 |
%%% Local Variables:
|
|
143 |
%%% mode: latex
|
|
144 |
%%% TeX-master: "isar-ref"
|
|
145 |
%%% End:
|