3082
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
1 |
\documentclass{svjour3}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
2 |
\usepackage{amsmath}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
3 |
\usepackage{amssymb}
|
3092
|
4 |
\usepackage{isabelle}
|
|
5 |
\usepackage{isabellesym}
|
3082
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
6 |
\usepackage{tikz}
|
3092
|
7 |
\usepackage{verbdef}
|
|
8 |
\usepackage{mathpartir}
|
|
9 |
\usepackage{pdfsetup}
|
|
10 |
\usepackage{times}
|
3082
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
11 |
\usepackage{stmaryrd}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
12 |
%\newtheorem{definition}{Definition}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
13 |
%\newtheorem{proposition}{Proposition}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
14 |
%\newtheorem{lemma}{Lemma}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
15 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
16 |
\urlstyle{rm}
|
3092
|
17 |
\isabellestyle{it}
|
|
18 |
\renewcommand{\isastyleminor}{\it}%
|
|
19 |
\renewcommand{\isastyle}{\normalsize\it}%
|
3082
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
20 |
\renewcommand{\isastylescript}{\it}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
21 |
\def\dn{\,\triangleq\,}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
22 |
\verbdef\singlearr|---->|
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
23 |
\verbdef\doublearr|===>|
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
24 |
\verbdef\tripple|###|
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
25 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
26 |
\renewcommand{\isasymequiv}{$\triangleq$}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
27 |
\renewcommand{\isasymemptyset}{$\varnothing$}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
28 |
%%\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
29 |
\renewcommand{\isasymUnion}{$\bigcup$}
|
3092
|
30 |
\renewcommand{\isacharunderscore}{\text{$\_\!\_$}}
|
3082
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
31 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
32 |
\newcommand{\isasymsinglearr}{$\mapsto$}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
33 |
\newcommand{\isasymdoublearr}{$\Mapsto$}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
34 |
\newcommand{\isasymtripple}{\tripple}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
35 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
36 |
\newcommand{\numbered}[1]{\refstepcounter{equation}{\rm(\arabic{equation})}\label{#1}}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
37 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
38 |
\begin{document}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
39 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
40 |
\title{Quotients Revisited for Isabelle/HOL}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
41 |
\author{Cezary Kaliszyk \and Christian Urban}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
42 |
\institute{C.~Kaliszyk \at University of Tsukuba, Japan
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
43 |
\and C.~Urban \at Technical University of Munich, Germany}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
44 |
\date{Received: date / Accepted: date}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
45 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
46 |
\maketitle
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
47 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
48 |
\begin{abstract}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
49 |
Higher-Order Logic (HOL) is based on a small logic kernel, whose only
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
50 |
mechanism for extension is the introduction of safe definitions and of
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
51 |
non-empty types. Both extensions are often performed in quotient
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
52 |
constructions. To ease the work involved with such quotient constructions, we
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
53 |
re-implemented in the %popular
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
54 |
Isabelle/HOL theorem prover the quotient
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
55 |
package by Homeier. In doing so we extended his work in order to deal with
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
56 |
compositions of quotients and also specified completely the procedure
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
57 |
of lifting theorems from the raw level to the quotient level.
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
58 |
The importance for theorem proving is that many formal
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
59 |
verifications, in order to be feasible, require a convenient reasoning infrastructure
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
60 |
for quotient constructions.
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
61 |
\end{abstract}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
62 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
63 |
%\keywords{Quotients, Isabelle theorem prover, Higher-Order Logic}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
64 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
65 |
\bibliographystyle{abbrv}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
66 |
\input{session}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
67 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
68 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
69 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
70 |
\end{document}
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
71 |
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
72 |
%%% Local Variables:
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
73 |
%%% mode: latex
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
74 |
%%% TeX-master: t
|
a6b0220fb8ae
Added an initial version of qpaper-jv and a TODO of things to write about.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
75 |
%%% End:
|