\documentclass[fontsize=10pt,DIV12,paper=a4,open=right,twoside,abstract=true]{scrreprt} \usepackage{fixltx2e} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{lmodern} \usepackage{textcomp} \usepackage[english]{babel} \usepackage{isabelle} \isatagannexa \usepackage{omg} \usepackage{draftwatermark} \SetWatermarkAngle{55} \SetWatermarkLightness{.9} \SetWatermarkFontSize{3cm} \SetWatermarkScale{1.4} \SetWatermarkText{\textbf{\textsf{Draft Proposal}}} \endisatagannexa \usepackage[nocolortable, noaclist,isasymonly,nocolor]{hol-ocl-isar} \renewcommand{\lfloor}{\isasymHolOclLiftLeft} \renewcommand{\rfloor}{\isasymHolOclLiftRight} \renewcommand{\lceil}{\isasymHolOclDropLeft} \renewcommand{\rceil}{\isasymHolOclDropRight} \renewcommand{\oclkeywordstyle}{\bfseries} \renewcommand{\javakeywordstyle}{\bfseries} \renewcommand{\smlkeywordstyle}{\bfseries} \renewcommand{\holoclthykeywordstyle}{} \usepackage{lstisar} \usepackage{railsetup} \usepackage[]{mathtools} \usepackage{% multirow, paralist, booktabs, % " " " threeparttable, longtable, % Mehrseitige Tabellen } \usepackage{graphicx} \usepackage[numbers, sort&compress, sectionbib]{natbib} \usepackage{chapterbib} \usepackage[caption=false]{subfig} \usepackage{tabu} \usepackage{prooftree} %\usepackage[draft]{fixme} \usepackage[pdfpagelabels, pageanchor=false, bookmarksnumbered, plainpages=false]{hyperref} \graphicspath{{data/},{figures/}} \makeatletter \renewcommand*\l@section{\bprot@dottedtocline{1}{1.5em}{2.8em}} \renewcommand*\l@subsection{\bprot@dottedtocline{2}{3.8em}{3.7em}} \renewcommand*\l@subsubsection{\bprot@dottedtocline{3}{7.0em}{5em}} \renewcommand*\l@paragraph{\bprot@dottedtocline{4}{10em}{6.2em}} %\renewcommand*\l@paragraph{\bprot@dottedtocline{4}{10em}{5.5em}} \renewcommand*\l@subparagraph{\bprot@dottedtocline{5}{12em}{7.7em}} %\renewcommand*\l@subparagraph{\bprot@dottedtocline{5}{12em}{6.5em}} \makeatother %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Overall the (rightfully issued) warning by Koma Script that \rm %%% etc. should not be used (they are deprecated since more than a %%% decade) \DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} \DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} \DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} \DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} \DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \setcounter{tocdepth}{3} % printed TOC not too detailed \hypersetup{bookmarksdepth=3} % more detailed digital TOC (aka bookmarks) \sloppy \allowdisplaybreaks[4] \raggedbottom \newcommand{\HOL}{HOL\xspace} \newcommand{\OCL}{OCL\xspace} \newcommand{\UML}{UML\xspace} \newcommand{\HOLOCL}{HOL-OCL\xspace} \newcommand{\FOCL}{Featherweight OCL\xspace} \renewcommand{\HolTrue}{\mathrm{true}} \renewcommand{\HolFalse}{\mathrm{false}} \newcommand{\ptmi}[1]{\using{\mi{#1}}} \newcommand{\Lemma}[1]{{\color{BrickRed}% \mathbf{\operatorname{lemma}}}~\text{#1:}\quad} \newcommand{\done}{{\color{OliveGreen}\operatorname{done}}} \newcommand{\apply}[1]{{\holoclthykeywordstyle% \operatorname{apply}}(\text{#1})} \newcommand{\fun} {{\holoclthykeywordstyle\operatorname{fun}}} \newcommand{\isardef} {{\holoclthykeywordstyle\operatorname{definition}}} \newcommand{\where} {{\holoclthykeywordstyle\operatorname{where}}} \newcommand{\datatype} {{\holoclthykeywordstyle\operatorname{datatype}}} \newcommand{\types} {{\holoclthykeywordstyle\operatorname{types}}} \newcommand{\pglabel}[1]{\text{#1}} \renewcommand{\isasymOclUndefined}{\ensuremath{\mathtt{invalid}}} \newcommand{\isasymOclNull}{\ensuremath{\mathtt{null}}} \newcommand{\isasymOclInvalid}{\isasymOclUndefined} \DeclareMathOperator{\inv}{inv} \newcommand{\Null}[1]{{\ensuremath{\mathtt{null}_\text{{#1}}}}} \newcommand{\testgen}{HOL-TestGen\xspace} \newcommand{\HolOption}{\mathrm{option}} \newcommand{\ran}{\mathrm{ran}} \newcommand{\dom}{\mathrm{dom}} \newcommand{\typedef}{\mathrm{typedef}} \newcommand{\typesynonym}{\mathrm{type\_synonym}} \newcommand{\mi}[1]{\,\text{#1}} \newcommand{\state}[1]{\ifthenelse{\equal{}{#1}}% {\operatorname{state}}% {\operatorname{\mathit{state}}(#1)}% } \newcommand{\mocl}[1]{\text{\inlineocl|#1|}} \DeclareMathOperator{\TCnull}{null} \DeclareMathOperator{\HolNull}{null} \DeclareMathOperator{\HolBot}{bot} \newcommand{\isaAA}{\mathfrak{A}} % urls in roman style, theory text in math-similar italics \urlstyle{rm} \isabellestyle{it} \newcommand{\ie}{i.\,e.\xspace} \newcommand{\eg}{e.\,g.\xspace} \newenvironment{isamarkuplazy_text}{\par \isacommand{lazy{\isacharunderscore}text}\isamarkupfalse\isacartoucheopen\isastyletext\begin{isapar}}{\end{isapar}\isacartoucheclose} \renewcommand{\isasymguillemotleft}{\isatext{\textquotedblleft}} \renewcommand{\isasymguillemotright}{\isatext{\textquotedblright}} \begin{document} \renewcommand{\subsubsectionautorefname}{Section} \renewcommand{\subsectionautorefname}{Section} \renewcommand{\sectionautorefname}{Section} \renewcommand{\chapterautorefname}{Chapter} \newcommand{\subtableautorefname}{\tableautorefname} \newcommand{\subfigureautorefname}{\figureautorefname} \isatagannexa \renewcommand\thepart{\Alph{part}} \renewcommand\partname{Annex} \endisatagannexa \newenvironment{matharray}[1]{\[\begin{array}{#1}}{\end{array}\]} % from 'iman.sty' \newcommand{\indexdef}[3]% {\ifthenelse{\equal{}{#1}}{\index{#3 (#2)|bold}}{\index{#3 (#1\ #2)|bold}}} % from 'isar.sty' \isatagafp \title{Featherweight OCL} \subtitle{A Proposal for a Machine-Checked Formal Semantics for OCL 2.5 %\\ %\includegraphics[scale=.5]{figures/logo_focl} } \endisatagafp \isatagannexa \title{A Formal Machine-Checked Semantics for OCL 2.5} \subtitle{A Proposal for the "Annex A" of the OCL Standard} \endisatagannexa \author{% \href{http://www.brucker.ch/}{Achim D. Brucker}\footnotemark[1] \and \href{https://www.lri.fr/~tuong/}{Fr\'ed\'eric Tuong}\footnotemark[2]~\footnotemark[3] \and \href{https://www.lri.fr/~wolff/}{Burkhart Wolff}\footnotemark[2]~\footnotemark[3]} \publishers{% \footnotemark[1]~SAP SE\\ Vincenz-Priessnitz-Str. 1, 76131 Karlsruhe, Germany \texorpdfstring{\\}{} \href{mailto:"Achim D. Brucker" }{achim.brucker@sap.com}\\[2em] % \footnotemark[2]~LRI, Univ. Paris-Sud, CNRS, CentraleSup\'elec, Universit\'e Paris-Saclay \\ b\^at. 650 Ada Lovelace, 91405 Orsay, France \texorpdfstring{\\}{} \href{mailto:"Frederic Tuong" }{frederic.tuong@lri.fr} \hspace{4.5em} \href{mailto:"Burkhart Wolff" }{burkhart.wolff@lri.fr} \\[2em] % \footnotemark[3]~IRT SystemX\\ 8 av.~de la Vauve, 91120 Palaiseau, France \texorpdfstring{\\}{} \href{mailto:"Frederic Tuong" }{frederic.tuong@irt-systemx.fr} \quad \href{mailto:"Burkhart Wolff" }{burkhart.wolff@irt-systemx.fr} } \maketitle \isatagannexa \cleardoublepage \endisatagannexa \isatagafp \begin{abstract} The Unified Modeling Language (UML) is one of the few modeling languages that is widely used in industry. While UML is mostly known as diagrammatic modeling language (\eg, visualizing class models), it is complemented by a textual language, called Object Constraint Language (OCL). OCL is a textual annotation language, originally based on a three-valued logic, that turns UML into a formal language. Unfortunately the semantics of this specification language, captured in the ``Annex A'' of the OCL standard, leads to different interpretations of corner cases. Many of these corner cases had been subject to formal analysis since more than ten years. The situation complicated with the arrival of version 2.3 of the OCL standard. OCL was aligned with the latest version of UML: this led to the extension of the three-valued logic by a second exception element, called \inlineocl{null}. While the first exception element \inlineocl{invalid} has a strict semantics, \inlineocl{null} has a non strict interpretation. The combination of these semantic features lead to remarkable confusion for implementors of OCL compilers and interpreters. In this paper, we provide a formalization of the core of OCL in HOL\@. It provides denotational definitions, a logical calculus and operational rules that allow for the execution of OCL expressions by a mixture of term rewriting and code compilation. Moreover, we describe a coding-scheme for UML class models that were annotated by code-invariants and code contracts. An implementation of this coding-scheme has been undertaken: it consists of a kind of compiler that takes a UML class model and translates it into a family of definitions and derived theorems over them capturing the properties of constructors and selectors, tests and casts resulting from the class model. However, this compiler is \emph{not} included in this document. Our formalization reveals several inconsistencies and contradictions in the current version of the OCL standard. They reflect a challenge to define and implement OCL tools in a uniform manner. Overall, this document is intended to provide the basis for a machine-checked text ``Annex A'' of the OCL standard targeting at tool implementors. \end{abstract} \tableofcontents \endisatagafp \part{Formal Semantics of OCL} \input{introduction} %\clearpage \isatagafp \input{session} \endisatagafp \isatagannexa \input{UML_Types.tex} \input{UML_Logic.tex} \input{UML_PropertyProfiles.tex} \input{UML_Boolean.tex} \input{UML_Void.tex} \input{UML_Integer.tex} \input{UML_Real.tex} \input{UML_String.tex} \input{UML_Pair.tex} \input{UML_Bag.tex} \input{UML_Set.tex} \input{UML_Sequence.tex} \input{UML_Library.tex} \input{UML_State.tex} \input{UML_Contracts.tex} %\input{UML_Tools.tex} %\input{UML_Main.tex} % \input{Design_UML.tex} % \input{Design_OCL.tex} \input{Analysis_UML.tex} \input{Analysis_OCL.tex} \part{Bibliography} \endisatagannexa \isatagafp \input{conclusion} %no conclusion for standard document \endisatagafp \bibliographystyle{abbrvnat} \bibliography{root} \isatagafp \appendix \part{Appendix} \endisatagafp \input{FOCL_Syntax} \isatagannexa \part{Table of Contents} \clearpage {\small \tableofcontents } \endisatagannexa \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: % LocalWords: implementors denotational OCL UML