% begin palatino.sty % copied from palatino.sty, except left ttdefault to CMTT \renewcommand{\rmdefault}{ppl} \renewcommand{\sfdefault}{phv} % \renewcommand{\ttdefault}{pcr} % end palatino.sty \usepackage{amssymb} \addtolength{\oddsidemargin}{30pt} \addtolength{\evensidemargin}{-22pt} \setlength{\inferLineSkip}{4pt} \newtheorem{exercise}{Exercise}[section] \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{falseclaim}[theorem]{False Claim} \newenvironment{proof}{\trivlist \item[\hskip \labelsep{\bf Proof:}]}{\hfill$\Box$ \endtrivlist} \newenvironment{attempt}{\trivlist \item[\hskip \labelsep{\bf Proof attempt:}]}{\hfill$\Diamond$ \endtrivlist} \newcommand{\highlight}[1]{\par%\vspace{1ex}% \framebox{\addtolength{\linewidth}{-1em}\begin{minipage}{\linewidth}#1\end{minipage}}} %\vspace{1ex} \def\thebibliography#1{%\subsection{References} \list {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth \advance\leftmargin\labelsep\itemsep 0pt% \usecounter{enumi}} \def\newblock{\hskip .11em plus .33em minus -.07em} \sloppy \sfcode`\.=1000\relax} \title{{\large 15-819K: Logic Programming}\\ {\large Lecture \lecnum}\\ \lectitle} \author{Frank Pfenning} \date{\lecdate} \pagestyle{fancyplain} \setlength{\headheight}{14pt} % \renewcommand{\chaptermark}[1]{\markboth{#1}{}} % \renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}} \lhead[\fancyplain{}{\bfseries L\lecnum.\thepage}]% {\fancyplain{}{\bfseries\lectitle}} \chead[]{} \rhead[\fancyplain{}{\bfseries\lectitle}]% {\fancyplain{}{\bfseries L\lecnum.\thepage}} \lfoot[{\small\scshape Lecture Notes}]{{\small\scshape Lecture Notes}} \cfoot[]{} \rfoot[{\small\scshape\lecdate}]{{\small\scshape\lecdate}} % For code environment, to get tt-style underscore % \renewcommand{\_}{\char`\_} % \renewcommand{\{}{\char`\{} % \renewcommand{\}}{\char`\}} % Some pervasively used definitions \newcommand{\blankline}{\mbox{}} % for \begin{code}...\end{code} \newcommand{\lowered}[1]{\raisebox{-0.75\baselineskip}{#1}} \newcommand{\jtrue}{\mathit{true}} \newcommand{\msf}[1]{\mathsf{#1}} \newcommand{\z}{\msf{z}} \newcommand{\s}{\msf{s}} \newcommand{\lif}{\mathrel{\leftarrow}} \newcommand{\DD}{\mathcal{D}} \newcommand{\EE}{\mathcal{E}} \newcommand{\under}{\mathrel{/}} \newcommand{\dom}{\mathrm{dom}} \newcommand{\cod}{\mathrm{cod}} \newcommand{\FV}{\mathrm{FV}} \newcommand{\PP}{\mathcal{P}} \newcommand{\limplies}{\supset} \newcommand{\ldot}{.\,} \newcommand{\xs}{\mathbf{x}} \newcommand{\ys}{\mathbf{y}} \newcommand{\zs}{\mathbf{z}} \newcommand{\resid}{>} \newcommand{\jtype}{\mathit{type}} \newcommand{\jtypes}{\mathbf{type}} \newcommand{\arrow}{\rightarrow} \newcommand{\boldsym}[1]{\mbox{\boldmath{$#1$}}} \newcommand{\taus}{\boldsym{\tau}} \newcommand{\sigmas}{\boldsym{\sigma}} \newcommand{\alphas}{\boldsym{\alpha}} \newcommand{\betas}{\boldsym{\beta}} \newcommand{\jres}{\mathit{res}} \newcommand{\ures}{\mathit{ures}} \newcommand{\ldash}{\mathrel{{\vdash}\kern-0.45em{\vdash}}} % \newcommand{\ldash}{\mathrel{\Vdash}} % \newcommand{\lwith}{\mathop{\mbox{\rmfamily \&}}} % not using stmaryrd \newcommand{\lwith}{\mathbin{\mathrm{\&}}} % not using stmaryrd \newcommand{\lolli}{\mathbin{\multimap}} \newcommand{\lone}{\mathbf{1}} \newcommand{\lbang}{\mathrm{!}} \newcommand{\lzero}{\mathbf{0}} \newcommand{\linif}{\mathbin{{\raisebox{0.8pt}{$\scriptstyle{\circ}$}}\!{-}}} \newcommand{\lfocus}{\mathrel{\ll}} \newcommand{\obang}{\mathbin{{\otimes}\lbang}} \newcommand{\rfocus}{\mathrel{\gg}} \newcommand{\gd}{\mathsf{g}} \newcommand{\gds}{\mathbf{g}} \newcommand{\uk}{\mathsf{u}} \newcommand{\uks}{\mathbf{u}} \newcommand{\approxes}{\preccurlyeq}