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\documentclass[dvipsnames,14pt,t]{beamer}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{beamerthemeplaincu}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%\usepackage[T1]{fontenc}
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%\usepackage[latin1]{inputenc}
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\usepackage{mathpartir}
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\usepackage[absolute,overlay]{textpos}
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\usepackage{ifthen}
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\usepackage{tikz}
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\usepackage{pgf}
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\usepackage{calc}
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\usepackage{ulem}
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\usepackage{courier}
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\usepackage{listings}
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\renewcommand{\uline}[1]{#1}
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\usetikzlibrary{arrows}
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\usetikzlibrary{automata}
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\usetikzlibrary{shapes}
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\usetikzlibrary{shadows}
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\usetikzlibrary{positioning}
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\usetikzlibrary{calc}
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\usetikzlibrary{plotmarks}
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\usepackage{graphicx}
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\setmonofont{Consolas}
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\definecolor{javared}{rgb}{0.6,0,0} % for strings
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\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
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\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
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\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\makeatletter
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\lst@CCPutMacro\lst@ProcessOther {"2D}{\lst@ttfamily{-{}}{-{}}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\@empty\z@\@empty
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\makeatother
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\lstdefinelanguage{scala}{
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morekeywords={abstract,case,catch,class,def,%
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do,else,extends,false,final,finally,%
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for,if,implicit,import,match,mixin,%
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new,null,object,override,package,%
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private,protected,requires,return,sealed,%
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super,this,throw,trait,true,try,%
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type,val,var,while,with,yield},
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otherkeywords={=>,<-,<\%,<:,>:,\#,@},
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sensitive=true,
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morecomment=[l]{//},
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morecomment=[n]{/*}{*/},
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morestring=[b]",
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morestring=[b]',
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morestring=[b]"""
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\lstdefinelanguage{while}{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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morekeywords={while, if, then. else, read, write},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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otherkeywords={=>,<-,<\%,<:,>:,\#,@},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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sensitive=true,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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morecomment=[l]{//},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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morecomment=[n]{/*}{*/},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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morestring=[b]",
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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morestring=[b]',
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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morestring=[b]"""
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\lstset{language=Scala,
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basicstyle=\ttfamily,
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keywordstyle=\color{javapurple}\bfseries,
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stringstyle=\color{javagreen},
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commentstyle=\color{javagreen},
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morecomment=[s][\color{javadocblue}]{/**}{*/},
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numbers=left,
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numberstyle=\tiny\color{black},
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stepnumber=1,
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numbersep=10pt,
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tabsize=2,
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showspaces=false,
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showstringspaces=false}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% beamer stuff
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\renewcommand{\slidecaption}{AFL 06, King's College London, 30.~October 2013}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{filecontents}{s-grammar1.data}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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1 0.01152
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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51 0.07973
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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101 0.09726
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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151 0.09320
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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201 0.10010
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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251 0.16997
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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301 0.26662
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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351 0.46118
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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401 0.62516
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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451 0.87247
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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501 1.16334
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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551 1.71152
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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601 2.10958
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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651 2.44360
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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701 2.98488
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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102 |
751 3.50326
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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801 4.11036
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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851 4.93394
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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901 5.77465
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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951 7.39123
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\end{filecontents}
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108 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{filecontents}{s-grammar2.data}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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1 0.01280
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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2 0.00064
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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3 0.00173
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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4 0.00355
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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5 0.00965
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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6 0.02674
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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7 0.06953
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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8 0.11166
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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9 0.18707
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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10 0.09189
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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11 0.12724
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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12 0.24337
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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13 0.59304
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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14 1.53594
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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15 4.01195
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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16 10.73582
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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17 29.51587
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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#18 73.14163
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\end{filecontents}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1>[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm]
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\LARGE Automata and \\[-2mm]
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\LARGE Formal Languages (6)\\[3mm]
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\end{tabular}}
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\normalsize
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Office: & S1.27 (1st floor Strand Building)\\
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Slides: & KEATS (also home work is there)\\
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\frametitle{\begin{tabular}{c}Regular Languages\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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While regular expressions are very useful for lexing,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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there is no regular expression that can recognise the language \bl{$a^nb^n$}.\bigskip
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\bl{$(((()()))())$} \;\;vs.\;\; \bl{$(((()()))()))$}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand{\qq}{\mbox{\texttt{"}}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Grammars\end{tabular}}
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A (context-free) grammar \bl{$G$} consists of
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\begin{itemize}
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\item a finite set of nonterminal symbols (upper case)
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\item a finite terminal symbols or tokens (lower case)
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\item a start symbol (which must be a nonterminal)
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\item a set of rules
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\begin{center}
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\bl{$A \rightarrow \text{rhs}$}
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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where \bl{rhs} are sequences involving terminals and nonterminals,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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including the empty sequence \bl{$\epsilon$}.\medskip\pause
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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We also allow rules
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\begin{center}
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\bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$}
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\end{center}
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Palindromes\end{tabular}}
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\begin{center}
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\bl{\begin{tabular}{lcl}
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$S$ & $\rightarrow$ & $\epsilon$ \\
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$S$ & $\rightarrow$ & $a\cdot S\cdot a$ \\
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$S$ & $\rightarrow$ & $b\cdot S\cdot b$ \\
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\end{tabular}}
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\end{center}\pause
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or
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\begin{center}
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\bl{\begin{tabular}{lcl}
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$S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
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\end{tabular}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
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\begin{center}
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\bl{\begin{tabular}{lcl}
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$E$ & $\rightarrow$ & $num\_token$ \\
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$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
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$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
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$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
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240 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
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\end{tabular}}
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\end{center}\pause
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\bl{\texttt{1 + 2 * 3 + 4}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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251 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
252 |
\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
253 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
254 |
\frametitle{\begin{tabular}{c}A CFG Derivation\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
255 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
256 |
\begin{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
257 |
\item Begin with a string containing only the start symbol, say \bl{$S$}\bigskip
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
258 |
\item Replace any nonterminal \bl{$X$} in the string by the
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
259 |
right-hand side of some production \bl{$X \rightarrow \text{rhs}$}\bigskip
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
260 |
\item Repeat 2 until there are no nonterminals
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
261 |
\end{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
262 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
263 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
264 |
\bl{$S \rightarrow \ldots \rightarrow \ldots \rightarrow \ldots \rightarrow \ldots $}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
265 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
266 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
267 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
268 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
269 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
270 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
271 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
272 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
273 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
274 |
\frametitle{\begin{tabular}{c}Example Derivation\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
275 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
276 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
277 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
278 |
$S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
282 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
283 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
\bl{$S$} & \bl{$\rightarrow$} & \bl{$aSa$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
& \bl{$\rightarrow$} & \bl{$abSba$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
& \bl{$\rightarrow$} & \bl{$abaSaba$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
& \bl{$\rightarrow$} & \bl{$abaaba$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
290 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
291 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
293 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
294 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
295 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
296 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
297 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
298 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
299 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
300 |
\frametitle{\begin{tabular}{c}Example Derivation\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
301 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
302 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
303 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
304 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
305 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
306 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
307 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
308 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
309 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
310 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
312 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
\begin{tabular}{@{}c@{}c@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
315 |
\begin{tabular}{l@{\hspace{1mm}}l@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
\bl{$E$} & \bl{$\rightarrow$} & \bl{$E*E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
317 |
& \bl{$\rightarrow$} & \bl{$E+E*E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
318 |
& \bl{$\rightarrow$} & \bl{$E+E*E+E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
319 |
& \bl{$\rightarrow^+$} & \bl{$1+2*3+4$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
320 |
\end{tabular} &\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
321 |
\begin{tabular}{l@{\hspace{1mm}}l@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
322 |
\bl{$E$} & \bl{$\rightarrow$} & \bl{$E+E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
323 |
& \bl{$\rightarrow$} & \bl{$E+E+E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
324 |
& \bl{$\rightarrow$} & \bl{$E+E*E+E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
325 |
& \bl{$\rightarrow^+$} & \bl{$1+2*3+4$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
326 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
327 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
328 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
329 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
330 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
331 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
332 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
334 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
335 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
336 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
337 |
\frametitle{\begin{tabular}{c}Language of a CFG\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
338 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
339 |
Let \bl{$G$} be a context-free grammar with start symbol \bl{$S$}.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
340 |
Then the language \bl{$L(G)$} is:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
341 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
342 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
343 |
\bl{$\{c_1\ldots c_n \;|\; \forall i.\; c_i \in T \wedge S \rightarrow^* c_1\ldots c_n \}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
344 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
345 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
346 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
347 |
\item Terminals, because there are no rules for replacing them.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
348 |
\item Once generated, terminals are ``permanent''.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
349 |
\item Terminals ought to be tokens of the language\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
350 |
(but can also be strings).
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
351 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
355 |
|
49
|
356 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
357 |
\mode<presentation>{
|
|
358 |
\begin{frame}[c]
|
50
|
359 |
\frametitle{\begin{tabular}{c}Parse Trees\end{tabular}}
|
49
|
360 |
|
|
361 |
\begin{center}
|
|
362 |
\bl{\begin{tabular}{lcl}
|
53
|
363 |
$E$ & $\rightarrow$ & $F \;|\; F \cdot * \cdot F$\\
|
|
364 |
$F$ & $\rightarrow$ & $T \;|\; T \cdot + \cdot T \;|\; T \cdot - \cdot T$\\
|
|
365 |
$T$ & $\rightarrow$ & $num\_token \;|\; ( \cdot E \cdot )$\\
|
49
|
366 |
\end{tabular}}
|
|
367 |
\end{center}
|
|
368 |
|
|
369 |
\begin{center}
|
|
370 |
\begin{tikzpicture}[level distance=8mm, blue]
|
50
|
371 |
\node {$E$}
|
|
372 |
child {node {$F$}
|
|
373 |
child {node {$T$}
|
|
374 |
child {node {(\,$E$\,)}
|
|
375 |
child {node{$F$ *{} $F$}
|
|
376 |
child {node {$T$} child {node {2}}}
|
|
377 |
child {node {$T$} child {node {3}}}
|
49
|
378 |
}
|
|
379 |
}
|
|
380 |
}
|
50
|
381 |
child {node {+}}
|
|
382 |
child {node {$T$}
|
|
383 |
child {node {(\,$E$\,)}
|
|
384 |
child {node {$F$}
|
|
385 |
child {node {$T$ +{} $T$}
|
49
|
386 |
child {node {3}}
|
|
387 |
child {node {4}}
|
|
388 |
}
|
|
389 |
}}
|
|
390 |
}};
|
|
391 |
\end{tikzpicture}
|
|
392 |
\end{center}
|
|
393 |
|
50
|
394 |
\begin{textblock}{5}(1, 6.5)
|
49
|
395 |
\bl{\texttt{(2*3)+(3+4)}}
|
|
396 |
\end{textblock}
|
|
397 |
|
|
398 |
\end{frame}}
|
|
399 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
407 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
408 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
409 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
410 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
\end{center}\pause\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
A CFG is \alert{left-recursive} if it has a nonterminal \bl{$E$} such
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
that \bl{$E \rightarrow^+ E\cdot \ldots$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
|
50
|
424 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
425 |
\mode<presentation>{
|
|
426 |
\begin{frame}[c]
|
|
427 |
\frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}}
|
|
428 |
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
A grammar is \alert{ambiguous} if there is a string that has at least two different parse trees.
|
50
|
430 |
|
|
431 |
|
|
432 |
\begin{center}
|
|
433 |
\bl{\begin{tabular}{lcl}
|
|
434 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
53
|
435 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
|
436 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
|
437 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
|
438 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
50
|
439 |
\end{tabular}}
|
|
440 |
\end{center}
|
|
441 |
|
|
442 |
\bl{\texttt{1 + 2 * 3 + 4}}
|
|
443 |
|
|
444 |
\end{frame}}
|
|
445 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
446 |
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
448 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
\frametitle{\begin{tabular}{c}Dangling Else\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
Another ambiguous grammar:\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
455 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
$E$ & $\rightarrow$ & if $E$ then $E$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
& $|$ & if $E$ then $E$ else $E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
& $|$ & \ldots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
\bl{\texttt{if a then if x then y else c}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
470 |
\frametitle{\begin{tabular}{c}Parser Combinators\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
471 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
Parser combinators: \bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
\begin{minipage}{1.1\textwidth}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
\mbox{}\hspace{-12mm}\mbox{}$\underbrace{\text{list of tokens}}_{\text{input}}$ \bl{$\Rightarrow$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
477 |
$\underbrace{\text{set of (parsed input, unparsed input)}}_{\text{output}}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
478 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
479 |
\end{minipage}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
480 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
482 |
\item sequencing
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
483 |
\item alternative
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
484 |
\item semantic action
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
485 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
487 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
489 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
490 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
491 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
492 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
493 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
494 |
Alternative parser (code \bl{$p\;||\;q$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
\item apply \bl{$p$} and also \bl{$q$}; then combine the outputs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
\large \bl{$p(\text{input}) \cup q(\text{input})$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
504 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
505 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
506 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
512 |
Sequence parser (code \bl{$p\sim q$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
513 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
514 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
\item apply first \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
\item then apply \bl{$q$} to the unparsed parts
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
517 |
\item then combine the results:\\ \mbox{}\;\;((output$_1$, output$_2$), unparsed part)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
518 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
519 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
520 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
521 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
522 |
\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
523 |
\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
524 |
\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
525 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
526 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
527 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
528 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
529 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
531 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
532 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
534 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
535 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
536 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
537 |
Function parser (code \bl{$p \Rightarrow f$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
538 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
539 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
540 |
\item apply \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
541 |
\item then apply the function \bl{$f$} to each first component
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
542 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
543 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
545 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
546 |
\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
547 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
548 |
\end{center}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
550 |
\bl{$f$} is the semantic action (``what to do with the parsed input'')
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
551 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
552 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
553 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
555 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
556 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
557 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
558 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
559 |
\frametitle{\begin{tabular}{c}Semantic Actions\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
560 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
561 |
Addition
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
562 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
563 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
564 |
\bl{$T \sim + \sim E \Rightarrow \underbrace{f((x,y), z) \Rightarrow x + z}_{\text{semantic action}}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
565 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
566 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
Multiplication
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
569 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
570 |
\bl{$F \sim * \sim T \Rightarrow f((x,y), z) \Rightarrow x * z$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
571 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
572 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
573 |
Parenthesis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
574 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
575 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
\bl{$\text{(} \sim E \sim \text{)} \Rightarrow f((x,y), z) \Rightarrow y$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
577 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
578 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
579 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
580 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
584 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
585 |
\frametitle{\begin{tabular}{c}Types of Parsers\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
586 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
587 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
588 |
\item {\bf Sequencing}: if \bl{$p$} returns results of type \bl{$T$}, and \bl{$q$} results of type \bl{$S$},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
589 |
then \bl{$p \sim q$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
590 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
591 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
592 |
\bl{$T \times S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
593 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
594 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
595 |
\item {\bf Alternative}: if \bl{$p$} returns results of type \bl{$T$} then \bl{$q$} \alert{must} also have results of type \bl{$T$},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
596 |
and \bl{$p \;||\; q$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
597 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
599 |
\bl{$T$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
601 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
602 |
\item {\bf Semantic Action}: if \bl{$p$} returns results of type \bl{$T$} and \bl{$f$} is a function from
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
603 |
\bl{$T$} to \bl{$S$}, then
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
604 |
\bl{$p \Rightarrow f$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
605 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
606 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
607 |
\bl{$S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
608 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
609 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
617 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
618 |
\frametitle{\begin{tabular}{c}Input Types of Parsers\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
619 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
620 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
621 |
\item input: \alert{string}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
622 |
\item output: set of (output\_type, \alert{string})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
\end{itemize}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
624 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
625 |
actually it can be any input type as long as it is a kind of sequence
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
(for example a string)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
634 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
635 |
\frametitle{\begin{tabular}{c}Scannerless Parsers\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
636 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
637 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
638 |
\item input: \alert{string}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
639 |
\item output: set of (output\_type, \alert{string})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
640 |
\end{itemize}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
but lexers are better when whitespaces or comments need to be filtered out;
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
643 |
then input is a sequence of tokens
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
644 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
645 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
646 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
647 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
649 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
651 |
\frametitle{\begin{tabular}{c}Successful Parses\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
652 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
654 |
\item input: string
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
655 |
\item output: \alert{set of} (output\_type, string)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
656 |
\end{itemize}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
658 |
a parse is successful whenever the input has been
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
659 |
fully ``consumed'' (that is the second component is empty)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
660 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
661 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
662 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
663 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
664 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
665 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
666 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
667 |
\begin{frame}[c]
|
170
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
668 |
\frametitle{Abstract Parser Class}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
\mbox{\lstset{language=Scala}\fontsize{10}{12}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
\texttt{\lstinputlisting{../progs/app7.scala}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
675 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
676 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
677 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
678 |
{\lstset{language=Scala}\fontsize{10}{12}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
679 |
\texttt{\lstinputlisting{../progs/app8.scala}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
680 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
681 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
682 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
683 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
684 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
685 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
686 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
687 |
\frametitle{\begin{tabular}{c}Two Grammars\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
689 |
Which languages are recognised by the following two grammars?
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
690 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
691 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
692 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
693 |
$S$ & $\rightarrow$ & $1 \cdot S \cdot S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
694 |
& $|$ & $\epsilon$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
695 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
696 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
697 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
698 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
699 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
700 |
$U$ & $\rightarrow$ & $1 \cdot U$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
701 |
& $|$ & $\epsilon$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
702 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
703 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
704 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
705 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
706 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
707 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
708 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
709 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
710 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
711 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
712 |
\frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
713 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
714 |
\mbox{}\\[-25mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
715 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
716 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
717 |
\begin{tikzpicture}[y=.2cm, x=.009cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
718 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
719 |
\draw (0,0) -- coordinate (x axis mid) (1000,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
720 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
721 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
722 |
\foreach \x in {0, 20, 100, 200,...,1000}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
723 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
724 |
node[anchor=north] {\small \x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
725 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
726 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
727 |
node[anchor=east] {\small\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
728 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
729 |
\node[below=0.6cm] at (x axis mid) {\bl{1}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
730 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
731 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
732 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
733 |
\draw[color=blue] plot[mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
734 |
file {s-grammar1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
735 |
\only<2->{\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
736 |
file {s-grammar2.data};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
737 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
738 |
\begin{scope}[shift={(400,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
739 |
\draw[color=blue] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
740 |
plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
741 |
node[right]{\small unambiguous};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
742 |
\only<2->{\draw[yshift=\baselineskip, color=red] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
743 |
plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
744 |
node[right]{\small ambiguous};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
745 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
746 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
747 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
748 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
749 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
750 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
751 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
752 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
753 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
754 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
755 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
756 |
\frametitle{\begin{tabular}{c}While-Language\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
757 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
758 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
759 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
760 |
\bl{\begin{tabular}{@{}lcl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
761 |
$Stmt$ & $\rightarrow$ & $\text{skip}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
762 |
& $|$ & $Id := AExp$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
763 |
& $|$ & $\text{if}\; B\!Exp \;\text{then}\; Block \;\text{else}\; Block$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
764 |
& $|$ & $\text{while}\; B\!Exp \;\text{do}\; Block$\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
765 |
$Stmts$ & $\rightarrow$ & $Stmt \;\text{;}\; Stmts$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
766 |
& $|$ & $Stmt$\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
767 |
$Block$ & $\rightarrow$ & $\{ Stmts \}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
768 |
& $|$ & $Stmt$\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
769 |
$AExp$ & $\rightarrow$ & \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
770 |
$BExp$ & $\rightarrow$ & \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
771 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
772 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
773 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
774 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
775 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
776 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
777 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
778 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
779 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
780 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
781 |
\frametitle{\begin{tabular}{c}An Interpreter\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
782 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
783 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
784 |
\bl{\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
785 |
$\{$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
786 |
\;\;$x := 5 \text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
787 |
\;\;$y := x * 3\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
788 |
\;\;$y := x * 4\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
789 |
\;\;$x := u * 3$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
790 |
$\}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
791 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
792 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
793 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
794 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
795 |
\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
796 |
\item \bl{\text{eval}(stmt, env)}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
797 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
798 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
799 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
800 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
801 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
802 |
|
50
|
803 |
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
804 |
|
53
|
805 |
|
51
|
806 |
|
49
|
807 |
\end{document}
|
|
808 |
|
|
809 |
%%% Local Variables:
|
|
810 |
%%% mode: latex
|
|
811 |
%%% TeX-master: t
|
|
812 |
%%% End:
|
|
813 |
|