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Commit 9b3fd4ff authored by W. Spencer Smith's avatar W. Spencer Smith
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Modification for spec quality and English to Math lectures

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Lectures/L24_SpecificationQuality/SpecificationQuality.pdf
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Lectures/L24_SpecificationQuality/SpecificationQuality.tex
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\documentclass[t,12pt,numbers,fleqn,handout]{beamer}
%\documentclass[t,12pt,numbers,fleqn]{beamer}
%\documentclass[t,12pt,numbers,fleqn,handout]{beamer}
\documentclass[t,12pt,numbers,fleqn]{beamer}
\usepackage{pgfpages}
\usepackage{hyperref}
......@@ -505,385 +505,4 @@ See
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Correct Syntax for Mathematics}
\begin{itemize}
\item Make sure the syntax of your mathematical expressions is correct
\item Correct syntax does not guarantee correct semantics
\item Incorrect syntax makes the mathematics ambiguous
\item Example problems to watch for
\begin{itemize}
\item Mismatch of types
\begin{itemize}
\item ($\mbox{p.xcoord()} + \mathit{width}) \wedge \mbox{p.xcoord()}$
\item $\neg(\mbox{integer})$
\item Set of sequences accessed by $[i]$
\item $\forall (i: \mathbb{N} \wedge j: \mathbb{N} ...)$
\end{itemize}
\item Use of programming language notation in mathematics
\begin{itemize}
\item Integer values instead of boolean
\item length $==$ MAX\_SIZE
\end{itemize}
\item $(x > 7) = \mathit{true}$ instead of $(x > 7)$ (bad form)
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Different World Views}
\begin{itemize}
\item English and other natural languages
\begin{itemize}
\item Express both static and dynamic views
\item States and actions (verbs of being and action)
\end{itemize}
\item Imperative programming languages
\begin{itemize}
\item Primarily dynamic world view (changes)
\end{itemize}
\item Functional programming languages
\begin{itemize}
\item Static world view
\end{itemize}
\item Mathematics
\begin{itemize}
\item Static world view only
\end{itemize}
\item Fundamental conceptual differences
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Static Versus Dynamic Views}
\begin{itemize}
\item These very different world views pose a conceptual hurdle for the translator
\item The translator must bridge the gap between
\begin{itemize}
\item Dynamic and static view of problem statement
\item Dynamic world view of programming and
\item Purely static world view of mathematics
\end{itemize}
\item Not hard, but requires conscious attention
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Translating Between Languages}
\begin{itemize}
\item Translating a statement from one language to another is a multistep (not single) process
\begin{enumerate}
\item Statement in source language to a mental understanding of the \structure{meaning} of the statement
\item Reformulate \structure{mental understanding} into target language view, concepts, culture
\item Mental understanding of the \structure{meaning} of the statement to a statement in the target language
\end{enumerate}
\item The first and last statement must \structure{mean} the same
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Translators}
\begin{itemize}
\item Knowing two languages: not enough to translate
\item A good translator knows well
\begin{itemize}
\item The two languages
\item AND the subject being translated
\item AND how to translate
\end{itemize}
\item These three things are \structure{different}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Organization and Style}
\begin{itemize}
\item When writing in English, or any other natural language, one pays careful
attention to
\begin{itemize}
\item Organization of the essay, report, etc.
\item Style of expression
\end{itemize}
\item When writing in Mathematics, to do the same:
\begin{itemize}
\item Clear, complete, conscise
\item KISSS (Keep it Simple Sharp and Straightforward)
\item Understandable
\item Interesting
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Strategies}
\begin{itemize}
\item Understand the meaning of the original
\item Obtain all needed information
\item Close the gap between the English text and mathematics
\item Divide and conquer (complexity)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Strategy: Understand the Original}
\begin{itemize}
\item Describe specific instance of general problem
\item Distinguish essentials from background
\item Draw a diagram
\item Express in intermediate or mixed language
\item Identify object referred to
\item Identify implicit (but false) ``information''
\item Identify missing information
\item Identify relationships between essential objects
\item Identify special cases
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Strategy: Obtain all Needed Information}
\begin{itemize}
\item Ask the author of the task description
\item Identify gaps in the description of the task
\item Identify implicit ``information''
\item Ask if implicit ``information'' may be assumed
\item Identify data present and ask about related details
\item Ask if missing information is really needed
\item Read \structure{carefully}, \structure{thoroughly}, \structure{precisely}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Strategy: Close Gap English -- Mathematics}
\begin{itemize}
\item Express implicit information explicitly
\item Reduce vagueness and ambiguity
\item Reword English text to be closer to mathematics (express in an intermediate, mixed language)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Strategy: Divide and Conquer}
\begin{itemize}
\item Construct a table
\item Distinguish between specific cases
\item Introduce an auxiliary mathematics function
\item Modularize
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Strategy: Draw Diagrams, Describe Specific Instances of the Given Problem}
\begin{itemize}
\item Graphical representations help understand the meaning of the message
\item For specific instances, think of extreme cases first to simplify
\begin{itemize}
\item $n=0$
\item $n=1$
\item $n=\inf$
\end{itemize}
\item Think of a normal sized problem, usually something like $n \geq 3$
\item You might want to write down truth tables
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{A Small Translator's Glossary}
\begin{tabular}{p{4cm} | p{6cm}}
\toprule
English & Mathematics\\
\midrule
and, but & $\wedge$\\
\hline
or & $\vee$\\
\hline
for all, each, every, any & $\forall$, $\wedge$ series, universal quantification\\
\hline
for no, none & $\forall$, $\wedge$ series, universal quantification, with a negated assertion\\
\hline
there is (are), there exist(s), for some, at least one & $\exists$, $\vee$ series, existential quantification\\
\hline
\bottomrule
\end{tabular}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{A Small Translator's Glossary Continued}
\begin{tabular}{p{4cm} | p{6cm}}
\toprule
English & Mathematics\\
\midrule
integer & $... \in \mathbb{Z}$\\
\hline
sorted & $\wedge_{i=0}^{n-2} A[i] \leq A[i+1]$, \newline
$\forall ( i : \mathbb{N} | 0 \leq i < n-1 : A[i] \leq A[i+1])$\\
\hline
if (when, whenever) ... then ... & ... $\rightarrow$ ..., sometimes $\wedge$ \\
\hline
search, find, equal, present & $=$\\
\hline
exchange, rearrange, different order, different sequence, merge, copy, sort & permutation\\
\hline
\bottomrule
\end{tabular}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Your Translator's Glossary}
\begin{itemize}
\item A professional translator compiles his/her own translation glossary
\begin{itemize}
\item Over time
\item Based on own accumulated experience
\end{itemize}
\item You should too!
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Exercise}
Consider an array $D$ with index values ranging from $1$ to $n$. The subject of this example is part of a specification
for a subprogram that will count how many times a particular given value occurs in the array $D$.\\
~\newline
The goal of this exercise is to write a postcondition for the subprogram, relating the various relevant variablesÕ
values when the search is complete.
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Exercise Continued}
Understand the task in the original language
\begin{itemize}
\item Identify objects referred to (look for nouns in the original English text)
\item<2-> \structure<2>{Array $D$, index value, times (count), particular given value, relevant variables's value}
\item Identify missing information
\item<3-> \structure<3>{Names of variable for: index, times (count), particular given value}
\item<4-> \structure<4>{Are there any other relevant variables?}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Exercise}
\begin{itemize}
\item Identify missing information
\item Names of variable for
\begin{itemize}
\item Index: assume $i$
\item Times (count): ask the author of the task, assume $\mathit{count}$
\item Particular given value: Ask the author of the task, assume $\mathit{key}$
\item Are there any other relevant variables? (no?)
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Reference}
\begin{itemize}
\item Baber, Robert L., \textit{Translating English to Mathematics}, 2002
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
\ No newline at end of file
Lectures/L25_EnglishToMath/EnglishToMath.pdf
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Lectures/L25_EnglishToMath/EnglishToMath.tex
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......@@ -23,7 +23,7 @@
\mode<presentation>{}
\input{../def-beamer}
\Drafttrue
\Draftfalse
\newcommand{\topicTitle}{25 English To Math}
\ifDraft
......@@ -47,7 +47,6 @@
\begin{itemize}
\item Administrative details
\item Line Formatter Example
\item English and mathematics as languages
\item Different world views
\item Translating between languages
......@@ -73,25 +72,19 @@ TBD
\item Midterm
\bi
\item Grades on Avenue
\item Out of 27 instead of 30
\bi
\item The test was more difficult than most expected
\item Final will also require knowledge of course material and attention to
detail
\item Remember the goal of the test is to measure your ability to design and
develop software as part of a University degree
\ei
\item Out of 29 instead of 30: Average around 70\%
\ei
\item A3 deadlines
\item A3
\begin{itemize}
\item Part 2 - Code: due 11:59 pm Mar 20
\item \structure{Part 1 spec available on Wednesday}
\item Part 1 - Specification: due 11:59 pm Mar 12
\item Part 1 - Solution: Mar 18
\item Part 2 - Code: due 11:59 pm Mar 26
\end{itemize}
\item A4
\bi
\item Your own design and specification
\item Due April 3 at 11:59 pm
\item Due April 9 at 11:59 pm
\ei
\end{itemize}
......@@ -102,196 +95,6 @@ TBD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Line Formatter}
\bi
\item \structure{Input} stream signalled with ET
\item Exactly one ET character in each input stream
\item \structure{Character} classifications:
\bi
\item Break character - BL (blank) and NL (new line)
\item Non Break Character - all others except ET
\item End of text indicator ET
\ei
\item \structure{Word} is a non-empty sequence of non break characters
\item \structure{Break} is a sequence of one or more break characters
\item \structure{Output} same sequence of words, except if there is an oversize
word
\bi
\item Oversize means more than MAXPOS characters, where MAXPOS is a positive
integer
\item If there is an oversize word
\bi
\item Set Alarm to TRUE
\item Exit the program
\ei
\ei
\ei
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Line Formatter}
\bi
\item Up to the point of an error, the program's output should have the
following properties
\bi
\item A new line should start only between words and at the beginning of the
output text, if any
\item A break in the input is reduced to a single break character in the output
\item As many words as possible should be placed on each line (i.e.\ between
successive NL characters)
\item No line may contain more than MAXPOS characters (words and BLs)
\ei
\ei
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Abstract?}
\uncover<2->{
\bi
\item Not abstract!
\item Specifies an implementation for error handling (variable named Alarm)
\item Do not have to name the variable Alarm
\item Could use exception handling (or another approach) instead
\item ET is a machine dependent (program domain) concept
\ei
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Correct?}
\uncover<2->{
\bi
\item The definition of line is incorrect!
\item A line is defined as being between NLs, which ignores text before the
first NL and after the last NL
\item The output file does not contain ET, which is either a bug in the spec or
a significant non-uniformity
\ei
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Unambiguous?}
\uncover<2->{
\bi
\item Ambiguous!
\item ``point of error'' is not defined
\item Output matches input to the last acceptable word, or the last acceptable character?
\item ``trailing blanks ending with ET'' is ambiguous
\item The program's output should be the same sequence of words as in the input
\bi
\item But the input is not a sequence of words
\item If the input were a sequence of words, what about leading or trailing
breaks?
\item ``As many words as possible should be placed on each line''
\bi
\item WHO WHAT ``NL'' WHEN
\item WHO ``NL'' WHAT WHEN
\ei
\ei
\ei
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Complete?}
\uncover<2->{
\bi
\item Not complete!
\item Meaning of NL and its relation to the concept of line is left implicit
\item Alarm is not specified if MAXPOS is never exceeded
\ei
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Consistent?}
\uncover<2->{
\bi
\item Not consistent!
\item ``non-empty'' and ``one or more'' (synonyms)
\item ``stream'' and ``sequence'' (synonyms)
\item Is the input a ``stream of characters'' or a ``sequence of words separated
by breaks''? -- sequence of T is not the same as sequence of sequence of T
\ei
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verifiable?}
\uncover<2->{
\bi
\item The specification cannot be verified, since it is ambiguous and incorrect
\ei
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Advantages and Disadvantages?}
\bi
\item \structure{Advantages and disadvantages of maintaining both
formal and a natural language spec?}
\ei
\uncover<2->{
\bi
\item Advantage of natural language - understandability
\item Advantage of formal spec
\bi
\item Unambiguous
\item Highlights difficult to informally detect cases
\item Checking for completeness and consistency
\item Amenable to tool support
\ei
\item Advantage of both - all of the above advantages
\item Disadvantages - have to maintain two specs
\item Automatic translation
\bi
\item Formal spec to natural language has been
researched
\item Natural language to formal spec has received more attention
\ei
\ei
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{English and Mathematics as Languages}
......
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