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zWfjP{Jye+^u>FHmbK#5zO$*g`=lyy84y*WIj(;mNM{xU(kjt4C+|wWI*|AiSSMPvp z{SL0_M|Hnv7O<v0P>T`X9(3h_)tv`QiL*rWSLN?JI&b2R*Nmqh9PIMHe_3@aZ&dWZ zX2;nQ-RJjRF<}ic$>7XPKf$<`yK;r_{Qqm)Umxway|~ix&*9rvrd{(_-@C2y?{w|l zS*qtmO0pQegfoI)u>2Bw;l03PAxnsAz*L8JC;khflN`L6zH<H*5}zNw@9BX#Kl$yS a<{zJ)d4^qv*Tlfg($s`YRn^tsjSB$z7Px`{ diff --git a/Lectures/L26_SpecificationQuality/SpecificationQuality.tex b/Lectures/L26_SpecificationQuality/SpecificationQuality.tex index db453c39..161aeb4b 100755 --- a/Lectures/L26_SpecificationQuality/SpecificationQuality.tex +++ b/Lectures/L26_SpecificationQuality/SpecificationQuality.tex @@ -37,7 +37,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} -\frametitle{Specification Via UML} +\frametitle{Specification Quality} \begin{itemize} \item Administrative details @@ -60,6 +60,8 @@ \begin{itemize} \item Part 1 - Specification: due 11:59 pm \structure{Mar 11} \item Part 2 - Code: due 11:59 pm Mar 20 +\item $\theta = \cos^{-1} \left ( \frac {\mathbf{u} \cdot \mathbf{v}}{|| \mathbf{u} || || +\mathbf{v} ||} \right )$ \end{itemize} \item A4 @@ -74,6 +76,54 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{A3 Hints} + +\begin{itemize} +\item Take advantage of what descriptive mathematical specification has to offer +\item You do not need to worry about how to calculate values, only how to + describe them +\item pointInRegion(p): A point p is considered to be in the Region if there + exists a point q, where q is in the Region, and the distance between the two + points is less than the allowed tolerance. +\item $\theta = \cos^{-1} \left ( \frac {\mathbf{u} \cdot \mathbf{v}}{|| \mathbf{u} || || +\mathbf{v} ||} \right )$ +\item A valid segment is valid if it is valid with respect to all obstacles +\bi +\item \structure{How would you say: For all obstacles the segment is valid?} +\item \uncover<2->{$\forall (i: \mathbb{N}| 0 \leq i < \mbox{Map.get\_obstacles.size()} : +\mbox{is\_valid\_segment\_for\_region}(p_1, p_2, i)$} +\ei +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{A3 Hints Continued} + +\begin{itemize} +\item \structure{What makes a segment valid wrt a given region?} +\bi +\item \uncover<2->{None of the points on the segment lie within the region} +\item \uncover<3->{For all points along the line NOT pointInRegion()} +\item \uncover<4->{All the points using the parametric rep of a line.} +\ei +\item \structure{What has to be true for a valid path?} +\bi +\item \uncover<5->{First point in the region for the safe zone} +\item \uncover<5->{Last point in the region for the safe zone} +\item \uncover<5->{For all destination there is a point on the path that is in + the region} +\item \uncover<5->{For all segments the segments are valid} +\ei +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} %\frametitle{Differences Between Interface and Abstract} \begin{itemize} @@ -375,4 +425,439 @@ successive NL characters) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{English and Mathematics as Languages} + +\begin{itemize} + +\item English is a language +\item So is Mathematics +\item Both have +\begin{itemize} +\item Rules of grammar (syntax) +\item Semantics +\end{itemize} +\item When writing in any language, pay attention to grammar and semantics. Get both right. + +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{English and Mathematics: A Difference} + +\begin{itemize} + +\item In English and other natural languages +\begin{itemize} +\item Ambiguity desired, intentionally possible +\item Unambiguous statements almost impossible +\end{itemize} +\item In Mathematics +\begin{itemize} +\item Ambiguity not desired, intentionally prevented +\item Ambiguous statements almost impossible (even in probability theory, fuzzy logic) +\end{itemize} + +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Mathematics and Engineering} + +\begin{itemize} + +\item Therefore, mathematics is the language of engineering + +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\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 -- GitLab