From a598f7f0989198508071d25fa6aba5d3cb07cbec Mon Sep 17 00:00:00 2001
From: Spencer Smith <smiths@mcmaster.ca>
Date: Fri, 10 Mar 2017 09:58:24 -0500
Subject: [PATCH] Updates to L26.

---
 .../SpecificationQuality.pdf                  | Bin 407741 -> 511122 bytes
 .../SpecificationQuality.tex                  | 487 +++++++++++++++++-
 2 files changed, 486 insertions(+), 1 deletion(-)

diff --git a/Lectures/L26_SpecificationQuality/SpecificationQuality.pdf b/Lectures/L26_SpecificationQuality/SpecificationQuality.pdf
index 313a9e760ebb46cc5841f0760a3fe110f40c5f80..7b595b43da044a234e2c67adb8146bf7d796eb19 100644
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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
-- 
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