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Lectures/L19_ModulesWithExternalInteraction/MazeTracingRobot.pdf create mode 100755 Lectures/L19_ModulesWithExternalInteraction/MazeTracingRobot.tex create mode 100644 Lectures/L19_ModulesWithExternalInteraction/UsesHierarchy.pdf create mode 100644 Lectures/L19_ModulesWithExternalInteraction/UsesHierarchyBetter.pdf create mode 100644 ReferenceMaterial/ExampleMaze_FormalSpec.pdf create mode 100644 ReferenceMaterial/vMohrenshildtAndPeters1998.pdf diff --git a/Lectures/L18_MazeTracingRobot/MazeTracingRobot.pdf b/Lectures/L18_MazeTracingRobot/MazeTracingRobot.pdf index 3fcfc51856aa2e8251f22c233346a19264744840..b11a3972e9c835c6773767d274f8a050f45c523b 100644 GIT binary patch literal 450374 zcmdqJ1z43$w=jIu4I<qwf`oK~NSAaA2%AlJ3J6<K=|)13?v^fTk?xXKk#6bQd^h?& zKF@Q``=0k)=llQbT>n2_``(K+Gxw}nvu4eT*)pj~%d&HE@L@6yk9U5?<l?8jPwQxA zLn|tZ$*Bx=uynJc<-5;M`>SAb%39mGL0xD$W$jGepwdu?qd62)TpZKY%>`;|kNI?_ zQ>!gv?EbB$lY1*`^5IiF5s=lo_eNFnV#BD;0Pb|LA$_&NelFJX=G%`iUL*P=jj|S6 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style -\documentclass[handout]{beamer} % for handout -%\documentclass{beamer} % for slides using uncover +%\documentclass[t,12pt,numbers,fleqn,handout]{beamer} +\documentclass[t,12pt,numbers,fleqn]{beamer} -\usepackage{logictheme} -\usepackage{amsmath} -\usepackage{bm} -\usepackage{ulem} - -\usepackage{hhline} -\usepackage{multirow} -\usepackage{multicol} -\usepackage{array} +\usepackage{pgfpages} \usepackage{hyperref} +\hypersetup{colorlinks=true, + linkcolor=blue, + citecolor=blue, + filecolor=blue, + urlcolor=blue, + unicode=false} +\urlstyle{same} + +\usepackage{booktabs} +\usepackage{multirow} -\usepackage{listings} +\useoutertheme{split} %so the footline can be seen, without needing pgfpages -\title[Maze Tracing Robot (slide \thepage)]{Maze Tracing Robot Example} -%\subtitle{???} -\author[Smith]{Dr.~Spencer Smith} -\institute{Computing and Software Department, McMaster University} -\date{\today} -\pgfdeclareimage[height=0.5cm]{logo}{../McMasterLogo} %McMaster logo in one folder up -\logo{\pgfuseimage{logo}} +% \pgfpagesuselayout{resize to}[letterpaper,border +% shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work -\setbeamercolor{alerted text}{fg=red!75!green!50!blue} -%\setbeamerfont{alerted text}{series=\bfseries} -\setbeamerfont{alerted text}{family=\rmfamily,series=\bfseries} +\mode<presentation>{} -%\setbeamertemplate{footline}{\insertpagenumber} % only has the page number +\input{../def-beamer} -\newcounter{temp} +\newcommand{\topic}{18 Maze Tracing Robot Example} + +\input{../titlepage} \begin{document} -% ================================================================================== -% Slide 1 -\maketitle -% ================================================================================== +\input{../footline} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Maze Tracing Robot Example} \begin{itemize} \item Administrative details -\item Dr.\ v.\ Mohrenschildt's maze tracing robot (see WebCT document) +\item Index set example +\item Solar water heating tank example +\item Dr.\ v.\ Mohrenschildt's maze tracing robot (see GitLab) \item MIS for maze\_storage \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} \frametitle{Administrative Details} \begin{itemize} -\item Assignment 3 deadlines +\item Assignment 2 \begin{itemize} -\item Minor modifications to posted file -\item Code due by midnight Feb 23 -\item E-mail your partner your code by Feb 24 -\item Lab report due by the beginning of class Mar 2 -\item Will discuss Assignment 3 during tutorial, time for questions +\item {Files due by 11:59 pm Feb 19} +\item {File automatically sent to partners on Feb 20} +\item Lab report due by 11:59 pm Feb 27 +\item {When returning an object, you can either create a new object or + return a reference} +\item {Remember: Deque is an Abstract Object, not an ADT} \end{itemize} + \item Midterm exam \begin{itemize} -\item March 4 during tutorial time -\item In T29/105, not our usual classroom +\item March 1, 7:00 pm, TSH/120 +\item 90 minute duration +\item Multiple choice - 30--40 questions? +\item Open book (any paper) \end{itemize} + \end{itemize} \end{frame} @@ -75,170 +78,151 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} -\frametitle{Modules with External Interaction} +\frametitle{Index Set} -\begin{itemize} -\item In general, some modules may interact with the environment or other modules -%\item The Display Point Masses Applet module does this -\item Environment might include the keyboard, the screen, the file system, motors, sensors, etc. -\item Sometimes the interaction is informally specified using prose (natural language) -\item Can introduce an environment variable -\begin{itemize} -\item Name, type -\item Interpretation -\end{itemize} -\item Environment variables include the screen, the state of a motor (on, direction of rotation, power level, etc.), -the position of a robot - -\end{itemize} +Write a function \texttt{indexSet(x, B)} that takes a value \texttt{x} and a +list of values \texttt{B} and returns a list of indices where \texttt{B[i] = + x}.\\ +~\newline +As a first step, how would you say this mathematically? \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} -\frametitle{External Interaction Continued} +\frametitle{Index Set} -\begin{itemize} -\item Some external interactions are hidden -\begin{itemize} -\item Present in the implementation, but not in the MIS -\item An example might be OS memory allocation calls -\end{itemize} -\item External interaction described in the MIS -\begin{itemize} -\item Naming access programs of the other modules -\item Specifying how the other module's state variables are changed -\item The MIS should identify what external modules are used -\end{itemize} -\end{itemize} +Write a function \texttt{indexSet(x, B)} that takes a value \texttt{x} and a +list of values \texttt{B} and returns a list of indices where \texttt{B[i] = + x}.\\ + +$$\mbox{indexSet}(x, B) \equiv \{i : \mathbb{N} | i \in [0 .. |B|-1] \wedge B_i = +x : i\}$$ + +How could you use \texttt{indexSet} to calculate \texttt{rank(x, A)}? \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -\frametitle{MIS for GUI Modules} -\begin{itemize} -\item Could introduce an environment variable -\item window: sequence [RES\_H][RES\_V] of pixelT -\begin{itemize} -\item Where window[r][c] is the pixel located at row r and column c, with numbering zero-relative and beginning at the -upper left corner -\item Would still need to define pixelT -\end{itemize} -\item Could formally specify the environment variable transitions -\item More often it is reasonable to specify the transition in prose -\item In some cases the proposed GUI might be shown by rough sketches -\end{itemize} +\begin{frame} +\frametitle{Anticipated Changes} + +\bi +\item The specific hardware on which the software is to run +\item The format of the initial input data +\item The format of the input parameters +\item The constraints on the input parameters +\item The format of the output data +\item The constraints on the output results +\item How the governing ODEs are defined using the input parameters +\item How the energy equations are defined using the input parameters +\item How the overall control of the calculations is orchestrated +\item The implementation of the sequence data structure +\item The algorithm used for the ODE solver +\item The implementation of plotting data +\ei \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} -\frametitle{Display Point Masses Module Syntax} +\frametitle{Module Hierarchy by Secrets} +\begin{table}[h!] +\centering +\begin{tabular}{p{0.3\textwidth} p{0.6\textwidth}} +\toprule +\textbf{Level 1} & \textbf{Level 2}\\ +\midrule + +{Hardware-Hiding Module} & ~ \\ +\midrule + +\multirow{6}{0.3\textwidth}{Behaviour-Hiding Module} & Input Format Module\\ +& Input Parameters Module\\ +& Output Format Module\\ +& Temperature ODEs Module\\ +& Energy Equations Module\\ +& Control Module\\ +\midrule + +\multirow{3}{0.3\textwidth}{Software Decision Module} & {Sequence Data Structure Module}\\ +& ODE Solver Module\\ +& Plotting Module\\ +\bottomrule -\textbf{Exported Access Programs}\\ -~\newline -\begin{tabular}{| l | l | l | l |} -\hline -\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exc.}\\ -\hline -DisplayPointMassesApplet & ~ & DisplayPointMassesApplet & ~\\ -\hline -paint & ~ & ~ & ~\\ -\hline \end{tabular} - +\caption{Module Hierarchy} +\label{TblMH} +\end{table} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} -\frametitle{Display Point Masses Module Semantics} +\frametitle{Example Modules from SWHS} -\textbf{Environment Variables}\\ -$\mathit{win}:$ 2D sequence of pixels displayed within a web-browser \\ +\textbf{Hardware Hiding Modules} -\noindent DisplayPointMassesApplet(): -\begin{itemize} -\item transition: The state of the abstract object ListPointMasses is modified as follows:\\ -ListPointMasses.init()\\ -ListPointMasses.add(0, PointMassT(20, 20, 10)\\ -ListPointMasses.add(1, PointMassT(120, 200, 20)\\ -... -\end{itemize} - -\noindent paint(): -\begin{itemize} -\item transition $win := $ Modify window so that the point masses in ListPointMasses -are plotted as circles. The centre of each circles should be the corresponding x and y coordinates and the radius should -be the mass of the point mass. -\end{itemize} +\begin{description} +\item[Secrets:]The data structure and algorithm used to implement the virtual + hardware. +\item[Services:]Serves as a virtual hardware used by the rest of the + system. This module provides the interface between the hardware and the + software. So, the system can use it to display outputs or to accept inputs. +\item[Implemented By:] OS +\end{description} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} -\frametitle{Assignment 3 Vector Module} +\frametitle{Example Modules from SWHS} -\textbf {Exported Access Programs}\\ -~\newline -\begin{tabular}{| l | l | l | p{0.75in} |} -\hline -\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\ -\hline -new vectorT & real $\rightarrow$ real & vectorT & ~\\ -\hline -getf & ~ & real $\rightarrow$ real & ~\\ -\hline -eval & real, real, integer & sequence of real & deltaNeg, nstepsNeg\\ -\hline -evalPrint & real, real, integer & ~ & deltaNeg, nstepsNeg\\ -\hline -\end{tabular} +\textbf{Input Verification Module} + +\begin{description} +\item[Secrets:] The rules for the physical and software constraints. +\item[Services:] Verifies that the input parameters comply with physical and + software constraints. Throws an error if a parameter violates a physical + constraint. Throws a warning if a parameter violates a software constraint. +\item[Implemented By:] SWHS +\end{description} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} -\frametitle{Vector Module Semantics} +\frametitle{Example Modules from SWHS} -\textbf{Environment Variables}\\ -$\mathit{screen}$ : two dimensional sequence of positions on the screen, which each position holding a character\\ -~\newline -\textbf{State Variables}\\ -$f$: real $\rightarrow$ real\\ -~\newline -\textbf{Access Routine Semantics}\\ -\noindent eval ($\mathit{startx}, \mathit{deltax}, \mathit{nsteps}$): -\begin{itemize} -\item output: $out := < f(\mathit{startx}), f(\mathit{startx} + \mathit{deltax}), f(\mathit{startx} + 2 \cdot \mathit{deltax}), ... -, f(\mathit{startx} + \mathit{nsteps} \cdot \mathit{deltax})>$ -\item exception: $exc := ((\mathit{deltax} < 0) \Rightarrow \mbox{deltaNeg} | (\mathit{nsteps} < 0) \Rightarrow -\mbox{nstepsNeg})$ -\end{itemize} +\textbf{ODE Solver Module} + +\begin{description} +\item[Secrets:] The algorithm to solve a system of first order ODEs. +\item[Services:] Provides solvers that take the governing equation, initial + conditions, and numerical parameters, and solve them. +\item[Implemented By:] Matlab +\end{description} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -\frametitle{Vector Module Semantics Continued} +\begin{frame}[plain, fragile] -\noindent evalPrint ($\mathit{startx}, \mathit{deltax}, \mathit{nsteps}$): -\begin{itemize} -\item transition: The state of $\mathit{screen}$ is modified so that the sequence returned by eval ($\mathit{startx}$, -$\mathit{deltax}$, $\mathit{nsteps}$) is displayed. -\item exception: $exc := ((\mathit{deltax} < 0) \Rightarrow \mbox{deltaNeg} | (\mathit{nsteps} < 0) \Rightarrow -\mbox{nstepsNeg})$ -\end{itemize} +\frametitle{SWHS Uses Hierarchy} + +\begin{center} +\includegraphics[scale=0.55]{UsesHierarchy.pdf} +\end{center} \end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Dr.\ v.\ Mohrenschildt's Maze Tracing Robot Example} @@ -254,7 +238,8 @@ $\mathit{deltax}$, $\mathit{nsteps}$) is displayed. \frametitle{Maze Tracing Robot Expected Changes} \begin{itemize} -\item Changes to the geometry of the robot such that the mapping from a position to the robot inputs is different +\item Changes to the geometry of the robot such that the mapping from a position + to the robot inputs is different \item Changes to the interface to the robot \item Changes to the format of the maze \item Changes to any constant values @@ -306,20 +291,23 @@ $\mathit{deltax}$, $\mathit{nsteps}$) is displayed. \begin{itemize} \item \structure<1>{Module name:} control \begin{itemize} -\item \structure<1>{Secret:} how the arm moves from position to position and how the buttons are checked +\item \structure<1>{Secret:} how the arm moves from position to position and how + the buttons are checked \item \structure<1>{Service:} controls the movement of the arm \item \structure<1>{Module prefix:} cn\_ \end{itemize} \item \structure<1>{Module name:} geometry \begin{itemize} -\item \structure<1>{Secret:} how the calculations from cell coords to robot coords are performed +\item \structure<1>{Secret:} how the calculations from cell coords to robot + coords are performed \item \structure<1>{Service:} handles geometric positioning of the arm \item \structure<1>{Module prefix:} gm\_ \end{itemize} \item \structure<1>{Module name:} hardware \begin{itemize} \item \structure<1>{Secret:} how it interfaces with the robot -\item \structure<1>{Service:} handles hardware aspects of arm (movement and button checking) +\item \structure<1>{Service:} handles hardware aspects of arm (movement and + button checking) \item \structure<1>{Module prefix:} hw\_ \end{itemize} \end{itemize} @@ -332,8 +320,10 @@ $\mathit{deltax}$, $\mathit{nsteps}$) is displayed. \begin{itemize} \item \structure<1>{Module name:} types\_constants \begin{itemize} -\item \structure<1>{Secret:} how the data structures are defined and constants defined -\item \structure<1>{Service:} provides standard variable types and constants to modules +\item \structure<1>{Secret:} how the data structures are defined and constants + defined +\item \structure<1>{Service:} provides standard variable types and constants to + modules \end{itemize} \end{itemize} \end{frame} @@ -410,8 +400,8 @@ cell = tuple of (x: integer, y: integer) % there could be one related to maximum size of the map ~\newline \textbf{Assumptions}\\ -~\newline -ms\_get\_maze\_start and ms\_get\_maze\_end are not called until after the corresponding set routines have been called. +~\newline ms\_get\_maze\_start and ms\_get\_maze\_end are not called until after +the corresponding set routines have been called. \end{frame} @@ -520,7 +510,6 @@ ms\_get\_maze\_start and ms\_get\_maze\_end are not called until after the corre \frametitle{Additional Specifications for Determining the Path} pathT = sequence of cell\\ -~\newline \noindent validPath : pathT $\rightarrow$ boolean \begin{itemize} diff --git a/Lectures/L18_MazeTracingRobot/UsesHierarchy.pdf b/Lectures/L18_MazeTracingRobot/UsesHierarchy.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a229222f5284ff31b7e96c88ae67d0c2a012bd50 GIT binary patch literal 59977 zcmV)HK)t^uP((&8F)lL-CB)_O<?E;OpwPs|3N#=vAa7!73Oqa@FHB`_XLM*FH6Sn` zQXnrzX>4?5av(28Y+-a|L}g=dWMv>eJ_>Vma%Ev{3U~pWy-SiMxsq+y_fhx+UeN!a zc8#E<8XQ0fOKu}CMT)P%>2s~U6@Zy%)a4^3CBqN&z!VDoLjlA2ug8CX{IAC+{`>rX zdHi^OdHlcrkH`Q0@&A1M-~R1?K0p5cpO4S^?|=TLhu{8l_xmfKo*w_o(|<ku<MBTq zUmpMOKKO6{5$Mz7fBc*1f4#k@{XgcDn128B@%0O&PfsAtrw@_+$K$_0NY2wEV?KXA zKfXS{)8YB!>(}?|<Lk@wueaBC`aOTX{(Abn034tGzuvyz*E63_zuuqTAH=`|U?_sG zuZ5t`xBU-#eE)i<@9WFcuW$M=YR3Qg_4bw#Uw*xPfo{J3>(L?q#q8dme|@g`_4E68 zXZZO1{`%|lBc#b2MtXn#_2JOZzlOZ`_g`Pk^guGf_qSh9Uu%9Kd3)+?|9TL^Q&7D8 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unicode=false} +\urlstyle{same} + +\usepackage{booktabs} +\usepackage{multirow} + +\useoutertheme{split} %so the footline can be seen, without needing pgfpages + +% \pgfpagesuselayout{resize to}[letterpaper,border +% shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work + +\mode<presentation>{} + +\input{../def-beamer} + +\newcommand{\topic}{18 Maze Tracing Robot Example} + +\input{../titlepage} + +\begin{document} + +\input{../footline} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Maze Tracing Robot Example} + +\begin{itemize} +\item Administrative details +\item Index set example +\item Solar water heating tank example +\item Modules with external interaction +\item Dr.\ v.\ Mohrenschildt's maze tracing robot (see GitLab) +\item MIS for maze\_storage +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Administrative Details} + +\begin{itemize} + +\item Assignment 2 +\begin{itemize} +\item {Files due by 11:59 pm Feb 19} +\item {File automatically sent to partners on Feb 20} +\item Lab report due by 11:59 pm Feb 27 +\item {When returning an object, you can either create a new object or + return a reference} +\item {\texttt{totalArea} is just the sum of the area of all circles, + do not worry about overlap} +\item {Removed POS exception from syntax} +\item {Implementation does NOT have to look like the + spec} +\end{itemize} + +\item Midterm exam +\begin{itemize} +\item March 1, 7:00 pm, TSH/120 +\item 90 minute duration +\item Multiple choice - 30--40 questions? +\item Open book (any paper) +\end{itemize} + +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Index Set} + +Write a function \texttt{indexSet(x, B)} that takes a value \texttt{x} and a +list of values \texttt{B} and returns a list of indices where \texttt{B[i] = + x}.\\ +~\newline +As a first step, how would you say this mathematically? + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Index Set} + +Write a function \texttt{indexSet(x, B)} that takes a value \texttt{x} and a +list of values \texttt{B} and returns a list of indices where \texttt{B[i] = + x}.\\ + +$$\mbox{indexSet}(x, B) \equiv \{i : \mathbb{N} | i \in [0 .. |B|-1] \wedge B_i = +x : i\}$$ + +How could you use \texttt{indexSet} to calculate \texttt{rank(x, A)}? + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Anticipated Changes} + +\bi +\item The specific hardware on which the software is to run +\item The format of the initial input data +\item The format of the input parameters +\item The constraints on the input parameters +\item The format of the output data +\item The constraints on the output results +\item How the governing ODEs are defined using the input parameters +\item How the energy equations are defined using the input parameters +\item How the overall control of the calculations is orchestrated +\item The implementation of the sequence data structure +\item The algorithm used for the ODE solver +\item The implementation of plotting data +\ei + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Module Hierarchy by Secrets} +\begin{table}[h!] +\centering +\begin{tabular}{p{0.3\textwidth} p{0.6\textwidth}} +\toprule +\textbf{Level 1} & \textbf{Level 2}\\ +\midrule + +{Hardware-Hiding Module} & ~ \\ +\midrule + +\multirow{6}{0.3\textwidth}{Behaviour-Hiding Module} & Input Format Module\\ +& Input Parameters Module\\ +& Output Format Module\\ +& Temperature ODEs Module\\ +& Energy Equations Module\\ +& Control Module\\ +\midrule + +\multirow{3}{0.3\textwidth}{Software Decision Module} & {Sequence Data Structure Module}\\ +& ODE Solver Module\\ +& Plotting Module\\ +\bottomrule + +\end{tabular} +\caption{Module Hierarchy} +\label{TblMH} +\end{table} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Example Modules from SWHS} + +\textbf{Hardware Hiding Modules} + +\begin{description} +\item[Secrets:]The data structure and algorithm used to implement the virtual + hardware. +\item[Services:]Serves as a virtual hardware used by the rest of the + system. This module provides the interface between the hardware and the + software. So, the system can use it to display outputs or to accept inputs. +\item[Implemented By:] OS +\end{description} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Example Modules from SWHS} + +\textbf{Input Verification Module} + +\begin{description} +\item[Secrets:] The rules for the physical and software constraints. +\item[Services:] Verifies that the input parameters comply with physical and + software constraints. Throws an error if a parameter violates a physical + constraint. Throws a warning if a parameter violates a software constraint. +\item[Implemented By:] SWHS +\end{description} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Example Modules from SWHS} + +\textbf{ODE Solver Module} + +\begin{description} +\item[Secrets:] The algorithm to solve a system of first order ODEs. +\item[Services:] Provides solvers that take the governing equation, initial + conditions, and numerical parameters, and solve them. +\item[Implemented By:] Matlab +\end{description} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}[plain, fragile] + +\frametitle{SWHS Uses Hierarchy} + +\begin{center} +\includegraphics[scale=0.55]{UsesHierarchy.pdf} +\end{center} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Modules with External Interaction} + +\begin{itemize} +\item In general, some modules may interact with the environment or other modules +%\item The Display Point Masses Applet module does this +\item Environment might include the keyboard, the screen, the file system, motors, sensors, etc. +\item Sometimes the interaction is informally specified using prose (natural language) +\item Can introduce an environment variable +\begin{itemize} +\item Name, type +\item Interpretation +\end{itemize} +\item Environment variables include the screen, the state of a motor (on, direction of rotation, power level, etc.), +the position of a robot + +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{External Interaction Continued} + +\begin{itemize} +\item Some external interactions are hidden +\begin{itemize} +\item Present in the implementation, but not in the MIS +\item An example might be OS memory allocation calls +\end{itemize} +\item External interaction described in the MIS +\begin{itemize} +\item Naming access programs of the other modules +\item Specifying how the other module's state variables are changed +\item The MIS should identify what external modules are used +\end{itemize} +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{MIS for GUI Modules} + +\begin{itemize} +\item Could introduce an environment variable +\item window: sequence [RES\_H][RES\_V] of pixelT +\begin{itemize} +\item Where window[r][c] is the pixel located at row r and column c, with numbering zero-relative and beginning at the +upper left corner +\item Would still need to define pixelT +\end{itemize} +\item Could formally specify the environment variable transitions +\item More often it is reasonable to specify the transition in prose +\item In some cases the proposed GUI might be shown by rough sketches +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Display Point Masses Module Syntax} + +\textbf{Exported Access Programs}\\ +~\newline +\begin{tabular}{| l | l | l | l |} +\hline +\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exc.}\\ +\hline +DisplayPointMassesApplet & ~ & DisplayPointMassesApplet & ~\\ +\hline +paint & ~ & ~ & ~\\ +\hline +\end{tabular} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Display Point Masses Module Semantics} + +\textbf{Environment Variables}\\ +$\mathit{win}:$ 2D sequence of pixels displayed within a web-browser \\ + +\noindent DisplayPointMassesApplet(): +\begin{itemize} +\item transition: The state of the abstract object ListPointMasses is modified as follows:\\ +ListPointMasses.init()\\ +ListPointMasses.add(0, PointMassT(20, 20, 10)\\ +ListPointMasses.add(1, PointMassT(120, 200, 20)\\ +... +\end{itemize} + +\noindent paint(): +\begin{itemize} +\item transition $win := $ Modify window so that the point masses in ListPointMasses +are plotted as circles. The centre of each circles should be the corresponding x and y coordinates and the radius should +be the mass of the point mass. +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Assignment 3 Vector Module} + +\textbf {Exported Access Programs}\\ +~\newline +\begin{tabular}{| l | l | l | p{0.75in} |} +\hline +\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\ +\hline +new vectorT & real $\rightarrow$ real & vectorT & ~\\ +\hline +getf & ~ & real $\rightarrow$ real & ~\\ +\hline +eval & real, real, integer & sequence of real & deltaNeg, nstepsNeg\\ +\hline +evalPrint & real, real, integer & ~ & deltaNeg, nstepsNeg\\ +\hline +\end{tabular} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Vector Module Semantics} + +\textbf{Environment Variables}\\ +$\mathit{screen}$ : two dimensional sequence of positions on the screen, which each position holding a character\\ +~\newline +\textbf{State Variables}\\ +$f$: real $\rightarrow$ real\\ +~\newline +\textbf{Access Routine Semantics}\\ +\noindent eval ($\mathit{startx}, \mathit{deltax}, \mathit{nsteps}$): +\begin{itemize} +\item output: $out := < f(\mathit{startx}), f(\mathit{startx} + \mathit{deltax}), f(\mathit{startx} + 2 \cdot \mathit{deltax}), ... +, f(\mathit{startx} + \mathit{nsteps} \cdot \mathit{deltax})>$ +\item exception: $exc := ((\mathit{deltax} < 0) \Rightarrow \mbox{deltaNeg} | (\mathit{nsteps} < 0) \Rightarrow +\mbox{nstepsNeg})$ +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Vector Module Semantics Continued} + +\noindent evalPrint ($\mathit{startx}, \mathit{deltax}, \mathit{nsteps}$): +\begin{itemize} +\item transition: The state of $\mathit{screen}$ is modified so that the sequence returned by eval ($\mathit{startx}$, +$\mathit{deltax}$, $\mathit{nsteps}$) is displayed. +\item exception: $exc := ((\mathit{deltax} < 0) \Rightarrow \mbox{deltaNeg} | (\mathit{nsteps} < 0) \Rightarrow +\mbox{nstepsNeg})$ +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Dr.\ v.\ Mohrenschildt's Maze Tracing Robot Example} + +\begin{figure} +\includegraphics[scale=0.42]{ExampleMaze.pdf} +\end{figure} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Maze Tracing Robot Expected Changes} + +\begin{itemize} +\item Changes to the geometry of the robot such that the mapping from a position to the robot inputs is different +\item Changes to the interface to the robot +\item Changes to the format of the maze +\item Changes to any constant values +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Maze Tracing Robot Uses Hierarchy} + +\begin{figure}[H] +\includegraphics[scale=0.42]{UsesHierarchyBetter.pdf} +\end{figure} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Maze Tracing Robot MG} +\begin{itemize} +\item \structure<1>{Module name:} maze\_storage +\begin{itemize} +\item \structure<1>{Secret:} how the maze is stored +\item \structure<1>{Service:} stores the maze +\item \structure<1>{Module prefix:} ms\_ +\end{itemize} +\item \structure<1>{Module name:} load\_maze +\begin{itemize} +\item \structure<1>{Secret:} where and how the maze file is read in +\item \structure<1>{Service:} loads the maze +\item \structure<1>{Module prefix:} lm\_ +\end{itemize} +\item \structure<1>{Module name:} find\_path +\begin{itemize} +\item \structure<1>{Secret:} the algorithm for finding the shortest path +\item \structure<1>{Service:} finds the shortest path through the maze +\item \structure<1>{Module prefix:} fp\_ +\end{itemize} +\end{itemize} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Maze Tracing Robot MG Continued} +\begin{itemize} +\item \structure<1>{Module name:} control +\begin{itemize} +\item \structure<1>{Secret:} how the arm moves from position to position and how the buttons are checked +\item \structure<1>{Service:} controls the movement of the arm +\item \structure<1>{Module prefix:} cn\_ +\end{itemize} +\item \structure<1>{Module name:} geometry +\begin{itemize} +\item \structure<1>{Secret:} how the calculations from cell coords to robot coords are performed +\item \structure<1>{Service:} handles geometric positioning of the arm +\item \structure<1>{Module prefix:} gm\_ +\end{itemize} +\item \structure<1>{Module name:} hardware +\begin{itemize} +\item \structure<1>{Secret:} how it interfaces with the robot +\item \structure<1>{Service:} handles hardware aspects of arm (movement and button checking) +\item \structure<1>{Module prefix:} hw\_ +\end{itemize} +\end{itemize} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Maze Tracing Robot MG Continued} +\begin{itemize} +\item \structure<1>{Module name:} types\_constants +\begin{itemize} +\item \structure<1>{Secret:} how the data structures are defined and constants defined +\item \structure<1>{Service:} provides standard variable types and constants to modules +\end{itemize} +\end{itemize} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{maze\_storage MIS} + +\textbf{Module}\\ +~\newline +maze\_storage\\ +~\newline + +\textbf{Uses}\\ +~\newline +types\_constants\\ +~\newline + +\textbf{Exported Access Programs}\\ +~\newline +\begin{tabular}{| l | l | l | l |} +\hline +\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\ +\hline +... & ... & ... & ...\\ +\hline +%any thoughts from the class on the design of the interface? +\end{tabular} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{maze\_storage Exported Access Programs} + +\begin{tabular}{| l | l | l | p{3.5cm} |} +\hline +\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\ +\hline +ms\_init & ~ & ~ & ~\\ +\hline +ms\_set\_maze\_start & cell & ~ & ms\_not\_initialized, ms\_cell\_out\_of\_range\\ +\hline +ms\_set\_maze\_end & cell & ~ & ms\_not\_initialized, ms\_cell\_out\_of\_range\\ +\hline +ms\_get\_maze\_start & ~ & cell & ms\_not\_initialized\\ +\hline +ms\_get\_maze\_end & ~ & cell & ms\_not\_initialized\\ +\hline +ms\_set\_wall & cell, cell & ~ & ms\_not\_initialized, ms\_not\_valid\_wall\\ +\hline +ms\_is\_connected & cell, cell & boolean & ms\_not\_initialized, ms\_cell\_out\_of\_range\\ +\hline +\end{tabular}\\ +~\newline +cell = tuple of (x: integer, y: integer) +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{maze\_storage Semantics} + +\textbf{State Variables}\\ +~\newline +\uncover<2->{\structure<2>{$\mathit{maze}$: set of tuple of ( cell, cell )}}\\ +\uncover<2->{\structure<2>{$\mathit{start}: \mbox{cell} $}}\\ +\uncover<2->{\structure<2>{$\mathit{end}: \mbox{cell} $}}\\ +\uncover<2->{\structure<2>{$\mathit{is\_init}: \mbox{boolean} := \mathit{false}$}}\\ + +~\newline +\textbf{State Invariant:} none\\ +% there could be one related to maximum size of the map +~\newline +\textbf{Assumptions}\\ +~\newline +ms\_get\_maze\_start and ms\_get\_maze\_end are not called until after the corresponding set routines have been called. + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Access Routine Semantics} + +\noindent ms\_init(): +\begin{itemize} +\item transition: \uncover<2->{\structure<2>{$\mathit{maze}, \mathit{is\_init} := \{ \}, \mathit{true}$}} +\item exception: \uncover<2->{\structure<2>{none}} +\end{itemize} + +\noindent ms\_set\_maze\_start(c): +\begin{itemize} +\item transition: \uncover<3->{\structure<3>{$start := c$}} +\item exception: \uncover<4->{\structure<4>{$exc := (\neg \mathit{is\_init} \Rightarrow \mbox{ms\_not\_initialized } | +\mbox{ } \neg \mbox{cell\_in\_range}(c) \Rightarrow \mbox{ms\_cell\_out\_of\_range})$}} +\end{itemize} + +\noindent ms\_set\_maze\_end(c): +\begin{itemize} +\item transition: \uncover<3->{\structure<3>{$end := c$}} +\item exception: \uncover<4->{\structure<4>{$exc := (\neg \mathit{is\_init} \Rightarrow \mbox{ms\_not\_initialized } | +\mbox{ } \neg \mbox{cell\_in\_range}(c) \Rightarrow \mbox{ms\_cell\_out\_of\_range})$}} +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Access Routine Semantics Continued} + +\noindent ms\_get\_maze\_start(): +\begin{itemize} +\item output: \uncover<2->{\structure<2>{$\mathit{out} := \mathit{start}$}} +\item exception: \uncover<3->{\structure<3>{$exc := (\neg \mathit{is\_init} \Rightarrow \mbox{ms\_not\_initialized})$}} +\end{itemize} + +\noindent ms\_get\_maze\_end(): +\begin{itemize} +\item output: \uncover<2->{\structure<2>{$\mathit{out} := \mathit{end}$}} +\item exception: \uncover<3->{\structure<3>{$exc := (\neg \mathit{is\_init} \Rightarrow \mbox{ms\_not\_initialized})$}} +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Access Routine Semantics Continued} + +\noindent ms\_set\_wall(c1, c2): +\begin{itemize} +\item transition: \uncover<2->{\structure<2>{$\mathit{maze} := \mathit{maze} \cup \{ < c1, c2 > \}$}} +\item exception: \uncover<3->{\structure<3>{$exc := (\neg \mathit{is\_init} \Rightarrow \mbox{ms\_not\_initialized } | +\mbox{ wall\_is\_point}(c1, c2) \vee \mbox{wall\_is\_diagonal}(c1, c2) \vee \mbox{wall\_is\_out\_of\_range}(c1, c2) +\Rightarrow \mbox{ms\_not\_valid\_wall})$}} +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Access Routine Semantics Continued} + +\noindent ms\_is\_connected(c1, c2): +\begin{itemize} +\item output: \uncover<2->{\structure<2>{$out := < c1, c2 > \in \mathit{maze}$}} +\item exception: \uncover<3->{\structure<3>{$exc := (\neg \mathit{is\_init} \Rightarrow \mbox{ms\_not\_initialized } | +\mbox{ } \neg \mbox{cell\_in\_range}(c1) \Rightarrow \mbox{ms\_cell\_out\_of\_range } | +\mbox{ } \neg \mbox{cell\_in\_range}(c2) \Rightarrow \mbox{ms\_cell\_out\_of\_range} )$}} +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Local Functions} + +\noindent cell\_in\_range : cell $\rightarrow$ boolean +\begin{itemize} +\item \uncover<2->{\structure<2>{cell\_in\_range (c) $\equiv (0 \leq c.x < \mbox{MAX\_NUM\_CELLS}) \wedge (0 \leq c.y < +\mbox{MAX\_NUM\_CELLS})$}} +\end{itemize} + +\noindent wall\_is\_point: cell $\times$ cell $\rightarrow$ boolean +\begin{itemize} +\item \uncover<3->{\structure<3>{wall\_is\_point (c1, c2) $\equiv c1 = c2$}} +\end{itemize} + +\noindent wall\_is\_diagonal: cell $\times$ cell $\rightarrow$ boolean +\begin{itemize} +\item \uncover<4->{\structure<4>{wall\_is\_diagonal (c1, c2) $\equiv \neg ( (c1.x = c2.x) \vee (c1.y = c2.y) )$}} +\end{itemize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Additional Specifications for Determining the Path} + +pathT = sequence of cell\\ +~\newline + +\noindent validPath : pathT $\rightarrow$ boolean +\begin{itemize} +\item \uncover<2->{\structure<2>{validPath (p) $\equiv (p[0] = \mbox{ms\_get\_maze\_start}() +\wedge p[|p| - 1] = \mbox{ms\_get\_maze\_end}() +\wedge \forall (i:\mathbb{N} | 0 \leq i \leq |p| - 2 : \mbox{ms\_is\_connected}(p[i], p[i+1]) )$}} +\end{itemize} +~\newline +\uncover<3->{\structure<3>{How would you specify the length of a wall?}}\\ +\uncover<4->{\structure<4>{lengthWall: tuple of cell $\rightarrow$ integer}}\\ +\uncover<4->{\structure<4>{$$\mbox{lengthWall}(<c1, c2>) \equiv (c1.x = c2.x \Rightarrow | c1.y - c2.y |$$}} +\uncover<4->{\structure<4>{$$ | c1.y = c2.y \Rightarrow | c1.x - c2.x |)$$}} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Shortest Path} + +How would you specify the length of a path?\\ +\uncover<2->{\structure<2>{lengthPath: pathT $\rightarrow$ integer}}\\ +\uncover<2->{\structure<2>{$$\mbox{lengthPath}(p) \equiv + (i: \mathbb{N} | 0 \leq i < (|p| -1 ) : \mbox{lengthWall}(<p_i, p_{i+1} >))+1$$}} +% the plus 1 is added because the length does not include the last point +\noindent How would you specify whether a path is the shortest path?\\ +\uncover<3->{\structure<3>{isShortest: pathT $\rightarrow$ boolean}}\\ +\uncover<3->{\structure<3>{$$\mbox{isShortest}(p) = \forall ( q : \mbox{pathT} $$}} +\uncover<3->{\structure<3>{$$|\mbox{validPath}(q) : \mbox{validPath}(p) \wedge \mbox{lengthPath}(p) \leq \mbox{lengthPath}(q))$$}} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\end{document} + diff --git 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