Changeset 956299b for doc/theses/jiada_liang_MMath/intro.tex

Timestamp:

Feb 8, 2024, 10:48:41 AM (7 months ago)

Author:

Peter A. Buhr <pabuhr@…>

Branches:

master

Children:

14755e5, 714e206

Parents:

211def2

Message:

copy enum proposal to enum thesis

File:

• doc/theses/jiada_liang_MMath/intro.tex (modified) (1 diff)

doc/theses/jiada_liang_MMath/intro.tex

@@ -1 +1 @@
 \chapter{Introduction}
 
-Testing glossy abbreviations \gls{foo} and \gls{bar}, and glossy definitions \gls{git} and \gls{gulp}.
+Naming values is a common practice in mathematics and engineering, e.g., $\pi$, $\tau$ (2$\pi$), $\phi$ (golden ratio), MHz (1E6), etc.
+Naming is also commonly used to represent many other numerical phenomenon, such as days of the week, months of a year, floors of a building (basement), specific times (noon, New Years).
+Many programming languages capture this important software-engineering capability through a mechanism called an \Newterm{enumeration}.
+An enumeration is similar to other programming-language types by providing a set of constrained values, but adds the ability to name \emph{all} the values in its set.
+Note, all enumeration names must be unique but different names can represent the same value (eight note, quaver), which are synonyms.
 
-And use the glossy abbreviations \gls{foo} and \gls{bar}, and definitions \gls{git} and \gls{gulp} again.
+Specifically, an enumerated type restricts its values to a fixed set of named constants.
+While all types are restricted to a fixed set of values because of the underlying von Neumann architecture, and hence, to a corresponding set of constants, e.g., @3@, @3.5@, @3.5+2.1i@, @'c'@, @"abc"@, etc., these values are not named, other than the programming-language supplied constant names.
+
+Fundamentally, all enumeration systems have an \Newterm{enumeration} type with an associated set of \Newterm{enumerator} names.
+An enumeration has three universal attributes, \Newterm{position}, \Newterm{label}, and \Newterm{value}, as shown by this representative enumeration, where position and value can be different.
+\begin{cquote}
+\small\sf\setlength{\tabcolsep}{3pt}
+\begin{tabular}{rccccccccccc}
+\it\color{red}enumeration & \multicolumn{7}{c}{\it\color{red}enumerators}       \\
+$\downarrow$\hspace*{25pt} & \multicolumn{7}{c}{$\downarrow$}                           \\
+@enum@ Weekday \{                               & Monday,       & Tuesday,      & Wednesday,    & Thursday,& Friday,    & Saturday,     & Sunday \}; \\
+\it\color{red}position                  & 0                     & 1                     & 2                             & 3                             & 4                     & 5                     & 6                     \\
+\it\color{red}label                             & Monday        & Tuesday       & Wednesday             & Thursday              & Friday        & Saturday      & Sunday        \\
+\it\color{red}value                             & 0                     & 1                     & 2                             & 3                             & 4                     & 5             & 6
+\end{tabular}
+\end{cquote}
+Here, the \Newterm{enumeration} @Weekday@ defines the ordered \Newterm{enumerator}s @Monday@, @Tuesday@, @Wednesday@, @Thursday@, @Friday@, @Saturday@ and @Sunday@.
+By convention, the successor of @Tuesday@ is @Monday@ and the predecessor of @Tuesday@ is @Wednesday@, independent of the associated enumerator constant values.
+Because an enumerator is a constant, it cannot appear in a mutable context, e.g. @Mon = Sun@ is meaningless, and an enumerator has no address, it is an \Newterm{rvalue}\footnote{
+The term rvalue defines an expression that can only appear on the right-hand side of an assignment.}.