Finish the basics of logic

Makefile

@@ -1,11 +1,15 @@
-1:
-	latexmk -f -xelatex -interaction=nonstopmode -output-directory=$(PWD)/build/ ep1.tex
-	pdftoppm -png -f 1 -l 1 -singlefile -r 1200 -scale-to-x 1920 -scale-to-y 1080 $(PWD)/build/ep1.pdf $(PWD)/build/ep1
-.PHONY: build
-build: cv.pdf
+%:
+	latexmk -f -xelatex -interaction=nonstopmode -output-directory=$(PWD)/build/ ep$@.tex
+	pdftoppm -png -f 1 -l 1 -singlefile -r 1200 -scale-to-x 1920 -scale-to-y 1080 $(PWD)/build/ep$@.pdf $(PWD)/build/ep$@
+
+deps:
+	@echo "Source San Pro font family must be installed"
+	tlmgr update --list
+	tlmgr install fontspec
+	tlmgr install sourcesanspro
+	tlmgr install fontawesome5
 
 .PHONY: clean
 clean:
 	rm -rf build
 	rm -f *~
-all: build

ep1.tex

@@ -28,7 +28,7 @@
 \maketitle
 \begin{frame}{So far\ldots}{}
   \begin{itemize}
-  \item In the first season we created a super simple compiler
+  \item In the first season, we created a super simple compiler
   \item We learned about the basics of LLVM and MLIR
   \item We created a basic platform to develop a programming language, that includes:
     \begin{itemize}
@@ -38,7 +38,7 @@
     \item and few other bits and pieces
     \end{itemize}
   \item BUT we didn't come up with a specification for \href{https://serene-lang.org}{Serene}
-  \item We didn't design the language yet
+  \item We didn't design the language, yet
   \item That's what we're going to do in this series
   \end{itemize}
 \end{frame}
@@ -47,7 +47,7 @@
   \begin{itemize}
   \item Not all the programming langs have specification
   \item A spec or standard brings clarity for users and developers
-  \item We could've just implement an already exist spec like \href{http://www.r6rs.org/}{R6RS} (Scheme)
+  \item We could've just implemented an already exist spec like \href{http://www.r6rs.org/}{R6RS} (Scheme)
   \item Or just create a language based on our intuition (many languages have done this)
   \item Or design a standard from scratch \\
     We can use about 100 years of Mathematics and Computer Science to our benefit
@@ -56,9 +56,9 @@
 
 \begin{frame}{Where to look?}
   \begin{itemize}
-  \item Based on the past experience we have some initial idea on where to look
-  \item Later on we will find out whether or not our initial ideas were good
-  \item For example
+  \item Based on the experience, we have some initial idea on where to look
+  \item Later on, we will find out whether our initial ideas were good
+  \item For example,
     \begin{itemize}
     \item I prefer functional programming
     \item Dynamic type systems
@@ -77,14 +77,14 @@
     \item Proof theory
     \end{itemize}
   \item They all describe the same world from different perspectives
-  \item Also, there are few papers that we need to look at, like the lisp paper
+  \item Furthermore, there are few papers that we need to look at, like the lisp paper
   \end{itemize}
 \end{frame}
 
 \begin{frame}{Required tools}
   \begin{itemize}
-  \item We need build up few mathematical skills
-  \item E.g We need to learn:
+  \item We need to build up few mathematical skills
+  \item E.g. We have to learn:
     \begin{itemize}
     \item Logic
     \item Set theory
@@ -95,32 +95,32 @@
 
 \begin{frame}{The Plan}{}
   \begin{itemize}
-  \item I like this series to be self contained as much as possible
+  \item I like this series to be self-contained as much as possible
   \item We're going to start from basics
   \item We will cover
     \begin{itemize}
-    \item What is mathematics? and why do we need it?
+    \item What is mathematics? And why do we need it?
     \item Mathematical thinking
     \item Discrete mathematics
     \item $\lambda$-calculus
     \item Type theory
     \item and the rest
     \end{itemize}
-  \item We will study the history of computer science an mathematics as well
+  \item We will study the history of computer science and mathematics as well.
   \item History is a great guide
   \end{itemize}
 \end{frame}
 
 \begin{frame}{Disclaimer}{}
   \begin{itemize}
-  \item I'm not a professional mathematician
-  \item I'm just sharing the result of my research and things that I learn. Take it with a grain of salt
+  \item I'm not a professional mathematician.
+  \item I'm just sharing the result of my research and things that I learn. Take it with a grain of salt.
   \item ``Nullius in verba''
   \end{itemize}
 \end{frame}
 
 \begin{frame}{Contact}{}
-  Please shared your thoughts and ideas or researches and papers that you want me to have a look at via:
+  Please, share your thoughts and ideas or researches and papers that you want me to have a look at via:
   \begin{itemize}
   \item Comment section on \href{https://youtube.com/c/lxsameer}{youtube}
   \item \href{https://lxsameer.com}{https://lxsameer.com}

ep2.tex

@@ -0,0 +1,128 @@
+%!TEX TS-program = xelatex
+%!TEX encoding = UTF-8 Unicode
+% Lxsameer's CV Latex class
+% Copyright (C) 2022 Sameer Rahmani <lxsameer@gnu.org>
+%
+% This program is free software; you can redistribute it and/or
+% modify it under the terms of the GNU General Public License
+% as published by the Free Software Foundation; either version 2
+% of the License, or (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program; if not, write to the Free Software
+% Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+
+\documentclass{lxpresent}
+
+\date{\today}
+\title{Mathematics of Programming Languages}
+\setep{02}{Basics of Logic}
+
+\begin{document}
+\maketitle
+
+\begin{frame}{Why logic?}{}
+  \begin{itemize}
+  \item Logic serves as the backbone of computer science
+  \item it provides the fundamental principles and tools necessary for understanding,
+    designing, and building complex systems
+  \item It forms the basis of logical reasoning, proofs, problem solving, and program correctness.
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{What is logic?}{}
+  \begin{itemize}
+  \item One of the key aspects of Mathematics is unambiguity
+  \item The study of the principles of reasoning
+  \item Logic is tool to remove ambiguity from our arguments and thoughts
+  \item Most of the definitions of formal logic have been developed so that they agree with the
+    natural or intuitive logic used by people.
+  \item The difference between formal logic and intuitive logic exists to avoid ambiguity and obtain consistency.
+  \item To put it simply logic is all about what counts as a good argument. A good argument is a valid argument. One that, preserves truth from premises to conclusion.
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Arguments}{Propositional logic}
+  \begin{itemize}
+  \item An argument is a sequence of statements aimed at demonstrating the truth of an assertion.
+  \item The assertion at the end of the sequence is called the \textbf{conclusion}.
+  \item The preceding statements are called \textbf{premises}.
+  \item As an example:\\
+    \begin{flalign*}
+      &\text{If} \overbrace{\text{Earth is a planet}}^{\textit{premise}} \text{then} \overbrace{\text{Earth is round}}^{\textit{conclusion}}\\
+      &\text{Earth is a planet}\\
+      \therefore \hspace{0.2em} &\text{Earth is round}.
+    \end{flalign*}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Arguments}{Symbolic logic}
+  \begin{itemize}
+  \item In logic, the form of an argument is distinguished from its content.
+  \item Logic, won't help you determine the intrinsic merit of an argument’s content.
+  \item It will help you analyze an argument’s form to determine whether the truth of the conclusion follows \textit{necessarily} from the truth of the premises.
+    \begin{flalign*}
+      &\text{If} \overbrace{\text{Earth is a planet}}^{\textit{p}} \text{then} \overbrace{\text{Earth is round}}^{\textit{q}}\\
+      &\overbrace{\text{Earth is a planet}}^{\textit{p}}\\
+      \therefore \hspace{0.2em} &\overbrace{\text{Earth is round}}^{\textit{q}}.
+    \end{flalign*}
+\item Convension: We will use letters \textit{p}, \textit{q}, and \textit{r} to represent
+component sentences.
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Proposition}{}
+  \begin{itemize}
+  \item In any mathematical theory, new terms are defined by using those that have been
+    previously defined. (E.g. A mathematical system)
+  \item This process has to start somewhere
+    \item In logic, the words \textbf{\textit{sentence}}, \textbf{\textit{true}}, \textbf{\textit{false}} are the initial
+      undefined terms
+  \item A \textbf{proposition} (or \textbf{statement}) is a sentence that is true or false but not both.
+  \item For example:
+    \begin{itemize}
+    \item ``Earth is a planet'' (true)
+    \item ``Earth is flat'' (false)
+    \item $x + 5 > 0$ (Depends on the value of $x$)
+    \item ``How are you?'' (not a proposition)
+
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Compound propositions}{}
+\begin{itemize}
+\item We can use \textbf{logical connectives} to connect propositions together to form compound propositions.
+\item For example:
+  \begin{itemize}
+  \item $\overbrace{\text{\say{Earth is a planet}}}^{\textit{p}}$ \textbf{or} $\overbrace{\text{\say{Sun is a planet}}}^{\textit{q}}$
+  \item $\overbrace{\text{\say{Alice is at work}}}^{\textit{p}}$ \textbf{and} $\overbrace{\text{\say{Bob is at work}}}^{\textit{q}}$
+  \item $\overbrace{\text{\say{Earth is \textbf{not} flat}}}^{\textit{p}}$
+  \end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}{More symbols}{}
+  Let's rewrite the propositions from before using symbolic variables:
+  \begin{itemize}
+  \item $\overbrace{\text{\say{Earth is a planet}}}^{\textit{p}}$ \textbf{or} $\overbrace{\text{\say{Sun is a planet}}}^{\textit{q}}$: ($p \lor q$)
+  \item $\overbrace{\text{\say{Alice is at work}}}^{\textit{p}}$ \textbf{and} $\overbrace{\text{\say{Bob is at work}}}^{\textit{q}}$: ($p \land q$)
+  \item $\overbrace{\text{\say{Earth is \textbf{not} flat}}}^{\textit{p}}$: ($\neg p$)
+  \end{itemize}
+
+\end{frame}
+\begin{frame}{Contact}{}
+  Please, share your thoughts and ideas or researches and papers that you want me to have a look at via:
+  \begin{itemize}
+  \item Comment section on \href{https://youtube.com/c/lxsameer}{youtube}
+  \item \href{https://lxsameer.com}{https://lxsameer.com}
+  \end{itemize}
+  \end{frame}
+\end{document}

ep3.tex

@@ -0,0 +1,10 @@
+\usepackage[sfdefault]{roboto}  %% Option 'sfdefault' only if the base font of the document is to be sans serif
+\usepackage[T1]{fontenc}
+\mdseries
+\documentclass{article}
+\begin{document}
+\begin{math}
+  \psi(x_b, t_b) = \int_{-\infty}^{+\infty} K(b, a)\psi(x_a, t_a)dx_a
+  \end{math}
+%% K(b, a) = (\frac{m}{ih(t_b - t_a)})^\frac{1}{2} exp \frac{im(x_b - x_a)^2}{2\hbar(t_b - t_a)}
+\end{document}

lxpresent.cls

@@ -30,6 +30,8 @@
 \RequirePackage[normalem]{ulem}
 \RequirePackage{amsmath}
 \RequirePackage{amssymb}
+\RequirePackage{mathtools}
+\RequirePackage{dirtytalk}
 \RequirePackage{capt-of}
 
 \newcommand*{\setep}[2]{\def\@ep{#1}\def\@eptitle{#2}}
@@ -44,7 +46,7 @@
 \setbeamercolor{palette secondary} {fg=spurple,bg=white}
 \setbeamercolor{structure}{fg=white,bg=spurple}
 \setbeamercolor{title in head/foot}{fg=white,bg=spurple}
-\setbeamercolor{date in head/foot}{fg=lightgray,bg=spurple}
+\setbeamercolor{date in head/foot}{fg=lightgray}
 \setbeamercolor{background canvas}{bg=spurple}
 \setbeamercolor{title}{fg=blue,bg=spurple}
 \setbeamercolor{normal text}{fg=white}
@@ -63,13 +65,10 @@
 % definition of the footline template
 \defbeamertemplate*{footline}{mytheme}{%
   \leavevmode%
-  \hbox{\begin{beamercolorbox}[wd=.3\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm]{title in head/foot}%
-    \makebox[2em][l]{{\usebeamerfont{title in head/foot}\textcolor{white}{\@ep}}}%
-    {\usebeamercolor{title in head/foot}{\@eptitle}}
-  \end{beamercolorbox}%
-  \begin{beamercolorbox}[wd=.3\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm,right]{title in head/foot}%
-  \end{beamercolorbox}}%
-  \vskip0pt%
+  \hspace{0.5em}
+  \hbox{
+    {\usebeamercolor{title in head/foot}{\@ep \- \@eptitle}}}
+  \vspace{0.5em}
 }
 
 % definition of the title page template
@@ -113,3 +112,7 @@
 \defbeamertemplate*{itemize item}{mysymbol}{\small\raise0.5pt\hbox{\mysymbol}}
 \defbeamertemplate*{itemize subitem}{mysymbol}{\footnotesize\raise0.5pt\hbox{\mysymbol}}
 \defbeamertemplate*{itemize subsubitem}{mysymbol}{\footnotesize\raise0.5pt\hbox{\mysymbol}}
+
+
+\newcommand{\pic}[2]{
+  \includegraphics[width=#2\textwidth]{#1}}