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Mark 2023-02-05 21:02:05 -08:00
parent e3e09c9c95
commit 494e91dc98
7 changed files with 574 additions and 612 deletions
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15
Advanced/Lambda Calculus/main.tex
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@ -1,13 +1,12 @@
% use [nosolutions] flag to hide solutions. % use [nosolutions] flag to hide solutions.
% use [solutions] flag to show solutions. % use [solutions] flag to show solutions.
\documentclass[ \documentclass[
solutions, nosolutions,
singlenumbering singlenumbering
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage{url} \usepackage{url}
\usepackage{mathtools} % for \coloneqq \usepackage{mathtools} % for \coloneqq
\usepackage{subfiles}
% An invisible marker, used to % An invisible marker, used to
% draw arrows in equations. % draw arrows in equations.
@ -51,11 +50,11 @@
\hfill \hfill
\subfile{parts/00 intro} \input{parts/00 intro}
\subfile{parts/01 combinators} \input{parts/01 combinators}
\subfile{parts/02 boolean} \input{parts/02 boolean}
\subfile{parts/03 numbers} \input{parts/03 numbers}
\subfile{parts/04 recursion} \input{parts/04 recursion}
\subfile{parts/05 challenges} \input{parts/05 challenges}
\end{document} \end{document}

7
Advanced/Lambda Calculus/parts/00 intro.tex
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@ -1,8 +1,3 @@
\documentclass[../main.tex]{subfiles}
\begin{document}
\section{Definitions} \section{Definitions}
\generic{$\lm$ Notation:} \generic{$\lm$ Notation:}
@ -250,5 +245,3 @@
\vfill \vfill
\pagebreak \pagebreak
\end{document}

8
Advanced/Lambda Calculus/parts/01 combinators.tex
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@ -1,8 +1,3 @@
\documentclass[../main.tex]{subfiles}
\begin{document}
\section{Combinators} \section{Combinators}
\definition{} \definition{}
@ -42,6 +37,3 @@
\vfill \vfill
\pagebreak \pagebreak
\end{document}

9
Advanced/Lambda Calculus/parts/02 boolean.tex
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@ -1,8 +1,3 @@
\documentclass[../main.tex]{subfiles}
\begin{document}
\section{Boolean Algebra} \section{Boolean Algebra}
The Kestrel selects its first argument, and the Kite selects its second. This \say{choosing} behavior is awfully similar to something you may have already seen... The Kestrel selects its first argument, and the Kite selects its second. This \say{choosing} behavior is awfully similar to something you may have already seen...
@ -53,6 +48,8 @@
It may be worth mentioning that OR $= \lm ab.(M~a~b)$ is also a solution. It may be worth mentioning that OR $= \lm ab.(M~a~b)$ is also a solution.
\end{solution} \end{solution}
\vfill
\problem{} \problem{}
To complete our boolean algebra, write the boolean equality check EQ. \\ To complete our boolean algebra, write the boolean equality check EQ. \\
What inputs should it take? What outputs should it produce? What inputs should it take? What outputs should it produce?
@ -67,5 +64,3 @@
\vfill \vfill
\pagebreak \pagebreak
\end{document}

6
Advanced/Lambda Calculus/parts/03 numbers.tex
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@ -1,7 +1,3 @@
\documentclass[../main.tex]{subfiles}
\begin{document}
\section{Numbers} \section{Numbers}
Since the only objects we have in $\lm$-calculus are functions, it's natural to think of quantities as \textit{adverbs} (once, twice, thrice,...) rather than \textit{nouns} (one, two, three ...) \\ Since the only objects we have in $\lm$-calculus are functions, it's natural to think of quantities as \textit{adverbs} (once, twice, thrice,...) rather than \textit{nouns} (one, two, three ...) \\
@ -222,5 +218,3 @@
\vfill \vfill
\pagebreak \pagebreak
\end{document}

6
Advanced/Lambda Calculus/parts/04 recursion.tex
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@ -1,7 +1,3 @@
\documentclass[../main.tex]{subfiles}
\begin{document}
\section{Recursion} \section{Recursion}
Say we want a function that computes the factorial of a positive integer. Here's one way we could define it: Say we want a function that computes the factorial of a positive integer. Here's one way we could define it:
@ -63,5 +59,3 @@
\vfill \vfill
\pagebreak \pagebreak
\end{document}

5
Advanced/Lambda Calculus/parts/05 challenges.tex
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@ -1,7 +1,3 @@
\documentclass[../main.tex]{subfiles}
\begin{document}
\section{Challenges} \section{Challenges}
Do \ref{Yfac} first, then finish the rest in any order. \\ Do \ref{Yfac} first, then finish the rest in any order. \\
@ -84,4 +80,3 @@
\problem{Bonus} \problem{Bonus}
Play with \textit{Lamb}, an automatic lambda expression evaluator. \\ Play with \textit{Lamb}, an automatic lambda expression evaluator. \\
\url{https://git.betalupi.com/Mark/lamb} \url{https://git.betalupi.com/Mark/lamb}
\end{document}