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winitzki committed Aug 16, 2024
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4 changes: 2 additions & 2 deletions sofp-src/tex/sofp-typeclasses.tex
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Expand Up @@ -1095,8 +1095,8 @@ \subsubsection{Example \label{subsec:tc-Example-Monoids}\ref{subsec:tc-Example-M

A semigroup with a designated \textsf{``}empty\textsf{''} value is called a \textbf{monoid}\index{monoid|textit}.
Formally, a type $T$ is a monoid when there is an associative binary
operation $\oplus_{T}$ and a chosen \textsf{``}empty\textsf{''} value ($e^{:T}$)
such that:
operation $\oplus_{T}$ and a chosen \textsf{``}empty\textsf{''} value ($e$ of type
$T$, also denoted by $e_{T}$) such that:
\begin{equation}
\text{for all }x^{:T}:\quad e\oplus_{T}x=x\quad,\quad\quad x\oplus_{T}e=x\quad.\label{eq:identity-laws-of-monoid}
\end{equation}
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6 changes: 3 additions & 3 deletions sofp-src/tex/sofp.tex
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{\footnotesize{}ISBN (e-book): 978-0-359-76877-6}\\
{\footnotesize{}ISBN: 978-0-359-76877-6}\\
\\
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{\scriptsize{}PDF file built on Thu, 15 Aug 2024 22:37:31 +0200 by pdfTeX 3.141592653-2.6-1.40.22 (TeX Live 2021) on Darwin}\\
{\scriptsize{}Source hash (sha256): 6d2c32ff2563fe31726d89631c315c93e6767fbcdcf275c18dfd4133aba3970e}\\
{\scriptsize{}Git commit: 6d0c698eea409a8a361e2274db6802396e7fa5fc}\\
{\scriptsize{}PDF file built on Thu, 15 Aug 2024 23:02:20 +0200 by pdfTeX 3.141592653-2.6-1.40.22 (TeX Live 2021) on Darwin}\\
~\\
{\scriptsize{}Permission is granted to copy, distribute and/or modify
this document under the terms of the GNU Free Documentation License,
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