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snowleopard committed Jul 1, 2019
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18 changes: 9 additions & 9 deletions paper/2-selective.tex
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Expand Up @@ -183,15 +183,15 @@ \section{Selective functors}\label{sec-selective}
\vspace{1mm}
\noindent
Here we tag a given function \hs{a}~\hs{->}~\hs{b} with \hs{Left} and turn a
value of type \hs{a} into the reverse function application
\hs{\}\hs{f}~\hs{->}~\hs{f}~\hs{a} that yields \hs{b} when given
\hs{a}~\hs{->}~\hs{b}, as desired. Since the \hs{Right} case is impossible, the
effect \hs{f}~\hs{a} is executed unconditionally. Note however, that the
equality \hs{(<*>)}~\hs{=}~\hs{apS} does not always hold. Selective functors
that satisfy the law \hs{(<*>)}~\hs{=}~\hs{apS} will be called \emph{rigid};
they will turn out to have a very simple normal form, which we will exploit in
the free construction in~\S\ref{sec-free}.
Here we tag the given function \hs{f}~\hs{::}~\hs{a}~\hs{->}~\hs{b} with
\hs{Left} and apply the reverse function application~(see Fig.~\ref{fig-std}) to
the value \hs{x}~\hs{::}~\hs{a}, thus matching the type signature
of \hs{select}. Since the \hs{Right} case is impossible, the effect
\hs{f}~\hs{a} is executed unconditionally. Note however, that the equality
\hs{(<*>)}~\hs{=}~\hs{apS} does not always hold. Selective functors that satisfy
the law \hs{(<*>)}~\hs{=}~\hs{apS} will be called \emph{rigid}; they will turn
out to have a simple normal form, which we will exploit in the free construction
in~\S\ref{sec-free}.
It is worth emphasising that the subclass relationships
\hs{Applicative}~\hs{f}~\hs{=>}~\hs{Selective}~\hs{f} and
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1 change: 1 addition & 0 deletions paper/main.tex
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Expand Up @@ -3,6 +3,7 @@
%%% The following is specific to ICFP '19 and the paper
%%% 'Selective Applicative Functors'
%%% by Andrey Mokhov, Georgy Lukyanov, Simon Marlow, and Jeremie Dimino.
%%%
\setcopyright{rightsretained}
\acmPrice{}
\acmDOI{10.1145/3341694}
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