Commit 0876cbad authored by Ralf Jung's avatar Ralf Jung

docs: one-shot

parent 11069713
Pipeline #324 passed with stage
......@@ -32,6 +32,36 @@ There are no interesting frame-preserving updates for $\agm(\cofe)$, but we can
\axiomH{ag-agree}{\ag(x) \mtimes \ag(y) \in \mval_n \Ra x \nequiv{n} y}
\end{mathpar}
\subsection{One-shot}
The purpose of the one-shot CMRA is to lazily initialize the state of a ghost location.
Given some CMRA $\monoid$, we define $\oneshotm(\monoid)$ as follows:
\begin{align*}
\monoid \eqdef{}& \ospending + \osshot(\monoid) + \munit + \bot \\
\mval_n \eqdef{}& \set{\ospending, \munit} \cup \setComp{\osshot(\melt)}{\melt \in \mval_n}
\end{align*}
\begin{align*}
\mcore{\ospending} \eqdef{}& \munit & \mcore{\osshot(\melt)} \eqdef{}& \mcore\melt \\
\mcore{\munit} \eqdef{}& \munit & \mcore{\bot} \eqdef{}& \bot
\end{align*}
\begin{align*}
\osshot(\melt) \mtimes \osshot(\meltB) \eqdef{}& \osshot(\melt \mtimes \meltB) \\
\munit \mtimes \ospending \eqdef{}& \ospending \mtimes \munit \eqdef \ospending \\
\munit \mtimes \osshot(\melt) \eqdef{}& \osshot(\melt) \mtimes \munit \eqdef \osshot(\melt)
\end{align*}
The remaining cases of composition go to $\bot$.
The step-indexed equivalence is inductively defined as follows:
\begin{mathpar}
\axiom{\ospending \nequiv{n} \ospending}
\infer{\melt \nequiv{n} \meltB}{\osshot(\melt) \nequiv{n} \osshot(\meltB)}
\axiom{\munit \nequiv{n} \munit}
\axiom{\bot \nequiv{n} \bot}
\end{mathpar}
$\oneshotm(-)$ is a locally non-expansive bifunctor from $\CMRAs$ to $\CMRAs$.
% \subsection{Exclusive monoid}
......
......@@ -335,7 +335,12 @@
\newcommand{\AuthInv}{\textsf{AuthInv}}
\newcommand{\Auth}{\textsf{Auth}}
%% STSs
% One-Shot
\newcommand{\oneshotm}{\ensuremath{\textmon{OneShot}}}
\newcommand{\ospending}{\textlog{pending}}
\newcommand{\osshot}{\textlog{shot}}
% STSs
\newcommand{\STSCtx}{\textlog{StsCtx}}
\newcommand{\STSSt}{\textlog{StsSt}}
\newcommand{\STSS}{\mathcal{S}} % states
......
Markdown is supported
0%
or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment