### docs: describe the part of the model that works for any UPred

parent 7c354ddb
 ... ... @@ -2,6 +2,7 @@ \subsection{COFE} This definition varies slightly from the original one in~\cite{catlogic}. \begin{defn}[Chain] Given some set $\cofe$ and an indexed family $({\nequiv{n}} \subseteq \cofe \times \cofe)_{n \in \mathbb{N}}$ of equivalence relations, a \emph{chain} is a function $c : \mathbb{N} \to \cofe$ such that $\All n, m. n \leq m \Ra c (m) \nequiv{n} c (n)$. \end{defn} ... ... @@ -94,7 +95,8 @@ Note that the composition of non-expansive (bi)functors is non-expansive, and th \All n, \melt, \meltB_1, \meltB_2.& \omit\rlap{$\melt \in \mval_n \land \melt \nequiv{n} \meltB_1 \mtimes \meltB_2 \Ra {}$} \\ &\Exists \meltC_1, \meltC_2. \melt = \meltC_1 \mtimes \meltC_2 \land \meltC_1 \nequiv{n} \meltB_1 \land \meltC_2 \nequiv{n} \meltB_2 \tagH{cmra-extend} \\ \text{where}\qquad\qquad\\ \melt \mincl \meltB \eqdef{}& \Exists \meltC. \meltB = \melt \mtimes \meltC \tagH{cmra-incl} \melt \mincl \meltB \eqdef{}& \Exists \meltC. \meltB = \melt \mtimes \meltC \tagH{cmra-incl}\\ \melt \mincl[n] \meltB \eqdef{}& \Exists \meltC. \meltB \nequiv{n} \melt \mtimes \meltC \tagH{cmra-inclN} \end{align*} \end{defn} ... ...
 ... ... @@ -25,7 +25,7 @@ where $\mProp$ is the set of meta-level propositions, \eg Coq's \texttt{Prop}. $\UPred(-)$ is a locally non-expansive functor from $\CMRAs$ to $\COFEs$. One way to understand this definition is to re-write it a little. We start by defining the COFE of \emph{step-indexed propositions}: We start by defining the COFE of \emph{step-indexed propositions}: For every step-index, we proposition either holds or does not hold. \begin{align*} \SProp \eqdef{}& \psetdown{\mathbb{N}} \\ \eqdef{}& \setComp{\prop \in \pset{\mathbb{N}}}{ \All n, m. n \geq m \Ra n \in \prop \Ra m \in \prop } \\ ... ... @@ -149,6 +149,7 @@ We obtain the following frame-preserving updates: {\osshot(\melt) \mupd \setComp{\osshot(\meltB)}{\meltB \in \meltsB}} \end{mathpar} %TODO: These need syncing with Coq % \subsection{Exclusive monoid} % Given a set $X$, we define a monoid such that at most one $x \in X$ can be owned. ... ... @@ -373,8 +374,6 @@ We obtain the following frame-preserving updates: % \subsection{STS with tokens monoid} % \label{sec:stsmon} % \ralf{This needs syncing with the Coq development.} % Given a state-transition system~(STS) $(\STSS, \ra)$, a set of tokens $\STSS$, and a labeling $\STSL: \STSS \ra \mathcal{P}(\STST)$ of \emph{protocol-owned} tokens for each state, we construct a monoid modeling an authoritative current state and permitting transitions given a \emph{bound} on the current state and a set of \emph{locally-owned} tokens. % The construction follows the idea of STSs as described in CaReSL \cite{caresl}. ... ...
 ... ... @@ -337,6 +337,7 @@ We can now derive the following rules for this derived form of the invariant ass {\knowInv\namesp\prop \proves \propB \vs[\mask] \propC} \end{mathpar} % TODO: These need syncing with Coq % \subsection{STSs with interpretation}\label{sec:stsinterp} % Building on \Sref{sec:stsmon}, after constructing the monoid $\STSMon{\STSS}$ for a particular STS, we can use an invariant to tie an interpretation, $\pred : \STSS \to \Prop$, to the STS's current state, recovering CaReSL-style reasoning~\cite{caresl}. ... ...
 ... ... @@ -221,7 +221,7 @@ \newcommand*{\knowInv}{\boxedassert{#2}[#1]} \newcommand*{\ownGhost}{\boxedassert[densely dashed]{#2}[#1]} \newcommand*{\ownGGhost}{\boxedassert[densely dashed]{#1}} \newcommand{\ownM}{\textlog{Own}(#1)} \newcommand{\ownPhys}{\textlog{Phy}(#1)} %% View Shifts ... ...
 ... ... @@ -33,8 +33,8 @@ \endgroup\clearpage\begingroup \input{logic} \endgroup\clearpage\begingroup %\input{model} %\endgroup\clearpage\begingroup \input{model} \endgroup\clearpage\begingroup \input{derived} \endgroup\clearpage\begingroup \printbibliography ... ...
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