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

docs/algebra.tex

@@ -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}
 

docs/constructions.tex

@@ -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}.

docs/derived.tex

@@ -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}.

docs/iris.sty

@@ -221,7 +221,7 @@
 \newcommand*{\knowInv}[2]{\boxedassert{#2}[#1]}
 \newcommand*{\ownGhost}[2]{\boxedassert[densely dashed]{#2}[#1]}
 \newcommand*{\ownGGhost}[1]{\boxedassert[densely dashed]{#1}}
-
+\newcommand{\ownM}[1]{\textlog{Own}(#1)}
 \newcommand{\ownPhys}[1]{\textlog{Phy}(#1)}
 
 %% View Shifts

docs/iris.tex

@@ -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