diff --git a/docs/derived.tex b/docs/derived.tex index 738a87bef2ca24dc77447175b5bdde8753ccc517..16c615a74f9fb7eeb2952e7623d1415971765b34 100644 --- a/docs/derived.tex +++ b/docs/derived.tex @@ -239,7 +239,21 @@ We can derive some specialized forms of the lifting axioms for the operational s % \end{mathpar} \subsection{Invariant identifier namespaces} -\ralf{Describe this.} + +Let $\namesp \ni \textlog{InvNamesp} \eqdef \textlog{list}(\textlog{InvName})$ be the type of \emph{namespaces} for invariant names. +Notice that there is an injection $\textlog{namesp\_inj}: \textlog{InvNamesp} \ra \textlog{InvName}$. +Whenever needed (in particular, for masks at view shifts and Hoare triples), we coerce $\namesp$ to its suffix-closure: $\namecl\namesp \eqdef \setComp{\iname}{\Exists \namesp'. \iname = \textlog{namesp\_inj}(\namesp' \dplus \namesp)}$ +We use the notation $\namesp.\iname$ for the namespace $[\iname] \dplus \namesp$. +We will overload the usual Iris notation for invariant assertions in the following: +$\knowInv\namesp\prop \eqdef \Exists \iname \in \namecl\namesp. \knowInv\iname{\prop}$ + +We define the inclusion relation on namespaces as $\namesp_1 \sqsubseteq \namesp_2 \Lra \Exists \namesp_3. \namesp_2 = \namesp_3 \dplus \namesp_1$, \ie $\namesp_1$ is a suffix of $\namesp_2$. +We have that $\namesp_1 \sqsubseteq \namesp_2 \Ra \namecl\namesp_2 \subseteq \namecl\namesp_1$. + +Similarly, we define $\namesp_1 \sep \namesp_2 \eqdef \Exists \namesp_1', \namesp_2'. \namesp_1' \sqsubseteq \namesp_1 \land \namesp_2' \sqsubseteq \namesp_2 \land |\namesp_1'| = |\namesp_2'| \land \namesp_1' \neq \namesp_2'$, \ie there exists a distinguishing suffix. +We have that $\namesp_1 \sep \namesp_2 \Ra \namecl\namesp_2 \sep \namecl\namesp_1$, and furthermore $\iname_1 \neq \iname_2 \Ra \namesp.\iname_1 \sep \namesp.\iname_2$. + +\ralf{Give derived rules for invariants.} % \subsection{STSs with interpretation}\label{sec:stsinterp} diff --git a/docs/iris.sty b/docs/iris.sty index 7692ff23597e2893b91238c3a10e5b3be4456db2..447207c1a5ebbe0836992d3fdb6527472e1e1bbe 100644 --- a/docs/iris.sty +++ b/docs/iris.sty @@ -184,6 +184,7 @@ \newcommand{\mask}{\mathcal{E}} \newcommand{\namesp}{\mathcal{N}} +\newcommand{\namecl}[1]{{\uparrow#1}} %% various pieces of Syntax \def\MU #1.{\mu #1.\spac}%