Commit 418eeacc by Aleš Bizjak

Fixed some typos in the appendix.

parent 97e8a9de
 ... @@ -46,14 +46,13 @@ We introduce an additional logical connective $\ownM\melt$, which will later be ... @@ -46,14 +46,13 @@ We introduce an additional logical connective $\ownM\melt$, which will later be For every definition, we have to show all the side-conditions: The maps have to be non-expansive and monotone. For every definition, we have to show all the side-conditions: The maps have to be non-expansive and monotone. \subsection{Iris model} \subsection{Iris model} \paragraph{Semantic domain of assertions.} \paragraph{Semantic domain of assertions.} The first complicated task in building a model of full Iris is defining the semantic model of $\Prop$. The first complicated task in building a model of full Iris is defining the semantic model of $\Prop$. We start by defining the functor that assembles the CMRAs we need to the global resource CMRA: We start by defining the functor that assembles the CMRAs we need to the global resource CMRA: \begin{align*} \begin{align*} \textdom{ResF}(\cofe^\op, \cofe) \eqdef{}& \record{\wld: \agm(\latert \cofe), \pres: \exm(\textdom{State}), \ghostRes: \iFunc(\cofe^\op, \cofe)} \textdom{ResF}(\cofe^\op, \cofe) \eqdef{}& \record{\wld: \mathbb{N} \fpfn \agm(\latert \cofe), \pres: \exm(\textdom{State}), \ghostRes: \iFunc(\cofe^\op, \cofe)} \end{align*} \end{align*} Remember that $\iFunc$ is the user-chosen bifunctor from $\COFEs$ to $\CMRAs$. Remember that $\iFunc$ is the user-chosen bifunctor from $\COFEs$ to $\CMRAs$. $\textdom{ResF}(\cofe^\op, \cofe)$ is a CMRA by lifting the individual CMRAs pointwise. $\textdom{ResF}(\cofe^\op, \cofe)$ is a CMRA by lifting the individual CMRAs pointwise. ... @@ -87,7 +86,7 @@ We only have to define the interpretation of the missing connectives, the most i ... @@ -87,7 +86,7 @@ We only have to define the interpretation of the missing connectives, the most i \wsatpre(n, \mask, \state, \rss, \rs) & \eqdef \begin{inbox}[t] \wsatpre(n, \mask, \state, \rss, \rs) & \eqdef \begin{inbox}[t] \rs \in \mval_{n+1} \land \rs.\pres = \exinj(\sigma) \land \rs \in \mval_{n+1} \land \rs.\pres = \exinj(\sigma) \land \dom(\rss) \subseteq \mask \cap \dom( \rs.\wld) \land {}\\ \dom(\rss) \subseteq \mask \cap \dom( \rs.\wld) \land {}\\ \All\iname \in \mask, \prop. (\rs.\wld)(\iname) \nequiv{n+1} \aginj(\latertinj(\wIso(\prop))) \Ra n \in \prop(\rss(\iname)) \All\iname \in \mask, \prop \in \iProp. (\rs.\wld)(\iname) \nequiv{n+1} \aginj(\latertinj(\wIso(\prop))) \Ra n \in \prop(\rss(\iname)) \end{inbox}\\ \end{inbox}\\ \wsat{\state}{\mask}{\rs} &\eqdef \set{0}\cup\setComp{n+1}{\Exists \rss : \mathbb{N} \fpfn \textdom{Res}. \wsatpre(n, \mask, \state, \rss, \rs \mtimes \prod_\iname \rss(\iname))} \wsat{\state}{\mask}{\rs} &\eqdef \set{0}\cup\setComp{n+1}{\Exists \rss : \mathbb{N} \fpfn \textdom{Res}. \wsatpre(n, \mask, \state, \rss, \rs \mtimes \prod_\iname \rss(\iname))} \end{align*} \end{align*} ... @@ -95,7 +94,7 @@ We only have to define the interpretation of the missing connectives, the most i ... @@ -95,7 +94,7 @@ We only have to define the interpretation of the missing connectives, the most i \typedsection{Primitive view-shift}{\mathit{pvs}_{-}^{-}(-) : \Delta(\pset{\mathbb{N}}) \times \Delta(\pset{\mathbb{N}}) \times \iProp \nfn \iProp} \typedsection{Primitive view-shift}{\mathit{pvs}_{-}^{-}(-) : \Delta(\pset{\mathbb{N}}) \times \Delta(\pset{\mathbb{N}}) \times \iProp \nfn \iProp} \begin{align*} \begin{align*} \mathit{pvs}_{\mask_1}^{\mask_2}(\prop) &= \Lam \rs. \setComp{n}{\begin{aligned} \mathit{pvs}_{\mask_1}^{\mask_2}(\prop) &= \Lam \rs. \setComp{n}{\begin{aligned} \All \rs_\f, m, \mask_\f, \state.& 0 < m \leq n \land (\mask_1 \cup \mask_2) \disj \mask_\f \land k \in \wsat\state{\mask_1 \cup \mask_\f}{\rs \mtimes \rs_\f} \Ra {}\\& \All \rs_\f, k, \mask_\f, \state.& 0 < k \leq n \land (\mask_1 \cup \mask_2) \disj \mask_\f \land k \in \wsat\state{\mask_1 \cup \mask_\f}{\rs \mtimes \rs_\f} \Ra {}\\& \Exists \rsB. k \in \prop(\rsB) \land k \in \wsat\state{\mask_2 \cup \mask_\f}{\rsB \mtimes \rs_\f} \Exists \rsB. k \in \prop(\rsB) \land k \in \wsat\state{\mask_2 \cup \mask_\f}{\rsB \mtimes \rs_\f} \end{aligned}} \end{aligned}} \end{align*} \end{align*} ... ...
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