Commit b6fb28b7 by Robbert Krebbers

### Docs: Do not abbreviate.

parent bf46989d
 ... ... @@ -448,7 +448,7 @@ Furthermore, we have the usual $\eta$ and $\beta$ laws for projections, $\textlo {\upd\plainly\prop \proves \prop} \end{mathpar} The premise in \ruleref{upd-update} is a \emph{meta-level} side-condition that has to be proven about$a$and$B$. %\ralf{Trouble is, we don't actually have$\in$inside the logic...} %\ralf{Trouble is, we do not actually have$\in$inside the logic...} \subsection{Consistency} ... ...  ... ... @@ -44,7 +44,7 @@ Noteworthy here is the fact that$\prop \proves \later\prop$can be derived from \subsection{Persistent Propositions} We call a proposition$\prop$\emph{persistent} if$\prop \proves \always\prop$. These are propositions that don't own anything'', so we can (and will) treat them like normal'' intuitionistic propositions. These are propositions that do not own anything'', so we can (and will) treat them like normal'' intuitionistic propositions. Of course,$\always\prop$is persistent for any$\prop$. Furthermore, by the proof rules given in \Sref{sec:proof-rules},$\TRUE$,$\FALSE$,$t = t'$as well as$\ownGhost\gname{\mcore\melt}$and$\mval(\melt)$are persistent. ... ...  ... ... @@ -32,7 +32,7 @@ Notice that these are immutable locations, so the maps-to proposition is persist The rule \ruleref{sprop-alloc} is then thought of as allocation, and the rule \ruleref{sprop-agree} states that a given location$\gname$can only store \emph{one} proposition, so multiple witnesses covering the same location must agree. %Compared to saved propositions in prior work, \ruleref{sprop-alloc} is stronger since the stored proposition can depend on the name being allocated. %\derek{Can't we cut the above sentence? This makes it sound like we are doing something weird that we ought not to be since prior work didn't do it. But in fact, I thought that in our construction we don't really need to rely on this feature at all! So I'm confused.} %\derek{Can't we cut the above sentence? This makes it sound like we are doing something weird that we ought not to be since prior work didn't do it. But in fact, I thought that in our construction we do not really need to rely on this feature at all! So I'm confused.} The conclusion of \ruleref{sprop-agree} usually is guarded by a$\later$. The point of this theorem is to show that said later is \emph{essential}, as removing it introduces inconsistency. % ... ... @@ -43,7 +43,7 @@$A(\gname) \eqdef \Exists \prop : \Prop. \always\lnot \prop \land \gname \Mapsto Intuitively, $A(\gname)$ says that the saved proposition named $\gname$ does \emph{not} hold, \ie we can disprove it. Using \ruleref{sprop-persist}, it is immediate that $A(\gname)$ is persistent. Now, by applying \ruleref{sprop-alloc} with $A$, we obtain a proof of $\prop \eqdef \gname \Mapsto A(\gname)$: this says that the proposition named $\gname$ is the proposition saying that it, itself, doesn't hold. Now, by applying \ruleref{sprop-alloc} with $A$, we obtain a proof of $\prop \eqdef \gname \Mapsto A(\gname)$: this says that the proposition named $\gname$ is the proposition saying that it, itself, does not hold. In other words, $\prop$ says that the proposition named $\gname$ expresses its own negation. Unsurprisingly, that leads to a contradiction, as is shown in the following lemma: \begin{lem} \label{lem:saved-prop-counterexample-not-agname} We have $\gname \Mapsto A(\gname) \proves \always\lnot A(\gname)$ and $\gname \Mapsto A(\gname) \proves A(\gname)$. \end{lem} ... ...
 ... ... @@ -521,7 +521,7 @@ Furthermore, as we construct more sophisticated and more interesting things that For the special case that $\prop = \propC$ and $\propB = \propB'$, we use the following notation that avoids repetition: $\Acc[\mask_1][\mask_2]\prop{\Ret x. \propB} \eqdef \prop \vs[\mask_1][\mask_2] \Exists\var. \propB * (\propB \vsW[\mask_2][\mask_1] \prop)$ This accessor is idempotent'' in the sense that it doesn't actually change the state. After applying it, we get our $\prop$ back so we end up where we started. This accessor is idempotent'' in the sense that it does not actually change the state. After applying it, we get our $\prop$ back so we end up where we started. %%% Local Variables: %%% mode: latex ... ...
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