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Proofreading TypesAndMutation

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Adam Chlipala 2018-04-08 14:15:51 -04:00
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frap_book.tex
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@ -3154,7 +3154,7 @@ More precisely, the limit on how many times we can run garbage collection in a r
The type-safety proof is fairly straightforward to update.
We prove progress by \emph{ignoring} the garbage-collection rule, since the existing rules were already enough to find a step for every nonvalue.
A bit more work is needed to update the proof of preservation; its case for the existing rules follows the same way as before, while we must prove a few lemmas on the way to handling the new rule.
A bit more work is needed to update the proof of preservation; its cases for the existing rules follow the same way as before, while we must prove a few lemmas on the way to handling the new rule.
\begin{lemma}[Transitivity for reachability]
If $\freeloc{e_1} \subseteq \freeloc{e_2}$, then $\reach{h}{e_1} \subseteq \reach{h}{e_2}$.