### fix some typos in the docs

parent ef669d81
 ... ... @@ -35,7 +35,7 @@ In order to solve the recursive domain equation in \Sref{sec:model} it is also e A function $f : \cofe \to \cofeB$ between two COFEs is \emph{non-expansive} (written $f : \cofe \nfn \cofeB$) if $\All n, x \in \cofe, y \in \cofe. x \nequiv{n} y \Ra f(x) \nequiv{n} f(y)$ It is \emph{contractive} if $\All n, x \in \cofe, y \in \cofe. (\All m < n. x \nequiv{m} y) \Ra f(x) \nequiv{n} f(x)$ $\All n, x \in \cofe, y \in \cofe. (\All m < n. x \nequiv{m} y) \Ra f(x) \nequiv{n} f(y)$ \end{defn} Intuitively, applying a non-expansive function to some data will not suddenly introduce differences between seemingly equal data. Elements that cannot be distinguished by programs within $n$ steps remain indistinguishable after applying $f$. ... ... @@ -211,7 +211,7 @@ Furthermore, discrete CMRAs can be turned into RAs by ignoring their COFE struct \end{defn} Note that every object/arrow in $\CMRAs$ is also an object/arrow of $\COFEs$. The notion of a locally non-expansive (or contractive) bifunctor naturally generalizes to bifunctors between these categories. \ralf{Discuss how we probably have a commuting square of functors between Set, RA, CMRA, COFE.} %TODO: Discuss how we probably have a commuting square of functors between Set, RA, CMRA, COFE. %%% Local Variables: %%% mode: latex ... ...
 ... ... @@ -135,7 +135,7 @@ Recursive predicates must be \emph{guarded}: in $\MU \var. \term$, the variable Note that $\always$ and $\later$ bind more tightly than $*$, $\wand$, $\land$, $\lor$, and $\Ra$. We will write $\pvs[\term] \prop$ for $\pvs[\term][\term] \prop$. If we omit the mask, then it is $\top$ for weakest precondition $\wpre\expr{\Ret\var.\prop}$ and $\emptyset$ for primitive view shifts $\pvs \prop$. \ralf{$\top$ is not a term in the logic. Neither is any of the operations on masks that we use in the rules for weakestpre.} %FIXME $\top$ is not a term in the logic. Neither is any of the operations on masks that we use in the rules for weakestpre. Some propositions are \emph{timeless}, which intuitively means that step-indexing does not affect them. This is a \emph{meta-level} assertion about propositions, defined as follows: ... ...
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