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feat: CN = 0 <=> TX_EXEC = 0 enforced by explicit constraint #99

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feat: CN = 0 <=> TX_EXEC = 0 enforced by explicit constraint #99

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feat: CN = 0 <=> TX_EXEC = 0 enforced by explicit constraint
OlivierBBB Feb 25, 2025
6bb882b
Update numbers.tex
OlivierBBB Feb 25, 2025
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13 changes: 8 additions & 5 deletions hub/generalities/context/numbers.tex
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Original file line number Diff line number Diff line change
@@ -1,7 +1,14 @@
This section presents some of the basic constraints pertaining to the context number columns $\cn$ and $\cn\new$.
\begin{enumerate}
\item $\cn$ and $\cn\new$ are hub-stamp-constant
\item \If $\txExec_{i} = 0$ \Then $\cn _{i} = 0$
\item \If $\cn _{i} = 0$ \Then $\txExec_{i} = 0$
\item \If $\cn _{i} \neq 0$ \Then $\txExec_{i} = 1$
\end{enumerate}
\saNote{} \label{hub: generalities: context: vanishing of context number outside of the execution phase}
The fact that $\CN$ is compelled to vanish \emph{precisely} when outside of the execution phase (i.e. whenever $\txExec \equiv 0$)
guarantees that the consistency argument from section~(\ref{hub: consistencies: execution environment: permutation}),
only take into account execution-rows (and not for instance pre-warming, initialization or skipping rows.)
\begin{enumerate}[resume]
\item \If $\txInit_{i} = 1$ \Then $\cn\new _{i} = 1 + \hubStamp_{i}$
\item \If $\txExec_{i} = 1$ \Then
\begin{enumerate}
Expand All @@ -25,10 +32,6 @@
\item \If $\xAhoy_{i} = 1$ \Then $\cn\new_{i} = \caller_{i}$
\item \If \big($\peekStack_{i} = 1$ \et $\haltFlag_{i} = 1$\big) \Then $\cn\new_{i} = \caller_{i}$
\end{enumerate}
\saNote{} \label{hub: generalities: context: vanishing of context number outside of the execution phase}
The vanishing of the $\CN$ outside of the execution phase (i.e. whenever $\txExec \equiv 0$)
guarantees that the consistency argument from section~(\ref{hub: consistencies: execution environment: permutation})
only take into execution-rows (and not for instance pre-warming, initialization or skipping rows.)

\saNote{} \label{hub: generalities: context: consequences of CMC and XAHOY}
Constraint~(\ref{hub: generalities: context: whenever the context may change the final row is a context row}) and
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