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12 changes: 9 additions & 3 deletions preamble.tex
Original file line number Diff line number Diff line change
Expand Up @@ -306,8 +306,7 @@
\newcommand*{\CgasHconst}{\mathsf{M}_{H,c}}
\newcommand*{\CgasHlinear}{\mathsf{M}_{H,\ell}}
\newcommand*{\CgasE}{\mathsf{M}_E}
\newcommand*{\CgasMconst}{\mathsf{M}_{M,c}}
\newcommand*{\CgasMlinear}{\mathsf{M}_{M,\ell}}
\newcommand*{\CgasM}{\mathsf{M}_{M}}
\newcommand*{\CgasPconst}{\mathsf{M}_{P,c}}
\newcommand*{\CgasPlinear}{\mathsf{M}_{P,\ell}}
\newcommand*{\CgasOconst}{\mathsf{M}_{O,c}}
Expand Down Expand Up @@ -337,6 +336,10 @@
\newcommand*{\CgasTaurus}{\mathsf{M}_{\Taurus}}
\newcommand*{\CgasAriesconst}{\mathsf{M}_{\Aries,c}}
\newcommand*{\CgasArieslinear}{\mathsf{M}_{\Aries,\ell}}
\newcommand*{\CgasGammamem}{\mathsf{M}_{\Gamma,\mathrm{m}}}
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\newcommand*{\CgasGammadb}{\mathsf{M}_{\Gamma,\mathrm{d}}}
\newcommand*{\CgasGammamemlinear}{\mathsf{M}_{\Gamma,\mathrm{m},\ell}}
\newcommand*{\CgasGammadblinear}{\mathsf{M}_{\Gamma,\mathrm{d},\ell}}

% String
\newcommand*{\Xavailable}{\mathsf{X}_A}
Expand Down Expand Up @@ -450,11 +453,11 @@

%%%%%%%%%%%%
% Named types (blackboard)
\newcommand*{\innerpvm}{\mathbb{I}}
\newcommand*{\pg¬code}{\pvm¬blob}
\newcommand*{\pg¬ram}{\mathbf{u}}
\newcommand*{\pg¬pc}{i}
\newcommand*{\pg¬gaschargedflag}{\tilde{g}}
\newcommand*{\pg¬handle}{h}

\newcommand*{\implications}{\mathbb{L}}
\newcommand*{\imX}{\mathbf{x}}
Expand Down Expand Up @@ -838,6 +841,9 @@
%%%%%%%%%%%%
% PVM-SPECIFIC ITEMS

\newcommand*{\pvm¬instance}{\mathbb{I}}

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pvm¬instance should stay where it was? The pattern in the "Named types" section is that you have the "named type" (eg pvm¬instance) followed by the names of the type's fields (for pvm¬instance these are pg¬code, pg¬ram, etc).

@koute koute Jul 28, 2026

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Hm, well, \pvm¬instance (\mathbb{I}) is the type of the instance, and \pvm¬module (\mathbb{B}) is the type of the module. To me it makes sense to keep them together? I can split them, but that seems to be somewhat confusing, considering they're inherently related (you create an instance from a module).

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I guess as \pvm¬module is a type it makes sense in the "Named types" section, but I found it confusing placed between the definition of \pvm¬instance and its fields. Anyway it doesn't really matter that much so I'll shut up now!

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Heh, okay, well, in general I'm fine with whatever you prefer. (:

\newcommand*{\pvm¬module}{\blob}
\newcommand*{\pvm¬module¬map}{\mathbf{c}}
\newcommand*{\jam¬blob}{\mathfrak{j}}
\newcommand*{\pvm¬blob}{\mathfrak{p}}
\newcommand*{\gascounter}{\varrho}
Expand Down
12 changes: 8 additions & 4 deletions text/definitions.tex
Original file line number Diff line number Diff line change
Expand Up @@ -38,7 +38,7 @@ \subsubsection{Custom Notation}
\item[$\edkey$] The set of Ed25519 public keys. A subset of $\blob[32]$. See section \ref{sec:signing}.
\item[$\bskey$] The set of Bandersnatch public keys. A subset of $\blob[32]$. See section \ref{sec:cryptography} and appendix \ref{sec:bandersnatch}.
\end{description}
\item[$\innerpvm$] The set representing the state of an $\mathbb{I}$nner \textsc{pvm} instance. See equation \ref{eq:innerpvm}.
\item[$\pvm¬instance$] The set representing the state of an $\mathbb{I}$nner \textsc{pvm} instance. See equation \ref{eq:innerpvm}.
\item[$\segment$] The set of data segments, equivalent to $\blob[\Csegmentsize]$. See equation \ref{eq:segment}.
\item[$\valkey$] The set of validator $\mathbb{K}$ey-sets. See equation \ref{eq:validatorkeys}.
\item[$\implications$] The set representing implications of accumulation. See equation \ref{eq:implications}.
Expand Down Expand Up @@ -111,12 +111,13 @@ \subsection{Functions}
\item[$\Omega_T$] Transfer host-call.
\item[$\Omega_U$] Upgrade-service host-call.
\item[$\Omega_W$] Write-storage host-call.
\item[$\Omega_X$] Expunge-\textsc{pvm} host-call.
\item[$\Omega_X$] Expunge an inner-\textsc{pvm} instance or a compiled program module host-call.
\item[$\Omega_Y$] Fetch data host-call.
\item[$\Omega_Z$] Pages inner-\textsc{pvm} memory host-call.
\item[$\Omega_\Taurus$] Yield accumulation trie result host-call.
\item[$\Omega_\Aries$] Provide preimage host-call.
\item[$\Omega_\Gemini$] Grow heap host-call.
\item[$\Omega_\Gamma$] Compile host-call.
\end{description}
\end{description}

Expand Down Expand Up @@ -317,8 +318,7 @@ \subsubsection{Host-function gas costs}
\item[$\CgasK = 968$] $\Omega_K$ (\texttt{invoke}) base gas cost.
\item[$\CgasLconst = 600$] $\Omega_L$ (\texttt{lookup}) base gas cost.
\item[$\CgasLlinear = 248$] $\Omega_L$ (\texttt{lookup}) gas per 1024 octets ($\fnmemgas(\CgasLlinear, \ell)$).
\item[$\CgasMconst = 1862$] $\Omega_M$ (\texttt{machine}) base gas cost.
\item[$\CgasMlinear = 112$] $\Omega_M$ (\texttt{machine}) gas per 1024 octets, program size ($\fnmemgas(\CgasMlinear, \ell)$).
\item[$\CgasM = 1862$] $\Omega_M$ (\texttt{machine}) gas cost.
\item[$\CgasN = 3855$] $\Omega_N$ (\texttt{new}) base gas cost.
\item[$\CgasOconst = 297$] $\Omega_O$ (\texttt{poke}) base gas cost.
\item[$\CgasOlinear = 224$] $\Omega_O$ (\texttt{poke}) gas per 1024 octets ($\fnmemgas(\CgasOlinear, \ell)$).
Expand Down Expand Up @@ -364,6 +364,10 @@ \subsubsection{Host-function gas costs}
\item[$\CgasArieslinear = 2264$] $\Omega_\Aries$ (\texttt{provide}) gas per 1024 octets ($\fnmemgas(\CgasArieslinear, \ell)$).
\item[$\CgasGeminiconst = 275$] $\Omega_\Gemini$ (\texttt{grow\_heap}) base gas cost.
\item[$\CgasGeminilinear = 121$] $\Omega_\Gemini$ (\texttt{grow\_heap}) gas per additional page.
\item[$\CgasGammamem = 1862$] $\Omega_\Gamma$ (\texttt{compile}) base gas cost when compiling from memory.
\item[$\CgasGammadb = 1862$] $\Omega_\Gamma$ (\texttt{compile}) base gas cost when compiling from the database.
\item[$\CgasGammamemlinear = 264$] $\Omega_\Gamma$ (\texttt{compile}) in-memory read gas per 1024 octets ($\fnmemgas(\CgasGammamemlinear, \ell)$).
\item[$\CgasGammadblinear = 366$] $\Omega_\Gamma$ (\texttt{compile}) database lookup read gas per 1024 octets ($\fnmemgas(\CgasGammadblinear, \ell)$).
\end{description}

\subsubsection{Signing Contexts}
Expand Down
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