Metropolis: static call

Paper.tex

@@ -600,8 +600,8 @@ \subsection{Execution}
 Evaluating $\boldsymbol{\sigma}_P$ from $\boldsymbol{\sigma}_0$ depends on the transaction type; either contract creation or message call; we define the tuple of post-execution provisional state $\boldsymbol{\sigma}_P$, remaining gas $g'$ and substate $A$:
 \begin{equation}
 (\boldsymbol{\sigma}_P, g', A) \equiv \begin{cases}
-\Lambda(\boldsymbol{\sigma}_0, S(T), T_o, &\\ \quad\quad g, T_p, T_v, T_\mathbf{i}, 0) & \text{if} \quad T_t = \varnothing \\
-\Theta_{3}(\boldsymbol{\sigma}_0, S(T), T_o, &\\ \quad\quad T_t, T_t, g, T_p, T_v, T_v, T_\mathbf{d}, 0) & \text{otherwise}
+\Lambda(\boldsymbol{\sigma}_0, S(T), T_o, &\\ \quad\quad g, T_p, T_v, T_\mathbf{i}, 0, \top) & \text{if} \quad T_t = \varnothing \\
+\Theta_{3}(\boldsymbol{\sigma}_0, S(T), T_o, &\\ \quad\quad T_t, T_t, g, T_p, T_v, T_v, T_\mathbf{d}, 0, \top) & \text{otherwise}
 \end{cases}
 \end{equation}
 
@@ -648,7 +648,7 @@ \section{Contract Creation} \label{ch:create}
 
 We define the creation function formally as the function $\Lambda$, which evaluates from these values, together with the state $\boldsymbol{\sigma}$ to the tuple containing the new state, remaining gas and accrued transaction substate $(\boldsymbol{\sigma}', g', A)$, as in section \ref{ch:transactions}:
 \begin{equation}
-(\boldsymbol{\sigma}', g', A) \equiv \Lambda(\boldsymbol{\sigma}, s, o, g, p, v, \mathbf{i}, e)
+(\boldsymbol{\sigma}', g', A) \equiv \Lambda(\boldsymbol{\sigma}, s, o, g, p, v, \mathbf{i}, e, w)
 \end{equation}
 
 The address of the new account is defined as being the rightmost 160 bits of the Keccak hash of the RLP encoding of the structure containing only the sender and the nonce. Thus we define the resultant address for the new account $a$:
@@ -691,7 +691,8 @@ \section{Contract Creation} \label{ch:create}
 I_s & \equiv & s \\
 I_v & \equiv & v \\
 I_\mathbf{b} & \equiv & \mathbf{i} \\
-I_e & \equiv & e
+I_e & \equiv & e \\
+I_w & \equiv & w
 \end{eqnarray}
 
 $I_\mathbf{d}$ evaluates to the empty tuple as there is no input data to this call. $I_H$ has no special treatment and is determined from the blockchain.
@@ -735,7 +736,7 @@ \section{Message Call} \label{ch:call}
 
 Aside from evaluating to a new state and transaction substate, message calls also have an extra component---the output data denoted by the byte array $\mathbf{o}$. This is ignored when executing transactions, however message calls can be initiated due to VM-code execution and in this case this information is used.
 \begin{equation}
-(\boldsymbol{\sigma}', g', A, \mathbf{o}) \equiv \Theta(\boldsymbol{\sigma}, s, o, r, c, g, p, v, \tilde{v}, \mathbf{d}, e)
+(\boldsymbol{\sigma}', g', A, \mathbf{o}) \equiv \Theta(\boldsymbol{\sigma}, s, o, r, c, g, p, v, \tilde{v}, \mathbf{d}, e, w)
 \end{equation}
 Note that we need to differentiate between the value that is to be transferred, $v$, from the value apparent in the execution context, $\tilde{v}$, for the {\small DELEGATECALL} instruction.
 
@@ -782,6 +783,7 @@ \section{Message Call} \label{ch:call}
 I_s & \equiv & s \\
 I_v & \equiv & \tilde{v} \\
 I_e & \equiv & e \\
+I_w & \equiv & w \\
 \text{Let} \; \mathtt{\tiny KEC}(I_\mathbf{b}) & = & \boldsymbol{\sigma}[c]_c
 \end{eqnarray}
 
@@ -827,6 +829,7 @@ \subsection{Execution Environment}
 \item $I_\mathbf{b}$, the byte array that is the machine code to be executed.
 \item $I_H$, the block header of the present block.
 \item $I_e$, the depth of the present message-call or contract-creation (i.e. the number of {\small CALL}s or {\small CREATE}s being executed at present).
+\item $I_w$, the permission to make modifications to the state.
 \end{itemize}
 
 The execution model defines the function $\Xi$, which can compute the resultant state $\boldsymbol{\sigma}'$, the remaining gas $g'$, the accrued substate $A$ and the resultant output, $\mathbf{o}$, given these definitions. For the present context, we will defined it as:
@@ -895,11 +898,20 @@ \subsubsection{Exceptional Halting}
 \mathbf{\delta}_w = \varnothing \quad \vee \\
 \lVert\boldsymbol{\mu}_\mathbf{s}\rVert < \mathbf{\delta}_w \quad \vee \\
 ( w \in \{ \text{\small JUMP}, \text{\small JUMPI} \} \quad \wedge \\ \quad \boldsymbol{\mu}_\mathbf{s}[0] \notin D(I_\mathbf{b}) ) \quad \vee \\
-\lVert\boldsymbol{\mu}_\mathbf{s}\rVert - \mathbf{\delta}_w + \mathbf{\alpha}_w > 1024 \quad
+ \lVert\boldsymbol{\mu}_\mathbf{s}\rVert - \mathbf{\delta}_w + \mathbf{\alpha}_w > 1024 \quad \vee \\
+ \neg I_w \wedge W(w, \boldsymbol{\mu})
+\end{array}
+\end{equation}
+where
+\begin{equation}
+W(w, \boldsymbol{\mu}) \equiv \begin{array}[t]{l}
+w \in \{\text{\small CREATE}, \text{\small SSTORE}, \text{\small SELFDESTRUCT}\} \quad \vee \\
+\text{\small LOG0} \le w \wedge w \le \text{\small LOG4} \quad \vee \\
+w \in \{\text{\small CALL}, \text{\small CALLCODE}\} \wedge \boldsymbol{\mu}_\mathbf{s}[2] \neq 0
 \end{array}
 \end{equation}
 
-This states that the execution is in an exceptional halting state if there is insufficient gas, if the instruction is invalid (and therefore its $\delta$ subscript is undefined), if there are insufficient stack items, if a {\small JUMP}/{\small JUMPI} destination is invalid or the new stack size would be larger then 1024. The astute reader will realise that this implies that no instruction can, through its execution, cause an exceptional halt.
+This states that the execution is in an exceptional halting state if there is insufficient gas, if the instruction is invalid (and therefore its $\delta$ subscript is undefined), if there are insufficient stack items, if a {\small JUMP}/{\small JUMPI} destination is invalid, the new stack size would be larger then 1024 or state modification is attempted during a static call. The astute reader will realise that this implies that no instruction can, through its execution, cause an exceptional halt.
 
 \subsubsection{Jump Destination Validity}
 
@@ -1948,7 +1960,7 @@ \subsection{Instruction Set}
 \textbf{Value} & \textbf{Mnemonic} & $\delta$ & $\alpha$ & \textbf{Description} \vspace{5pt} \\
 0xf0 & {\small CREATE} & 3 & 1 & Create a new account with associated code. \\
 &&&& $\mathbf{i} \equiv \boldsymbol{\mu}_\mathbf{m}[ \boldsymbol{\mu}_\mathbf{s}[1] \dots (\boldsymbol{\mu}_\mathbf{s}[1] + \boldsymbol{\mu}_\mathbf{s}[2] - 1) ]$ \\
-&&&& $(\boldsymbol{\sigma}', \boldsymbol{\mu}'_g, A^+) \equiv \begin{cases}\Lambda(\boldsymbol{\sigma}^*, I_a, I_o, L(\boldsymbol{\mu}_g), I_p, \boldsymbol{\mu}_\mathbf{s}[0], \mathbf{i}, I_e + 1) & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[0] \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge\; I_e < 1024\\ \big(\boldsymbol{\sigma}, \boldsymbol{\mu}_g, \varnothing\big) & \text{otherwise} \end{cases}$ \\
+&&&& $(\boldsymbol{\sigma}', \boldsymbol{\mu}'_g, A^+) \equiv \begin{cases}\Lambda(\boldsymbol{\sigma}^*, I_a, I_o, L(\boldsymbol{\mu}_g), I_p, \boldsymbol{\mu}_\mathbf{s}[0], \mathbf{i}, I_e + 1, I_w) & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[0] \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge\; I_e < 1024\\ \big(\boldsymbol{\sigma}, \boldsymbol{\mu}_g, \varnothing\big) & \text{otherwise} \end{cases}$ \\
 &&&& $\boldsymbol{\sigma}^* \equiv \boldsymbol{\sigma} \quad \text{except} \quad \boldsymbol{\sigma}^*[I_a]_n = \boldsymbol{\sigma}[I_a]_n + 1$ \\
 &&&& $A' \equiv A \Cup A^+$ which implies: $A'_\mathbf{s} \equiv A_\mathbf{s} \cup A^+_\mathbf{s} \quad \wedge \quad A'_\mathbf{l} \equiv A_\mathbf{l} \cdot A^+_\mathbf{l} \quad \wedge \quad A'_\mathbf{r} \equiv A_\mathbf{r} + A^+_\mathbf{r}$ \\
 &&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv x$ \\
@@ -1962,7 +1974,7 @@ \subsection{Instruction Set}
 \midrule
 0xf1 & {\small CALL} & 7 & 1 & Message-call into an account. \\
 &&&& $\mathbf{i} \equiv \boldsymbol{\mu}_\mathbf{m}[ \boldsymbol{\mu}_\mathbf{s}[3] \dots (\boldsymbol{\mu}_\mathbf{s}[3] + \boldsymbol{\mu}_\mathbf{s}[4] - 1) ]$ \\
-&&&& $(\boldsymbol{\sigma}', g', A^+, \mathbf{o}) \equiv \begin{cases}\begin{array}{l}\Theta(\boldsymbol{\sigma}, I_a, I_o, t, t,\\ \quad C_{\text{\tiny CALLGAS}}(\boldsymbol{\mu}), I_p, \boldsymbol{\mu}_\mathbf{s}[2], \boldsymbol{\mu}_\mathbf{s}[2], \mathbf{i}, I_e + 1)\end{array} & \begin{array}{l}\text{if} \quad \boldsymbol{\mu}_\mathbf{s}[2] \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge \\ \quad\quad I_e < 1024\end{array}\\ (\boldsymbol{\sigma}, g, \varnothing, ()) & \text{otherwise} \end{cases}$ \\
+&&&& $(\boldsymbol{\sigma}', g', A^+, \mathbf{o}) \equiv \begin{cases}\begin{array}{l}\Theta(\boldsymbol{\sigma}, I_a, I_o, t, t,\\ \quad C_{\text{\tiny CALLGAS}}(\boldsymbol{\mu}), I_p, \boldsymbol{\mu}_\mathbf{s}[2], \boldsymbol{\mu}_\mathbf{s}[2], \mathbf{i}, I_e + 1, I_w)\end{array} & \begin{array}{l}\text{if} \quad \boldsymbol{\mu}_\mathbf{s}[2] \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge \\ \quad\quad I_e < 1024\end{array}\\ (\boldsymbol{\sigma}, g, \varnothing, ()) & \text{otherwise} \end{cases}$ \\
 &&&& $n \equiv \min(\{ \boldsymbol{\mu}_\mathbf{s}[6], |\mathbf{o}|\})$ \\
 &&&& $\boldsymbol{\mu}'_\mathbf{m}[ \boldsymbol{\mu}_\mathbf{s}[5] \dots (\boldsymbol{\mu}_\mathbf{s}[5] + n - 1) ] = \mathbf{o}[0 \dots (n - 1)]$ \\
 &&&& $\boldsymbol{\mu}'_g \equiv \boldsymbol{\mu}_g + g'$ \\
@@ -1996,7 +2008,7 @@ \subsection{Instruction Set}
 \midrule
 0xf2 & {\small CALLCODE} & 7 & 1 & Message-call into this account with an alternative account's code. \\
 &&&& Exactly equivalent to {\small CALL} except: \\
-&&&& $(\boldsymbol{\sigma}', g', A^+, \mathbf{o}) \equiv \begin{cases}\begin{array}{l}\Theta(\boldsymbol{\sigma}^*, I_a, I_o, I_a, t,\\\quad C_{\text{\tiny CALLGAS}}(\boldsymbol{\mu}), I_p, \boldsymbol{\mu}_\mathbf{s}[2], \boldsymbol{\mu}_\mathbf{s}[2], \mathbf{i}, I_e + 1)\end{array} & \begin{array}{l}\text{if} \quad \boldsymbol{\mu}_\mathbf{s}[2] \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge\\ \quad\quad{}I_e < 1024\end{array} \\ (\boldsymbol{\sigma}, g, \varnothing, ()) & \text{otherwise} \end{cases}$ \\
+&&&& $(\boldsymbol{\sigma}', g', A^+, \mathbf{o}) \equiv \begin{cases}\begin{array}{l}\Theta(\boldsymbol{\sigma}^*, I_a, I_o, I_a, t,\\\quad C_{\text{\tiny CALLGAS}}(\boldsymbol{\mu}), I_p, \boldsymbol{\mu}_\mathbf{s}[2], \boldsymbol{\mu}_\mathbf{s}[2], \mathbf{i}, I_e + 1, I_w)\end{array} & \begin{array}{l}\text{if} \quad \boldsymbol{\mu}_\mathbf{s}[2] \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge\\ \quad\quad{}I_e < 1024\end{array} \\ (\boldsymbol{\sigma}, g, \varnothing, ()) & \text{otherwise} \end{cases}$ \\
 &&&& Note the change in the fourth parameter to the call $\Theta$ from the 2nd stack value $\boldsymbol{\mu}_\mathbf{s}[1]$\\
 &&&& (as in {\small CALL}) to the present address $I_a$. This means that the recipient is in fact the\\
 &&&& same account as at present, simply that the code is overwritten.\\
@@ -2016,12 +2028,19 @@ \subsection{Instruction Set}
 &&&& argument is $\boldsymbol{\mu}_\mathbf{s}[2]$. As a result, $\boldsymbol{\mu}_\mathbf{s}[3]$, $\boldsymbol{\mu}_\mathbf{s}[4]$, $\boldsymbol{\mu}_\mathbf{s}[5]$ and $\boldsymbol{\mu}_\mathbf{s}[6]$ in the definition of {\small CALL} \\
 &&&& should respectively be replaced with $\boldsymbol{\mu}_\mathbf{s}[2]$, $\boldsymbol{\mu}_\mathbf{s}[3]$, $\boldsymbol{\mu}_\mathbf{s}[4]$ and $\boldsymbol{\mu}_\mathbf{s}[5]$. \\
 &&&& Otherwise exactly equivalent to {\small CALL} except: \\
-&&&& $(\boldsymbol{\sigma}', g', A^+, \mathbf{o}) \equiv \begin{cases}\begin{array}{l}\Theta(\boldsymbol{\sigma}^*, I_s, I_o, I_a, t,\\\quad \boldsymbol{\mu}_\mathbf{s}[0], I_p, 0, I_v, \mathbf{i}, I_e + 1)\end{array} & \text{if} \quad I_v \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge\; I_e < 1024 \\ (\boldsymbol{\sigma}, g, \varnothing, ()) & \text{otherwise} \end{cases}$ \\
+&&&& $(\boldsymbol{\sigma}', g', A^+, \mathbf{o}) \equiv \begin{cases}\begin{array}{l}\Theta(\boldsymbol{\sigma}^*, I_s, I_o, I_a, t,\\\quad \boldsymbol{\mu}_\mathbf{s}[0], I_p, 0, I_v, \mathbf{i}, I_e + 1, I_w)\end{array} & \text{if} \quad I_v \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge\; I_e < 1024 \\ (\boldsymbol{\sigma}, g, \varnothing, ()) & \text{otherwise} \end{cases}$ \\
 &&&& Note the changes (in addition to that of the fourth parameter) to the second \\
 &&&& and ninth parameters to the call $\Theta$.\\
 &&&& This means that the recipient is in fact the same account as at present, simply\\
 &&&& that the code is overwritten {\it and} the context is almost entirely identical.\\
 \midrule
+0xfa & {\small STATICCALL} & 6 & 1 & Static message-call into an account. \\
+&&&& Exactly equivalent to {\small CALL} except: \\
+&&&& The argument $\boldsymbol{\mu}_\mathbf{s}[2]$ is replaced with $0$. \\
+&&&& The deeper argument $\boldsymbol{\mu}_\mathbf{s}[3]$, $\boldsymbol{\mu}_\mathbf{s}[4]$, $\boldsymbol{\mu}_\mathbf{s}[5]$ and $\boldsymbol{\mu}_\mathbf{s}[6]$ are respectively replaced with \\
+&&&& $\boldsymbol{\mu}_\mathbf{s}[2]$, $\boldsymbol{\mu}_\mathbf{s}[3]$, $\boldsymbol{\mu}_\mathbf{s}[4]$ and $\boldsymbol{\mu}_\mathbf{s}[5]$. \\
+&&&& The last argument of $\Theta$ is $\bot$. \\
+\midrule
 0xfe & {\small INVALID} & $\varnothing$ & $\varnothing$ & Designated invalid instruction. \\
 \midrule
 0xff & {\small SELFDESTRUCT} & 1 & 0 & Halt execution and register account for later deletion. \\