∥μo∥) ∨ ∥μs∥−δw+αw>1024 ∨
(¬Iw ∧ W(w,μ)) ∨
(w = SSTORE ∧ μg Gcallstipend)
w ∈ {CREATE, CREATE2, SSTORE, SELFDESTRUCT} ∨
LOG0≤w ∧ w≤LOG4 ∨ w=CALL ∧ μs[2]̸=0
where
(139) (140) (141) (142)
This states that
ing state if there is insufficient gas, if the instruction is invalid (and therefore its δ subscript is undefined), if there are insufficient stack items, if a JUMP/JUMPI destination is invalid, the new stack size would be larger than 1024 or state modification is attempted during a static call. The as- tute reader will realise that this implies that no instruction can, through its execution, cause an exceptional halt. Also, the execution is in an exceptional halting state if the gas left prior to executing an SSTORE instruction is less than or equal to the call stipend Gcallstipend. The last condition was introduced in EIP-1706 by Forshtat and Weiss [2019]
(part of EIP-2200 by Tang [2019]).
9.4.3. Jump Destination Validity. We previously used D as the function to determine the set of valid jump desti- nations given the code that is being run. We define this as any position in the code occupied by a JUMPDEST instruction.
All such positions must be on valid instruction bound- aries, rather than sitting in the data portion of PUSH operations and must appear within the explicitly defined portion of the code (rather than in the implicitly defined STOP operations that trail it).
(143) w ≡
Ib[μpc] STOP
if μpc < ∥Ib∥ otherwise
ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 13
(138)
X(σ, μ, A, I) ≡ ∅,μ,A,I,o
(a,b,c,d) · e ≡ μ′ ≡ μ′g ≡
(a,b,c,d,e)
μ except:
μg −C(σ,μ,A,I)
μpc ≡ μm ≡
μ ≡ i
μs ≡ μo ≡
∅,μ,A,I,∅
′
O(σ,μ,A,I)·o if o̸=∅
X O(σ,μ,A,I)
o ≡ H(μ,I)
otherwise
Note that, when we evaluate Ξ, we drop the fourth element I′ and extract the remaining gas μ′g from the resultant machine state μ′.
X is thus cycled (recursively here, but implementations are generally expected to use a simple iterative loop) until either Z becomes true indicating that the present state is exceptional and that the machine must be halted and any changes discarded or until H becomes a series (rather than the empty set) indicating that the machine has reached a controlled halt.
9.4.1. Machine State. The machine state μ is defined as the tuple (g,pc,m,i,s) which are the gas available, the program counter pc ∈ N256 , the memory contents, the active number of words in memory (counting continuously from position 0), and the stack contents. The memory contents μm are a series of zeroes of size 2256.
For the ease of reading, the instruction mnemonics, written in small-caps (e.g. ADD), should be interpreted as their numeric equivalents; the full table of instructions and their specifics is given in Appendix H.
For the purposes of defining Z, H and O, we define w as the current operation to be executed:
Formally: (146)
where: (147)
DJ(c,i) ≡
D(c) ≡ DJ(c,0)
{}
{i} ∪ DJ (c, N (i, c[i]))
if c[i] = JUMPDEST DJ (c, N (i, c[i]))
if i∥c∥
otherwise
We also assume the fixed amounts of δ and α, specifying the stack items removed and added, both subscriptable on the instruction and an instruction cost function C eval- uating to the full cost, in gas, of executing the given instruction.
where N is the next valid instruction position in the code, skipping the data of a PUSH instruction, if any: (148)
if Z(σ,μ,A,I)
if w=REVERT
where (145)
W (w, μ) ≡
the execution is in an exceptional halt-
i + w − PUSH1 + 2
N (i, w) ≡ if w ∈ [PUSH1, PUSH32] i + 1
otherwise
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