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Jakob Botsch Nielsen authored
This specifies an initial version of blockchain semantics. The semantics are specified as several relations: ChainStep : Environment -> Action -> Tx -> Environment -> list Action -> Prop. This relation captures the semantics of a single step/action in the chain. Such an action can either be a transfer, contract deployment or contract call. It specifies that when an action is executed in some starting environment, then the blockchain records a transaction (Tx) on the chain and performs certain updates to the environment. Finally, the step also results in possible new actions to be executed due to contract execution. An environment is for now simply a Chain (which contracts can interact with) and a collection of contracts that have been deployed to some addresses. The Chain contains various useful operations for contracts such as the current block number or ability to query transactions and user balances. For example, for a simple transfer action we may have ChainStep pre act tx post []. Then the ChainStep relation will capture that the only thing that has changed in the post environment is that tx has been added to the chain (so that the appropriate account balances have been updated), but for instance also that no new contracts have appeared. Since this is just a transfer, there also cannot be any new actions to execute. The semantics of the environment updates are captured in an abstract manner to allow for different implementations of blockchains. Specifically, we use an equivalence relation EnvironmentEquiv : Environment -> Environment -> Prop and just require that the environment is equivalent (under this relation) to an obvious implementation of an environment. We implement an obvious blockchain, LocalBlockchain, which uses finite maps with log n access times rather than the linear maps used in the default semantics. A single block, when added to a blockchain, consists of a list of these actions to execute. In each block this list of actions must then be executed (in a correct manner) until no more actions are left. This is captured in BlockTrace : Environment -> list Action -> Environment -> list Action -> Prop. For all intents and purposes this can be seen as just a transitive reflexive closure of the ChainStep relation above. Right now it only allows blocks to reduce steps in a depth-first order, but this relation should be simple to update to other or more general orders of reduction. Note that ChainStep and BlockTrace say nothing about new blocks, but only about execution within blocks. The semantics of how blocks are added to the chain is captured in ChainTrace : Environment -> Environment -> Prop. This is a collection of block traces and representing additions of blocks. At each block added, ChainTrace also captures that the environment must be updated accordingly so that contracts can access information about block numbers correctly. Finally, a blockchain must always be able to prove that there is a ChainTrace from its initial environment (the genesis blockchain) to its current environment. There are several TODOs left in the semantics: 1. We need to account for gas and allow execution failures 2. We need to put restrictions on when contracts can appear as the source of actions 3. We need to capture soundness of the add_block function in blockchain implementations We also provide to sanity checks for these semantics: 1. We prove them for a simple block chain (LocalBlockchain.v). 2. We prove a "circulation" theorem for any blockchain satisfying the semantics. That is, we show the following theorem: Theorem chain_trace_circulation {env_start env_end : Environment} (trace : ChainTrace env_start env_end) : circulation env_end = (circulation env_start + coins_created (block_height (block_header env_start)) (block_height (block_header env_end)))%Z.
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