Commit 71ea5d00 authored by Jakob Botsch Nielsen's avatar Jakob Botsch Nielsen
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Specify and prove an initial blockchain semantics

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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