Stretch Goal: prove x*y=k

[d-xo]

Adding this just as a note really, and the idea is stolen from this issue in k-dss.

We could introduce a new kind of block into act: invariant that would look something like this:

invariant K of UniswapV2Exchange

storage

    reserve0_reserve1_blockTimestampLast |-> #WordPackUInt112UInt112UInt32(Reserve0, Reserve1, _) => _
    totalSupply |-> TotalSupply => _
    kLast       |-> KLast => _

such that

    (Reserve0 * Reserve1) / (TotalSupply ^ 2) == KLast

This would generate a K spec with symbolic calldata that proves that the generalized invariant holds at the end of every possible call to the contract. This proof could be made fast by implicitly reusing all the other specs (i.e. implicitly including every other spec for UniswapV2Exchange in a calls block for each invariant block).

[d-xo]

Some related discussion from the chat: https://matrix.to/#/!faGfrHRNsAJdJzQRoy:matrix.dapp.org.uk/$QiMm72WNyGF9mFz5-zSirSVP_dr76JVow--TfRB7B6k?via=matrix.dapp.org.uk

[d-xo]

Perhaps we could even just directly append the ensures statements to the existing specs without even having to create a new spec specifically for the invariants