Group elements generator

[vlasin]

Adds an executable to symbolic-base that computes a set of group points of the form g^(x^n) for the input x. This is useful for public testing to ensure x is not leaked. For production, we need to either use an already precomputed set of points or do an MPC setup ceremony.

Also, fixes some unsafe operations in PlonkUp and makes corrections to UtxoAccumulator example.

[TurtlePU]

Instead of storing just a name of a group, you can directly store the required operations, like this:

data Group = forall pt. (CyclicGroup pt, Show pt, ToJSON pt) => Group

supportedGroups :: [(String, Group)]
supportedGroups =
    [ ("bn254-g1", Group @BN254_G1_Point)
    , ("bn254-g2", Group @BN254_G1_Point)
    , ("bls12381-g1", Group @BLS12_381_G1_Point)
    , ("bls12381-g2", Group @BLS12_381_G2_Point)
    ]

But that's just a suggestion, the code looks 🔥 🔥 🔥 as is

[vlasin]

Hmm, apparently, this approach requires TypeAbstractions to work, which requires GHC 9.14.

When we upgrade to that version, we can use something like this:

case optGroup opts of
    Group @pt -> pointGen @pt

[TurtlePU]

Hmm, that's strange, the extension page says that it's available since 9.8.
And the following basic example runs fine for me on GHC 9.6:

{-# LANGUAGE AllowAmbiguousTypes       #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE ScopedTypeVariables       #-}
{-# LANGUAGE TypeApplications          #-}

data Mon = forall a. (Monoid a, Show a) => Mon

runMon :: Mon -> String
runMon (Mon @a) = show (mempty @a <> mempty)

main :: IO ()
main = putStrLn $ runMon (Mon @[Int])

[TurtlePU]

🔥 🔥 🔥