Automatic plaf instance - Issue #129

[jae-cuz]

Resolves #129. Implemented automatic plaf instance generation.
use chiquito::plonkish::backend::plaf::PlafInstance would enable plaf_circuit.instance().

Ready for review @leolara @qwang98

• Collect copy constraints btw witness_column & public_column, and index and offset of them
• instance_with_offsets: vector of pair (witness value, public offset), where public offset indicates the order to be returned
• sort the vector instance_with_offsets with public offset
• instance_values: convert witness values in instance_with_offsets to field
• and return the instance vector

See along with example :

// when we use expose, plaf.copys is assigned like
[
    CopyC {
        columns: (
            Column {
                kind: Public,
                index: 0,
            },
            Column {
                kind: Witness,
                index: 1,
            },
        ),
        offsets: [
            (
                0,
                10,
            ),
        ],
    },
    CopyC {
        columns: (
            Column {
                kind: Public,
                index: 0,
            },
            Column {
                kind: Witness,
                index: 2,
            },
        ),
        offsets: [
            (
                1,
                10,
            ),
        ],
    },
]
// which means that values to be exposed are "witness[column 1][row 10]" and "witness[column 2][row 10]"
// in order 0, 1, respectively.

[jae-cuz]

Tried generalizaiton with reference to https://github.com/Dhole/polyexen/blob/master/src/plaf/backends/halo2.rs#L346-L367

[leolara]

So, actually this is better if we do in plaf codebase, because it is in their responsability boundary,. So I would send this as a PR there. But keep this open in case they don't accept it we can add it here.

[leolara]

Please, paste here the link to the PR to plaf when you have sent it, so we can track if it gets merged.

[jae-cuz]

Here is my PR to plaf : Dhole/polyexen#3

I would make a new issue if it is merged :) Thanks

[jae-cuz]

Move to #144.