chore!: cleanup recursion interface

[kevaundray]

This PR aims to fix some of the long-standing issues with the recursion interface, in particular:

• Users needing to manually handle the aggregation objects

• asking users to pass the barretenberg proofs as inputs, and the public inputs.

• The first is fixed by removing the notion of aggregation objects from the Noir program and defining it as a "proof system public input".

• The second is fixed by defining a proof as only containing the proof elements and public inputs separately. (There is a PR up to do this more extensively, but it was temporarily shelved as we applied the changes more upstream to see what broke, after the recursion changes are made, I think we can merge that PR).

There are a few other things that I'd like to address but may be left for another PR (due to them being significant breaking changes):

• Users need to convert their proof and VK from bytes to packed fields. We currently have a 30K budget in terms of gates so it should be possible to do this conversion in circuit. The benefits of this is that proofs no longer look

• is_recursive can be added as a circuit definition, removing the need for the is_recursive flag

Checklist:

Remove the checklist to signal you've completed it. Enable auto-merge if the PR is ready to merge.

• If the pull request requires a cryptography review (e.g. cryptographic algorithm implementations) I have added the 'crypto' tag.
• I have reviewed my diff in github, line by line and removed unexpected formatting changes, testing logs, or commented-out code.
• Every change is related to the PR description.
• I have linked this pull request to relevant issues (if any exist).

[kevaundray]

This seems to be failing tests because the recursion tests don't actually set the inner public inputs, this was never flagged up before because we were using the values in the proof

[kevaundray]

One last thing to note, is the fact that this PR does not allow one to pass a proof with an aggregation object to a std::verify_proof anymore. What we'd need to do is add the prepend the aggregation object to the proof since its a "proof system public input".

Before doing this, we should clarify the possible usecases, that would require nested aggregation object and the usecases that would only require threading the output aggregation object

[AztecBot]

Benchmark results

No metrics with a significant change found.

Detailed results

All benchmarks are run on txs on the Benchmarking contract on the repository. Each tx consists of a batch call to create_note and increment_balance, which guarantees that each tx has a private call, a nested private call, a public call, and a nested public call, as well as an emitted private note, an unencrypted log, and public storage read and write.

This benchmark source data is available in JSON format on S3 here.

Values are compared against data from master at commit a60b71a5 and shown if the difference exceeds 1%.

L2 block published to L1

Each column represents the number of txs on an L2 block published to L1.

Metric	8 txs	32 txs	128 txs
l1_rollup_calldata_size_in_bytes	45,444	179,588	716,132
l1_rollup_calldata_gas	223,008	868,148	3,447,992
l1_rollup_execution_gas	842,095	3,595,256	22,203,654
l2_block_processing_time_in_ms	1,344	5,112	21,064 (-1%)
note_successful_decrypting_time_in_ms	347 (+1%)	1,042 (-6%)	3,871 (+1%)
note_trial_decrypting_time_in_ms	58.2 (+9%)	38.5 (+3%)	145 (+5%)
l2_block_building_time_in_ms	13,543	53,909	217,167
l2_block_rollup_simulation_time_in_ms	9,981	39,678 (-1%)	160,581
l2_block_public_tx_process_time_in_ms	3,530	14,161 (+2%)	56,348

L2 chain processing

Each column represents the number of blocks on the L2 chain where each block has 16 txs.

Metric	5 blocks	10 blocks
node_history_sync_time_in_ms	15,430 (-4%)	29,426
note_history_successful_decrypting_time_in_ms	2,507 (-1%)	5,067
note_history_trial_decrypting_time_in_ms	79.0 (-7%)	145 (+4%)
node_database_size_in_bytes	3,920,649	4,260,907
pxe_database_size_in_bytes	29,940	59,499

Circuits stats

Stats on running time and I/O sizes collected for every circuit run across all benchmarks.

Circuit	circuit_simulation_time_in_ms	circuit_input_size_in_bytes	circuit_output_size_in_bytes
private-kernel-init	205 (+3%)	43,109	20,441
private-kernel-ordering	114 (-1%)	25,833	9,689
base-rollup	2,053	244,144	881
root-rollup	86.7 (-2%)	4,088	889
private-kernel-inner	259	64,516	20,441
public-kernel-private-input	172	25,203	20,441
public-kernel-non-first-iteration	171	25,245	20,441
merge-rollup	11.2 (-2%)	2,608	881

Miscellaneous

Transaction sizes based on how many contracts are deployed in the tx.

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	10,323	26,359

[vezenovm]

LGTM. We have things we need to discuss with regards to nested agg object and the add_recursive_method but this can all be handled in follow-up work as this is a good improvement on the current interface.

[kevaundray]

We can fixup the nits in a separate PR and add the nested aggregation object

[kevaundray]

Will re-merge this into master when #3729 is merged