Add support for preprocessed columns
- Dominant language
- Rust
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- 96
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Description
To make AirScript constraint scope capture [randomized AIR with preprocessing (RAP)](https://hackmd.io/@aztec-network/plonk-arithmetiization-air) (and not limiting it to AIR with injected verifier randomness), it would be necessary to add support for preprocessed columns. This would make AirScript a DSL ready to be used in other projects, since RAPs are the most generic way we have at the moment to capture computations of a computational model. For example, RAPs can easily describe Plonk or R1CS constraint systems, making it able to capture arithmetic circuits.
Based on the idea of how periodic columns are handled in AirScript and knowing that preprocessed columns are publicly known to both the prover and the verifier before the STARK generation, it makes sense to invent a syntax for preprocessed columns that is explicit.
I think that one of the two following approaches would work (I use python-like syntax to denote the preprocessed columns shape):
1. Add a new declaration for preprocessed columns in the `trace_columns` section, e.g.:
```
trace_columns:
main: [a,b]
aux: [c,d]
pre:
L1: [1] + [0]*(T-1)
```
2. Create a section for preprocessed columns, e.g.:
```
preprocessed_columns:
L1: [1] + [0]*(T-1)
```
I the previous examples, I have used `T`for denoting the number of rows in the execution trace.
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