pilopt: equal-constrained witness columns removal

[gzanitti]

Resolves #2081

[chriseth]

Nice! Did you try what the result on test_data/std/poseidon_gl_test.asm is?

[gzanitti]

Nice! Did you try what the result on test_data/std/poseidon_gl_test.asm is?

Yes, it went from Removed 164 witness and 154 fixed columns. Total count now: 99 witness and 50 fixed columns. to Removed 175 witness and 154 fixed columns. Total count now: 88 witness and 50 fixed columns.

[chriseth]

This looks great now! One last annoying thing to test: Array elements. The issue is that we cannot remove them (because we would need to shorten the array by one element and update the indices, etc - it's very tricky).

Can you add a test of the form let w: col[20]; w[4] = w[7]; and see what happens? Please also include some references to the (potentially) removed witness column both in other identities and in hints / prover functions.

[chriseth]

I think remove_constant_witness_columns already avoids removing arrays, but I think it does not correctly avoid removing array elements (.is_array() only returns true on the first element of the array or on the array itself). The function build_poly_id_to_definition_name_lookup already creates a lookup table that could be extended to also supply the information if the PolyID is an array element or not.