cairo-vm is a Rust implementation of the Cairo VM. Cairo (CPU Algebraic Intermediate Representation) is a programming language for writing provable programs, where one party can prove to another that a certain computation was executed correctly without the need for this party to re-execute the same program.
In the Cairo1-run crate we should implement the option to return the Air Private Inputs.
To implement this we should see how they are implemented in the Python VM
Here is and example on how to execute them
cairo-run --program cairo_programs/proof_programs/_keccak.json --layout starknet_with_keccak --air_public_input=_keccak_public_input.json --air_private_input=_keccak_private_input.json --trace_file=_keccak_trace.json --memory_file=_keccak_memory.json --print_output --proof_mode
In the Cairo1-run crate we should implement the option to return the Air Private Inputs. To implement this we should see how they are implemented in the Python VM
https://github.com/starkware-libs/cairo-lang/blob/caba294d82eeeccc3d86a158adb8ba209bf2d8fc/src/starkware/cairo/lang/vm/cairo_run.py#L430-L431
Here is and example on how to execute them
cairo-run --program cairo_programs/proof_programs/_keccak.json --layout starknet_with_keccak --air_public_input=_keccak_public_input.json --air_private_input=_keccak_private_input.json --trace_file=_keccak_trace.json --memory_file=_keccak_memory.json --print_output --proof_mode