Proof checking for delayed finite field arithmetic using floating point operators
Résumé
Formal proof checkers such as Coq, PVS and HOL light are capable of validating proofs on finite field arithmetics and their implementations but they require extensive training from potential users. We propose here to use a tool named Gappa that can be learned in a matter of minutes to hide technicalities of such formal proof checkers. We present how we overcame one limitation of Gappa for the delayed solution of a triangular system over a finite field using floating point arithmetic. We did not produce a certificate of validity of the delayed algorithm independent of all the parameters but we contributed to the trust that readers and users may have in this algorithm by spanning a large number of domains for the inputs. As they are easily implemented we hope that such practices may become routinely used during software design and tests.
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