19,952 research outputs found
The three dimensions of proofs
In this document, we study a 3-polygraphic translation for the proofs of SKS,
a formal system for classical propositional logic. We prove that the free
3-category generated by this 3-polygraph describes the proofs of classical
propositional logic modulo structural bureaucracy. We give a 3-dimensional
generalization of Penrose diagrams and use it to provide several pictures of a
proof. We sketch how local transformations of proofs yield a non contrived
example of 4-dimensional rewriting.Comment: 38 pages, 50 figure
A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4
Being able to soundly estimate roundoff errors of finite-precision
computations is important for many applications in embedded systems and
scientific computing. Due to the discrepancy between continuous reals and
discrete finite-precision values, automated static analysis tools are highly
valuable to estimate roundoff errors. The results, however, are only as correct
as the implementations of the static analysis tools. This paper presents a
formally verified and modular tool which fully automatically checks the
correctness of finite-precision roundoff error bounds encoded in a certificate.
We present implementations of certificate generation and checking for both Coq
and HOL4 and evaluate it on a number of examples from the literature. The
experiments use both in-logic evaluation of Coq and HOL4, and execution of
extracted code outside of the logics: we benchmark Coq extracted unverified
OCaml code and a CakeML-generated verified binary
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