Arbitrary-precision integer libraries such as GMP are a critical building block of computer algebra systems. provides state-of-the-art algorithms that intricate enough to justify formal verification. In this paper, we present C library has been formally verified using the Why3 verification platform in about four person-years. This deals not only with safety, but full functional correctness. It ...

We formally verify executable algorithms for solving Markov decision processes (MDPs) in the interactive theorem prover Isabelle/HOL. build on existing formalizations of probability theory to analyze expected total reward criterion finite and infinite-horizon problems. Our developments formalize Bellman equation give conditions under which optimal policies exist. Based this analysis, we dynamic...