For the last year the Axiom effort has focused on proving Axiom correct. There has been much progress on that front. Soon there will be a survey paper on prior cooperation between computer algebra systems and proof systems. The work is now entering a new phase looking at verification.
On that topic, I strongly recommend Benjamin Pierce's keynote talk on The Science of Deep Specification https://www.youtube.com/watch?v=IPNdsnRWBkk Youtube also hosts the DeepSpec Summer School videos from Summer 2017. Tim
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