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Recent years have seen remarkable successes in rigorous engineering: using mathematically rigorous semantic models (not just idealised calculi) of real-world processors, programming languages, protocols, and security mechanisms, for testing, proof, analysis, and design. Building these models is challenging, requiring experimentation, dialogue with vendors or standards bodies, and validation; their scale adds engineering issues akin to those of programming to the task of writing clear and usable mathematics. But language and tool support for specification is lacking. Proof assistants can be used but bring their own difficulties, and a model produced in one, perhaps requiring many person-years effort and maintained over an extended period, cannot be used by those familiar with another.

We introduce Lem, a language for engineering reusable large-scale semantic models. The Lem design takes inspiration both …