Abstract
In a world where trusting software systems is problematic, formal methods and formal proofs should be able to help. Proof checking can play an important role in establishing trust since such checkers can be smaller and easier to verify than, for example, entire theorem provers or model checkers. Proof checking has played an important role in the history of programming languages and, I argue, in its future. In general, proof checkers rely on programming languages which must also be trusted. In many modern proof checkers and theorem provers, that programming language is a functional programming language, often a variant of ML. In fact, parts of ML (eg., strong typing, abstract datatypes, and higher-order programming) were designed to make ML into a trustworthy metalanguage for the finding and checking proofs in LCF [2].
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