A tale of four theorem provers, or: A (reasonably) opinionated comparison of Isabelle/HOL, Lean, HOL4, and Agda
6.6 relevance
Score Breakdown
technical depth 9
novelty 6
actionability 5
community 6
strategic 5
personal 6
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Comparison of theorem provers is technically deep but not directly actionable for most engineers.
Summary
In which I compare Lean, Isabelle/HOL, Agda, and HOL4 with only mild regard for "fairness". All four of the above are theorem proving applications; that is, their purpose is to computer-formalize mathematics. Broadly speaking, both Lean and Agda are dependent-types based systems, utilizing the Curry-Howard correspondence to prove theorems via a complex type system, whereas Isabelle/HOL and HOL4 are LCF-style systems, with a small "proof kernel" containing base rules (e.g.forall x, x = x) that all proofs must be constructed via.