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Four theorem provers compared across proof discovery and manipulation

blueberrywren.dev 40 min read Editor score 6/10

The comparison covers Lean, Isabelle/HOL, HOL4, and Agda, including proof discovery, manipulation, and the author’s rankings. Engineers choosing or studying formal verification tools get a practical, if explicitly opinionated, perspective.

What

Lean, Isabelle/HOL, HOL4 and Agda are theorem provers for computer-formalizing mathematics.

How

Lean and Agda use dependent types; Isabelle/HOL and HOL4 use LCF-style kernels. The review formalizes Euclid’s proof of infinitely many primes in all four.

Why it matters

These contrasts help engineers choose proof tooling based on foundations, interactivity and automation.

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