  the isabelle theorem prover is an interactive theorem prover, successor of the higher order logic (hol) theorem prover. it is an lcf-style theorem prover (written in standard ml), so it is based on a small logical core guaranteeing logical correctness. isabelle is generic: it provides a meta-logic (a weak type theory), which is used to encode object logics like first-order logic (fol), higher-order logic (hol) or zermeloâfraenkel set theory (zfc). isabelle's main proof method is a higher-order version of resolution, based on higher-order unification. though interactive, isabelle also features efficient automatic reasoning tools, such as a term rewriting engine and a tableaux prover, as well as various decision procedures. isabelle has been used to formalize numerous theorems from mathematics and computer science, like gÃ¶del's completeness theorem, gÃ¶del's theorem about the consistency of the axiom of choice, the prime number theorem, correctness of security protocols, and properties of programming language semantics. the isabelle theorem prover is free software, released under the revised bsd license. ==example proof== isabelle's proof language isar aims to support proofs that are both human-readable and machine-checkable. for example, the proof that the square root of two is not rational can be written as follows.  sqrt2_not_rational:       m n :: nat  n_nonzero:   sqrt_rat:   lowest_terms:  ..  n_nonzero  sqrt_rat    simp    (auto
Free_theorem_provers Proof_assistants Theorem_proving_software_systems