Editing Isabelle (proof assistant) (section)

==Features<!--'Intelligible semi-automated reasoning', 'Isar (Isabelle)', 'Locale (Isabelle)', 'Metis (theorem prover)', 'Nitpick (Isabelle)', 'Nunchaku (Isabelle)', and 'Sledgehammer (Isabelle)' redirect here-->==
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 [[Zermelo–Fraenkel set theory]] (ZFC). The most widely used object logic is Isabelle/HOL, although significant set theory developments were completed in Isabelle/ZF. Isabelle's main proof method is a higher-order version of [[First-order resolution|resolution]], based on higher-order [[unification (computing)|unification]].

Though interactive, Isabelle features efficient automatic reasoning tools, such as a [[term rewriting]] engine and a [[Method of analytic tableaux|tableaux prover]], various decision procedures, and, through the '''Sledgehammer'''<!--boldface per WP:R#PLA--> proof-automation interface, external [[satisfiability modulo theories]] (SMT) solvers (including [[CVC4]]) and [[Resolution (logic)|resolution]]-based [[automated theorem prover]]s (ATPs), including [[E (theorem prover)|E]], [[SPASS]], and [[Vampire (theorem prover)|Vampire]] (the '''Metis'''<!--boldface per WP:R#PLA-->{{efn|{{IPAc-en|ˈ|m|iː|t|ɪ|s}}}} proof method reconstructs resolution proofs generated by these ATPs).<ref>Jasmin Christian Blanchette, Lukas Bulwahn, Tobias Nipkow, [https://people.mpi-inf.mpg.de/~jblanche/frocos2011-dis-proof.pdf "Automatic Proof and Disproof in Isabelle/HOL"], in: Cesare Tinelli, Viorica Sofronie-Stokkermans (eds.), [https://books.google.com/books?id=TT18o_HohVwC&dq= ''International Symposium on Frontiers of Combining Systems – FroCoS 2011''], Springer, 2011.</ref> It also features two [[Model theory|model]] finders ([[counterexample]] generators): '''Nitpick'''<!--boldface per WP:R#PLA--><ref name=:0>Jasmin Christian Blanchette, Mathias Fleury, Peter Lammich & Christoph Weidenbach, [https://www.cs.vu.nl/~jbe248/sat.pdf "A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality"], ''Journal of Automated Reasoning'' '''61''':333–365 (2018).</ref> and '''Nunchaku'''<!--boldface per WP:R#PLA-->.<ref>Andrew Reynolds, Jasmin Christian Blanchette, Simon Cruanes, Cesare Tinelli, [http://homepage.divms.uiowa.edu/~ajreynol/ijcar16a.pdf "Model Finding for Recursive Functions in SMT"], in: Nicola Olivetti, Ashish Tiwari (eds.), [https://books.google.com/books?id=HxFkDAAAQBAJ&dq= ''8th International Joint Conference on Automated Reasoning''], Springer, 2016.</ref>

Isabelle features '''locales'''<!--boldface per WP:R#PLA--> which are modules that structure large proofs. A locale fixes types, constants, and assumptions within a specified scope<ref name=:0/> so that they do not have to be repeated for every [[Lemma (mathematics)|lemma]]. 

'''Isar'''<!--boldface per WP:R#PLA--> ("'''intelligible semi-automated reasoning'''<!--boldface per WP:R#PLA-->") is Isabelle's formal proof language. It is inspired by the [[Mizar system]].<ref name=:0/>