Isabelle

A generic proof assistantinteractive theorem proving, n.: Writing a proof in a precise computer language so that software checks every step: the person supplies the ideas, the computer fills in small steps and guarantees that nothing is wrong. whose most widely used instance, Isabelle/HOL, is based on higher-order logic. Following the LCF design, every proof is checked by a small trusted kernel. Users write structured, human-readable proofs in the Isar language, and the Sledgehammer tool sends goals to external automated proversautomated theorem proving, n.: Getting computers to prove mathematical or logical statements by themselves, by searching for a chain of valid steps that leads from basic assumptions to the statement. and SMT solverssatisfiability modulo theories, n.: An extension of logic-puzzle solving that also understands arithmetic, arrays and other data types, so it can check whether conditions in software, such as 'x + y > 10 and x < 3', can ever be met. and then reconstructs their proofs inside Isabelle, an approach to proof automation that other systems have imitated. The Archive of Formal Proofs, a refereed online collection begun in 2004, holds a large body of formalized mathematics and computer science. Isabelle/HOL was used to verify the seL4 operating-system microkernel and, alongside LeanLean, prop. n.: A programming language and proof checker in which mathematicians write proofs that the computer verifies line by line. It has become the main language in which AI systems produce checkable proofs., appears in machine-learning theorem-proving benchmarks such as miniF2F.