Isabelle is a generic proof assistant.
It allows mathematical formulas to be expressed in a formal language and provides tools for proving those formulas in a logical calculus. The main application is the formalization of mathematical proofs and in particular formal verification, which includes proving the correctness of computer hardware or software and proving properties of computer languages and protocols.
The most widespread instance of Isabelle nowadays is Isabelle/HOL, which provides a higher-order logic theorem proving environment that is ready to use for big applications.
Isabelle/HOL includes powerful specification tools, e.g. for (co)datatypes, (co)inductive definitions and recursive functions with complex pattern matching.
Proofs are conducted in the structured proof language Isar, allowing for proof text naturally understandable for both humans and computers.
For proofs, Isabelle incorporates some tools to improve the user’s productivity. In particular, Isabelle’s classical reasoner can perform long chains of reasoning steps to prove formulas. The simplifier can reason with and about equations. Linear arithmetic facts are proved automatically, various algebraic decision procedures are provided. External first-order provers can be invoked through sledgehammer.
Isabelle may serve as a generic framework for rapid prototyping of deductive systems. These are formulated within Isabelle’s logical framework Isabelle/Pure, which is suitable for a variety of formal calculi (e.g. axiomatic set theory).
Isabelle allows proofs to be written in two different styles, the procedural and the declarative.
This is free and open source software.
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