<theory, tool> A generic theorem prover with support for several object-logics, developed by Lawrence C. Paulson <Larry.Paulson@cl.cam.ac.uk> in collaboration with Tobias Nipkow (http://in.tum.de/~nipkow/) at the Technical University of Munich.
Isabelle supports first-order logic - constructive and classical versions; higher-order logic, similar to Gordon's HOL; Zermelo Fränkel set theory; an extensional version of Martin Löf's type theory, the classical first-order sequent calculus, LK; the modal logics T, S4, and S43; and Logic for Computable Functions.
An object logic's syntax and inference rules are specified declaratively allowing single-step proof construction. Proof procedures can be expressed using "tactics" and "tacticals". Isabelle provides control structures for expressing search procedures and generic tools such as simplifiers and classical theorem provers which can be applied to object-logics. Isabelle is built on top of Standard ML and uses its user interface.
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