HOL: Higher-Order Logic
These are the main sources of the Isabelle system for Higher-Order Logic.
There are also several example sessions:
- Algebra
- rings and univariate polynomials
- Auth
- a new approach to verifying authentication protocols
- AxClasses
- a few basic examples of using axiomatic type classes
- BCV
- generic model of bytecode verification, i.e. data-flow analysis
for assembly languages with subtypes
- HOL-Complex
- a development of the complex numbers, the reals, and the hyper-reals,
which are used in non-standard analysis (builds the image HOL-Complex)
- HOL-Complex-HahnBanach
- the Hahn-Banach theorem for real vector spaces (in Isabelle/Isar)
- HOL-Complex-ex
- miscellaneous real ans complex number examples
- Hoare
- verification of imperative programs (verification conditions are
generated automatically from pre/post conditions and loop invariants)
- IMP
- mechanization of a large part of a semantics text by Glynn Winskel
- IMPP
- extension of IMP with local variables and mutually recursive
procedures
- IOA
- a simple theory of Input/Output Automata
- Induct
- examples of (co)inductive definitions
- Isar_examples
- several introductory examples using Isabelle/Isar
- Lambda
- fundamental properties of lambda-calculus (Church-Rosser and termination)
- Lattice
- lattices and order structures (in Isabelle/Isar)
- MicroJava
- formalization of a fragment of Java, together with a corresponding
virtual machine and a specification of its bytecode verifier and a
lightweight bytecode verifier, including proofs of type-safety.
- Modelcheck
- basic setup for integration of some model checkers in Isabelle/HOL
- NumberTheory
- fundamental Theorem of Arithmetic, Chinese Remainder Theorem,
Fermat/Euler Theorem, Wilson's Theorem
- Prolog
- a (bare-bones) implementation of Lambda-Prolog
- Subst
- defines a theory of substitution and unification.
- TLA
- Lamport's Temporal Logic of Actions (with separate example sessions)
- UNITY
- Chandy and Misra's UNITY formalism
- W0
- a precursor of MiniML, without let-expressions
- ex
- miscellaneous examples
Useful references on Higher-Order Logic:
- P. B. Andrews,
An Introduction to Mathematical Logic and Type Theory
(Academic Press, 1986).
- A. Church,
A Formulation of the Simple Theory of Types
(Journal of Symbolic Logic, 1940).
- M. J. C. Gordon and T. F. Melham (editors),
Introduction to HOL: A theorem proving environment for higher order logic
(Cambridge University Press, 1993).
- J. Lambek and P. J. Scott,
Introduction to Higher Order Categorical Logic
(Cambridge University Press, 1986).