## 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
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)
Hoare
  verification of imperative programs (verification conditions are generated automatically from pre/post conditions and loop invariants)
HoareParallel
  verification of shared-variable imperative programs a la Owicki-Gries. (verification conditions are generated automatically)
Hyperreal
  Nonstandard analysis. Builds on Real and is part of Complex.
IMP
  mechanization of a large part of a semantics text by Glynn Winskel
IMPP
  extension of IMP with local variables and mutually recursive procedures
Import
  theories imported from other (HOL) theorem provers.
Induct
  examples of (co)inductive definitions
IOA
  a simple theory of Input/Output Automata
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)
Library
  A collection of generic theories
Matrix
  two-dimensional matrices
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
NanoJava
  Haore Logic for a tiny fragment of Java
NumberTheory
  fundamental Theorem of Arithmetic, Chinese Remainder Theorem, Fermat/Euler Theorem, Wilson's Theorem, Quadratic Reciprocity
Prolog
  a (bare-bones) implementation of Lambda-Prolog
Real
  the real numbers, part of Complex
Real/HahnBanach
  the Hahn-Banach theorem for real vector spaces (in Isabelle/Isar)
SET-Protocol
  verification of the SET Protocol
Subst
  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