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-Real
a development of the reals and hyper-reals, which are used in non-standard analysis (builds the image HOL-Real)
HOL-Real-HahnBanach
the Hahn-Banach theorem for real vector spaces (in Isabelle/Isar)
HOL-Real-ex
miscellaneous real 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)
Lex
verification of a simple lexical analyzer generator
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.
MiniML
formalization of type inference for the language Mini-ML
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: