HOL: Higher-Order Logic

This directory contains the ML sources of the Isabelle system for Higher-Order Logic.

There are several subdirectories with examples:

ex
general examples
Auth
a new approach to verifying authentication protocols
AxClasses
a few axiomatic type class examples:
Tutorial
Some simple axclass demos that go along with the axclass Isabelle document (isatool doc axclass).
Group
Some bits of group theory.
Lattice
Basic theory of lattices and orders.
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
Induct
examples of (co)inductive definitions
Integ
a development of the integers including efficient integer calculations (part of the standard HOL environment)
IOA
a simple theory of Input/Output Automata
Isar_examples
some Isabelle/Isar proof documents
Lambda
a proof of the Church-Rosser theorem for lambda-calculus
Lex
verification of a simple lexical analyzer generator
MiniML
formalization of type inference for the language Mini-ML
Real
a development of the reals and hyper-reals, which are used in non-standard analysis. Also includes the positive rationals. Used to build the image HOL-Real.
Subst
defines a theory of substitution and unification.
TLA
Lamport's Temporal Logic of Actions
Tools
holds code used to provide support for records, datatypes, induction, etc.
UNITY
Chandy and Misra's UNITY formalism.
W0
a precursor of MiniML, without let-expressions
Useful references on Higher-Order Logic: