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.
- BCV
- generic model of bytecode verification, i.e. data-flow analysis
for assembly languages with subtypes.
- 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
- several introductory Isabelle/Isar examples
- 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.
- Real/HahnBanach
- the Hahn-Banach theorem for real vectorspaces (Isabelle/Isar).
- 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:
- 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).