Unification Utilities for Isabelle/ML

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

This article provides various unification utilities for Isabelle/ML, most prominently:

First-order and higher-order pattern E-unification and E-matching. While unifiers in Isabelle/ML only consider the $α β η$ -equational theory of the $λ$ -calculus, unifiers in this article may take an extra background theory, in the form of an equational prover, into account. For example, the unification problem $n + 1 \equiv ? m + S u c 0$ may be solved by providing a prover for the background theory $\forall n . n + 1 \equiv n + S u c 0$ .
Tactics, methods, and attributes with adjustable unifiers (e.g.\ resolution, fact, assumption, OF).
A generalisation of unification hints. Unification hints are a flexible extension for unifiers. Among other things, they can be used for reflective tactics, to provide canonical unification instances, or to simply strengthen the background theory of a unifier in a controlled manner.
Simplifier integration for e-unifiers.
Practical combinations of unification algorithms, e.g. a combination of first-order and higher-order pattern unification.
A hierarchical logger for Isabelle/ML, including per logger configurations with log levels, output channels, message filters.

While this entry works with every object logic, some extra setup for Isabelle/HOL and application examples are provided. All unifiers are tested with SpecCheck.

License

BSD License

Topics

Tools

Session ML_Unification

Depends on

SpecCheck - Specification-Based Testing for Isabelle/ML

Used by

Transport via Partial Galois Connections and Equivalences