Unification Utilities for Isabelle/ML

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 $\alpha\beta\eta$-equational theory of the $\lambda$-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 $n + 1 \equiv {}?m + Suc\; 0$ may be solved by providing a prover for the background theory $\forall n.\ n + 1 \equiv n + Suc\; 0$.
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