kappelmann/ml-unification-isabelle

This formalisation is now part of the AFP. Please refer to https://www.isa-afp.org/entries/ML_Unification.html

ML-Unification

Content

1. First-order and higher-order pattern [E-unification](https://en.wikipedia.org/wiki/Unification_(computer_science%29#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 = ?m + Suc 0 may be solved by providing a prover for the background theory forall n. n + 1 = n + Suc 0.
2. Tactics, methods, and attributes with adjustable unifiers (e.g.\ resolution, fact, assumption, OF).
3. 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.
4. Simplifier integration for e-unifiers.
5. Practical combinations of unification algorithms, e.g. a combination of first-order and higher-order pattern unification.
6. A hierarchical logger for Isabelle/ML, including per logger configurations with log levels, output channels, message filters. See Logger/README.md for details.

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.

See Examples/ for some application examples.

Build

Requirements:

1. The Isabelle development version
2. The AFP development version

Future Tasks

1. Add higher-order unifier E-unification and matching
2. tests:
   • adapt tests to work for open terms