15-816 Linear Logic

Lecture 26: Linear Unification

We examine the question of unification in the context of the linear lambda-calculus.

Because of beta-conversion, the problem is significantly harder than for first-order terms as in Lolli and in fact turns out to be undecidable. Reasonable semi-decision procedures exist, and one is described in the extended abstract below.

In practice, however, this algorithm is not directly useful for a linear logic programming because of its inherent non-determinism.

We will discuss unification for the so-called pattern fragment which guarantees most general unifiers, but cannot handle all kinds of equations. In practice, equations outside this fragment are simply postponed and carried along as constraints, sometime yielding conditional answers.

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Frank Pfenning