## 15-816 Linear Logic |

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.

- Linear Higher-Order
Pre-Unification,

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.

Frank Pfenning fp@cs