15-816 Linear Logic
Lecture 13: Linear Logic Programming

A logic programming language arises from a logic by fixing a particular search strategy. Computation in this paradigm is then search according to the fixed strategy, which allows algorithms to be implemented faithfully and predicable.

In this lecture we consider goal-directed proof search as the foundation of linear logic programming. In order to allow both declarative and operational readings of a program, we restrict ourselves to the right asynchronous connectives of linear logic. For those connectives, goal-directed search is sound and non-deterministically complete. The resulting language of linear hereditary Harrop formulas (LHHF) has first been proposed by Hodas and Miller and has been implemented in the Lolli language.

We concentrate on specifying search via the notion of uniform proof, a specialization of the concept of focusing to right asynchronous connectives, and discuss informally how the remaining non-determinism is resolved in order to obtain an operational semantics. In the next lecture we will experiment with the actual implementation of the Lolli language.

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Frank Pfenning