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.