Summary: Computational Interpretations of Linear Logic
Department of Computing
Imperial College of Science, Technology and Medicine
180 Queen's Gate, London SW7 2BZ, England
To appear in Theoretical Computer Science
February 27, 1992
We study Girard's Linear Logic from the point of view of giving a concrete compu
tational interpretation of the logic, based on the CurryHoward isomorphism. In the
case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus,
giving finer control over order of evaluation and storage allocation, while maintain
ing the logical content of programs as proofs, and computation as cutelimination.
In the classical case, it leads to a concurrent process paradigm with an operational
semantics in the style of Berry and Boudol's Chemical Abstract Machine. This opens
up a promising new approach to the parallel implementation of functional program
ming languages; and offers the prospect of typed concurrent programming in which
correctness is guaranteed by the typing.