Computational Aspects of Linear Logic (Foundations of Computing Series)

Linear logic, first introduced by Jean-Yves Girard in 1987 as a resource-conscious logic, is a refinement of classical logic that has now matured into a rich area of active research that includes linear logic semantics, proof theory, complexity, and applications to the theory of concurrent and distributed systems. This monograph investigates several issues in the proof theory of linear logic, showing that linear logic is a computational logic behind logics, that is about computation rather than about "Truth". In addressing both complexity and programming language issues, Lincoln's main theoretical concern is to strengthen the conceptual underpinnings necessary to apply proof theory to reason about computation. The principal contribution is the author's investigation of two computational interpretations of linear logic. He first demonstrates the power of a correspondence, advocated by Girard, between proofs and computations. Lincoln next revisits the Curry-Howard correpondence between proofs and programmes, originally observed for intuitionistic logic, and shows that linear logic adds a greater degree of control over the resource-usage of programmes.