Logic Programming and Meta-Logic

The theory of cut-free sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, lambda Prolog and its linear logic refinement, Lolli, provide for various forms of abstraction (modules, abstract data types, and higher-order programming) but lack primitives for concurrency. The logic programming language LO (Linear Objects) provides some primitives for concurrency but lacks abstraction mechanisms. A logic programming presentation of all of higher-order linear logic, named Forum, modularly extends these other languages and also allows for abstractions and concurrency in specifications. To illustrate the expressive strengths of Forum, we specify in it a sequent calculus proof system and the operational semantics of a programming language that incorporates side-effects.