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A typed foundation for directional logic programming
 In Proc. Workshop on Extensions to Logic Programming
, 1992
"... Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and d ..."
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Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and deadlockfreedom) and controlling concurrency. By using Girard’s linear logic, we are able to devise a type system that combines types and modes into a unified framework, and enables one to express directionality declaratively. The rich power of the type system allows outputs to be embedded in inputs and vice versa. Type checking guarantees that values have unique producers, but multiple consumers are still possible. From a theoretical point of view, this work provides a “logic programming interpretation ” of (the proofs of) linear logic, adding to the concurrency and functional programming interpretations that are already known. It also brings logic programming into the broader world of typed languages and typesaspropositions paradigm, enriching it with static scoping and higherorder features.
Languages, Theory
"... Every functional programmer knows about sum and product types, a+b and a×b respectively. Negative and fractional types, a−b and a/b respectively, are much less known and their computational interpretation is unfamiliar and often complicated. We show that in a programming model in which information i ..."
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Every functional programmer knows about sum and product types, a+b and a×b respectively. Negative and fractional types, a−b and a/b respectively, are much less known and their computational interpretation is unfamiliar and often complicated. We show that in a programming model in which information is preserved (such as the model introduced in our recent paper on Information Effects), these types have particularly natural computational interpretations. Intuitively, values of negative types are values that flow “backwards ” to satisfy demands and values of fractional types are values that impose constraints on their context. The combination of these negative and fractional types enables greater flexibility in programming by breaking global invariants into local ones that can be autonomously satisfied by a subcomputation. Theoretically, these types give rise to two function spaces and to two notions of continuations, suggesting that the previously observed duality of computation conflated two orthogonal notions: an additive duality that corresponds to backtracking and a multiplicative duality that corresponds to constraint propagation.