On the unity of duality

Most type systems are agnostic regarding the evaluation strategy for the underlying languages, with the value restriction for ML which is absent in Haskell as a notable exception. As type systems become more precise, however, detailed properties of the operational semantics may become visible because properties captured by the types may be sound under one strategy but not the other. For example, intersection types distinguish between call-by-name and call-by-value functions, because the subtyping law (A B) (A C) A (B C) is unsound for the latter in the presence of effects. In this paper we develop a proof-theoretic framework for analyzing the interaction of types with evaluation order, based on the notion of polarity. Polarity was discovered through linear logic, but we propose a fresh origin in Dummett's program of justifying the logical laws through alternative verifica

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Noam Zeilberger
• Keywords: Agnostic Regarding, APAL 2008, Most Type Systems, Type Systems