Bounded linear types in a resource semiring

Abstract. Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce a bounded linear typing discipline on a general notion of resource which can be modeled in a semiring. For this type system we provide both a general type-inference procedure, parameter-ized by the decision procedure of the semiring equational theory, and a (coherent) categorical semantics. This could be a useful type-theoretic and denotational framework for resource-sensitive compilation, and it represents a generalization of several existing type systems. As a non-trivial instance, motivated by hardware compilation, we present a com-plex new application to calculating and controlling timing of execution in a (recursion-free) higher-order functional programming language with local store. 1 Resource-aware types and semantics The two important things about a computer program are what it computes an