Abstract

If we view functions as processes, then their resources are their arguments, supplied through application, and used by the function to produce a result. In this paper, we define resource use for functions, based on the syntactic notion of needed redexes from [BKKS86]. We introduce a variant of neededhess, tail-neededness, and define packets of needed descendants of redexes in order to mea- sure the degree of neededhess. These results are generalised to produce a semantic characterisation of the resource use properties of functions, using a term-model. By means of the Curry-Howard isomorphism, we apply these ideas to proof trees of propositions in Intuitionistic Logic to demonstrate that propositions, i.e. types, can be used to express the usage properties of functions. A resource-aware type system capable of inferring such types for A-terms is presented.

Citations