Interpreting Localized Computational Effects Using Operators of Higher Type

Abstract

We outline a general approach to providing intensional models for languages with computational effects, whereby the problem of interpreting a given effect reduces to that of finding an operator of higher type satisfying certain equations. Our treatment consolidates and generalizes an idea that is already implicit in the literature on game semantics. As an example, we work out our approach in detail for the case of fresh name generation, and discuss some particular models to which it applies.

A Graph Model for Imperative Computation

“…We note also that Longley has recently shown how a similar category, built from an untyped graph-style model using the monad of finite multisets, as opposed to finite sets or finite sequences, provides a model of fresh name generation [12]. In future work, we plan to investigate the relationships between all these models in greater detail, and explore the constructions at the higher level of generality proposed by Hyland et al…”

“…The utility of a universal type for establishing properties of a model is well-known, and was explained in detail by Longley [11]. The central idea of this paper, of modifying Scott's graph model to record slightly different information, has also been used by Longley in [12] to obtain a model of fresh name generation. A similar model construction has been investigated by Hyland et al [7].…”