A Game Semantics of Local Names and Good Variables

Abstract

Abstract. We describe a game semantics for local names in a functional setting. It is based on a category of dialogue games acted upon by the automorphism group of the natural numbers; this allows properties of names such as freshness and locality to be characterized semantically. We describe a model of the nu-calculus in this category, and extend it with named references (without bad variables) using names as pointers to a store. After refining the semantics via a notion of garbage collection, we prove that the compact elements are definable as terms, and hence obtain a full abstraction result.

Nominal Game Semantics

“…Since 2004, the nominal approach has led to a series of new full abstraction results. The languages covered are the ν-calculus [3] (purely functional language with names), λν [25] (a higher-order language with storage of untyped names), Reduced ML [31] (a higher-order language with integer-valued storage), RefML [32] (higher-order references) and Middleweight Java [34]. Nominal game semantics has also been used to model Concurrent ML [26] and exceptions [34].…”

Capsules and Closures: A Small-Step Approach

“…State is typically modeled by some form of heap from which storage locations can be allocated and deallocated [7,15,20,21]. Others have used game semantics to reason about local state [4,5,10]. Mason and Talcott [12][13][14] and Felleisen and Hieb [6] present a semantics based on a heap and storage locations.…”

Relational Semantics for Higher-Order Programs

“…Others have used game semantics to reason about programs with local state [19][20][21][22]. Several full abstraction results have come from using game semantics to represent languages with state and higher-order constructs.…”