A game semantics of names and pointers

J. Laird
2008 Annals of Pure and Applied Logic  
We describe a fully abstract semantics for a simple functional language with locally declared names which may be used as pointers to names. It is based on a category of dialogue games acted upon by the group of natural number automorphisms. This allows a formal, semantic characterization of the key properties of names such as freshness and locality. We describe a model of the call-by-value λ-calculus (a closed Freyd category) based on these games, and show that it can be used to interpret the
more » ... -calculus of Pitts and Stark. We then construct a model of our pointer-language by extending our category of games with an explicit representation of the store, using a notion of semantic garbage-collection to erase inaccessible pointers. Using factorization and decomposition techniques, we show that the compact elements of our model are definable as terms, and hence it is fully abstract.
doi:10.1016/j.apal.2007.10.006 fatcat:twc3zxtizvajvnwhvrdn3sqgsi