Games for syntactic control of interference

This thesis proposes a game semantics for languages that adhere to the design principles first proposed by John Reynolds in Syntactic Control of Interference. A pair of subterms of a program written in a language adherent to the SCI principles enjoy the property that the evaluation of one will have no impact on the subsequent evaluation of the other if they contain no free identifier in common. The proposed model relies upon a novel notion of view based on partial orders of moves, rather than sequences of moves, to capture the inability of programs to discern the order of execution of non-interfering side-effects. Three languages from the literature that obey the SCI principles are interpreted in the model: PCF This language controls interference by eschewing any imperative features. Basic SCI At the other extreme, this language outlaws aliasing and thus prevents subterms containing distinct free identifiers from accessing the same parts of the store. SCIR Aliasing is outlawed for those identifiers that can affect the store but may be permissible for those that cannot. It incorporates a sophisticated notion of passive type; containing no phrases which assign to non-local store. This notion is distinct from that of passive use: identifiers in the context of a typing judgement that are perhaps not of passive type but that are used only passively in the term. The games model defined in this thesis is shown to possess the definability property for each of the three languages: every finite element of the model is the denotation of a term of the language in question. Using this property, the model can be used to characterize program equivalence in each of the languages precisely; that is, a fully abstract model can be built.