Combining and Relating Control Effects and their Semantics

Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a programming language which includes these features, as well as higher-order references. They are obtained by contrasting methodologies: by annotating sequences of moves with "control pointers" indicating where exceptions are thrown and caught, and by composing the exceptions and continuations monads. The former approach allows an explicit representation of control flow in games for exceptions, and hence a straightforward proof of definability (full abstraction) by factorization, as well as offering the possibility of a semantic approach to control flow analysis of exception-handling. However, establishing soundness of such a concrete and complex model is a non-trivial problem. It may be resolved by establishing a correspondence with the monad semantics, based on erasing explicit exception moves and replacing them with control pointers.Comment: In Proceedings COS 2013, arXiv:1309.092

A Fully Abstract Game Semantics for Parallelism with Non-Blocking Synchronization on Shared Variables

We present a fully abstract game semantics for an Algol-like parallel language with non-blocking synchronization primitive. Elaborating on Harmer\u27s game model for nondeterminism, we develop a game framework appropriate for modeling parallelism. The game is a sophistication of the wait-notify game proposed in a previous work, which makes the signals for thread scheduling explicit with a certain set of extra moves. The extra moves induce a Kleisli category of games, on which we develop a game semantics of the Algol-like parallel language and establish the full abstraction result with a significant use of the non-blocking synchronization operation

Game semantics for first-order logic

We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results. We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of first-order classical logic. We present some relations with Krivine's classical realizability and applications to type isomorphisms

FULL ABSTRACTION FOR NOMINAL GENERAL REFERENCES

Copyright for articles published in Logical Methods in Computer Science is retained by the authors. Logical Methods in Computer Science is an open-access journal. All journal content is licensed under a Creative Commons license (http://creativecommons.org/licenses/by-nd/2.0/)Published in Logical Methods in Computer Science Vol. 5 (3:8) 2009, pp. 1–69 www.lmcs-online.orgResearch financially supported by the Engineering and Physical Sciences Research Council, the Eugenides Foundation, the A. G. Leventis Foundation and Brasenose College

A fully abstract game semantics of local exceptions

A fully abstract game semantics for an extension of Idealized Algol with locally declared exceptions is presented. It is based on "Hyland-Ong games", but as well as relaxing the constraints which impose functional behaviour (as in games models of other computational effects such as continuations and references), new structure is added to plays in the form of additional pointers which track the flow of control. The semantics is proved to be fully abstract by a factorization of strategies into a 'new-exception generator' and a strategy with local control flow. It is shown, using examples, that there is no model of exceptions which is a conservative extension of the semantics of Idealized Algol without the new pointers

Imperative Programs as Proofs via Game Semantics

Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this thesis we describe a logical counterpart to this extension, in which proofs denote such strategies. The system is expressive: it contains all of the connectives of Intuitionistic Linear Logic, and first-order quantification. Use of a novel sequoid operator allows proofs with imperative behaviour to be expressed. Thus, we can embed first-order Intuitionistic Linear Logic into this system, Polarized Linear Logic, and an expressive imperative total programming language. We can use the first-order structure to express properties on the imperative programs. The proof system has a tight connection with a simple game model, where games are forests of plays. Formulas are modelled as games, and proofs as history-sensitive winning strategies. We provide a strong full and faithful completeness result with respect to this model: each finitary strategy is the denotation of a unique analytic (cut-free) proof. Infinite strategies correspond to analytic proofs that are infinitely deep. Thus, we can normalise proofs, via the semantics. The proof system makes novel use of the fact that the sequoid operator allows the exponential modality of linear logic to be expressed as a final coalgebra.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A Fully Abstract Game Semantics of Local Exceptions

Abstract A fully abstract game semantics for an extension of Idealized Algol with locally declared exceptions is presented. It is based on "Hyland-Ong games", but as well as relaxing the constraints which impose functional behaviour (as in games models of other computational effects such as continuations and references), new structure is added to plays in the form of additional pointers which track the flow of control. The semantics is proved to be fully abstract by a factorization of strategies into a `new-exception generator ' and a strategy with local control flow. It is shown, using examples, that there is no model of exceptions which is a conservative extension of the semantics of Idealized Algol without the new pointers