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Documents authored by Laird, James D.


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Laird, James D.

Document
A Fully Abstract Game Semantics for Countable Nondeterminism

Authors: W. John Gowers and James D. Laird

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)


Abstract
The concept of fairness for a concurrent program means that the program must be able to exhibit an unbounded amount of nondeterminism without diverging. Game semantics models of nondeterminism show that this is hard to implement; for example, Harmer and McCusker's model only admits infinite nondeterminism if there is also the possibility of divergence. We solve a long standing problem by giving a fully abstract game semantics for a simple stateful language with a countably infinite nondeterminism primitive. We see that doing so requires us to keep track of infinitary information about strategies, as well as their finite behaviours. The unbounded nondeterminism gives rise to further problems, which can be formalized as a lack of continuity in the language. In order to prove adequacy for our model (which usually requires continuity), we develop a new technique in which we simulate the nondeterminism using a deterministic stateful construction, and then use combinatorial techniques to transfer the result to the nondeterministic language. Lastly, we prove full abstraction for the model; because of the lack of continuity, we cannot deduce this from definability of compact elements in the usual way, and we have to use a stronger universality result instead. We discuss how our techniques yield proofs of adequacy for models of nondeterministic PCF, such as those given by Tsukada and Ong.

Cite as

W. John Gowers and James D. Laird. A Fully Abstract Game Semantics for Countable Nondeterminism. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 24:1-24:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gowers_et_al:LIPIcs.CSL.2018.24,
  author =	{Gowers, W. John and Laird, James D.},
  title =	{{A Fully Abstract Game Semantics for Countable Nondeterminism}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.24},
  URN =		{urn:nbn:de:0030-drops-96918},
  doi =		{10.4230/LIPIcs.CSL.2018.24},
  annote =	{Keywords: semantics, nondeterminism, games and logic}
}

Laird, James

Document
Dinaturality Meets Genericity: A Game Semantics of Bounded Polymorphism

Authors: James Laird

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)


Abstract
We study subtyping and parametric polymorphism, with the aim of providing direct and tractable semantic representations of type systems with these expressive features. The liveness order uses the Player-Opponent duality of game semantics to give a simple representation of subtyping: we generalize it to include graphs extracted directly from second-order intuitionistic types, and use the resulting complete lattice to interpret bounded polymorphic types in the style of System F_<:, but with a more tractable subtyping relation. To extend this to a semantics of terms, we use the type-derived graphs as arenas, on which strategies correspond to dinatural transformations with respect to the canonical coercions ("on the nose" copycats) induced by the liveness ordering. This relationship between the interpretation of generic and subtype polymorphism thus provides the basis of the semantics of our type system.

Cite as

James Laird. Dinaturality Meets Genericity: A Game Semantics of Bounded Polymorphism. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 33:1-33:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{laird:LIPIcs.FSCD.2023.33,
  author =	{Laird, James},
  title =	{{Dinaturality Meets Genericity: A Game Semantics of Bounded Polymorphism}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.33},
  URN =		{urn:nbn:de:0030-drops-180171},
  doi =		{10.4230/LIPIcs.FSCD.2023.33},
  annote =	{Keywords: Subtyping, Bounded Polymorphism, Game Semantics, Dinaturality}
}
Document
Sequoidal Categories and Transfinite Games: A Coalgebraic Approach to Stateful Objects in Game Semantics

Authors: William John Gowers and James Laird

Published in: LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)


Abstract
The non-commutative sequoid operator (/) on games was introduced to capture algebraically the presence of state in history-sensitive strategies in game semantics, by imposing a causality relation on the tensor product of games. Coalgebras for the functor A (/) _ - i.e., morphisms from S to A (/) S --- may be viewed as state transformers: if A (/) _ has a final coalgebra, !A, then the anamorphism of such a state transformer encapsulates its explicit state, so that it is shared only between successive invocations. We study the conditions under which a final coalgebra !A for A (/) _ is the carrier of a cofree commutative comonoid on A. That is, it is a model of the exponential of linear logic in which we can construct imperative objects such as reference cells coalgebraically, in a game semantics setting. We show that if the tensor decomposes into the sequoid, the final coalgebra !A may be endowed with the structure of the cofree commutative comonoid if there is a natural isomorphism from !(A × B)to !A (x) !B. This condition is always satisfied if !A is the bifree algebra for A (/) _, but in general it is necessary to impose it, as we establish by giving an example of a sequoidally decomposable category of games in which plays will be allowed to have transfinite length. In this category, the final coalgebra for the functor A (/)_ is not the cofree commutative comonoid over A: we illustrate this by explicitly contrasting the final sequence for the functor A (/) _ with the chain of symmetric tensor powers used in the construction of the cofree commutative comonoid as a limit by Melliès, Tabareau and Tasson.

Cite as

William John Gowers and James Laird. Sequoidal Categories and Transfinite Games: A Coalgebraic Approach to Stateful Objects in Game Semantics. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 13:1-13:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{gowers_et_al:LIPIcs.CALCO.2017.13,
  author =	{Gowers, William John and Laird, James},
  title =	{{Sequoidal Categories and Transfinite Games: A Coalgebraic Approach to Stateful Objects in Game Semantics}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Bonchi, Filippo and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.13},
  URN =		{urn:nbn:de:0030-drops-80454},
  doi =		{10.4230/LIPIcs.CALCO.2017.13},
  annote =	{Keywords: Game Semantics, Stateful Languages, Transfinite Games, Sequoid Operator}
}
Document
Polymorphic Game Semantics for Dynamic Binding

Authors: James Laird

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)


Abstract
We present a game semantics for an expressive typing system for block-structured programs with late binding of variables and System F style polymorphism. As well as generic programs and abstract datatypes, this combination may be used to represent behaviour such as dynamic dispatch and method overriding. We give a denotational models for a hierarchy of programming languages based on our typing system, including variants of PCF and Idealized Algol. These are obtained by extending polymorphic game semantics to block-structured programs. We show that the categorical structure of our models can be used to give a new interpretation of dynamic binding, and establish definability properties by imposing constraints which are identical or similar to those used to characterize definability in PCF (innocence, well-bracketing, determinacy). Moreover, relaxing these can similarly allow the interpretation of side-effects (state, control, non-determinism) - we show that in particular we may obtain a fully abstract semantics of polymorphic Idealized Algol with dynamic binding by following exactly the methodology employed in the simply-typed case.

Cite as

James Laird. Polymorphic Game Semantics for Dynamic Binding. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 27:1-27:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{laird:LIPIcs.CSL.2016.27,
  author =	{Laird, James},
  title =	{{Polymorphic Game Semantics for Dynamic Binding}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.27},
  URN =		{urn:nbn:de:0030-drops-65671},
  doi =		{10.4230/LIPIcs.CSL.2016.27},
  annote =	{Keywords: Game semantics, denotational models, PCF, Idealized Algol}
}
Document
Weighted Relational Models for Mobility

Authors: James Laird

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)


Abstract
We investigate operational and denotational semantics for computational and concurrent systems with mobile names which capture their computational properties. For example, various properties of fixed networks, such as shortest or longest path, transition probabilities, and secure data flows, correspond to the ``sum'' in a semiring of the weights of paths through the network: we aim to model networks with a dynamic topology in a similar way. Alongside rich computational formalisms such as the lambda-calculus, these can be represented as terms in a calculus of solos with weights from a complete semiring $R$, so that reduction associates a weight in R to each reduction path. Taking inspiration from differential nets, we develop a denotational semantics for this calculus in the category of sets and R-weighted relations, based on its differential and compact-closed structure, but giving a simple, syntax-independent representation of terms as matrices over R. We show that this corresponds to the sum in R of the values associated to its independent reduction paths, and that our semantics is fully abstract with respect to the observational equivalence induced by sum-of-paths evaluation.

Cite as

James Laird. Weighted Relational Models for Mobility. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 24:1-24:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{laird:LIPIcs.FSCD.2016.24,
  author =	{Laird, James},
  title =	{{Weighted Relational Models for  Mobility}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.24},
  URN =		{urn:nbn:de:0030-drops-59982},
  doi =		{10.4230/LIPIcs.FSCD.2016.24},
  annote =	{Keywords: Concurrency, Mobility, Denotational Semantics}
}
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