G. Winskel - Academia.edu (original) (raw)

Papers by G. Winskel

Theoretical Computer Science, 1996

Models for concurrency can be classified with respect to three relevant parameters: behaviour/sys... more Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. In this paper, we move a step towards a classification of models for concurrency based on the parameters above. Formally, we choose a representative of any of the eight classes of models obtained by varying the three parameters, and we study the formal relationships between using the language of category theory.

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Lecture Notes in Computer Science, 2013

Just as traditional games are represented by trees, so distributed/concurrent games are represent... more Just as traditional games are represented by trees, so distributed/concurrent games are represented by event structures. We show the determinacy of such concurrent games with Borel sets of configurations as winning conditions, provided the games are race-free and bounded-concurrent. Both restrictions are shown necessary. The determinacy proof proceeds via a reduction to the determinacy of tree games, and the determinacy of these in turn reduces to the determinacy of Gale-Stewart games.

because functicns like that of example 8.2.5 which are not sequential but still included. By indu... more because functicns like that of example 8.2.5 which are not sequential but still included. By induction on types Berry shows that the stable ordering is "hidden" in the fully abstract model of PCF and that the functions in it are stable with respect to it. As remarked above the fullyabstract model cannot contain all such functions. For first order types (of the form (@, ,... rn; ?$ where ci and 7 are ground types) he shows that the stable order is the image of the syntactic order and that the extensional order is the image of Plotkin's operational preorder 5 on terms. He conjectures that this state of affairs holds at all types in the fully-abstract model. The work of Berry and Curien ([Ber and Cur], [Cur]) on models of algorithms shows the stable ordering will be very important for a semantic construction of the full*y-abstract model. Some obvious approaches do not work however. The stable ordering alone does not support sequential functions; both parts of axioms Q for...

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, 2018

Foundations of Software Science and Computation Structures, 2018

The hiding operation, crucial in the compositional aspect of game semantics, removes computation ... more The hiding operation, crucial in the compositional aspect of game semantics, removes computation paths not leading to observable results. Accordingly, games models are usually biased towards angelic non-determinism: diverging branches are forgotten. We present here new categories of games, not suffering from this bias. In our first category, we achieve this by avoiding hiding altogether; instead morphisms are uncovered strategies (with neutral events) up to weak bisimulation. Then, we show that by hiding only certain events dubbed inessential we can consider strategies up to isomorphism, and still get a category-this partial hiding remains sound up to weak bisimulation, so we get a concrete representations of programs (as in standard concurrent games) while avoiding the angelic bias. These techniques are illustrated with an interpretation of affine nondeterministic PCF which is adequate for weak bisimulation; and may, must and fair convergences.

because functicns like that of example 8.2.5 which are not sequential but still included. By indu... more because functicns like that of example 8.2.5 which are not sequential but still included. By induction on types Berry shows that the stable ordering is "hidden" in the fully abstract model of PCF and that the functions in it are stable with respect to it. As remarked above the fullyabstract model cannot contain all such functions. For first order types (of the form (@, ,... rn; ?$ where ci and 7 are ground types) he shows that the stable order is the image of the syntactic order and that the extensional order is the image of Plotkin's operational preorder 5 on terms. He conjectures that this state of affairs holds at all types in the fully-abstract model. The work of Berry and Curien ([Ber and Cur], [Cur]) on models of algorithms shows the stable ordering will be very important for a semantic construction of the full*y-abstract model. Some obvious approaches do not work however. The stable ordering alone does not support sequential functions; both parts of axioms Q for...

because functicns like that of example 8.2.5 which are not sequential but still included. By indu... more because functicns like that of example 8.2.5 which are not sequential but still included. By induction on types Berry shows that the stable ordering is "hidden" in the fully abstract model of PCF and that the functions in it are stable with respect to it. As remarked above the fullyabstract model cannot contain all such functions. For first order types (of the form (@, ,... rn; ?$ where ci and 7 are ground types) he shows that the stable order is the image of the syntactic order and that the extensional order is the image of Plotkin's operational preorder 5 on terms. He conjectures that this state of affairs holds at all types in the fully-abstract model. The work of Berry and Curien ([Ber and Cur], [Cur]) on models of algorithms shows the stable ordering will be very important for a semantic construction of the full*y-abstract model. Some obvious approaches do not work however. The stable ordering alone does not support sequential functions; both parts of axioms Q for...

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, 2018

We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with s... more We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with symmetry, recently introduced by Castellan et al, with probability. This model supports two interpretations of PPCF, one sequential and one parallel. We make the case for this model by exploiting the causal structure of probabilistic concurrent strategies. First, we show that the strategies obtained from PPCF programs have a deadlock-free interaction, and therefore deduce that there is an interpretation-preserving functor from our games to the probabilistic relational model recently proved fully abstract by Ehrhard et al. It follows that our model is intensionally fully abstract. Finally, we propose a definition of probabilistic innocence and prove a finite definability result, leading to a second (independent) proof of full abstraction.

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, 2018

We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with s... more We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with symmetry, recently introduced by Castellan et al, with probability. This model supports two interpretations of PPCF, one sequential and one parallel. We make the case for this model by exploiting the causal structure of probabilistic concurrent strategies. First, we show that the strategies obtained from PPCF programs have a deadlock-free interaction, and therefore deduce that there is an interpretation-preserving functor from our games to the probabilistic relational model recently proved fully abstract by Ehrhard et al. It follows that our model is intensionally fully abstract. Finally, we propose a definition of probabilistic innocence and prove a finite definability result, leading to a second (independent) proof of full abstraction.

Foundations of Software Science and Computation Structures, 2018

The hiding operation, crucial in the compositional aspect of game semantics, removes computation ... more The hiding operation, crucial in the compositional aspect of game semantics, removes computation paths not leading to observable results. Accordingly, games models are usually biased towards angelic non-determinism: diverging branches are forgotten. We present here new categories of games, not suffering from this bias. In our first category, we achieve this by avoiding hiding altogether; instead morphisms are uncovered strategies (with neutral events) up to weak bisimulation. Then, we show that by hiding only certain events dubbed inessential we can consider strategies up to isomorphism, and still get a category-this partial hiding remains sound up to weak bisimulation, so we get a concrete representations of programs (as in standard concurrent games) while avoiding the angelic bias. These techniques are illustrated with an interpretation of affine nondeterministic PCF which is adequate for weak bisimulation; and may, must and fair convergences.

Foundations of Software Science and Computation Structures, 2018

The hiding operation, crucial in the compositional aspect of game semantics, removes computation ... more The hiding operation, crucial in the compositional aspect of game semantics, removes computation paths not leading to observable results. Accordingly, games models are usually biased towards angelic non-determinism: diverging branches are forgotten. We present here new categories of games, not suffering from this bias. In our first category, we achieve this by avoiding hiding altogether; instead morphisms are uncovered strategies (with neutral events) up to weak bisimulation. Then, we show that by hiding only certain events dubbed inessential we can consider strategies up to isomorphism, and still get a category-this partial hiding remains sound up to weak bisimulation, so we get a concrete representations of programs (as in standard concurrent games) while avoiding the angelic bias. These techniques are illustrated with an interpretation of affine nondeterministic PCF which is adequate for weak bisimulation; and may, must and fair convergences.

Journal of the London Mathematical Society, 2007

The concept of generalised species of structures between small categories and, correspondingly, t... more The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These definitions encompass most notions of combinatorial species considered in the literature-including of course Joyal's original notion-together with their associated substitution operation. Our first main result exhibits the substitution calculus of generalised species as arising from a Kleisli bicategory for a pseudo-comonad on profunctors. Our second main result establishes that the bicategory of generalised species of structures is cartesian closed.

ABSTRACT Many original motivations and intuitions were formed around the model of transition syst... more ABSTRACT Many original motivations and intuitions were formed around the model of transition systems. Through the medium of presheaves, we are able to cope uniformly with a range of models and their equivalences, from interleaving to independence models, and at the same time, by altering our view a little, see the approach as only a slight adjustment in the perspective that motivated Park and Milner’s definition of strong bisimulation.

ABSTRACT Many original motivations and intuitions were formed around the model of transition syst... more ABSTRACT Many original motivations and intuitions were formed around the model of transition systems. Through the medium of presheaves, we are able to cope uniformly with a range of models and their equivalences, from interleaving to independence models, and at the same time, by altering our view a little, see the approach as only a slight adjustment in the perspective that motivated Park and Milner’s definition of strong bisimulation.

These notes are designed to accompany 8-10 lectures on denotational semantics for Part II of the ... more These notes are designed to accompany 8-10 lectures on denotational semantics for Part II of the Cambridge University Computer Science Tripos. Some of the material of this course (roughly, the first half) used to form part of courses on semantics of programming languages for Parts IB/II. The Part IB course on Semantics of Programming Languages is a prerequisite. Tripos questions Of the many past Tripos questions on programming language semantics, here are those which are relevant to the current course and predate those available from the Lab webpage-all denotational semantics questions available from the Lab webpage are relevant.

Category Theory and Computer Science, 1997

Abstract. Recent work has shown that presheaf categories provide a general model of concurrency, ... more Abstract. Recent work has shown that presheaf categories provide a general model of concurrency, with an inbuilt notion of bisimulation based on open maps. Here it is shown how this approach can also han-dle systems where the language of actions may change ...

Theoretical Computer Science, 1996

Models for concurrency can be classified with respect to three relevant parameters: behaviour/sys... more Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. In this paper, we move a step towards a classification of models for concurrency based on the parameters above. Formally, we choose a representative of any of the eight classes of models obtained by varying the three parameters, and we study the formal relationships between using the language of category theory.

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Lecture Notes in Computer Science, 2013

Just as traditional games are represented by trees, so distributed/concurrent games are represent... more Just as traditional games are represented by trees, so distributed/concurrent games are represented by event structures. We show the determinacy of such concurrent games with Borel sets of configurations as winning conditions, provided the games are race-free and bounded-concurrent. Both restrictions are shown necessary. The determinacy proof proceeds via a reduction to the determinacy of tree games, and the determinacy of these in turn reduces to the determinacy of Gale-Stewart games.

because functicns like that of example 8.2.5 which are not sequential but still included. By indu... more because functicns like that of example 8.2.5 which are not sequential but still included. By induction on types Berry shows that the stable ordering is "hidden" in the fully abstract model of PCF and that the functions in it are stable with respect to it. As remarked above the fullyabstract model cannot contain all such functions. For first order types (of the form (@, ,... rn; ?$ where ci and 7 are ground types) he shows that the stable order is the image of the syntactic order and that the extensional order is the image of Plotkin's operational preorder 5 on terms. He conjectures that this state of affairs holds at all types in the fully-abstract model. The work of Berry and Curien ([Ber and Cur], [Cur]) on models of algorithms shows the stable ordering will be very important for a semantic construction of the full*y-abstract model. Some obvious approaches do not work however. The stable ordering alone does not support sequential functions; both parts of axioms Q for...

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, 2018

Foundations of Software Science and Computation Structures, 2018

The hiding operation, crucial in the compositional aspect of game semantics, removes computation ... more The hiding operation, crucial in the compositional aspect of game semantics, removes computation paths not leading to observable results. Accordingly, games models are usually biased towards angelic non-determinism: diverging branches are forgotten. We present here new categories of games, not suffering from this bias. In our first category, we achieve this by avoiding hiding altogether; instead morphisms are uncovered strategies (with neutral events) up to weak bisimulation. Then, we show that by hiding only certain events dubbed inessential we can consider strategies up to isomorphism, and still get a category-this partial hiding remains sound up to weak bisimulation, so we get a concrete representations of programs (as in standard concurrent games) while avoiding the angelic bias. These techniques are illustrated with an interpretation of affine nondeterministic PCF which is adequate for weak bisimulation; and may, must and fair convergences.

because functicns like that of example 8.2.5 which are not sequential but still included. By indu... more because functicns like that of example 8.2.5 which are not sequential but still included. By induction on types Berry shows that the stable ordering is "hidden" in the fully abstract model of PCF and that the functions in it are stable with respect to it. As remarked above the fullyabstract model cannot contain all such functions. For first order types (of the form (@, ,... rn; ?$ where ci and 7 are ground types) he shows that the stable order is the image of the syntactic order and that the extensional order is the image of Plotkin's operational preorder 5 on terms. He conjectures that this state of affairs holds at all types in the fully-abstract model. The work of Berry and Curien ([Ber and Cur], [Cur]) on models of algorithms shows the stable ordering will be very important for a semantic construction of the full*y-abstract model. Some obvious approaches do not work however. The stable ordering alone does not support sequential functions; both parts of axioms Q for...

because functicns like that of example 8.2.5 which are not sequential but still included. By indu... more because functicns like that of example 8.2.5 which are not sequential but still included. By induction on types Berry shows that the stable ordering is "hidden" in the fully abstract model of PCF and that the functions in it are stable with respect to it. As remarked above the fullyabstract model cannot contain all such functions. For first order types (of the form (@, ,... rn; ?$ where ci and 7 are ground types) he shows that the stable order is the image of the syntactic order and that the extensional order is the image of Plotkin's operational preorder 5 on terms. He conjectures that this state of affairs holds at all types in the fully-abstract model. The work of Berry and Curien ([Ber and Cur], [Cur]) on models of algorithms shows the stable ordering will be very important for a semantic construction of the full*y-abstract model. Some obvious approaches do not work however. The stable ordering alone does not support sequential functions; both parts of axioms Q for...

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, 2018

We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with s... more We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with symmetry, recently introduced by Castellan et al, with probability. This model supports two interpretations of PPCF, one sequential and one parallel. We make the case for this model by exploiting the causal structure of probabilistic concurrent strategies. First, we show that the strategies obtained from PPCF programs have a deadlock-free interaction, and therefore deduce that there is an interpretation-preserving functor from our games to the probabilistic relational model recently proved fully abstract by Ehrhard et al. It follows that our model is intensionally fully abstract. Finally, we propose a definition of probabilistic innocence and prove a finite definability result, leading to a second (independent) proof of full abstraction.

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, 2018

We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with s... more We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with symmetry, recently introduced by Castellan et al, with probability. This model supports two interpretations of PPCF, one sequential and one parallel. We make the case for this model by exploiting the causal structure of probabilistic concurrent strategies. First, we show that the strategies obtained from PPCF programs have a deadlock-free interaction, and therefore deduce that there is an interpretation-preserving functor from our games to the probabilistic relational model recently proved fully abstract by Ehrhard et al. It follows that our model is intensionally fully abstract. Finally, we propose a definition of probabilistic innocence and prove a finite definability result, leading to a second (independent) proof of full abstraction.

Foundations of Software Science and Computation Structures, 2018

The hiding operation, crucial in the compositional aspect of game semantics, removes computation ... more The hiding operation, crucial in the compositional aspect of game semantics, removes computation paths not leading to observable results. Accordingly, games models are usually biased towards angelic non-determinism: diverging branches are forgotten. We present here new categories of games, not suffering from this bias. In our first category, we achieve this by avoiding hiding altogether; instead morphisms are uncovered strategies (with neutral events) up to weak bisimulation. Then, we show that by hiding only certain events dubbed inessential we can consider strategies up to isomorphism, and still get a category-this partial hiding remains sound up to weak bisimulation, so we get a concrete representations of programs (as in standard concurrent games) while avoiding the angelic bias. These techniques are illustrated with an interpretation of affine nondeterministic PCF which is adequate for weak bisimulation; and may, must and fair convergences.

Foundations of Software Science and Computation Structures, 2018

The hiding operation, crucial in the compositional aspect of game semantics, removes computation ... more The hiding operation, crucial in the compositional aspect of game semantics, removes computation paths not leading to observable results. Accordingly, games models are usually biased towards angelic non-determinism: diverging branches are forgotten. We present here new categories of games, not suffering from this bias. In our first category, we achieve this by avoiding hiding altogether; instead morphisms are uncovered strategies (with neutral events) up to weak bisimulation. Then, we show that by hiding only certain events dubbed inessential we can consider strategies up to isomorphism, and still get a category-this partial hiding remains sound up to weak bisimulation, so we get a concrete representations of programs (as in standard concurrent games) while avoiding the angelic bias. These techniques are illustrated with an interpretation of affine nondeterministic PCF which is adequate for weak bisimulation; and may, must and fair convergences.

Journal of the London Mathematical Society, 2007

The concept of generalised species of structures between small categories and, correspondingly, t... more The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These definitions encompass most notions of combinatorial species considered in the literature-including of course Joyal's original notion-together with their associated substitution operation. Our first main result exhibits the substitution calculus of generalised species as arising from a Kleisli bicategory for a pseudo-comonad on profunctors. Our second main result establishes that the bicategory of generalised species of structures is cartesian closed.

ABSTRACT Many original motivations and intuitions were formed around the model of transition syst... more ABSTRACT Many original motivations and intuitions were formed around the model of transition systems. Through the medium of presheaves, we are able to cope uniformly with a range of models and their equivalences, from interleaving to independence models, and at the same time, by altering our view a little, see the approach as only a slight adjustment in the perspective that motivated Park and Milner’s definition of strong bisimulation.

ABSTRACT Many original motivations and intuitions were formed around the model of transition syst... more ABSTRACT Many original motivations and intuitions were formed around the model of transition systems. Through the medium of presheaves, we are able to cope uniformly with a range of models and their equivalences, from interleaving to independence models, and at the same time, by altering our view a little, see the approach as only a slight adjustment in the perspective that motivated Park and Milner’s definition of strong bisimulation.

These notes are designed to accompany 8-10 lectures on denotational semantics for Part II of the ... more These notes are designed to accompany 8-10 lectures on denotational semantics for Part II of the Cambridge University Computer Science Tripos. Some of the material of this course (roughly, the first half) used to form part of courses on semantics of programming languages for Parts IB/II. The Part IB course on Semantics of Programming Languages is a prerequisite. Tripos questions Of the many past Tripos questions on programming language semantics, here are those which are relevant to the current course and predate those available from the Lab webpage-all denotational semantics questions available from the Lab webpage are relevant.

Category Theory and Computer Science, 1997

Abstract. Recent work has shown that presheaf categories provide a general model of concurrency, ... more Abstract. Recent work has shown that presheaf categories provide a general model of concurrency, with an inbuilt notion of bisimulation based on open maps. Here it is shown how this approach can also han-dle systems where the language of actions may change ...