Traced monoidal categories

Joyal, André; Street, Ross; Verity, Dominic

doi:10.1017/s0305004100074338

Cited by 385 publications

(560 citation statements)

References 11 publications

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“…These lemmas show that T has enough structure so that we can apply the Int construction [12,9] (with respect to coproducts) to it and obtain a category Int(T) that models interactive computation. We shall describe the interpretation of terms in Int(T) concretely and refer to loc.…”

Section: Definitionmentioning

confidence: 97%

“…For example Ghica et al have developed methods for hardware synthesis based on game semantics [7]. A related semantic approach based on the Int construction [12] has been the used to design a functional programming language for sublinear space computation [4].…”

Section: Introductionmentioning

confidence: 99%

“…The interactive model that corresponds to CPS translation and defunctionalization is constructed using the Int construction [12], which captures a canonical way of constructing a model of higher-order computation from a first-order one. As this model validates call-by-name, it is natural to consider a call-by-name CPS translation; we use a variant of the one of Hofmann and Streicher [10].…”

Section: Introductionmentioning

confidence: 99%

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On Interaction, Continuations and Defunctionalization

Schöpp

2013

Lecture Notes in Computer Science

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Abstract. In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. in Ghica's approach to hardware synthesis, or in joint work with Dal Lago on programming with sublinear space. This paper relates such semantically motivated nonstandard compilation methods to more standard techniques in the compilation of functional programming languages, such as continuation passing and defunctionalization. We first show for the linear λ -calculus that interpretation in a model of computation by interaction can be described as a call-by-name CPS transformation followed by a defunctionalization procedure that takes into account controlflow information. We then use the interactive model to guide the extension of the compositional translation to source languages with full contraction and recursion.

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Section: Definitionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Interaction, Continuations and Defunctionalization

Schöpp

2013

Lecture Notes in Computer Science

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“…The first step in constructing a model of INTML[WEC] from a model of WEC is to apply the Int-construction [11] to the category of computations. This construction is wellknown in the context of game semantics; it has been used by Abramsky and Jagadeesan to model AJM-games [2].…”

Section: Trace and Int-constructionmentioning

confidence: 99%

Computation-by-Interaction with Effects

Schöpp

2011

Programming Languages and Systems

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Abstract. A successful approach in the semantics of programming languages is to model programs by interaction dialogues. While dialogues are most often considered abstract mathematical objects, it has also been argued that they are useful for actual computation. A manual implementation of interaction dialogues can be complicated, however. To address this issue, we consider a general method for extending a given language with a metalanguage that supports the implementation of dialogues. This method is based on the construction by Dal Lago and the author of the programming language INTML, which applies interaction dialogues to sublinear space computation. We show that only few assumptions on the programming languages are needed to implement a useful INTML-like metalanguage. We identify a weak variant of the Enriched Effect Calculus (EEC) of Egger, Møgelberg & Simpson as a convenient setting for capturing the structure needed for the construction of the metalanguage. In particular, function types are not needed for the construction and iteration by means of a Conway operator is sufficient. By using EEC we show how computational effects can be accounted for in the implementation of interaction dialogues.In game semantics and related areas of programming language semantics there is a long tradition of modelling programs by interaction dialogues. Programs are modelled as entities that may engage in a dialogue with their environment. The interpretation of a program explains what kinds of queries it can receive and how it may answer. Large programs are composed of smaller ones that interact with each other, so that the whole execution of a program may be considered an interaction process. The question/answer dialogues that make up such models tend to have very concrete nature, which has lead to interesting applications, for example in algorithmic game semantics.The premise of this paper is that interaction dialogues are useful not only for interpreting programming languages, but also as an actual implementation method. There are many examples where dialogues have been used for the implementation of programs, e.g. [17,6,13]. Two recent examples provide the main motivation for the work reported here. First, Ghica introduces the Geometry of Synthesis [6] as a method of hardware synthesis. His approach is to construct a game model by implementing interaction dialogues by digital circuits and then to interpret a variant of Idealized Algol in the thus constructed game model. With this approach one can write a program in an high-level language (Idealized Algol) and by interpretation in the game model have it translated to a low-level language for digital circuits (Verilog). In this way, the implementation of dialogues is used as a method for hardware synthesis.A similar example has been studied by Dal Lago and the author in the context of computation with sublinear space [13]. There the problem is how to write programs

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“…and specifically [5] for the algebraic presentation of multiset relations), even if mostly relevant in recent years have been the graphical characterization of traced monoidal categories [6], and their duality with compact closed categories.…”

mentioning

confidence: 99%