Towards a uniform topological treatment of streams and functions on streams

Bakker, J. W. de; Kok, Joost N.

doi:10.1007/bfb0015739

Cited by 11 publications

(2 citation statements)

References 16 publications

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“…The applications to stream programming were recognized early, but not followed up on: in a surprisingly little-cited 1985 paper [9], de Bakker and Kok proposed an ultrametric semantics for a language of first-order stream programs over integers and wrote "We think there are no problems when we allow functions of higher order[. .…”

Section: Discussionmentioning

confidence: 99%

A semantic model for graphical user interfaces

Krishnaswami

Benton

2011

SIGPLAN Not.

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We give a denotational model for graphical user interface (GUI) programming using the Cartesian closed category of ultrametric spaces. The ultrametric structure enforces causality restrictions on reactive systems and allows well-founded recursive definitions by a generalization of guardedness. We capture the arbitrariness of user input (e.g., a user gets to decide the stream of clicks she sends to a program) by making use of the fact that the closed subsets of an ultrametric space themselves form an ultrametric space, allowing us to interpret nondeterminism with a "powerspace" monad.Algebras for the powerspace monad yield a model of intuitionistic linear logic, which we exploit in the definition of a mixed linear/non-linear domain-specific language for writing GUI programs. The non-linear part of the language is used for writing reactive stream-processing functions whilst the linear sublanguage naturally captures the generativity and usage constraints on the various linear objects in GUIs, such as the elements of a DOM or scene graph.We have implemented this DSL as an extension to OCaml, and give examples demonstrating that programs in this style can be short and readable.

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Section: Discussionmentioning

confidence: 99%

A semantic model for graphical user interfaces

Krishnaswami

Benton

2011

SIGPLAN Not.

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“…Defining observable behavior in terms of input/output implants a dataflow essence within ABTs akin to such dataflow-like networks and calculi as [10], [32], and especially [14]. The coalgebraic model of ABT presented here differs from all of the above-mentioned work in a number of respects.…”

Section: Abstract Behavior Typesmentioning

confidence: 99%

Abstract Behavior Types: a foundation model for components and their composition

Arbab

2005

Science of Computer Programming

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The notion of Abstract Data Type (ADT) has served as a foundation model for structured and object oriented programming for some thirty years. The current trend in software engineering toward component based systems requires a foundation model as well. The most basic inherent property of an ADT, i.e., that it provides a set of operations, subverts some highly desirable properties in emerging formal models for components that are based on the object oriented paradigm. We introduce the notion of Abstract Behavior Type (ABT) as a higher-level alternative to ADT and propose it as a proper foundation model for both components and their composition. An ABT defines an abstract behavior as a relation among a set of timed-data-streams, without specifying any detail about the operations that may be used to implement such behavior or the data types it may manipulate for its realization. The ABT model supports a much looser coupling than is possible with the ADT's operational interface, and is inherently amenable to exogenous coordination. We propose that both of these are highly desirable, if not essential, properties for models of components and their composition. To demonstrate the utility of the ABT model, we describe Reo: an exogenous coordination language for compositional construction of component connectors based on a calculus of channels. We show the expressive power of Reo, and the applicability of ABT, through a number of examples.

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Denotational semantics of nets with nondeterminism

Kok¹

1986

Esop 86

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We define a topological framework for streams of traces. With this approach Kahn's method generalizes to nets with bounded nondeterminism. We consider fixpoints of multivalued functions. We have a standard fixed point theorem, which can be used to model feed back loops. These fixed points can also be obtained by iteration. We give a general syntax of nets and see how we can analyze them in our streamframework. We show how to avoid the Brock-Ackerman and Keller anomalies. We are able to model the fair merge, which is a continuous function in our framework, and delay along lines. We prove a lemma that says that the order in which we connect nodes in our networks does not matter. If we have nets with nodes with unbounded nondeterminism, we can still use these fixpoints, but we do lose in our topological framework our iteration theorem.

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Towards a uniform topological treatment of streams and functions on streams

Cited by 11 publications

References 16 publications

A semantic model for graphical user interfaces

A semantic model for graphical user interfaces

Abstract Behavior Types: a foundation model for components and their composition

Denotational semantics of nets with nondeterminism

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