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Ultrametric Semantics of Reactive Programs
"... Abstract—We describe a denotational model of higherorder functional reactive programming using ultrametric spaces and nonexpansive maps, which provide a natural Cartesian closed generalization of causal stream functions and guarded recursive definitions. We define a type theory corresponding to thi ..."
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Cited by 8 (3 self)
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Abstract—We describe a denotational model of higherorder functional reactive programming using ultrametric spaces and nonexpansive maps, which provide a natural Cartesian closed generalization of causal stream functions and guarded recursive definitions. We define a type theory corresponding to this semantics and show that it satisfies normalization. Finally, we show how reactive programs written in this language may be implemented efficiently using an imperatively updated dataflow graph, and give a separation logic proof that this lowlevel implementation is correct with respect to the highlevel semantics. I.
A Semantic Model for Graphical User Interfaces
, 2011
"... We give a denotational model for graphical user interface (GUI) programming in terms of the cartesian closed category of ultrametric spaces. The metric structure allows us to capture natural restrictions on reactive systems, such as causality, while still allowing recursively defined values. We capt ..."
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Cited by 7 (1 self)
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We give a denotational model for graphical user interface (GUI) programming in terms of the cartesian closed category of ultrametric spaces. The metric structure allows us to capture natural restrictions on reactive systems, such as causality, while still allowing recursively defined values. 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 a metric space themselves form a metric space under the Hausdorff metric, allowing us to interpret nondeterminism with a “powerspace ” monad on ultrametric spaces. The powerspace monad is commutative, and hence gives rise to a model of linear logic. We exploit this fact by constructing a mixed linear/nonlinear domainspecific language for GUI programming. The linear sublanguage naturally captures the 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.
Representing Contractive Functions on Streams
 UNDER CONSIDERATION FOR PUBLICATION IN THE JOURNAL OF FUNCTIONAL PROGRAMMING
, 2011
"... Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce welldefined streams? In this article we present a new approach to this problem, bas ..."
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Cited by 1 (0 self)
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Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce welldefined streams? In this article we present a new approach to this problem, based upon the topological notion of contractive functions on streams. In particular, we give a sound and complete representation theorem for contractive functions on streams, illustrate the use of this theorem as a practical means to produce welldefined streams, and show how the efficiency of the resulting definitions can be improved using another representation of contractive functions.
Representing Contractive Functions on Streams (Extended Version)
 UNDER CONSIDERATION FOR PUBLICATION IN THE JOURNAL OF FUNCTIONAL PROGRAMMING
, 2011
"... Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce welldefined streams? In this article we present a new approach to this problem, bas ..."
Abstract
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Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce welldefined streams? In this article we present a new approach to this problem, based upon the topological notion of contractive functions on streams. In particular, we give a sound and complete representation theorem for contractive functions on streams, illustrate the use of this theorem as a practical means to produce welldefined streams, and show how the efficiency of the resulting definitions can be improved using another representation of contractive functions.