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Causal commutative arrows

Part of: JFP Research Articles

Published online by Cambridge University Press:  29 June 2011

HAI LIU ,
ERIC CHENG  and
PAUL HUDAK
HAI LIU
Affiliation:
Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail: hai.liu@aya.yale.edu, eric.cheng@aya.yale.edu, paul.hudak@yale.edu)
ERIC CHENG
Affiliation:
Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail: hai.liu@aya.yale.edu, eric.cheng@aya.yale.edu, paul.hudak@yale.edu)
PAUL HUDAK
Affiliation:
Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail: hai.liu@aya.yale.edu, eric.cheng@aya.yale.edu, paul.hudak@yale.edu)
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Abstract

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Arrows are a popular form of abstract computation. Being more general than monads, they are more broadly applicable, and, in particular, are a good abstraction for signal processing and dataflow computations. Most notably, arrows form the basis for a domain-specific language called Yampa, which has been used in a variety of concrete applications, including animation, robotics, sound synthesis, control systems, and graphical user interfaces. Our primary interest is in better understanding the class of abstract computations captured by Yampa. Unfortunately, arrows are not concrete enough to do this with precision. To remedy this situation, we introduce the concept of commutative arrows that capture a noninterference property of concurrent computations. We also add an init operator that captures the causal nature of arrow effects, and identify its associated law. To study this class of computations in more detail, we define an extension to arrows called causal commutative arrows (CCA), and study its properties. Our key contribution is the identification of a normal form for CCA called causal commutative normal form (CCNF). By defining a normalization procedure, we have developed an optimization strategy that yields dramatic improvements in performance over conventional implementations of arrows. We have implemented this technique in Haskell, and conducted benchmarks that validate the effectiveness of our approach. When compiled with the Glasgow Haskell Compiler (GHC), the overall methodology can result in significant speedups.

Type
Articles
Information
Journal of Functional Programming , Volume 21 , Special Issue 4-5: Dedicated to ICFP 2009 , September 2011 , pp. 467 - 496
Copyright
Copyright © Cambridge University Press 2011

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