An Ode to Arrows

Liu, Hai; Hudak, Paul

doi:10.1007/978-3-642-11503-5_14

Cited by 3 publications

(1 citation statement)

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“…Even though in Functional Reactive Programming (FRP) or dataflow programming, we tend to think very operationally of init as a unit delay, there is no reason to confine CCA only to this application domain. For instance, CCA also forms the basis of a DSL for ordinary differential equations (ODEs), and arrows are indeed a better choice in implementation DSL level let-expressions in comparison to tagged AST, or higher-order abstract syntax (HOAS), because they help maintain the sharing of computation and avoid space leaks (Liu & Hudak, 2010). Many dataflow and stream programming languages provide conditionals, such as if -then-else, as part of the language (Wadge & Ashcroft, 1985;Caspi et al, 1987).…”

Section: Expressiveness and Extensionsmentioning

confidence: 99%

Causal commutative arrows

2011

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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.

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Section: Expressiveness and Extensionsmentioning

confidence: 99%