Causal Commutative Arrows


Hai (Paul) Liu, Eric Chang, and Paul Hudak


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 non-interference 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 speed-ups.


  ,author="Paul Liu and Eric Cheng and Paul Hudak"
  ,title="Causal Commutative Arrows"
  ,journal="Journal of Functional Programming"
  ,number="Special Issue 4-5"
  ,publisher="Cambridge University Press"