Causal Commutative Arrows Revisited Jeremy Yallop Hai Liu University of Cambridge, UK Intel Labs, USA
[email protected] [email protected] Abstract init which construct terms of an overloaded type arr. Most of the Causal commutative arrows (CCA) extend arrows with additional code listings in this paper uses these combinators, which are more constructs and laws that make them suitable for modelling domains convenient for defining instances, in place of the notation; we refer such as functional reactive programming, differential equations and the reader to Paterson (2001) for the details of the desugaring. synchronous dataflow. Earlier work has revealed that a syntactic Unfortunately, speed does not always follow succinctness. Al- transformation of CCA computations into normal form can result in though arrows in poetry are a byword for swiftness, arrows in pro- significant performance improvements, sometimes increasing the grams can introduce significant overhead. Continuing with the ex- speed of programs by orders of magnitude. In this work we refor- ample above, in order to run exp, we must instantiate the abstract mulate the normalization as a type class instance and derive op- arrow with a concrete implementation, such as the causal stream timized observation functions via a specialization to stream trans- transformer SF (Liu et al. 2009) that forms the basis of signal func- formers to demonstrate that the same dramatic improvements can tions in the Yampa domain-specific language for functional reactive be achieved without leaving the language. programming (Hudak et al. 2003): newtype SF a b = SF {unSF :: a → (b, SF a b)} Categories and Subject Descriptors D.1.1 [Programming tech- niques]: Applicative (Functional) Programming (The accompanying instances for SF , which define the arrow operators, appear on page 6.) Keywords arrows, stream transformers, optimization, equational Instantiating exp with SF brings an unpleasant surprise: the reasoning, type classes program runs orders of magnitude slower than an equivalent pro- gram that does not use arrows.