Functional reactive programming, or FRP, is a paradigm for programming hybrid systems -- i.e., systems containing a combination of both continuous and discrete components -- in a high-level, declarative way. The key ideas in FRP are its notions of continuous, time-varying values, and time-ordered sequences of discrete events.

Functional Reactive Programming (FRP) is a high-level declarative language for programming reactive systems. Previous work on FRP has demonstrated its utility in a wide range of application domains, including animation, graphical user interfaces, and robotics. FRP has an elegant continuous-time denotational semantics. However, it guarantees no bounds on execution time or space, thus making it unsuitable for many embedded real-time applications. To alleviate this problem, we recently developed Real-Time FRP (RT-FRP), whose operational semantics permits us to formally guarantee bounds on both execution time and space. In this paper we present a formally verifiable compilation strategy from a new language based on RT-FRP into imperative code. The new language, called Event-Driven FRP (E-FRP), is more tuned to the paradigm of having multiple external events. While it is smaller than RT-FRP, it features a key construct that allows us to compile the language into efficient code. We have used this language and its compiler to generate code for a small robot controller that runs on a PIC16C66 micro-controller. Because the formal specification of compilation was crafted more for clarity and for technical convenience, we describe an implementation that produces more efficient code.

With this machinery, we can give a common structure to programs based on different notions of computation. The generality of arrows tends to force one into a point-free style, which is useful for proving general properties. However it is not to everyone's taste, and can be awkward for programming specific instances. The solution is a point-wise notation for arrows, which is automatically translated to the functional language Haskell. Each notion of computation thus defines a special sublanguage of Haskell. 1 Notions of computation We shall explore what we mean by a notion of computation using four varied examples. As a point of comparison, we shall consider how the following operator on functions may be generalized to the various types of `function-like ' components.

A limited form of dependent types, called Generalized Algebraic Data Types (GADTs), has recently been added to the list of Haskell extensions supported by the Glasgow Haskell Compiler. Despite not being full-fledged dependent types, GADTs still offer considerably enlarged scope for enforcing important code and data invariants statically. Moreover, GADTs offer the tantalizing possibility of writing more efficient programs since capturing invariants statically through the type system sometimes obviates entire layers of dynamic tests and associated data markup. This paper is a case study on the applications of GADTs in the context of Yampa, a domainspecific language for Functional Reactive Programming in the form of a self-optimizing, arrow-based Haskell combinator library. The paper has two aims. Firstly, to explore what kind of optimizations GADTs make possible in this context. Much of that should also be relevant for other domain-specific embedded language implementations, in particular arrow-based ones. Secondly, as the actual performance impact of the GADT-based optimizations is not obvious, to quantify this impact, both on tailored micro benchmarks, to establish the effectiveness of individual optimizations, and on two fairly large, realistic applications, to gauge the overall impact. The performance gains for the micro benchmarks are substantial. This implies that the Yampa API could be simplified as a number of “pre-composed ” primitives that were there mainly for performance reasons are no longer needed. As to the applications, a worthwhile performance gain was obtained in one case whereas the performance was more or less unchanged in the other.

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. 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 kind of non-interference property of concurrent computations. We also add an init operator, and identify a crucial law that captures the causal nature of arrow effects. We call the resulting computational model causal commutative arrows. To study this class of computations in more detail, we define an extension to the simply typed lambda calculus 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 combined with stream fusion, the overall methodology can result in speed-ups of greater than two orders of magnitude.

Abstract. Functional reactive programming integrates dynamic dataflow with functional programming to offer an elegant and powerful model for expressing computations over time-varying values. Developing realistic applications, however, requires access to libraries, such as those for GUIs, that are written in mainstream object-oriented languages. Previous work has developed functional reactive interfaces for GUI toolkits but has not provided an account of the principles underlying the implementation strategy. In this paper, we investigate this problem by studying the adaptation of the objectoriented toolkit MrEd to the functional reactive language FrTime. The heart of this problem is how to communicate state changes between the application and the toolkit’s widget objects. After presenting a basic strategy for adaptation, we discuss abstraction techniques based on mixins and macros that allow us to adapt numerous properties in many widget classes with minimal code duplication. This results in a wrapper for the entire MrEd toolkit in only a few hundred lines of code. We also briefly discuss a spreadsheet developed with the resulting toolkit. 1

Abstract. We introduce the arrow calculus, a metalanguage for manipulating Hughes’s arrows with close relations both to Moggi’s metalanguage for monads and to Paterson’s arrow notation. Arrows are classically defined by extending lambda calculus with three constructs satisfying nine (somewhat idiosyncratic) laws. In contrast, the arrow calculus adds four constructs satisfying five laws. Two of the constructs are arrow abstraction and application (satisfying beta and eta laws) and two correspond to unit and bind for monads (satisfying left unit, right unit, and associativity laws). The five laws were previously known to be sound; we show that they are also complete, and hence that the five laws may replace the nine. We give a translation from classic arrows into the arrow calculus to complement Paterson’s desugaring and show that the two translations form an equational correspondence in the sense of Sabry and Felleisen. We are also the first to publish formal type rules (which are unusual in that they require two contexts), which greatly aided our understanding of arrows. The first fruit of our new calculus is to reveal some redundancies in the classic formulation: the nine classic arrow laws can be reduced to eight, and the three additional classic arrow laws for arrows with apply can be reduced to two. The calculus has also been used to clarify the relationship between idioms, arrows and monads and as the inspiration for a categorical semantics of arrows. 1

Invertible programming occurs in the area of data conversion where it is required that the conversion in one direction is the inverse of the other. For that purpose, we introduce bidirectional arrows (biarrows). The bi-arrow class is an extension of Haskell’s arrow class with an extra combinator that changes the direction of computation. The advantage of the use of bi-arrows for invertible programming is the preservation of invertibility properties using the biarrow combinators. Programming with bi-arrows in a polytypic or generic way exploits this the most. Besides bidirectional polytypic examples, including invertible serialization, we give the definition of a monadic bi-arrow transformer, which we use to construct a bidirectional parser/pretty printer.

Abstract: Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals. FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discrete-time signals (hybrid systems). What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order data-flow constructs. This raises a range of implementation challenges. This paper contributes towards advancing the state of the art of FRP implementation by studying the notion of signal change and change propagation in a setting of hybrid signal function networks with dynamic structure. To sidestep some problems of certain previous FRP implementations that are structured using arrows, we suggest working with a notion of composable, multi-input and multi-output signal functions. A clear conceptual distinction is also made between continuous-time and discrete-time signals. We then show how establishing change-related properties of the signal functions in a network allows such networks to be simplified (static optimisation) and can help reducing the amount of computation needed for executing the networks (dynamic optimisation). Interestingly, distinguishing between continuous-time and discrete-time signals allows us to characterise the change-related properties of signal functions more precisely than what we otherwise would have been able to, which is helpful for optimisation.

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on time-varying values (signals). FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discretetime signals (hybrid systems). What sets FRP apart from most other reactive languages is its support for systems with highly dynamic structure (dynamism) and higher-order reactive constructs (higher-order data-flow). However, the price paid for these features has been the loss of the safety and performance guarantees provided by other, less expressive, reactive languages. Statically guaranteeing safety properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checksthatguaranteedomain-specificconstraints, suchasfeedbackbeingwell-formed(causality analysis). However, comparedwithFRP,theyarelimitedintheircapacitytosupportdynamism andhigher-orderdata-flow. Ontheotherhand, asestablishedstatictechniquesdonotsufficefor highly structurally dynamic systems, FRP generally enforces few domain-specific constraints, leaving the FRP programmer to manually check that the constraints are respected. Thus, there