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.

This paper presents an embedded security sublanguage for enforcing information-flow policies in the standard Haskell programming language. The sublanguage provides useful information-flow control mechanisms including dynamic security lattices, run-time code privileges and declassification, without modifying the base language. This design avoids the redundant work of producing new languages, lowers the threshold for adopting security-typed languages, and also provides great flexibility and modularity for using security-policy frameworks. The embedded security sublanguage is designed using a standard combinator interface called arrows. Computations constructed in the sublanguage have static and explicit control-flow components, making it possible to implement information-flow control using static-analysis techniques at run time, while providing strong security guarantees. This paper presents a concrete Haskell implementation and an example application demonstrating the proposed techniques. 1.

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.

We show that quantum computation can be decomposed in a pure classical (functional) part and an effectful part modeling probabilities and measurement. The effectful part can be modeled using a generalization of monads called arrows. Both the functional and effectful parts can be elegantly expressed in the Haskell programming language. 1

Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure context-dependent computation. In particular, we develop a generic comonadic interpreter of languages for context-dependent computation and instantiate it for stream-based computation. We also discuss distributive laws of a comonad over a monad as a means to structure combinations of effectful and context-dependent computation. We apply the latter to analyse clocked dataflow (partial stream based) computation. 1

Monads are by now well-established as programming construct in functional languages. Recently, the notion of “Arrow ” was introduced by Hughes as an extension, not with one, but with two type parameters. At first, these Arrows may look somewhat arbitrary. Here we show that they are categorically fairly civilised, by showing that they correspond to monoids in suitable subcategories of bifunctors C op ×C → C. This shows that, at a suitable level of abstraction, arrows are like monads — which are monoids in categories of functors C → C. Freyd categories have been introduced by Power and Robinson to model computational effects, well before Hughes ’ Arrows appeared. It is often claimed (informally) that Arrows are simply Freyd categories. We shall make this claim precise by showing how monoids in categories of bifunctors exactly correspond to Freyd categories.

Certain programs making use of monads need to perform recursion over the values of monadic actions. Although the do-notation of Haskell provides a convenient framework for monadic programming, it lacks the generality to support such recursive bindings. In this paper, we describe an enhanced translation schema for the donotation and its integration into Haskell. The new translation allows variables to be bound recursively, provided the underlying monad comes equipped with an appropriate fixed-point operator.

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 dataflow 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 reactive constructs. Statically guaranteeing correctness 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 checks that guarantee domain-specific properties, such as feedback loops always being well-formed. However, they are limited in their capabilities to support dynamism and higher-order data-flow compared with FRP. Thus, the onus of ensuring such properties of FRP programs has so far been on the programmer as established static techniques do not suffice. In this paper, we show how dependent types allow this concern to be addressed. We present an implementation of FRP embedded in the dependently-typed language Agda, leveraging the type system of the host language to craft a domain-specific (dependent) type system for FRP. The implementation constitutes a discrete, operational semantics of FRP, and as it passes the Agda type, coverage, and termination checks, we know the operational semantics is total, which means our type system is safe. Categories and Subject Descriptors D.3.2 [Programming Languages]: Language Classifications—applicative (functional) languages, data-flow languages, specialized application languages General Terms Languages Keywords dependent types, domain-specific languages, DSELs, FRP, functional programming, reactive programming, synchronous data-flow

Abstract. Monads have been employed in programming languages for modeling various language features, most importantly those that involve side effects. In particular, Haskell’s IO monad provides access to I/O operations and mutable variables, without compromising referential transparency. Cyclic definitions that involve monadic computations give rise to the concept of value-recursion, where the fixed-point computation takes place only over the values, without repeating or losing effects. In this paper, we describe a semantics for a lazy language based on Haskell, supporting monadic I/O, mutable variables, usual recursive definitions, and value recursion. Our semantics is composed of two layers: A natural semantics for the functional layer, and a labeled transition semantics for the IO layer. Mathematics Subject Classification. 68N18, 68Q55, 18C15.

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