Paul Hudak

Functional reactive animation

Fran (Functional Reactive Animation) is a collection of data types and functions for composing richly interactive, multimedia animations. The key ideas in Fran are its notions of behaviors and events. Behaviors are time-varying, reactive values, while events are sets of arbitrarily complex conditions, carrying possibly rich information. Most traditional values can be treated as behaviors, and when images are thus treated, they become animations. Although these notions are captured as data types rather than a programming language, we provide them with a denotational semantics, including a proper treatment of real time, to guide reasoning and implementation. A method to effectively and efficiently perform event detection using interval analysis is also described, which relies on the partial information structure on the domain of event times. Fran has been implemented in Hugs, yielding surprisingly good performance for an interpreter-based system. Several examples are given, including the ability to describe physical phenomena involving gravity, springs, velocity, acceleration, etc. using ordinary differential equations.

Monad transformers and modular interpreters

We show how a set of building blocks can be used to construct programming language interpreters, and present implementations of such building blocks capable of supporting many commonly known features, including simple expressions, three different function call mechanisms (call-by-name, call-by-value and lazy evaluation), references and assignment, nondeterminism, first-class continuations, and program tracing. The underlying mechanism of our system is monad transformers, a simple form of abstraction for introducing a wide range of computational behaviors, such as state, I/O, continuations, and exceptions. Our work is significant in the following respects. First, we have succeeded in designing a fully modular interpreter based on monad transformers that incudes features missing from Steeles, Espinosas, and Wadlers earlier efforts. Second, we have found new ways to lift monad operations through monad transformers, in particular difficult cases not achieved in Moggis original work. Third, we have demonstrated that interactions between features are reflected in liftings and that semantics can be changed by reordering monad transformers. Finally, we have implemented our interpreter in Gofer, whose constructor classes provide just the added power over Haskells type classes to allow precise and convenient expression of our ideas. This implementation includes a method for constructing extensible unions and a form of subtyping that is interesting in its own right.

Modular domain specific languages and tools

A domain specific language (DSL) allows one to develop software for a particular application domain quickly and effectively, yielding programs that are easy to understand, reason about, and maintain. On the other hand, there may be a significant overhead in creating the infrastructure needed to support a DSL. To solve this problem, a methodology is described for building domain specific embedded languages (DSELs), in which a DSL is designed within an existing, higher-order and typed, programming language such as Haskell or ML. In addition, techniques are described for building modular interpreters and tools for DSELs. The resulting methodology facilitates reuse of syntax semantics, implementation code, software tools, as well as look-and-feel.

Conception, evolution, and application of functional programming languages

The foundations of functional programming languages are examined from both historical and technical perspectives. Their evolution is traced through several critical periods: early work on lambda calculus and combinatory calculus, Lisp, Iswim, FP, ML, and modern functional languages such as Miranda1 and Haskell. The fundamental premises on which the functional programming methodology stands are critically analyzed with respect to philosophical, theoretical, and pragmatic concerns. Particular attention is paid to the main features that characterize modern functional languages: higher-order functions, lazy evaluation, equations and pattern matching, strong static typing and type inference, and data abstraction. In addition, current research areas—such as parallelism, nondeterminism, input/output, and state-oriented computations—are examined with the goal of predicting the future development and application of functional languages.

A gentle introduction to Haskell

Permission is hereby granted, free of charge, to any person obtaining a copy of “A Gentle Introduction to Haskell” (the Text), to deal in the Text without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Text, and to permit persons to whom the Text is furnished to do so, subject to the following condition: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Text.

A history of Haskell: being lazy with class

This paper describes the history of Haskell, including its genesis and principles, technical contributions, implementations and tools, and applications and impact.

Functional reactive programming from first principles

Functional Reactive Programming, or FRP, is a general framework for programming hybrid systems in a high-level, declarative manner. The key ideas in FRP are its notions of behaviors and events. Behaviors are time-varying, reactive values, while events are time-ordered sequences of discrete-time event occurrences. FRP is the essence of Fran, a domain-specific language embedded in Haskell for programming reactive animations, but FRP is now also being used in vision, robotics and other control systems applications. In this paper we explore the formal semantics of FRP and how itrelates to an implementation based on streams that represent (and therefore only approximate) continuous behaviors. We show that, in the limit as the sampling interval goes to zero, the implementation is faithful to the formal, continuous semantics, but only when certain constraints on behaviors are observed. We explore the nature of these constraints, which vary amongst the FRP primitives. Our results show both the power and limitations of this approach to language design and implementation. As an example of a limitation, we show that streams are incapable of representing instantaneous predicate events over behaviors.

Arrows, Robots, and Functional Reactive Programming

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. Yampa is an instantiation of FRP as a domain-specific language embedded in Haskell. This paper describes Yampa in detail, and shows how it can be used to program a particular kind of hybrid system: a mobile robot. Because performance is critical in robotic programming, Yampa uses arrows (a generalization of monads) to create a disciplined style of programming with time-varying values that helps ensure that common kinds of timeand space-leaks do not occur. No previous experience with robots is expected of the reader, although a basic understanding of physics and calculus is assumed. No knowledge of arrows is required either, although we assume a good working knowledge of Haskell. This paper is dedicated in memory of Edsger W. Dijkstra for his influential insight that mathematical logic is and must be the basis for sensible computer program construction.

A semantic model of reference counting and its abstraction (detailed summary)

Most interpreters for functional languages (as well as Lisp) employ at some level in the implementation a notion of sharing, whether manifested indirectly through an environment or directly via pointers. Sharing is essential to an efficient implementation, saving time by not recomputing values, and saving space by having only one copy of each value. From the perspective of lambda calculus, sharing arises whenever a beta-reduction results in substitution for more than one occurrence of a particular bound variable.

Lambda in Motion: Controlling Robots with Haskell

We present our experiences using a purely functional language, Haskell, in what has been traditionally the realm of low-level languages: robot control. Frob (Functional Robotics) is a domain-specific language embedded in Haskell for robot control. Frob is based on Functional Reactive Programming (FRP), as initially developed for Fran, a language of reactive animations. Frob presents the interaction between a robot and its stimuli, both onboard sensors and messages from other agents, in a purely functional manner. This serves as a basis for composable high level abstractions supporting complex control regimens in a concise and reusable manner.