The use of monads to structure functional programs is described. Monads provide a convenient framework for simulating e ects found in other languages, such as global state, exception handling, output, or non-determinism. Three case studies are looked at in detail: how monads ease the modi cation of a simple evaluator; how monads act as the basis of a datatype of arrays subject to in-place update; and how monads can be used to build parsers.

We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example functions in Bird and Wadler's "Introduction to Functional Programming" can be expressed using these operators. 1 Introduction Among the many styles and methodologies for the construction of computer programs the Squiggol style in our opinion deserves attention from the functional programming community. The overall goal of Squiggol is to calculate programs from their specification in the way a mathematician calculates solutions to differential equations, or uses arithmetic to solve numerical problems. It is not hard to state, prove and use laws for well-known operations such as addition, multiplication and ---at the function level--- composition. It is, however, quite hard to state, prove and use laws for arbitrarily recursively ...

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, callby -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 includes features missing from Steele's, Espinosa's, and Wadler's earlier efforts. Second, we have found new ways to lift monad operations through monad transformers, in particular difficult cases not achieved in Moggi's original work. ...

This paper presents a type-based information flow analysis for a call-by-value λ-calculus equipped with references, exceptions and let-polymorphism, which we refer to as Core ML. The type system is constraint-based and has decidable type inference. Its noninterference proof is reasonably light-weight, thanks to the use of a number of orthogonal techniques. First, a syntactic segregation between values and expressions allows a lighter formulation of the type system. Second, noninterference is reduced to subject reduction for a nonstandard language extension. Lastly, a semi-syntactic approach to type soundness allows dealing with constraint-based polymorphism separately.

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 e#ectively 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 di#erential equations.

Lists are often used as "glue" to connect separate parts of a program together. We propose an automatic technique for improving the efficiency of such programs, by removing many of these intermediate lists, based on a single, simple, local transformation. We have implemented the method in the Glasgow Haskell compiler.

This paper describes a flexible type system which combines overloading and higher-order polymorphism in an implicitly typed language using a system of constructor classes -- a natural generalization of type classes in Haskell. We present a wide range of examples which demonstrate the usefulness of such a system. In particular, we show how constructor classes can be used to support the use of monads in a functional language. The underlying type system permits higher-order polymorphism but retains many of many of the attractive features that have made the use of Hindley/Milner type systems so popular. In particular, there is an effective algorithm which can be used to calculate principal types without the need for explicit type or kind annotations. A prototype implementation has been developed providing, amongst other things, the first concrete implementation of monad comprehensions known to us at the time of writing. 1 An overloaded map function Many functional programs use the map ...

this paper. Pleasingly, the arrow interface turned out to be applicable to other kinds of non-monadic library also, for example the fudgets library for graphical user interfaces [CH93], and a new library for programming active web pages. These applications will be described in sections 6 and 9. While arrows are a little less convenient to use than monads, they have significantly wider applicability. They can therefore be used to bring the benefits of monad-like programming to a much wider class of applications. 2 Background: Library Design Using Monads

Various models and languages for describing and manipulating hierarchically structured data have been proposed. Algebraic, calculus-based and logic-programming oriented languages have all been considered. This paper presents a general model for complex objects, and languages for it based on the three paradigms. The algebraic language generalizes those presented in the literature; it is shown to be related to the functional style of programming advocated by Backus. The notion of domain independence familiar from relational databases is defined, and syntactic restrictions (referred to as safety conditions) on calculus queries are formulated, that guarantee domain independence. The main results are: The domain-independent calculus, the safe calculus, the algebra, and the logic-programming oriented language have equivalent expressive power. In particular, recursive queries, such as the transitive closure, can be expressed in each of the languages. For this result, the algebra needs the pow...

We investigate the properties of a simple programming language whose main computational engine is structural recursion on sets. We describe a progression of sublanguages in this paradigm that (1) have increasing expressive power, and (2) illustrate robust conceptual restrictions thus exhibiting interesting additional properties. These properties suggest that we consider our sublanguages as candidates for "query languages". Viewing query languages as restrictions of our more general programming language has several advantages. First, there is no "impedance mismatch" problem; the query languages are already there, so they share common semantic foundation with the general language. Second, we suggest a uniform characterization of nested relational and complex-object algebras in terms of some surprisingly simple operators; and we can make comparisons of expressiveness in a general framework. Third, we exhibit differences in expressive power that are not always based on complexity arguments...