Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, debuggers, equality functions, unifiers, pattern matchers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of user-defined datatypes. This paper extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions using an extension of Jones ' theories of qualified types and higher-order polymorphism. The semantics of the programs in the extended language is obtained by adding type arguments to functions in a dictionary passing style. Programs in the extended language are translated to Haskell. 1

How canweintegrate interaction into a purely declarative language? This tutorial describes a solution to this problem based on a monad. The solution has been implemented in the functional language Haskell and the declarative language Escher. Comparisons are given to other approaches to interaction based on synchronous streams, continuations, linear logic, and side effects.

PolyP extends a functional language (a subset of Haskell) with a construct for defining polytypic functions by induction on the structure of user-defined datatypes. Programs in the extended language are translated to Haskell. PolyLib contains powerful structured recursion operators like catamorphisms, maps and traversals, as well as polytypic versions of a number of standard functions from functional programming: sum, length, zip, (==), (6), etc. Both the specification of the library and a PolyP implementation are presented.

When type classes were first introduced in Haskell they were regarded as a fairly experimental language feature, and therefore warranted a fairly conservative design. Since that time, practical experience has convinced many programmers of the benefits and convenience of type classes. However, on occasion, these same programmers have discovered examples where seemingly natural applications for type class overloading are prevented by the restrictions imposed by the Haskell design. It is possible to extend the type class mechanism of Haskell in various ways to overcome these limitations, but such proposals must be designed with great care. For example, several different extensions have been implemented in Gofer. Some of these, particularly the support for multi-parameter classes, have proved to be very useful, but interactions between other aspects of the design have resulted in a type system that is both unsound and undecidable. Another illustration is the introduction of constructor cla...

This paper describes a new approach to generic functional programming, which allows us to define functions generically for all datatypes expressible in Haskell. A generic function is one that is defined by induction on the structure of types. Typical examples include pretty printers, parsers, and comparison functions. The advanced type system of Haskell presents a real challenge: datatypes may be parameterized not only by types but also by type constructors, type definitions may involve mutual recursion, and recursive calls of type constructors can be arbitrarily nested. We show that--- despite this complexity---a generic function is uniquely defined by giving cases for primitive types and type constructors (such as disjoint unions and cartesian products). Given this information a generic function can be specialized to arbitrary Haskell datatypes. The key idea of the approach is to model types by terms of the simply typed -calculus augmented by a family of recursion operators. While co...

this paper is to marry effects to monads, writing T for a computation that yields a value in and may have effects delimited by oe. Now we have that ( is

Lacking support for generic traversal, functional programming languages suffer from a scalability problem when applied to largescale program transformation problems. As a solution, we introduce functional strategies: typeful generic functions that not only can be applied to terms of any type, but which also allow generic traversal into subterms.

A polytypic function definition is a function definition that is parametrised with a datatype. It embraces a class of algorithms. As an example we define a simple polytypic "crush" combinator that can be used to calculate polytypically. The ability to define functions polytypically adds another level of flexibility in the reusability of programming idioms and in the design of libraries of interoperable components.

Many functions can be dened completely generically for all datatypes. Examples include pretty printers (eg show), parsers (eg read), data converters, equality and comparison functions, mapping functions, and so forth. This paper proposes a generic programming extension that enables the user to dene such functions in Haskell. In particular, the proposal aims at generalizing Haskell's deriving construct, which is commonly considered decient since instance declarations can only be derived for a few predened classes. Using generic denitions derived instances can be specied for arbitrary user-dened type classes and for classes that abstract over type constructors of rst-order kind. 1 Introduction Generic or polytypic programming aims at relieving the programmer from repeatedly writing functions of similar functionality for dierent datatypes. Typical examples for socalled generic functions include pretty printers (eg show), parsers (eg read), functions that convert data into a u...

We describe a monadic interface to low-level hardware features that is a suitable basis for building operating systems in Haskell. The interface includes primitives for controlling memory management hardware, user-mode process execution, and low-level device I/O. The interface enforces memory safety in nearly all circumstances. Its behavior is specified in part by formal assertions written in a programming logic called P-Logic. The interface has been implemented on bare IA32 hardware using the Glasgow Haskell Compiler (GHC) runtime system. We show how a variety of simple O/S kernels can be constructed on top of the interface, including a simple separation kernel and a demonstration system in which the kernel, window system, and all device drivers are written in Haskell.