The algebra of recursive graph transformation language UnCAL: complete axiomatisation and iteration categorical semantics

The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About 20 years ago, Bunemanet al. developed a graph database query language UnQL on the top of a functional meta-language UnCAL for describing and manipulating graphs. Recently, the functional programming community has shown renewed interest in UnCAL, because it provides an efficient graph transformation language which is useful for various applications, such as bidirectional computation.In order to make UnCAL more flexible and fruitful for further extensions and applications, in this paper, we give a more conceptual understanding of UnCAL using categorical semantics. Our general interest of this paper is to clarify what is the algebra of UnCAL. Thus, we give an equational axiomatisation and categorical semantics of UnCAL, both of which are new. We show that the axiomatisation is complete for the original bisimulation semantics of UnCAL. Moreover, we provide a clean characterisation of the computation mechanism of UnCAL called ‘structural recursion on graphs’ using our categorical semantics. We show a concrete model of UnCAL given by the λG-calculus, which shows an interesting connection to lazy functional programming.

The Genuine Sieve of Eratosthenes

A much beloved and widely used example showing the elegance and simplicity of lazy functional programming represents itself as “The Sieve of Eratosthenes.” This paper shows that this example is not the sieve and presents an implementation that actually is.

Special Double Issue on Haskell

Since its inception in 1987, Haskell has provided a focal point for research in lazy functional programming. During this time the language has continually evolved, as a result of both theoretical advances and practical experience. Haskell has proved to be a powerful tool for many kinds of programming tasks, and an excellent vehicle for many aspects of computing pedagogy and research. The recent definition of Haskell 98 provides a long-awaited stable version of the language, but there are many exciting possibilities for future versions of Haskell.

Special issue on Haskell

Since its inception in 1987, Haskell has provided a focal point for research in lazy functional programming. During this time the language has continually evolved, as a result of both theoretical advances and practical experience. Haskell has proved to be a powerful tool for many kinds of programming tasks, and applications in industry are beginning to emerge. The recent definition of Haskell 98 provides a long-awaited stable version of the language, but there are many exciting possibilities for future versions of Haskell.The fourth Haskell Workshop will be held as part of the PLI 2000 colloquium on Principles, Logics, and Implementations of high-level programming languages in Montreal, 17th September 2000. Previous Haskell Workshops have been held in Paris (1999), Amsterdam (1997) and La Jolla (1995). Following on from these workshops, a special issue of the Journal of Functional Programming will be devoted to Haskell. Possible topics include, but are not limited to:* Critiques of Haskell 98;* New proposals for Haskell;* Applications or case studies;* Programming techniques;* Reasoning about programs;* Semantic issues;* Pedagogical issues;* Implementation.Contributors to any of the Haskell workshops are invited to submit full papers to the special issue on Haskell, but submission is open to everyone. Submissions should be sent to guest editor (address below), with a copy to Nasreen Ahmad ([email protected]). Submitted articles should be sent in postscript format, preferably gzipped and uuencoded. In addition, please send, as plain text, title, abstract, and contact information. The submission deadline is 1st February 2001. For other submission details, please consult an issue of the Journal of Functional Programming or see the Journal's web pages.