Stratego is a language for the specification of transformation rules and strategies for applying them. The basic actions of transformations are matching and building instantiations of first-order term patterns. The language supports concise formulation of generic and data type-specific term traversals. One of the unusual features of Stratego is the separation of scope from matching, allowing sharing of variables through traversals. The combination of first-order patterns with strategies forms an expressive formalism for pattern matching. In this paper we discuss three examples of strategic pattern matching: (1) Contextual rules allow matching and replacement of a pattern at an arbitrary depth of a subterm of the root pattern. (2) Recursive patterns can be used to characterize concisely the structure of languages that form a restriction of a larger language. (3) Overlays serve to hide the representation of a language in another (more generic) language. These techniques are illustrated by...

Graph algorithms expressed in functional languages often suffer from their inherited imperative, state-based style. In particular, this impedes formal program manipulation. We show how to model persistent graphs in functional languages by graph constructors. This provides a decompositional view of graphs which is very close to that of data types and leads to a "more functional" formulation of graph algorithms. Graph constructors enable the definition of general fold operations for graphs. We present a promotion theorem for one of these folds that allows program fusion and the elimination of intermediate results. Fusion is not restricted to the elimination of tree-like structures, and we prove another theorem that facilitates the elimination of intermediate graphs. We describe an ML-implementation of persistent graphs which efficiently supports the presented fold operators. For example, depth-first-search expressed by a fold over a functional graph has the same complexity as the corresp...

In Standard ML, as in many other languages, programmers are often confronted with an unpleasant choice between pattern matching and abstraction. Because pattern matching can only be performed on concrete datatypes, programmers must often sacrifice either the convenience of pattern matching or the engineering benefits of abstraction. Views relieve this tension by allowing pattern matching on abstract datatypes. We propose a modest extension of Standard ML with views and define its semantics via a source-to-source translation back into Standard ML without views. We claim no particular technical innovation; rather, we have attempted to engineer a solution that blends as seamlessly as possible with the rest of the language, including the module system and the stateful features of the language. 1 Introduction The convenience of pattern matching is one of the most seductive aspects of languages like Standard ML [6]. Not until the newcomer tries to write large programs does she encounter the...

Abstract. Data in object-oriented programming is organized in a hierarchy of classes. The problem of object-oriented pattern matching is how to explore this hierarchy from the outside. This usually involves classifying objects by their run-time type, accessing their members, or determining some other characteristic of a group of objects. In this paper we compare six different pattern matching techniques: object-oriented decomposition, visitors, type-tests/type-casts, typecase, case classes, and extractors. The techniques are compared on nine criteria related to conciseness, maintainability and performance. The paper introduces case classes and extractors as two new pattern-matching methods and shows that their combination works well for all of the established criteria. 1

Pattern abstractions increase the expressiveness of pattern matching, enabling the programmer to describe a broader class of regular forests with patterns. Furthermore, pattern abstractions support code reuse and code factoring, features that facilitate maintenance and evolution of code. Past research on pattern abstractions has generally ignored the aspect of compile-time checks for exhaustiveness and redundancy. In this paper we propose a class of expressive patterns that admits these compile-time checks.

We propose a new style of writing graph algorithms in functional languages which is based on an alternative view of graphs as inductively defined data types. We show how this graph model can be implemented efficiently, and then we demonstrate how graph algorithms can be succinctly given by recursive function definitions based on the inductive graph view. We also regard this as a contribution to the teaching of algorithms and data structures in functional languages since we can use the functional-style graph algorithms instead of the imperative algorithms that are dominant today. Keywords: Graphs in Functional Languages, Recursive Graph Algorithms, Teaching Graph Algorithms in Functional Languages

We propose three extensions to patterns and pattern matching in Haskell. The first, pattern guards, allows the guards of a guarded equation to match patterns and bind variables, as well as to test boolean condition. For this we introduce a natural generalisation of guard expressions to guard qualifiers. A frequently-occurring special case is that a function should be applied to a matched value, and the result of this is to be matched against another pattern. For this we introduce a syntactic abbreviation, transformational patterns, that is particularly useful when dealing with views. These proposals can be implemented with very modest syntactic and implementation cost. They are upward compatible with Haskell; all existing programs will continue to work. We also offer a third, much more speculative proposal, which provides the transformational-pattern construct with additional power to explicitly catch pattern match failure. We demonstrate the usefulness of the proposed extension by several examples, in particular, we compare our proposal with views, and we also discuss the use of the new patterns in combination with equational reasoning.

Abstract. Pattern matching is advantageous for understanding and reasoning about function definitions, but it tends to tightly couple the interface and implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to abstract datatypes based on a rightinvertible language rinv—every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation (implemented as abstract datatypes), while maintaining simple and sound reasoning.

Abstract. Pattern matching is a widely used technique in functional languages, especially those in the ML and Haskell traditions, where it is at the core of the semantics. In languages in the Lisp tradition, in contrast, pattern matching it typically provided by libraries built with macros. We present match, a sophisticated pattern matcher for Racket, implemented as language extension. using macros. The system supports novel and widely-useful pattern-matching forms, and is itself extensible. The extensibility of match is implemented via a general technique for creating extensible language extensions. 1 Extending Pattern Matching The following Racket 1 [12] program finds the magnitude of a complex number, represented in either Cartesian or polar form as a 3-element list, using the first element as a type tag: (define (magnitude n) (cond [(eq? (first n) ’cart) (sqrt (+ (sqr (second n)) (sqr (third n))))]