We describe a design pattern for writing programs that traverse data structures built from rich mutually-recursive data types. Such programs often have a great deal of "boilerplate" code that simply walks the structure, hiding a small amount of "real" code that constitutes the reason for the traversal. Our technique allows most...

Abstract. Generic programming enables the programmer to define functions by induction on the structure of types. Defined once, such a generic function can be used to generate a specialized function for any user defined data type. Several ways to support generic programming in functional languages have been proposed, each with its own pros and cons. In this paper we describe a combination of two existing approaches, which has the advantages of both of them. In our approach overloaded functions with class variables of an arbitrary kind can be defined generically. A single generic definition defines a kind-indexed family of overloaded functions, one for each kind. For instance, the generic mapping function generates an overloaded mapping function for each kind. Additionally, we propose a separate extension that allows to specify a customized instance of a generic function for a type in terms of the generated instance for that type. 1

Term rewriting is an appealing technique for performing program analysis and program transformation. Tree (term) traversal is frequently used but is not supported by standard term rewriting.

The Visitor design pattern allows the encapsulation of polymorphic behavior outside the class hierarchy on which it operates. A common application of Visitor is the encapsulation of tree traversals. Unfortunately, visitors resist composition and allow little traversal control.

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.

Strategic programming is a generic programming idiom for processing compound data such as terms or object structures. At the heart of the approach is the separation of two concerns: basic dataprocessing computations vs. traversal schemes. Actual traversals are composed by passing the former as arguments to the latter. Traversal schemes can be defined by the strategic programmer using a combinator style that relies on primitives for layered traversal. In this paper, we take a look at strategic programming from an aspect-oriented programming perspective. Throughout the paper, we compare strategic programming with adaptive programming, which is a well-established aspectual approach to the traversal of object structures. We start from the observation that aspect-oriented programming terms, e.g., crosscutting, join point, and advice can be instantiated for aspectual traversal approaches.

A typed model of strategic term rewriting is developed. The key innovation is that generic. The calculus traversal is covered. To this end, we define a typed rewriting calculus S ′ γ employs a many-sorted type system extended by designated generic strategy types γ. We consider two generic strategy types, namely the types of type-preserving and type-unifying strategies. S ′ γ offers traversal combinators to construct traversals or schemes thereof from many-sorted and generic strategies. The traversal combinators model different forms of one-step traversal, that is, they process the immediate subterms of a given term without anticipating any scheme of recursion into terms. To inhabit generic types, we need to add a fundamental combinator to lift a many-sorted strategy s to a generic type γ. This step is called strategy extension. The semantics of the corresponding combinator states that s is only applied if the type of the term at hand fits, otherwise the extended strategy fails. This approach dictates that the semantics of strategy application must be type-dependent to a certain extent. Typed strategic term rewriting with coverage of generic term traversal is a simple but expressive model of generic programming. It has applications in program

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We demonstrate how the concept of strategies originating from term rewriting can be introduced in a typed, functional setting. We provide a model of strategies based on a further generalisation of updatable, monadic, generalised fold algebras. We show how strategies can be used as a structuring device for functional programming. 1

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