Hierarchy in Generic Programming Libraries

Generic programming (GP) is a form of abstraction in programming languages that serves to reduce code duplication by exploiting the regular structure of algebraic datatypes. Several different approaches to GP in Haskell have surfaced, giving rise to the problem of code duplication across GP libraries. Given the original goals of GP, the is a rather unfortunate turn of events. Fortunately, we can convert between the different representations of each approach, which allows us to “borrow” generic functions from different approaches, avoiding the need to reimplement every generic function in every single GP library. In previous work we have shown how existing GP libraries relate to each other. In this paper we go one step further and advocate “hierarchical GP”: through proper design of different GP approaches, each library can fit neatly in a hierarchy, greatly minimizing the amount of supporting infrastructure necessary for each approach, and allowing each library to be specific and concise, while eliminating code duplication overall. We introduce a new library for GP in Haskell intended to sit at the top of the “GP hierarchy”. This library contains a lot of structural information, and is not intended to be used directly. Instead, it is a good starting point for generating generic representations for other libraries. This approach is also suitable for being the only library with native compiler support; all other approaches can be obtained from this one by simple conversion of representations in plain Haskell code

Multifocal: a strategic bidirectional transformation language for XML schemas

Lenses are one of the most popular approaches to define bidirectional transformations between data models. However, writing a lens transformation typically implies describing the concrete steps that convert values in a source schema to values in a target schema. In contrast, many XML-based languages allow writing structure-shy programs that manipulate only specific parts of XML documents without having to specify the behavior for the remaining structure. In this paper, we propose a structure-shy bidirectional two-level transformation language for XML Schemas, that describes generic type-level transformations over schema representations coupled with value-level bidirectional lenses for document migration. When applying these two-level programs to particular schemas, we employ an existing algebraic rewrite system to optimize the automatically-generated lens transformations, and compile them into Haskell bidirectional executables. We discuss particular examples involving the generic evolution of recursive XML Schemas, and compare their performance gains over non-optimized definitions.Fundação para a Ciência e a Tecnologi

Transformation of structure-shy programs with application to XPath queries and strategic functions

Various programming languages allow the construction of structure-shy programs. Such programs are defined generically for many different datatypes and only specify specific behavior for a few relevant subtypes. Typical examples are XML query languages that allow selection of subdocuments without exhaustively specifying intermediate element tags. Other examples are languages and libraries for polytypic or strategic functional programming and for adaptive object-oriented programming. In this paper, we present an algebraic approach to transformation of declarative structure-shy programs, in particular for strategic functions and XML queries. We formulate a rich set of algebraic laws, not just for transformation of structure-shy programs, but also for their conversion into structure-sensitive programs and vice versa. We show how subsets of these laws can be used to construct effective rewrite systems for specialization, generalization, and optimization of structure-shy programs. We present a type-safe encoding of these rewrite systems in Haskell which itself uses strategic functional programming techniques. We discuss the application of these rewrite systems for XPath query optimization and for query migration in the context of schema evolution

Generic Views

Structural polymorphism allows for generic functions to be defined by induction over the structure of types. In Generic Haskell, the structure of a type is perceived as a nested sum of products. Over the last few years it has been shown that a great amount of generic programs can be defined in terms of this perception. Still, there are applications for which viewing data types as sums of products limits the expressiveness of Generic Haskell. As it turns out, different perceptions of the structure of types enable the definition of generic programs that are more efficient, more elegant, and more expressive. We show how these different perceptions, which we call generic views, can be implemented and used in Generic Haskell

Generic views on data types

Abstract. A generic function is defined by induction on the structure of types. The structure of a data type can be defined in several ways. For example, in PolyP a pattern functor gives the structure of a data type viewed as a fixed point, and in Generic Haskell a structural representation type gives an isomorphic type view of a data type in terms of sums of products. Depending on this generic view on the structure of data types, some generic functions are easier, more difficult, or even impossible to define. Furthermore, the efficiency of some generic functions can be improved by choosing a different view. This paper introduces generic views on data types and shows why they are useful. Furthermore, it shows how generic views have been added to Generic Haskell, an extension of the functional programming language Haskell that supports the construction of generic functions. The separation between inductive definitions on type structure and generic views allows us to combine many approaches to generic programming in a single framework.