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Polytypic Values Possess Polykinded Types
, 2000
"... A polytypic value is one that is defined by induction on the structure of types. In Haskell the type structure is described by the socalled kind system, which distinguishes between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to ..."
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Cited by 107 (20 self)
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A polytypic value is one that is defined by induction on the structure of types. In Haskell the type structure is described by the socalled kind system, which distinguishes between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to polytypic programming were restricted in that they only allowed to parameterize values by types of one fixed kind. In this paper we show how to define values that are indexed by types of arbitrary kinds. It appears that these polytypic values possess types that are indexed by kinds. We present several examples that demonstrate that the additional exibility is useful in practice. One paradigmatic example is the mapping function, which describes the functorial action on arrows. A single polytypic definition yields mapping functions for datatypes of arbitrary kinds including first and higherorder functors. Polytypic values enjoy polytypic properties. Using kindindexed logical relations we prove...
Generic programming: An introduction
 3rd International Summer School on Advanced Functional Programming
, 1999
"... ..."
The Essence of the Visitor Pattern
, 1997
"... . For objectoriented programming, the Visitor pattern enables the definition of a new operation on an object structure without changing the classes of the objects. The price has been that the set of classes must be fixed in advance, and they must each have a socalled accept method. In this paper w ..."
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Cited by 82 (4 self)
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. For objectoriented programming, the Visitor pattern enables the definition of a new operation on an object structure without changing the classes of the objects. The price has been that the set of classes must be fixed in advance, and they must each have a socalled accept method. In this paper we demonstrate how to program visitors without relying on accept methods and without knowing all classes of the objects in advance. The idea, derived from related work on shape polymorphism in functional programming, is to separate (1) accessing subobjects, and (2) acting on them. In the objectoriented setting, reflection techniques support access to subobjects, as demonstrated in our Java class, Walkabout. It supports all visitors as subclasses, and they can be programmed without any further use of reflection. Thus a program using the Visitor pattern can now be understood as a specialized version of a program using the Walkabout class. 1 Introduction Design patterns [3] aim to make object...
Nested datatypes
 In MPC’98, volume 1422 of LNCS
, 1998
"... Abstract. A nested datatype, also known as a nonregular datatype, is a parametrised datatype whose declaration involves different instances of the accompanying type parameters. Nested datatypes have been mostly ignored in functional programming until recently, but they are turning out to be both th ..."
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Cited by 79 (5 self)
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Abstract. A nested datatype, also known as a nonregular datatype, is a parametrised datatype whose declaration involves different instances of the accompanying type parameters. Nested datatypes have been mostly ignored in functional programming until recently, but they are turning out to be both theoretically important and useful in practice. The aim of this paper is to suggest a functorial semantics for such datatypes, with an associated calculational theory that mirrors and extends the standard theory for regular datatypes. Though elegant and generic, the proposed approach appears more limited than one would like, and some of the limitations are discussed. 1
Generic Haskell: practice and theory
 In Generic Programming, Advanced Lectures, volume 2793 of LNCS
, 2003
"... Abstract. Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes describe the basic constructs of Generic Haskell and highlight the underlying theory. Generic programming aims at making programming more effective by making it more general. ..."
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Cited by 65 (23 self)
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Abstract. Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes describe the basic constructs of Generic Haskell and highlight the underlying theory. Generic programming aims at making programming more effective by making it more general. Generic programs often embody nontraditional kinds of polymorphism. Generic Haskell is an extension of Haskell [38] that supports the construction of generic programs. Generic Haskell adds to Haskell the notion of structural polymorphism, the ability to define a function (or a type) by induction on the structure of types. Such a function is generic in the sense that it works not only for a specific type but for a whole class of types. Typical examples include equality, parsing and pretty printing, serialising, ordering, hashing, and so on. The lecture notes on Generic Haskell are organized into two parts. This first part motivates the need for genericity, describes the basic constructs of Generic Haskell, puts Generic Haskell into perspective, and highlights the underlying theory. The second part entitled “Generic Haskell: applications ” delves deeper into the language discussing three nontrivial applications of Generic Haskell: generic dictionaries, compressing XML documents, and a generic version of the zipper data type. The first part is organized as follows. Section 1 provides some background discussing type systems in general and the type system of Haskell in particular. Furthermore, it motivates the basic constructs of Generic Haskell. Section 2 takes a closer look at generic definitions and shows how to define some popular generic functions. Section 3 highlights the theory underlying Generic Haskell and discusses its implementation. Section 4 concludes. 1
A Generic Programming Extension for Haskell
 Utrecht University
, 1999
"... 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 ..."
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Cited by 40 (5 self)
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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 userdened type classes and for classes that abstract over type constructors of rstorder 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...
Dealing with Large Bananas
 Universiteit Utrecht
, 2000
"... Abstract. Many problems call for a mixture of generic and speci c programming techniques. We propose a polytypic programming approach based on generalised (monadic) folds where a separation is made between basic fold algebras that model generic behaviour and updates on these algebras that model spec ..."
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Cited by 29 (12 self)
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Abstract. Many problems call for a mixture of generic and speci c programming techniques. We propose a polytypic programming approach based on generalised (monadic) folds where a separation is made between basic fold algebras that model generic behaviour and updates on these algebras that model speci c behaviour. We identify particular basic algebras as well as some algebra combinators, and we show how these facilitate structured programming with updatable fold algebras. This blend of genericity and speci city allows programming with folds to scale up to applications involving large systems of mutually recursive datatypes. Finally, we address the possibility of providing generic de nitions for the functions, algebras, and combinators that we propose. 1
Typed Generic Traversal With Term Rewriting Strategies
 Journal of Logic and Algebraic Programming
, 2002
"... 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 manysorted type system extended by designated generic strategy types γ. We consider two generic strategy t ..."
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Cited by 26 (8 self)
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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 manysorted type system extended by designated generic strategy types γ. We consider two generic strategy types, namely the types of typepreserving and typeunifying strategies. S ′ γ offers traversal combinators to construct traversals or schemes thereof from manysorted and generic strategies. The traversal combinators model different forms of onestep 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 manysorted 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 typedependent 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
Polytypic Data Conversion Programs
 Science of Computer Programming
, 2001
"... Several generic programs for converting values from regular datatypes to some other format, together with their corresponding inverses, are constructed. Among the formats considered are shape plus contents, compact bit streams and pretty printed strings. The different data conversion programs are co ..."
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Cited by 25 (9 self)
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Several generic programs for converting values from regular datatypes to some other format, together with their corresponding inverses, are constructed. Among the formats considered are shape plus contents, compact bit streams and pretty printed strings. The different data conversion programs are constructed using John Hughes' arrow combinators along with a proof that printing (from a regular datatype to another format) followed by parsing (from that format back to the regular datatype) is the identity. The printers and parsers are described in PolyP, a polytypic extension of the functional language Haskell.
Polytypic compact printing and parsing
 In Doaitse Swierstra, editor, ESOP’99, volume 1576 of LNCS
, 1999
"... Abstract. A generic compact printer and a corresponding parser are constructed. These programs transform values of any regular datatype to and from a bit stream. The algorithms are constructed along with a proof that printing followed by parsing is the identity. Since the binary representation is ve ..."
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Cited by 22 (7 self)
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Abstract. A generic compact printer and a corresponding parser are constructed. These programs transform values of any regular datatype to and from a bit stream. The algorithms are constructed along with a proof that printing followed by parsing is the identity. Since the binary representation is very compact, the printer can be used for compressing data possibly supplemented with some standard algorithm for compressing bit streams. The compact printer and the parser are described in the polytypic Haskell extension PolyP. 1