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Polytypic Programming With Ease
, 1999
"... A functional polytypic program is one that is parameterised by datatype. Since polytypic functions are defined by induction on types rather than by induction on values they typically operate on a higher level of abstraction than their monotypic counterparts. However, polytypic programming is not nec ..."
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Cited by 13 (5 self)
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A functional polytypic program is one that is parameterised by datatype. Since polytypic functions are defined by induction on types rather than by induction on values they typically operate on a higher level of abstraction than their monotypic counterparts. However, polytypic programming is not necessarily more complicated than conventional programming. We show that a polytypic function is uniquely defined by its action on constant functors, projection functors, sums, and products. This information is sufficient to specialize a polytypic function to arbitrary polymorphic datatypes, including mutually recursive datatypes and nested datatypes. The key idea is to use infinite trees as index sets for polytypic functions and to interpret datatypes as algebraic trees. This approach appears both to be simpler, more general, and more efficient than previous ones which are based on the initial algebra semantics of datatypes. Polytypic functions enjoy polytypic properties. We show that wellkno...
Final Dialgebras: From Categories to Allegories
 Workshop on Fixed Points in Computer Science
, 1999
"... The study of inductive and coinductive types (like finite lists and streams, respectively) is usually conducted within the framework of category theory, which to all intents and purposes is a theory of sets and functions between sets. Allegory theory, an extension of category theory due to Freyd, is ..."
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Cited by 6 (3 self)
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The study of inductive and coinductive types (like finite lists and streams, respectively) is usually conducted within the framework of category theory, which to all intents and purposes is a theory of sets and functions between sets. Allegory theory, an extension of category theory due to Freyd, is better suited to modelling relations between sets as opposed to functions between sets. The question thus arises of how to extend the standard categorical results on the existence of final objects in categories (for example, coalgebras and products) to their existence in allegories. The motivation is to streamline current work on generic programming, in which the use of a relational theory rather than a functional theory has proved to be desirable. In this paper, we define the notion of a relational final dialgebra and prove, for an important class of dialgebras, that a relational final dialgebra exists in an allegory if and only if a final dialgebra exists in the underlying category of map...
Functional polytypic programming  use and implementation
, 1997
"... Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern matchers, equ ..."
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Cited by 5 (2 self)
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Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern matchers, equality functions, unifiers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of userdefined datatypes. This thesis introduces polytypic functions, shows how to construct and reason about polytypic functions and describes the implementation of the polytypic programming system PolyP. PolyP extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions. Programs in the extended language are translated to Haskell.
Generic Operations on Nested Datatypes
, 2001
"... Nested datatypes are a generalisation of the class of regular datatypes, which includes familiar datatypes like trees and lists. They typically represent constraints on the values of regular datatypes and are therefore used to minimise the scope for programmer error. ..."
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Cited by 4 (0 self)
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Nested datatypes are a generalisation of the class of regular datatypes, which includes familiar datatypes like trees and lists. They typically represent constraints on the values of regular datatypes and are therefore used to minimise the scope for programmer error.
Chapter 1 Extensible and Modular Generics for the Masses
"... Abstract: A generic function is a function that is defined on the structure of data types: with a single definition, we obtain a function that works for many data types. In contrast, an adhoc polymorphic function requires a separate implementation for each data type. Previous work by Hinze on light ..."
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Abstract: A generic function is a function that is defined on the structure of data types: with a single definition, we obtain a function that works for many data types. In contrast, an adhoc polymorphic function requires a separate implementation for each data type. Previous work by Hinze on lightweight generic programming has introduced techniques that allow the definition of generic functions directly in Haskell. A severe drawback of these approaches is that generic functions, once defined, cannot be extended with adhoc behaviour for new data types, precluding the design of an extensible and modular generic programming library based on these techniques. In this paper, we present a revised version of Hinze’s Generics for the masses approach that overcomes this limitation. Using our new technique, writing an extensible and modular generic programming library in Haskell 98 is possible. 1.1
Patterns as first class citizens
, 2008
"... Abstract. The pure pattern calculus generalises the pure lambdacalculus by basing computation on patternmatching instead of betareduction. The simplicity and power of the calculus derive from allowing any term to be a pattern. As well as supporting a uniform approach to functions, it supports a u ..."
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Abstract. The pure pattern calculus generalises the pure lambdacalculus by basing computation on patternmatching instead of betareduction. The simplicity and power of the calculus derive from allowing any term to be a pattern. As well as supporting a uniform approach to functions, it supports a uniform approach to data structures which underpins two new forms of polymorphism. Path polymorphism supports searches or queries along all paths through an arbitrary data structure. Pattern polymorphism supports the dynamic creation and evaluation of patterns, so that queries can be customised in reaction to new information about the structures to be encountered. In combination, these features provide a natural account of tasks such as programming with XML paths. As the variables used in matching can now be eliminated by reduction it is necessary to separate them from the binding variables used to control scope. Then standard techniques suffice to ensure that reduction progresses and to establish confluence of reduction. 1
unknown title
"... Abstract Generic programming allows you to write a function once, and use it many times at different types. A lot of good foundational work on generic programming has been done. The goal of this paper is to propose a practical way of supporting generic programming within the Haskell language, withou ..."
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Abstract Generic programming allows you to write a function once, and use it many times at different types. A lot of good foundational work on generic programming has been done. The goal of this paper is to propose a practical way of supporting generic programming within the Haskell language, without radically changing the language or its type system. The key idea is to present generic programming as a richer language in which to write default method definitions in a class declaration. On the way, we came across a separate issue, concerning typeclass overloading where higher kinds are involved. We propose a simple typeclass system extension to allow the programmer to write richer contexts than is currently possible.
Nested collections and polytypism
"... A pointfree calculus of socalled collection types is presented similar to the monadic calculus of Tannen Buneman and Wong We observe that our calculus is parametrised by a monad thus making the calculus polytypic A novel contribution of the paper is to discuss situations in which a single appli ..."
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A pointfree calculus of socalled collection types is presented similar to the monadic calculus of Tannen Buneman and Wong We observe that our calculus is parametrised by a monad thus making the calculus polytypic A novel contribution of the paper is to discuss situations in which a single application involves more than one collection type In particular we outline the contribution to database research that may be obtained by exploiting current developments in polytypic programming Introduction and overview Collection types such as trees lists and bags have been studied extensively in computing science In particular in the research area of formal program development the observation attributed by LMeertens to HBoom that these types form a hierarchy has proved