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Bananas in Space: Extending Fold and Unfold to Exponential Types
, 1995
"... Fold and unfold are general purpose functionals for processing and constructing lists. By using the categorical approach of modelling recursive datatypes as fixed points of functors, these functionals and their algebraic properties were generalised from lists to polynomial (sumofproduct) datatypes ..."
Abstract

Cited by 96 (6 self)
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Fold and unfold are general purpose functionals for processing and constructing lists. By using the categorical approach of modelling recursive datatypes as fixed points of functors, these functionals and their algebraic properties were generalised from lists to polynomial (sumofproduct) datatypes. However, the restriction to polynomial datatypes is a serious limitation: it precludes the use of exponentials (functionspaces) , whereas it is central to functional programming that functions are firstclass values, and so exponentials should be able to be used freely in datatype definitions. In this paper we explain how Freyd's work on modelling recursive datatypes as fixed points of difunctors shows how to generalise fold and unfold from polynomial datatypes to those involving exponentials. Knowledge of category theory is not required; we use Gofer throughout as our metalanguage, making extensive use of constructor classes. 1 Introduction During the 1980s, Bird and Meertens [6, 22] d...
Type Parametric Programming
, 1993
"... We introduce a new abstraction mechanism, type parametric combinators, which supports abstraction over type constructors defined by datatype declarations found in functional languages such as Miranda, Haskell, and ML. This mechanism allows the definition and use of high level abstractions not pos ..."
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Cited by 13 (5 self)
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We introduce a new abstraction mechanism, type parametric combinators, which supports abstraction over type constructors defined by datatype declarations found in functional languages such as Miranda, Haskell, and ML. This mechanism allows the definition and use of high level abstractions not possible in traditional languages and could be used to define user programmable derived instance declarations for type classes in Haskel. We illustrate its use in an actual programming language by giving examples in the ML dialect CRML.
Abstract Bananas in Space: Extending Fold and Unfold to Exponential Types
"... Fold and unfold are general purpose functionals for processing and constructing lists. By using the categorical approach of modelling recursive datatypes as fixed points of functors, these functionals and their algebraic properties were generalised from lists to polynomial (sumofproduct) datatypes ..."
Abstract
 Add to MetaCart
Fold and unfold are general purpose functionals for processing and constructing lists. By using the categorical approach of modelling recursive datatypes as fixed points of functors, these functionals and their algebraic properties were generalised from lists to polynomial (sumofproduct) datatypes. However, the restriction to polynomial datatypes is a serious limitation: it precludes the use of exponentials (functionspaces), whereas it is central to functional programming that functions are firstclass values, and so exponentials should be able to be used freely in datatype definitions. In this paper we explain how Freydâ€™s work on modelling recursive datatypes as fixed points of difunctors shows how to generalise fold and unfold from polynomial datatypes to those involving exponentials. Knowledge of category theory is not required; we use Gofer throughout as our metalanguage, making extensive use of constructor classes. 1