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Strong Categorical Datatypes I
, 1991
"... An endofunctor of a cartesian closed category is often called strong if it is enriched over the exponential. Equivalently this strength can be provided as a natural transformation ` A;X : F (A) \Theta X \Gamma! F (A \Theta X) satisfying some elementary coherence conditions. This latter formulation ..."
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An endofunctor of a cartesian closed category is often called strong if it is enriched over the exponential. Equivalently this strength can be provided as a natural transformation ` A;X : F (A) \Theta X \Gamma! F (A \Theta X) satisfying some elementary coherence conditions. This latter formulation
Datatypes in Memory
"... Abstract. Besides functional correctness, specifications must describe other properties of permissible implementations. We want to use simple algebraic techniques to specify resource usage alongside functional behaviour. In this paper we examine the space behaviour of datatypes, which depends on the ..."
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Cited by 1 (0 self)
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Abstract. Besides functional correctness, specifications must describe other properties of permissible implementations. We want to use simple algebraic techniques to specify resource usage alongside functional behaviour. In this paper we examine the space behaviour of datatypes, which depends
Strong Categorical Datatypes II: A term logic for categorical programming
, 1995
"... This paper lifts the categorytheoretic results of [4] to the level of an abstract language suitable for basing categorical programming language implementations. The earlier work built a fibrationbased stronglynormalizing categorical combinator reduction system based entirely on functorial strengt ..."
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strength that allows the distribution of context to the interior of a strong data structure. Strong typeforming functors accompanied by (1) a collection of constructor combinators (initial datatypes) or destructor combinators (final datatypes) and (2) a capability for building new state
Induction and Recursion on Datatypes
, 1995
"... this paper we introduce a notion of induction over an arbitrary datatype and go on to show how the notion is used to establish unicity of a certain (broad) class of equations. Our overall goal is to develop a calculational theory of mathematical induction. That is we want to be able to calculate rel ..."
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Cited by 16 (7 self)
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this paper we introduce a notion of induction over an arbitrary datatype and go on to show how the notion is used to establish unicity of a certain (broad) class of equations. Our overall goal is to develop a calculational theory of mathematical induction. That is we want to be able to calculate
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.
Staging Algebraic Datatypes
"... We describe a mechanism for staging algebraic datatype definitions. This is a generalization of the notion of partially static data, and allows runtime code generators to generate more efficient code. The idea is to capture static information, made evident by dynamic case analysis, and propagate th ..."
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We describe a mechanism for staging algebraic datatype definitions. This is a generalization of the notion of partially static data, and allows runtime code generators to generate more efficient code. The idea is to capture static information, made evident by dynamic case analysis, and propagate
DatatypeGeneric Termination Proofs
"... Datatypegeneric programs are programs that are parameterised by a datatype. We review the allegorical foundations of a methodology of designing datatypegeneric programs. The notion of Freductivity, where F parametrises a datatype, is reviewed and a number of its properties are presented. The prop ..."
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Datatypegeneric programs are programs that are parameterised by a datatype. We review the allegorical foundations of a methodology of designing datatypegeneric programs. The notion of Freductivity, where F parametrises a datatype, is reviewed and a number of its properties are presented
Elements of a Relational Theory of Datatypes
 Formal Program Development, volume 755 of Lecture Notes in Computer Science
, 1993
"... The "Boom hierarchy" is a hierarchy of types that begins at the level of trees and includes lists, bags and sets. This hierarchy forms the basis for the calculus of total functions developed by Bird and Meertens, and which has become known as the "BirdMeertens formalism". This p ..."
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Cited by 43 (0 self)
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. The context of this work is a relational theory of datatypes, rather than a calculus of total functions. Elements of the theory necessary to the later discussion are summarised at the beginning of the paper. 1 Introduction This paper reports on an experiment into the design of a programming algebra
Generic Programming for Indexed Datatypes
 WGP'11
, 2011
"... An indexed datatype is a type that uses a parameter as a typelevel tag; a typical example is the type of vectors, which are indexed over a typelevel natural number encoding their length. Since the introduction of generalised algebraic datatypes, indexed datatypes have become commonplace in Haskell ..."
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An indexed datatype is a type that uses a parameter as a typelevel tag; a typical example is the type of vectors, which are indexed over a typelevel natural number encoding their length. Since the introduction of generalised algebraic datatypes, indexed datatypes have become commonplace
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