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Generic pointfree lenses
 In International Conference on Mathematics of Program Construction (MPC), Québec City, QC
, 2010
"... Abstract. Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with viewupdate, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a ba ..."
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Cited by 16 (8 self)
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Abstract. Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with viewupdate, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a backward transformation instructing how to translate an abstract view to an update over concrete models. In this paper we show that most of the standard pointfree combinators can be lifted to lenses with suitable backward semantics, allowing us to use the pointfree style to define powerful bidirectional transformations by composition. We also demonstrate how to define generic lenses over arbitrary inductive data types by lifting standard recursion patterns, like folds or unfolds. To exemplify the power of this approach, we “lensify ” some standard functions over naturals and lists, which are tricky to define directly “byhand ” using explicit recursion.
Recursive coalgebras from comonads
 Inform. and Comput
, 2006
"... The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of struct ..."
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Cited by 14 (3 self)
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The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of structured recursion in programming semantics, list some basic facts about recursive coalgebras and, centrally, give new conditions for the recursiveness of a coalgebra based on comonads, comonadcoalgebras and distributive laws of functors over comonads. We also present an alternative construction using countable products instead of cofree comonads.
DatatypeGeneric Reasoning
"... Datatypegeneric programs are programs that are parameterised by a datatype. Designing datatypegeneric programs brings new challenges and new opportunities. We review the allegorical foundations of a methodology of designing datatypegeneric programs. The effectiveness of the methodology is demons ..."
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Datatypegeneric programs are programs that are parameterised by a datatype. Designing datatypegeneric programs brings new challenges and new opportunities. We review the allegorical foundations of a methodology of designing datatypegeneric programs. The effectiveness of the methodology is demonstrated by an extraordinarily concise proof of the wellfoundedness of a datatypegeneric occursin relation.