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Primitive (co)recursion and courseofvalues (co)iteration, categorically
 Informatica
, 1999
"... Abstract. In the mainstream categorical approach to typed (total) functional programming, datatypes are modelled as initial algebras and codatatypes as terminal coalgebras. The basic function definition schemes of iteration and coiteration are modelled by constructions known as catamorphisms and ana ..."
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Cited by 13 (6 self)
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Abstract. In the mainstream categorical approach to typed (total) functional programming, datatypes are modelled as initial algebras and codatatypes as terminal coalgebras. The basic function definition schemes of iteration and coiteration are modelled by constructions known as catamorphisms and anamorphisms. Primitive recursion has been captured by a construction called paramorphisms. We draw attention to the dual construction of apomorphisms, and show on examples that primitive corecursion is a useful function definition scheme. We also put forward and study two novel constructions, viz., histomorphisms and futumorphisms, that capture the powerful schemes of courseofvalue iteration and its dual, respectively, and argue that even these are helpful.
The Calculation of a Polytypic Parser
, 1996
"... In this paper it is shown how inverses can be used to calculate a parser. A polytypic unparser is given and by using rules for calculating inverses a polytypic parser is calculated from it. It can be instantiated automatically for all data types that can be described by a regular functor. The idea t ..."
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Cited by 5 (0 self)
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In this paper it is shown how inverses can be used to calculate a parser. A polytypic unparser is given and by using rules for calculating inverses a polytypic parser is calculated from it. It can be instantiated automatically for all data types that can be described by a regular functor. The idea that a parser can be calculated as the inverse of an unparser is not new, but because polytypical functions are used here the calculated parser is very general. Inverses are defined in a general way and rules are given to calculate them. The set monad has a strong connection with inverses and for many monadic concepts the instantiation with this monad gives rise to rules about inverses. In this way the inverses of catamorphisms and anamorphisms can be characterized. As we know that the unparser and the rules that were used in the calculation are correct, the calculated parser is known to be correct too. In general the parser that results from such a calculation is not very efficient and it is possible to construct much more efficient parsers by hand. Because it is possible to prove the equality of these two parsers, this parser is correct too. An implementation of parsers for a small subset of html and latex is given as an illustration of how the polytypic functions are instantiated for a particular datatype. Contents 1