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Extra resources for Conception, Evolution, And Application Of Functional Programming Languages

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Using type classes we can thus treat overloading in a consistent, arguably elegant, way. Another nice feature is that type classes naturally support a notion of inheritance. For example, we may define a class Eq by class Eq a where (==) :: a + a + Boo1 Given this class, we would certainly expect all members of the class Num, say, to have == defined on them. Thus the class declaration for Num could be changed to class Eq a * Num a where ::a+a+a (+I negate :: a + a which can be read as “only members of the class Eq may be members of the class Num, and a type a belongs to the class Num if.

For example, rotate (Polar r t) angle = Polar r (t+angle) As the example stands, objects of type Complex are concretely represented with the Rectangular constructor, but this decision could be reversed by making Polar the concrete constructor and Rectangular the view, without altering any of the functions that manipulate objects of type Complex. Whereas traditionally abstract data types are regarded as hiding the representation, with views we can reveal as many representations (zero, one, or more) as are required.

For example, consider the following list-of-factorials program, again using a ring of processors: (map fat [2,3,4]) on 0 where map f [] = [I f (xxs) = f x : ((map f xs) on (right self)) ACM Computing Surveys, Vol. 21, No. 3, September 1989 400 ’ Paul Hudak Note that the recursive call to map is mapped onto the processor to the right of the current one, and thus the elements 2, 6, and 24 in the result list are computed on processors 0, 1, and 2, respectively. Parafunctional programming languages have been shown to be adequate in expressing a wide range of deterministic parallel algorithms clearly and concisely [Hudak 1986c; Hudak and Smith 19861.

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