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Program Structuring in Haskell Slide 11 |
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The third extension that I want to tell you about is known as "multiple parameter classes". This is also based on ideas that have been around for quite a long time, but they are only now beginning to appear in full Haskell implementations. The intuition here is that a multiple parameter type class corresponds to a predicate on multiple arguments, or, in simple terms, to an n-ary relation between types and constructors. The example on this slide shows a fragment of a library for working with collection classes, a mainstay for traditional object-oriented class libraries. The class relates collection constructors "c" to element types "a", and provides operations for building empty collections, inserting new elements, and enumerating the existing elements. A full version would, of course, provide many other operations, and would perhaps use a hierarchy of classes to distinguish different kinds of collection. The two instance declarations provide implementations of collections involving lists (presumably, without worrying about ordering or duplication of elements) and for some abstract datatype of sets. The element type "a" is completely unconstrained in the first instance declaration, but is restricted to equality types in the second. (The implementation of sets used here requires an equality operation to build and use "Set" values.) Once again, we can use the operations of the class to build generic functions that can be used with any collection type. In effect, these features just provide an extension of parametric polymorphism, together with all the benefits for modularity that polymorphism usually brings. |