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Program Structuring in Haskell Slide 6 |
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In fact, the syntax of Haskell takes a dual approach, describing type classes in terms of predicates on types (i.e., characteristic functions) rather than sets of types. From a mathematical perspective, there is little to distinguish between the two. However, predicates seem to fit more comfortably into the language, and have a natural implementation. The declaration at the top of this slide introduces the Eq class by giving it a name, and by listing the operators that it's elements (or "instances", as they are called) are expected to support. The variable "a" used here represents an arbitrary instance of the class, and serves as a placeholder for the argument of the Eq predicate, and for the arguments of the equality operator (==). Instance declarations are required to populate a class. For example, the two fragments shown here specify that Bool is an equality type, and that lists are equality types if the component values are themselves of an equality type. (The actual definitions of equality in each case would be written in place of the "..." shown here.) An important point here is that the instance declarations for a class can be distributed across the modules for a large program, and the class can be extended at will to include new types are they are defined. With these definitions in place, the Haskell type system can determine which version of equality is required for any given use of the (==) symbol. In the example shown here, we are using the operator to compare lists of booleans, so it is clear that we expect [Bool] to be an equality type (i.e., that the predicate Eq [Bool] holds), which follows directly by combining the two instance declarations on this slide. |