By Kenneth B Stolarsky
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Additional resources for Algebraic numbers and Diophantine approximation
Write a function that takes two lists of type [Maybe Int] and examines the pair of list heads before looking at the rest of the lists. It returns a list in which the Ints of each pair have been added if both are of the form Just n, preserving any Just n value otherwise. 10. TYPE CLASSES AND OVERLOADING 31 Exercise 10. Deﬁne a data type that represents six diﬀerent metals and automatically creates versions of (==) and show. Exercise 11. Suppose that you have some coins that have been sorted into piles, each of which contains only one kind of coin.
8 Common Functions on Lists Haskell provides a number of operations on lists. A few of the most important ones are presented in this section. We will have more to say about these functions later in the book, where we will use them in a variety of practical applications, show how they are implemented, and prove theorems stating some of their mathematical properties. ] =>
For example, the (+) function can be applied to integers or ﬂoating point numbers (as well as several other kinds of number). This means that there are two completely diﬀerent implementations of this function, one for integers and another for ﬂoating point. And that raises a question: what is the type of (+)? 7. On the other hand, it would be too general to specify (+) :: a -> a -> a because this says that any type can be added, allowing nonsensical expressions like True+False and "cat"+"mouse".