By Richard Bird
Overseas model. similar content material. See photograph of booklet.
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Additional resources for Introduction to Functional Programming (Prentice Hall International Series in Computing Science)
Consider, for instance, the following definition: three num -t num 3 three x Suppose we submit the above definition to the evaluator, enter a session and type three ( 1 /0) . 6 FUNCTIONS 41 ? three (1/0) 3 What has happened is that the evaluator does not require the value of the argument to three in order to determine the result , so it does not attempt to evaluate it. l and the function is non-strict. For a number of reasons, a non-strict semantics is preferable to a strict one. First, it makes reasoning about equality easier.
We suppose: (+) : : num --+ num --+ num 1st : : (a, (3 ) --+ a As a necessary first step, we must take account of the fact that the two occurrences of the polymorphic function 1st need not receive the same in stantiations for the type variables a and (3 . After all , the expression: 1st ( 1 , True) + 1st ( 1 , 42) is well-typed, even though the first occurrence of 1st has type (num, bool) --+ num, and the second has type ( num, num) --+ num. To deal with this point, we rewrite the definition of I in the form: Ixy = Istl X + Ist 2 y and assume two different instantiations: Istl .
1 Numb ers The data type num consists of whole numbers ( or integers) and fractional numbers ( also calle d floating-point numbers). A whole number is a number whose fractional part is zero. 0 Although there are infinitely many numbers, computers have finite ca pacities and can only store a limited range. Even within a finite range there are infinitely many fractional numbers, so not all numbers can be stored ex actly. It is wise to be aware that a limitation exists, especially since it can cause what appears to be a mathematically correct program to fail or return unexpected results.
Introduction to Functional Programming (Prentice Hall International Series in Computing Science) by Richard Bird