Discrete Mathematics

Download e-book for kindle: APL with a mathematical accent by C.A. Reiter, W.R. Jones

By C.A. Reiter, W.R. Jones

ISBN-10: 0534128645

ISBN-13: 9780534128647

This e-book could be of curiosity to arithmetic scientists operating within the parts of linear algebra, summary algebra, quantity idea, numerical research, operations examine and mathematical modelling

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Extra resources for APL with a mathematical accent

Example text

Thus an object is a collection of data elements and operations that act on these data elements. The operations are called methods. A uniform mechanism, called message passing, is provided for invoking the correct piece of code when a function is called, or as we now prefer to say, a message is passed to an object to execute a certain method. Methods are usually not defined for each object separately but are collected in a class. Objects then belong to a class from which they take their methods.

Searching these rules will get slower as the number of data types increases. In the second case (using upvalues) there is one rule list for each data type and it grows with the number of operations. As an example, the built-in arithmetic operations take potentially many data types, so it is usually better to store these rules with the data type. m by defining a general rule for applying methods to objects. Instead of putting the dispatch function inside the object, the constructor returns only a symbol and defines the necessary rules for it.

The methods are given as a list of pairs, the first element of each pair is the name of the method, the second element is the (pure) function that implements the method. Methods that simply inspect the internal state, for example returning the balance, are written as functions without any additional arguments. The method new is automatically called by the constructor makeAccount to initialize the internal state of each new object. The statement Apply[(switch[#l] = #2)&, accountmethods, {1}] defines the methods as values of the symbol switch in such a way that switch[mef/*] gives the function used to implement the method named meth.

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APL with a mathematical accent by C.A. Reiter, W.R. Jones


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