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Many processes, both in mathematics and in nature, involve addition You are familiar with the discrete process of addition, in which you add nitely many numbers to obtain a sum or aggregate But there are important instances in which we wish to add in nitely many terms One important example is in the calculation of area especially the area of an unusual (non-rectilinear) shape A standard strategy is to approximate the desired area by the sum of small, thin rectangular regions (whose areas are easy to calculate) A second example is the calculation of work, in which we think of the work performed over an interval or curve as the aggregate of small increments of work performed over very short intervals We need a mathematical formalism for making such summation processes natural and comfortable Thus we will develop the concept of the integral

// Override GetOb() public override T GetOb() { ConsoleWrite("Gen2 s GetOb(): "); return ob; } } // Demonstrate generic method override class OverrideDemo { static void Main() { // Create a Gen object for int Gen<int> iOb = new Gen<int>(88); // This calls Gen s version of GetOb() ConsoleWriteLine(iObGetOb());

// Now, create a Gen2 object and assign its // reference to iOb (which is a Gen<int> variable) iOb = new Gen2<int>(99); // This calls Gen2 s version of GetOb() ConsoleWriteLine(iObGetOb()); } }

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555 030076 031423 032786 034165 035558 036965 038383 039812 041250 042696 044149 045607 047069 048534 050000 17467 17523 17564 17588 17596 07693 05778 03856 01929 00000 86 87 88 89 90 16950 17084 17204 17307 17395 17082 15237 13373 11493 09599 81 82 83 84 85 078780 079951 081095 082212 083299 084358 085387 086384 087350 088282 16051 16260 16455 16635 16800 25952 24233 22484 20708 18907 76 77 78 79 80 072561 073850 075117 076362 077583 15590 15340 15075 14798 14508 14206 13892 13566 13229 12882 12524 12156 11778 11392 10997

The output is shown here:

Gen s GetOb(): 88 Gen2 s GetOb(): 99

Let f be a given function We have already seen in the theory of falling bodies (Section 34) that it can be useful to nd a function F such that F = f We call

As the output confirms, the overridden version of GetOb( ) is called for an object of type Gen2, but the base class version is called for an object of type Gen

11 12 13 14 15 023638 024883 026150 027439 028748 16635 16455 16260 16051 15828 14798 15075 15340 15590 15828 34034 32493 30912 29294 27640 71 72 73 74 75 065835 067214 068577 069924 071252

Part I:

iOb = new Gen2<int>(99);

000834 001069 001341 001650 001998

.

is valid because iOb is a variable of type Gen<int> Thus, it can refer to any object of type Gen<int> or any object of a class derived from Gen<int>, including Gen2<int> Of course, iOb couldn t be used to refer to an object of type Gen2<double>, for example, because of the type mismatch

Methods that use type parameters to declare method parameters can be overloaded However, the rules are a bit more stringent than they are for methods that don t use type parameters In general, a method that uses a type parameter as the data type of a parameter can be overloaded as long as the signatures of the two versions differ This means the type and/or number of their parameters must differ However, the determination of type difference is not based on the generic type parameter, but on the type argument substituted for the type parameter when a constructed type is created Therefore, it is possible to overload a method that uses type parameters in such a way that it looks right, but won t work in all specific cases For example, consider this generic class:

02610 03040 03484 03939 04399

// Ambiguity can result when overloading methods that // use type parameters // // This program will not compile using System; // A generic class that contains a potentially ambiguous // overload of the Set() method class Gen<T, V> { T ob1; V ob2; // // In some cases, these two methods // will not differ in their parameter types public void Set(T o) { ob1 = o; } public void Set(V o) { ob2 = o; } } class AmbiguityDemo { static void Main() { Gen<int, double> ok = new Gen<int, double>();

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