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We conjecture that the required formula is a second-degree polynomial in n, say a + bn + en2, and then calculate the coefficients a, b and c Here is how the calculation goes For brevity, let us use Pn to denote the proposition ( Z k : l^k^n: k) = a + bn + cn2 Then (Vn :: ( Z f e : l ^ f e ^ n : f c ) = a + bn + cn2) { principle of mathematical induction, definition of Pn } ( S k : l < f e ^ 0 : f e ) = a + bO + cO2 A<Vn::P(n+l)<=Pn> = { empty range and arithmetic } 0 = a A (Vn::P(n+l)< =Pn) So the basis of the induction has allowed us to deduce that a, the coefficient of n , is 0.



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acquire a DomainModelInfo object from an initialized store, and how to query it for its constituents:

return true; default: return false; } } } }

Because the compiler takes the yield return statement and generates classes that correspond to what you probably would have written manually, iterators in C# exhibit the same performance characteristics as classes that implement the enumerator design pattern manually Although there is no performance improvement, the programmer productivity gained is significant

Now we calculate b and c To do so, we make the induction hypothesis.

Store store = new Store(typeof(IssueStateModelsDomainModel));





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Creating Multiple Iterators in a Single Class Previous iterator examples implemented IEnumerable<T>GetEnumerator() This is the method that foreach seeks implicitly Sometimes you might want different iteration sequences, such as iterating in reverse, filtering the results, or iterating over an object projection other than the default You can declare additional iterators in the class by encapsulating them within properties or methods that return IEnumerable<T> or IEnumerable If you want to iterate over the elements of Pair<T> in reverse, for example, you provide a GetReverseEnumerator() method, as shown in Listing 1620

public struct Pair<T>: IEnumerable<T> { public IEnumerable<T> GetReverseEnumerator() { yield return Second; yield return First; } } public void Main() { Pair<string> game = new Pair<string>("Redskins", "Eagles");

that 0 ^ n and P.n is true. Then = { { { definition of P, a = 0 } range splitting } assumption: P.n, a = 0. That is, (I k : 1 ^ k ^ n : k> = bn + cn2 } bn + en2 + n + I = b(n+l) + c(n+l}2 { = o C-

foreach (string name in gameGetReverseEnumerator()) { ConsoleWriteLine(name); } }

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DomainModel dm = storeGetDomainModel<IssueStateModelsDomainModel>(); DomainModelInfo dmi = dmDomainModelInfo; ReadOnlyCollection<DomainClassInfo> domainClasses = dmiDomainClasses; ReadOnlyCollection<DomainRelationshipInfo> domainRelationships = dmiDomainRelationships;

Note that you return IEnumerable<T>, not IEnumerator<T> This is different from IEnumerable<T>GetEnumerator(), which returns IEnumerator<T> The code in Main() demonstrates how to call GetReverseEnumerator() using a foreach loop

(Ik : l^k^n+l : k) = fc(n+l) -t-c(n-i-l) 2 (Sk: l ^ k ^ n : k ) + n + l = b(n+l) + c(n+l) 2

yield Statement Characteristics You can declare the yield return statement only in members that return an IEnumerator<T> or IEnumerable<T> type, or their nongeneric equivalents More specifically, you can use yield only in GetEnumerator() methods that return IEnumerator<T>, or in methods that return IEnumerable<T> but are not called GetEnumerator() Methods that include a yield return statement may not have a simple return If the method uses the yield return statement, then the C# compiler generates the necessary code to maintain the state machine for the iterator In contrast, if the method uses the return statement instead of yield return, the programmer is responsible for maintaining his own state machine and returning an instance of one of the iterator interfaces Further, just as all code paths in a method with a return type must contain a return statement accompanied by a value (assuming they don t throw an exception), all code paths in an iterator must contain a yield return statement if they are to return any data Additional restrictions on the yield statement that result in compiler errors are as follows

In this chapter we talked about de ning domain models for DomainSpeci c Languages These models are the foundation for language de nition By now you should have learned: How to build a basic domain model using the DSL designer What the DSL domain model notation means How to do basic programming against the DSL API to make a model All of the other aspects of the language de nition described by the next few chapters notation, serialization, validation, code-generation, and user interface are based on having a domain model that properly represents the concepts, properties, and relationships of the domain

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arithmetic } comparing coefficients } arithmetic }

clauses of the try statement Furthermore, a yield statement may appear in a try block only if there is no catch block

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