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In the 1930s (a fertile time for computing theory!) two mathematicians named Church and Kleene devised a formal system for investigating the properties of functions. This was called lambda calculus, and (as further developed by Curry and others) it is still a staple part of computational theory for computer scientists. Fast-forward 70 or so years, and we see just a hint of this theory peeking through in C# s lambda expressions only a hint, though, so bear with it. As we saw before, you can think of a function as an expression that maps a set of inputs (the parameters) to an output (the return value). Mathematicians sometimes use a notation similar to this to define a function: (x,y,z) x + y + z You can read this as defining a function that operates on three parameters (x, y, and z). The result of the function is just the sum of the three parameters, and, by definition, it can have no side effects on the system. The parameters themselves aren t modified by the function; we just map from the input parameters to a result. Lambda expressions in C# use syntax very similar to this to define functional expressions. Here s the C# equivalent of that mathematical expression we used earlier:

(x,y,z) => x + y + z;

Notice how it rather cutely uses => as the programming language equivalent of . C++ users should not mistake this for the -> operator it is quite different!

This defines a lambda expression that takes three parameters and returns the sum of those three parameters.

Some languages enforce the no side effects constraint; but in C# there is nothing to stop you from writing a lambda expression such as this one:

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n this chapter, we discuss message authentication codes (MACs) and digital signature schemes. Recall from Section 1.5 that a MAC is a sequence of bits that can be attached to a message to verify where it originated and that it has not been tampered with. We will describe two types of MACs: one based on block ciphers and one based on hash functions. The MACs we describe require the sender and receiver to share a key. In many cases, it might be useful to allow anyone (without possession of a shared key) to be able to verify the originator of message, and we will thus describe how digital signatures allow you to do so. There are many other types of MAC and signature schemes that have been developed in this chapter, we sample just a few of the more commonly used. Choosing the right MAC and signature schemes for your software design may sometimes be a nontrivial decision, and we encourage you to consult a security expert prior to doing so. The goal of this chapter is to give you some fluency in exploring potential solutions and discussing the options with a security expert. We first introduce secure hash functions as they are used as a component in the MAC and digital signature schemes we describe.

(x,y,z) => { SomeStaticClass.CrashAndBurnAndMessWithEverything(); x.ModifyInternalState(); return x + y + z; }

(Incidentally, this form of lambda expression, using braces to help define its body, is called a statement-form lambda.) In C#, a lambda is really just a concise way to write an anonymous method. We re just writing normal code, so we can include operations that have side effects. So, although C# brings along some functional techniques with lambda syntax, it is not a pure functional language like ML or F#. Nor does it intend to be. So, what use is a lambda, then We ll see some very powerful techniques in 8 and 14, where lambdas play an important role in LINQ. Some of the data access features of the .NET Framework use the fact that we can convert lambdas into data structures called expression trees, which can be composed to create complex query-like expressions over various types of data. For now, we re merely going to take advantage of the fact that we can implicitly create a delegate from a lambda, resulting in less cluttered code. How do we write our anonymous delegate as a lambda Here s the original:

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Predicate<Document> predicate = delegate(Document doc ) { return !doc.Text.Contains(" "); }

And here it is rewritten using a lambda expression:

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