# rec03 - Recitation 3 Higher-order Functions Anonymous...

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Recitation 3 Higher-order Functions, Anonymous Functions, Currying, Side effects, Printing and Exceptions This lecture covers: higher-order functions anonymous functions currying side-effects and printing exceptions Higher-order functions Functions are values just like any other value in OCaml. What does that mean exactly? This means that we can pass functions around as arguments to other functions, that we can store functions in data structures, that we can return functions as a result from other functions. The full implication of this will not hit you until later, but believe us, it will. Let us look at why it is useful to have higher-order functions. The first reason is that it allows you to write more general code, hence more reusable code. As a running example, consider functions double and square on integers: let double (x:int):int = 2 * x let square (x:int):int = x * x Let us now come up with a function to quadruple a number. We could do it directly, but for utterly twisted motives decide to use the function double above: let quad (x:int):int = double (double (x)) Straightforward enough. What about a function to raise an integer to the fourth power? let fourth (x:int):int = square (square (x)) There is an obvious similarity between these two functions: what they do is apply a given function twice to a value. By passing in the function to apply_twice as an argument, we can abstract this functionality and thus reuse code: let applyTwice ((f:int -> int), (x:int)):int = f (f (x)) Using this, we can write: let quad (x:int):int = applyTwice(double,x) let fourth (x:int):int = applyTwice(square,x) The advantage is that the similarity between these two functions has been made manifest. Doing this is very helpful. If someone comes up with an improved (or corrected) version of applyTwice , then every function

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that uses it profits from the improvement. The function applyTwice is a so-called higher-order function: it is a function from functions to other values. Notice the type of applyTwice is ((int -> int) * int) -> int . To avoid polluting the top-level namespace, it can be useful to locally define the function to pass in as an argument. For example: let fourth (x:int):int = let square (y:int):int = y * y in applyTwice (square,x) What happens when we evaluate an expression that uses a higher-order function? We use the same rules as
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## This note was uploaded on 10/25/2009 for the course PHYS 2214 at Cornell.

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rec03 - Recitation 3 Higher-order Functions Anonymous...

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