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One common use case for local functions is when we want to use recursion In these cases, the enclosing function is called, sets things up, and then makes the rst call to a local recursive function Recursive functions (or methods) are ones that call themselves Structurally, all directly recursive functions can be seen as having two cases: the base case and the recursive case The base case is used to stop the recursion Recursive functions can be computationally expensive because for every recursive call another stack frame is used; however, some algorithms are most naturally expressed using recursion Most Python implementations have a xed limit to how many recursive calls can be made The limit is returned by sysgetrecursionlimit() and can be changed by syssetrecursionlimit(), although increasing the limit is most often a sign that the algorithm being used is inappropriate or that the implementation has a bug The classic example of a recursive function is one that is used to calculate factorials For example, factorial(5) will calculate 5! and return 120, that is, 1 2 3 4 5:

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def factorial(x): if x <= 1: return 1 return x * factorial(x - 1)

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This is not an ef cient solution, but it does show the two fundamental features of recursive functions If the given number, x, is 1 or less, 1 is returned and no recursion occurs this is the base case But if x is greater than 1 the value returned is x * factorial(x - 1), and this is the recursive case because here the factorial function calls itself The function is guaranteed to terminate because if the initial x is less than or equal to 1 the base case will be used and the function will nish immediately, and if x is greater than 1, each recursive call will be on a number one less than before and so will eventually be 1 To see both local functions and recursive functions in a meaningful context we will study the indented_list_sort() function from module le IndentedListpy This function takes a list of strings that use indentation to create a hierarchy, and a string that holds one level of indent, and returns a list with the same strings but where all the strings are sorted in case-insensitive alphabetical order, with indented items sorted under their parent item, recursively, as the before and after lists shown in Figure 81 illustrate Given the before list, the after list is produced by this call: after = IndentedListindented_list_sort(before) The default indent value is four spaces, the same as the indent used in the before list, so we did not need to set it explicitly

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FIGURE 111 The customer table from the Mountain View Music database promised, but also this table contains the passwords customers use when they log on to the Mountain View Music Web site For these reasons we need tight controls that limit who and what can access this table For example, let s say that all the customer service employees need to be able to read and write to tbl_customer If you grant them all read and write access to the table, they will be able to read and write all the data in the table This means that they can see the password, even if it s encrypted Why let them see it and have the opportunity to change it and affect your customers We know what you might be thinking: Permissions can be applied on a column basis, and thus you could prevent them from seeing this information Although that is true, have you ever tried to manage security to this level It can be a pain to keep track of who has access to what Instead, you can create a view as follows

before = ["Nonmetals", " Hydrogen", " Carbon", " Nitrogen", " Oxygen", "Inner Transitionals", " Lanthanides", " Cerium", " Europium", " Actinides", " Uranium", " Curium", " Plutonium", "Alkali Metals", " Lithium", " Sodium", " Potassium"]

after = ["Alkali Metals", " Lithium", " Potassium", " Sodium", "Inner Transitionals", " Actinides", " Curium", " Plutonium", " Uranium", " Lanthanides", " Cerium", " Europium", "Nonmetals", " Carbon", " Hydrogen", " Nitrogen", " Oxygen"]

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We will begin by looking at the indented_list_sort() function as a whole, and then we will look at its two local functions

def indented_list_sort(indented_list, indent=" KEY, ITEM, CHILDREN = range(3) def add_entry(level, key, item, children): def update_indented_list(entry): entries = [] for item in indented_list: level = 0 i = 0 while itemstartswith(indent, i): i += len(indent) level += 1 key = itemstrip()lower() add_entry(level, key, item, entries) indented_list = [] for entry in sorted(entries): update_indented_list(entry) return indented_list "):

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