Python Chapter 6: Functions Design

Chapter 6: Design with Functions

• This chapter covers functions in Python, focusing on structuring code, assigning tasks, and defining recursive functions.
• Objectives include explaining the usefulness of functions in structuring programs, employing top-down design to assign tasks, and defining recursive functions, along with managing namespaces, using higher-order functions, and understanding the costs and benefits of recursion.
• Functions as Abstraction Mechanisms: Abstractions hide details, allowing a person to view many things as a single thing. Abstractions are commonly used to represent everyday tasks in a concise manner, such as "doing my laundry".
• Functions Eliminate Redundancy: Functions serve to eliminate repetitive code, thereby improving efficiency and reducing errors.
• Functions Hide Complexity: Functions encapsulate processes, hiding the complex code underpinning those processes. This allows the programmer focusing on the function's purpose without getting bogged down in implementation details.
• Functions Support General Methods with Systematic Variations: An algorithm, a set of defined steps to accomplish a task, should be general enough to create solutions to many different problem instances. A function should be a general method providing systematic variations.
• Functions Support Division of Labor: In a well-organized system, each part does its own job toward a shared goal. Functions in a program likewise perform logical, divided tasks.
• Problem Solving with Top-Down Design: Top-down design breaks down a complex problem into smaller, more manageable subproblems, a process also known as problem decomposition. As each subproblem is identified, its solution is assigned to a specific function.
• Design of Text Analysis Program: A structure chart illustrates the relationships among functions in a text analysis program. Data types are shown—such as integer (int), strings(string), and floating-point numbers (float).
• Design of Sentence Generator Program: A structure chart illustrates the functions and data type relationships in a sentence generator program.
• Design of Doctor Program: A structure chart illustrates data type relationships in a doctor program. Data types such as strings(string) are shown.
• Design with Recursive Functions: Recursive functions break down a complex problem into smaller problems of the same form. In top-down design, recursive functions solve these smaller problems using the same function.
• Defining a Recursive Function: A recursive function calls itself, which requires a mechanism (a base case) to stop the recursive calls after a certain point to prevent the program from continuing indefinitely.
• Making displayRange Recursive (Continued): An example using a recursive function to display a list of numbers. This demonstrates the step-wise refinement in top-down design.
• Most Recursive Functions Expect at Least One Argument: One or more arguments are an expected feature for many recursive functions, especially those needing data to be solved.
• Another Example: Recursive version of sum: A recursive function example to calculate the sum of numbers between two bounds, and provides an illustration of the program call tracing the calculations with examples.
• Tracing a Recursive Function: Tracing shows the recursive calls and return values, illustrated by an example using the sum function.
• Using Recursive Definitions to Construct Recursive Functions: Recursive functions often rely on the recursive definition of a problem; understanding the problem's recursive definition is key for function design.
• Example Fibonacci Sequence: Recursive calculations, as seen in the Fibonacci sequence, demonstrate recursive structure.
• Recursion in Sentence Structure: Recursive functions help define the structure of sentences in language. They can modify noun phrases using prepositional phrases, often including a recursive call.
• Infinite Recursion: Infinite recursion occurs when recursive calls occur without a base case to terminate. This can lead to the program running out of memory resources to handle this recursive process.
• The Costs and Benefits of Recursion: This section examines the space and time efficiencies of recursive calls. Recursive function calls require memory space for each call in a call stack; iterative functions do not have this cost.
• Higher-Order Functions (Advanced Topic): Higher-order functions accept functions as arguments; they can handle sequences of data and return results or a sequence of results. These functions separate the task of transforming values from the task of accumulating results.
• Functions as First-Class Data Objects: Functions can be treated like data. They can be assigned to variables, passed as arguments, returned as values, and stored in structures.
• Mapping: Mapping applies a function to every value in a sequence. This returns a new sequence based on the result of the function applications.
• Filtering: The predicate is a function that is applied to each value in a sequence. If the predicate returns a value True, the value is added to a filtered list. Otherwise, it's excluded.
• Reducing: Reducing function takes a list of values and applies a function repeatedly to accumulate a single data value.
• Using Lambda Functions to Create Anonymous Functions: Lambda functions, anonymous functions, represent a short, simple expression that can be directly used in operations, such as reduce or map.
• Creating Jump Tables: Create a dictionary keyed on command names; a simple program execution approach using the jump table.
• Summary: A function acts as an abstraction, helps eliminate redundant code, and decomposes complex problems via top-down design where they can be assigned to functions. Recursive functions treat complex problems like smaller problems of the same form and call themselves.
• Summary (continued): A recursive function calls itself with base cases to terminate the recursive call process. A program's namespace contains module variables, parameters, temporary variables, and scopes. The lifetime of a variable is the duration of program execution.
• Summary (continued): Python treats functions like data. Higher-order functions accept functions as arguments, potentially return functions, and can work with data. Filtering and mapping functions do these data transformations. Reducing function applies to a sequence of values to reduce to a single result value.