Question

Define a procedure last-pair that returns the list that contains only the last element of a given (nonempty) list: (last-pair (list 2372149 34)) (34)

Short answer

Define `last-pair` function and use recursion to return last element as a list.

Step-by-step solution

Understand the Problem

The task requires us to create a procedure, `last-pair`, that accepts a non-empty list and returns a list containing only the last element from the input list. For example, given the input `(list 2372149 34)`, the expected output is `(34)`.

Create a base function

In a Lisp-like language, let's define a function `last-pair` that will handle our operation. We can use recursion to traverse the list until we reach the last element. For our implementation, we will need to identify single-element lists, as these represent the last element in a longer list.

Check for the base case

Implement the base case in the procedure. If the list has only one element, return the list immediately: ``` (define (last-pair lst) (if (null? (cdr lst)) lst (last-pair (cdr lst)))) ``` Here, `(null? (cdr lst))` checks if there is a next element. If there is not, the current list is the last element.

Recursive step

If the list is not a single-element list, recursively call `last-pair` on the rest of the list (i.e., the cdr) until you reach the single-element list: ``` (last-pair (cdr lst)) ``` This step ensures that we are working through the list one step at a time until only one element remains.

Run the function on the given example

Using the defined `last-pair` procedure, test it with the provided example to check if it returns the correct result. Example: `(last-pair (list 2372149 34))` should return `(34)`.

Key concepts

Functional Programming

Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions. It avoids changing state and mutable data. This style of programming is centered around the use of functions and avoids side-effects, making it different from imperative programming.
In functional programming, functions are first-class citizens. This means that functions can be passed as arguments to other functions, returned as values from other functions, and assigned to variables. This leads to clean and understandable code, which is very powerful in reducing bugs.
One of the key concepts is recursion, a method where the solution to a problem depends on solutions to smaller instances of the same problem. It is a natural fit in functional programming because it replaces loops, which often rely on mutable state. With recursion, we define functions in a way that allows them to invoke themselves, typically breaking down a task into smaller, easily manageable parts.

Lisp Programming Language

Lisp, short for "LISt Processing," is one of the oldest and most well-known functional programming languages. Created in the late 1950s, Lisp has a unique syntax that uses lots of parentheses, which can initially be intimidating, but is straightforward once you get accustomed to it.
Lisp is particularly associated with list processing because of its efficient handling of lists, which are a primary data structure in the language. Lists in Lisp can contain other lists, allowing for the construction of complex data structures. This makes Lisp very powerful for tasks like symbolic reasoning and AI applications.
Lisp's philosophy centers around code that is data, meaning programs can manipulate and transform other programs, a feature known as metaprogramming. This feature, along with dynamic typing, garbage collection, and first-class functions, makes Lisp a versatile choice in many domains.

List Processing

List processing refers to the handling and manipulation of lists, which are collections of elements typically of the same type. Lists are a fundamental data structure in many programming languages, especially those that are based on or support functional programming.
In list processing, there are typical operations like mapping, filtering, and reducing, which allow for the transformation and reduction of lists into simpler forms. For example, mapping applies a function to each element in a list, producing a new list of results. Meanwhile, filtering selects elements that satisfy a condition.
Recursion plays a significant role in list processing as it allows functions to operate over lists that can be of indefinite length or structure. By defining base cases and recursive cases, list processing functions manage to navigate and manipulate lists effectively, as seen in the `last-pair` function that recursively selects the last element of a list.