Question

Consider the following Scheme function: (define (mystery input-list) (cond ((null? input-list) 0) (else (+ 1 (mystery (cdr input-list)) )) )) What is the result of invoking the function as follows? (mystery (list 34 5)) Explain what this function does in general.

Short answer

The function returns 2 and it computes the length of a list.

Step-by-step solution

Understanding the Function Definition

The function `mystery` takes a single argument `input-list`. It checks whether `input-list` is empty with `(null? input-list)`. If so, it returns 0.

Recursive Call when List is Not Empty

If `input-list` is not empty, the function performs a recursive call by passing the 'cdr' (the rest) of the list to itself. It adds 1 to the result of this recursive call. This essentially counts each element in the list.

Applying the Function to the Example Input

Now, consider the input `(list 34 5)`. The function will first add 1 to the result of calling `mystery` on `(cdr (list 34 5))`, which is `(list 5)`. Then, `mystery` will add 1 to the result of calling itself on `(cdr (list 5))`, which is an empty list `()`. The call on the empty list returns 0.

Final Computation

Combining the recursive calls, we have: `1 + (1 + (mystery '())) = 1 + (1 + 0) = 2`. Thus, the function returns 2.

General Explanation

In general, this function calculates the length of a given list by counting the number of elements within it.

Key concepts

Scheme Programming

Scheme is a minimalist dialect of the Lisp programming language family. It emphasizes a very clean and simple design, with a small core that allows for flexibility and functionality through extensions. Scheme is popular in educational contexts due to its straightforward syntax and strong focus on recursion. The language makes it easy to express logical ideas and operations clearly.

Each Scheme program consists of expressions written in S-expression notation. An S-expression is a list where the first element is the operator and the following elements are the operands. For example, `(define (mystery input-list) ...)` defines a function called `mystery` in Scheme. This function handles list operations in a recursive manner, as detailed in our exercise.

Scheme relies heavily on recursion for iteration. This property is seen in the `mystery` function, which recursively processes each element of its input list to determine the list's length.

List Processing

List processing is fundamental in Scheme and many functional programming languages. Lists are a core data structure, providing a flexible way to handle a sequence of elements. In Scheme, a list can be manipulated using various built-in functions such as `car`, `cdr`, and `cons`.

The `car` function returns the first element of a list, while `cdr` returns the remainder of the list after the first element. These functions are essential for breaking down lists into manageable parts. In our example, `(cdr input-list)` is used to obtain a smaller list for further processing.

The mystery function utilizes these list techniques to achieve its goal. It systematically processes the list, treating it like a stack, counting each item until it encounters an empty list. This explains why it returns 0 when it reaches the terminal condition of an empty list. Through such recursion, Scheme efficiently performs operations that might traditionally require iterative looping in other languages.

Function Definition

Defining functions in Scheme is straightforward. A function is created with `define`, providing a name, parameters, and the body of the function. In the exercise example, the function `mystery` is defined to accept a single parameter, `input-list`.

Conditional execution is implemented via `cond`, which provides a clean way to execute different paths based on the conditions provided. In this particular function, it checks if `input-list` is empty using `(null? input-list)`. If true, it returns 0, marking the end of recursion.

This structure demonstrates how functions can call themselves recursively, a common pattern in functional languages. It emphasizes condition checking and state reduction. By invoking itself with a reduced problem, `mystery` solves a larger problem through simplicity. The recursive process accumulates results via addition, highlighting the power of function definition in Scheme to elegantly solve problems.