## Homework Assignment 4

### Structurally Recursive Functions

#### Introduction

This assignment asks you to write recursive functions in Racket. The primary goal of this assignment is to gain experience with recursion and Racket lists. For this assignment:

Template Source File

This file includes a provide clause that exports your five public functions. This enables me to load your module and test your functions using my own Rackunit tests.

With provide, you must define all five functions. If you don't have time to solve a problem, define a function that takes the correct number of arguments and returns a legal default value, such as 0 or '().
Do Not Use...
• ... any of Racket's primitive higher-order functions in any of your solutions, including map, apply, and filter.
• ... any function that converts a list argument to another datatype. Process the list.
• ... a let expression or an internal define in any of your solutions.
Organizing Code
• Use a comment to indicate where the code for each problem begins and ends. The template already does that for you.
• For each problem, write at least three test expressions to test your solution. Depending on the type of value that the function produces, use check-equal?, check-=, or check-true/false. You may use my example as one of your tests. Be sure that you test other key cases, too.
• Put any helper functions you write for a problem between the main function in your solution and the tests for the main function.

#### Problems

1. Write a recursive function (string* str n) that takes two arguments: a string x and a non-negative integer n. The non-negative integers are defined inductively as:
```     <number> ::= 0
| <number> + 1
```
string* returns a string consisting of n occurrences of str. For example:
```     > (string* "Eugene" 3)
"EugeneEugeneEugene"
```
You will want to use Racket's string-append function. Remember that the base case when recurring on a non-negative integer is 0.

2. Write a structurally recursive function (collect f lon) that takes two arguments, a one-argument function f and a list of numbers lon.
```     <list-of-numbers> ::= ()
| (<number> . <list-of-numbers>)
```
collect returns a list of items f(i) for every i in lon. For example:
```     > (collect sqr '(1 2 -1 -2 3 -3 5 -4 4))   ; sqr squares its arg
'(1 4 1 4 9 9 25 16 16)
```
3. Write a structurally recursive function (insert-before new-sym sym los) that takes as arguments two symbols, new-sym and sym, and a list of symbols, los.
```     <list-of-symbols> ::= ()
| (<synbol> . <list-of-symbols>)
```
insert-before returns a list just like los, except with new-sym occurring before the first occurrence of sym. For example:
```     > (insert-before 'a 'b '(c b b i e))
'(c a b b i e)
```
4. Write a structurally recursive function (any? test? lon) that takes two arguments, a function of one number, test?, and list of numbers, lon. any? returns #t if any number in lon passes the test?, and #f otherwise. For example:
```     > (any? negative? '(26 37 41 25 12))
#f
> (any? even? '(37 41 25 26 12)))
#t
```
5. Write a structurally recursive function (positions-of s los) that takes two arguments, a symbol s and a list of symbols los. positions-of returns a list containing the zero-based positions of all occurrences of s in los. For example:
```     > (positions-of 'a '(a b a c d a e f g a h i j k))
'(0 2 5 9)
```
Make positions-of an interface procedure that calls a structurally recursive helper function with the symbol and list of symbols as the first two arguments, and an initial value for the counter as the third.

#### Deliverables

By the due time and date, submit the following files:

• homework04.rkt, the source file containing your function definitions and test cases

Be sure that your submission follows the submission requirements.

Eugene Wallingford ..... wallingf@cs.uni.edu ..... February 16, 2023