Assignment 1: Learning Scheme¶

In this assignment, your task is to learn basic Scheme programming. We’ll do this by implementing a number of basic Scheme functions.

Your solutions are restricted to use only the following:

define, lambda, let, let*, cond/else, if
null?, car, cdr, cons, list?, list
not, and, or, #t, #f, equal?
basic arithmetic operators like +, /, mod, <, >=, …
data types: numbers, strings, symbols, lists

Any functions you define in this assignment must use only these elementary forms. You can (should!) create helper functions, and you may also use functions from previous questions in the answers to later questions.

Functions that start with my- are versions of existing Scheme functions. Of course, don’t use the existing Scheme function in your code!

Implement a function called (singleton? x) that returns #t if x is a list with exactly 1 element, and #f otherwise. For example:
```
> (singleton? '(4 mouse ()))
#f

> (singleton? '(xy))
#t

> (singleton? 4)
#f
```
Implement a function called (my-make-list n x) that returns a list containing n copies of x. For example:
```
> (my-make-list 3 'a)
(a a a)

> (my-make-list 2 '(1 2 3))
((1 2 3) (1 2 3))

> (my-make-list 2 (my-make-list 3 '(a b)))
(((a b) (a b) (a b)) ((a b) (a b) (a b)))
```
If n is 0 or less, then return the empty list.

You can assume n is a valid integer. If it’s not, it’s fine if your function crashes.
Implement a function called (all-same? lst) that returns #t if lst is empty, or if all the elements in it are equal to each other (using equal?). For example:
```
> (all-same? '())
#t

> (all-same? '(cat))
#t

> (all-same? '(cat cat cat))
#t

> (all-same? '(cat cat dog cat))
#f
```
You can assume lst is a valid list. If it’s not, it’s fine if your function crashes.
Implement a function called (my-iota n) that returns a list containing the numbers from 0 to n-1. For example:
```
> (my-iota 0)
()

> (my-iota 1)
(0)

> (my-iota 2)
(0 1)

> (my-iota 5)
(0 1 2 3 4)
```
If n is 0 or less, then return the empty list.

You can assume n is a valid integer. If it’s not, it’s fine if your function crashes.
Implement a function called (my-length lst) that returns that returns the number of items in lst. For example:
```
> (my-length '())
0

> (my-length '(a))
1

> (my-length '(a (b c)))
2

> (my-length '(a (b c) d))
3
```
You can assume lst is a valid list. If it’s not, it’s fine if your function crashes.
Implement a function called (nth lst i) that returns that returns the item at index location i in lst. The indexing is 0-based, so, the first element is at index location 0, the second element is at index location 1, and so on. For example:
```
> (nth '(a b c) 0)
a

> (nth '(a b c) 1)
b

> (nth '(a b c) 2)
c

> (nth '(a b c) 3)
;bad index
```
You can assume lst is a valid list and i is a valid integer. If not, it’s fine if your function crashes.

If i is less than 0, or if its greater than or equal to the length of lst, call the error function.
Implement a function called (my-last lst) that returns the last element of lst. For example:
```
> (my-last '(cat))
cat

> (my-last '(cat dog))
dog

> (my-last '(cat dog (1 2 3)))
(1 2 3)

> (my-last '())
my-last: empty list
```
Notice that calling my-last on the empty list prints the error message “my-last: empty list”. Use the error function to do this, e.g. (error "my-last: empty list").

You can assume lst is a valid list. If it’s not, it’s fine if your function crashes.
Implement a function called (middle lst) that returns a list that is the same as lst, but the first element and the last element have been removed. For example:
```
> (middle '(a b c d e))
(b c d)

> (middle '(6 4 cat m egg))
(4 cat m)
```
If lst has 2, or fewer, elements, then return the empty list.

You can assume lst is a valid list. If it’s not, it’s fine if your function crashes.
Implement a function called (my-filter pred lst) that returns a list containing just the elements of lst that satisfied the predicate function pred. For example:
```
> (my-filter odd? '(5 7 0 -6 4))
(5 7)

> (my-filter odd? '(10 5 7 0 11 4))
(5 7 11)

> (my-filter list? '(hat (left right) 4 ()))
((left right) ())

> (my-filter (lambda (x) (or (= x 5) (< x 0))) '(5 6 9 -6 2 5 0 5))
(5 -6 5 5)
```
You can assume pred is a predicate function that takes one input, and returns either #t or #f. If it’s not, it’s fine if your function crashes.

You can assume lst is a valid list. If it’s not, it’s fine if your function crashes.
Implement a function called (my-append A B) that returns a list that has all the elements of A followed by all the elements of B. For example:
```
> (my-append '(1 2 3) '(4 5 6 7))
(1 2 3 4 5 6 7)

> (my-append '(1 2 3) '(4))
(1 2 3 4)

> (my-append '() '(4))
(4)
```
You can assume A and B are valid lists. If they’re not, it’s fine if your function crashes.
Implement a function called (append-all lol) that returns a list that has all the lists of lol appended into one list. For example:
```
> (append-all '())
()

> (append-all '((a)))
(a)

> (append-all '((a) (b c)))
(a b c)

> (append-all '((a) (b c) (d)))
(a b c d)

> (append-all '((a) (b c) (d) (e f)))
(a b c d e f)
```
You can assume lol a valid list of lists, i.e. lol is a list whose elements are all lists. If lol is not a list of lists, it’s fine if your function crashes.
Implement a function called (my-sort lst) that returns the numbers on lst in sorted order. For example:
```
> (my-sort '())
()

> (my-sort '(3))
(3)

> (my-sort '(4 1 3 7 5 5 1))
(1 1 3 4 5 5 7)
```
You can assume lst a valid list of numbers. If it’s not, it’s fine if your function crashes.

It’s fine if your algorithm runs in quadratic time.

Hint: Recursive sorting algorithms, like quicksort or mergesort, are good choices for Scheme
Implement a function called (all-bits n) that returns a list of \(2^n\) sub-lists, where each sub-list is a different pattern of n 0s and 1s. For example:
```
> (all-bits 0)
()

> (all-bits 1)
((0) (1))

> (all-bits 2)
((0 0) (0 1) (1 0) (1 1))
```
The order of the sub-lists doesn’t matter, as long the returned list contains exactly all \(2^n\) possible bit lists.

Important: your function should, at least in theory, work for any n no matter how big. Do not use any tricks that assume a limit on the size of n.

If n is less than or equal to 0, return the empty list.

You can assume n is a valid integer. If it’s not, it’s fine if your function crashes.

What to Submit¶

Put all your code into a single Scheme source file called a1.scm, and this submit this online in Canvas.

Please make sure to use exactly the function names and inputs as described above, otherwise your functions will get marked as incorrect.

Assignment 1: Learning Scheme¶

What to Submit¶

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