SI 413 Fall 2023 / Homeworks

This is the archived website of SI 413 from the Fall 2023 semester. Feel free to browse around; you may also find more recent offerings at my teaching page.

Homework 3: Scheme Evaluation

Many of these exercises are programming exercises, but you do not need to submit them electronically.

1 Symbol Mixup

Write a function (mixup x) that takes an argument x, which can be any symbol or any number, and produces the opposite type of thing, either the number 5 if x is a symbol, or the symbol 'num if x is a number.

For example, (mixup 20) should produce 'num, and (mixup 'hello) should produce 5.

2 Building Blocks

In the C programming language, give an example of each of the following types of code fragments.

  1. An atom (or literal)

  2. A value that is not an atom

  3. An expression that is not a value

  4. A statement that does not end in a semicolon

3 Nested Quotes

When you type 5 into the interpreter, it returns 5.

When you type (quote 5), it still returns the number 5.

But when you type (quote (quote 5)) or ''5, it returns '5.

What do you think is going on here? Why do you need two quotes to make the symbol 5?

(Caution: this is pretty tricky. Think about how evaluation works. Play around, experiment, discuss.)

4 Find the symbol

Write a function (has-symbol? name expr) that recursively searches through any quoted expression expr and returns true or false depending on whether that expression contains the given symbol name.

Note that the expression can contain nested sub-expressions!

For example, this would return #t:

(has-symbol? 'x '(* 2 (+ x 3)))

whereas this would return #f:

(has-symbol? 'y '(* 2 (+ x 3)))

5 Homoiconicity

The Wikipedia page on homoiconicity claims that raw machine code can be considered homoiconic, just like Scheme.

Explain what this means in a few sentences of your own.

Then tell me what properties of most homoiconic languages (like Scheme) does machine code definitely not have.

6 And Transformation

You know that there is a built-in function called and in Scheme. The built-in version actually takes any number of arguments, and always returns either #t or #f, but for this exercise we’ll assume that and only takes two arguments.

You should be able to convince yourself that every and could be re-written as an if. For example, consider the following function that tests whether the number x is a “teen”.

(define (teen? x)
  (and (>= x 13)
       (< x 20)))

Well this is exactly the same as:

(define (teen? x)
  (if (< x 13)
      (< x 20)))

Your task is to write a Scheme function (and->if expr) that takes a quoted and expression and returns an equivalent quoted if expression that computes the same thing. (Note: the expression your code produces might not look exactly like what I have above, but it should be equivalent computationally.)

If you then eval the result, it should work. For example, the following should produce #t:

(define x 18)
(eval (and->if '(and (>= x 13) (< x 20))))