Conditionals

Exercises

Exercise 0: Preparation

Read the reading on conditionals. You may also want to rescan the reading on numbers and reading on Boolean values, which includes information on predicates.

Exercise 1: What is it?

Define and test a Scheme predicate atom-or-list? that takes one argument and returns #t if the argument is either an atom (symbol) or a list, #f if it is neither.

Exercise 2: Between, Revisited

Define and test a Scheme predicate between? that takes three arguments, all real numbers, and determines whether the second one lies strictly between the first and third (returning #t if it is, #f if it is not). For example, 6 lies strictly between 5 and 13, so both (between? 5 6 13) and (between? 13 6 5) should have the value #t.

Exericse 3: Triangulation

Three line segments can be assembled into a triangle if, and only if, the length of each of them is less than the sum of the lengths of the other two. Define a Scheme predicate triangle? that takes three arguments, all positive real numbers, and determines whether line segments of those three lengths (assumed to be measured in the same units) could be assembled into a triangle.

Exercise 4: Being Neighborly

Define and test a Scheme procedure neighbor that takes one argument, an integer, and returns the next higher integer if its argument is even, the next lower integer if its argument is odd. (Start by writing a comment that describes the purpose of the procedure.)

Exercise 5: Non-Boolean Tests

For each of the following expressions, guess what the output should be and then test it in Scheme.

• (if #t 'aardvark 'zebra)
• (if #f 'aardvark 'zebra)
• (if (null? null) 'aardvark 'zebra)
• (if (null? (list 'a 'b 'c)) 'aardvark 'zebra
• (if () 'aardvark 'zebra)
• (if (list 'a 'b 'c) 'aardvark 'zebra)
• (if 2 'aardvark 'zebra)
• (if 'true 'aardvark 'zebra)
• (if 'false 'aardvark 'zebra)

Exercise 6: Categorizing Lists

Define and test a Scheme procedure list-type that takes one argument, a list, and returns the symbol empty if the argument is the empty list, the symbol non-empty otherwise.

Exercise 7: Who Won?

Define and test a Scheme procedure report-victory that takes one argument, a real number, and returns the string "I won!" if that number is positive, the string "You won!" if it is negative, and the string "It's a tie!" if it is zero.

a. Use if for all your tests.

b. Use cond for all your tests.

Exercise 8: The Sphinx's Riddle

As you may know, one of the famous riddles of the Sphinx goes something like the following:

What is it that walks upon four legs, then two legs, then three legs?

The answer is ``humans''.

Write a Scheme predicate, legs, that, given someone's age, tells how many legs they walk upon. (You get to choose reasonable ages for the three phases of life.)

Exercise 9: Categorizing Data

Write and test a Scheme procedure, type, that returns the a symbol that represents the type of its argument. For example,

> (type 3)
integer
> (type '(1 2 3))
list
> (type "hello")
string
> (type 2/3)
rational
> (type 'type)
symbol
> (type type)
procedure

Notes