Held: Wednesday, 28 January 2004
Summary:
Today we begin to learn how to tell Scheme to make decisions. The
procedures used to make decisions are called conditionals.
Today's class will be a large group design effort rather than an individual
or small group design effort.
Related Pages:
Due
Assignments:
Notes:
- As a change of pace, today's class will primarily focus on group problem solving.
Overview:
- A problem: Turning numbers into letters (in English and Scheme).
- Making life easier: Conditionals.
- What kinds of tests can you use in conditionals?
- Suppose that for fairness's sake, I'd like a program that converts
numeric grades to letter grades.
- We'll look at two related grading schemes.
- 94-100: A, 90-93: A-, 87-89: B+, 84-86: B, ...
- 10:A+ 9:A, 8:A-, 7:B+, 6:B, 5:B-, 4:C+ 3:C 2:C- 1:D 0:F
- How might you explain to someone how to turn a number into a grade?
- In either schema, can you write a procedure that turns a number
into a grade, using only the Scheme you already know?
- As you may have noted from your narrative, we are often tempted
to describe the procedure in terms of the word
if
. For
example, if the grade is at least 94, then give the student
an A, otherwise, if the grade is between 90 and 93, ...
- In Scheme, you can write such expressions as
(if condition
success-expression
failure-expression)
- Note that
if does not behave according to
Marie's evaluation pattern (in which all the arguments
to a procedure are computed before the procedure is applied).
- In particular, only one of the success-expression and
failure-expression is computed.
- Given the Scheme that you know right now, the only effect is
on efficiency.
- Later, you'll see that this decision affects other things, too.
- For example
- We can nest these conditions.
(if (>= grade 94)
'A
(if (<= 90 grade 93)
'Aminus
(if (<= 87 grade 90)
...)))
- As you may have noticed, the code is somewhat hard to read (and
awfully indented). Another alternative is to use Scheme's
cond, which more closely resembles a table.
- Here's what a
cond expression looks like
(cond
((condition1) exp1)
((condition2) exp2)
((condition3) exp3)
...
(else default-exp))
- In this case, the conditions are evaluted one-by-one until one
holds true. The value of the corresponding expression
is the then returned.
- For our problem, this format seems particularly appropriate.
(cond
((>= grade 94) 'A)
((<= 90 grade 93) 'Aminus)
...)
- To permit you to write useful tests and conditions for conditionals,
Scheme provides a wide variety of mechanisms for building those tests.
- Tests should return true (
#t) or false
(#f).
- Scheme treats anything that's not false as true.
- We call the tests Boolean expressions in honor of the logician
George Boole.
- We call procedures that return true or false predicates.
- The simplest tests: Type Predicates.
- These procedures (whose names invariably end with question marks)
determine whether a value falls within a particular type.
- They include:
number?,
list?, and
symbol?.
- There are many numeric comparators, including
< (strictly less than),
<= (less than or equal to),
= (equal to),
>= (greater than or equal to),
and
> (strictly greater than).
- There are also a variety of equality comparators, including
=,
eq?,
eqv?, and
equal?.
-
= is used for numbers.
-
eq? typically determines if two
values share the same memory location.
-
eqv? determines if two
primitive values are equal.
-
equal? also looks within
compound types (such as lists) and compares the components of those types.
- Scheme also lets you combine Boolean expressions with
and,
or, and not.
- You will have an opportunity to experiment with all of these
in the lab.
;
Check with Bobby