define
keywordI use the words "function", "operator", and "program" almost interchangeably. All three words mean "something that takes in some information, does some computation, and produces some information as a result".
The word "operator" tends to be used for built-in arithmetic functions like addition, subtraction, multiplication, division, square root, and comparison. The word "program" tends to be used for functions you or I have defined. The word "function" applies equally to both. Don't worry too much about this distinction.
For example, consider the familiar arithmetic operators
"+
", "-
", etc. from grade school:
in the algebraic expression 3 + 4
, the
operator "+" operates on the two pieces of information "3"
and "4" and produces the result "7".
+, -, *, /
all take two or more numbers
and return a numbersqrt
takes one number and returns a
numberremainder
and modulo
(two
names for the same operator) both take two integers and
return an integer: they divide the first operand by the
second, returning not the quotient but the
remainder.Examples:
(sqrt (+ (* 3 (remainder 5 3)) (* 4
4)))
(sqrt 3 4)
sqrt
function only accepts one
parameter.pi
has the value 3.14159....e
has the value 2.71828182....define
keywordThe define
keyword is used in two common
ways: defining variables
and defining
functions.
true
and false
are the two
built-in boolean values.<, >, =, <=, >=
all take two
or more numbers and return a booleaneq?
takes two objects (numbers, symbols,
booleans, or anything else) and returns a booleanand, or
each takes two or more booleans
and returns a booleannot
takes a boolean and returns a
booleanzero?, positive?, negative?
all take a
number and return a boolean.(zero? x)
is just another way of saying
(= x 0)
.(positive? x)
is just another way of saying
(> x 0)
.(negative? x)
is just another way of saying
(< x 0)
.Examples:
(or (<= price 10.00) (eq? my-symbol
'bluebird))
price
is
less than or equal to 10.00; if so, it returns
true
. If not, it then tests whether
my-symbol
is the symbol 'bluebird
; if
so, it returns true
, otherwise
false
.(or 3 4)
or
works on booleans,
not numbers(< true false)
(+ 3 (< 4 5))
(+ 3 true)
, because the value of (<
4 5)
is true
. The second step fails
because +
only works on numbers, not on a
number and a boolean.Scheme contains several conditional constructs, but the
only one we need in this course is cond
.
The
define-struct
keyword allows you to add new
aggregate data types to the language.
empty
is a variable, not a function; its
value is the empty list.cons
takes an object and a list, and
returns a new list with the specified object as its first
element, and the specified list as the rest. In Beginner
mode, it signals an error if the second parameter is not
a list.first
takes a non-empty list and returns
the first element. It signals an error message if it is
given an empty list or anything other than a list.rest
takes a non-empty list and returns
a list of everything but the first element. It signals an
error message if it is given an empty list or anything
other than a list.empty?
takes an object and returns a
boolean indicating whether it is the empty list.cons?
takes an object and returns a
boolean indicating whether it is a non-empty list.Examples:
(cons 'bluebird empty)
(define bird-list (cons 'bluebird (cons 'mallard (cons 'crow empty)))
bird-list
to be a list of three symbols.bird-list
(cons 'bluebird (cons 'mallard (cons
'crow empty)))
(first bird-list)
'bluebird
(rest bird-list)
(cons 'mallard (cons 'crow
empty))
(first (rest bird-list))
'mallard
(empty? bird-list)
false
(cons? bird-list)
true
(empty? (rest (rest (rest bird-list))))
true