Vocabulary of Minimal Scheme


Functions, Operators, and Programs

I 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".

Arithmetic operators


Predefined numeric constants
The define keyword

The define keyword is used in two common ways: defining variables and defining functions.

Boolean operators


(or (<= price 10.00) (eq? my-symbol 'bluebird))
Legal. This determines whether 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)
Illegal because or works on booleans, not numbers
(< true false)
Illegal because < works on numbers, not booleans
(+ 3 (< 4 5))
The first step of simplification turns this into (+ 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.

Defining structures

The define-struct keyword allows you to add new aggregate data types to the language.



(cons 'bluebird empty)
returns exactly the same thing
(define bird-list (cons 'bluebird (cons 'mallard (cons 'crow empty)))
returns nothing, but defines bird-list to be a list of three symbols.
returns (cons 'bluebird (cons 'mallard (cons 'crow empty)))
(first bird-list)
returns 'bluebird
(rest bird-list)
returns (cons 'mallard (cons 'crow empty))
(first (rest bird-list))
returns 'mallard
(empty? bird-list)
returns false
(cons? bird-list)
returns true
(empty? (rest (rest (rest bird-list))))
returns true

Last modified: Wed Jun 13 11:26:59 EDT 2001
Stephen Bloch / sbloch@adelphi.edu