Terminology

Sam’s quick and dirty attempt to summarize recent vocabulary. If you find something confusing, please ask me to clarify. If there are other terms you’d like defined, let me know.

Integer

A number with no fractional part. A number that can be obtained by repeatedly adding 1 to 0 or repeatedly subtracting 1 from 0. For example, 5 is an integer because 5 = 0 + 1 + 1 + 1 + 1 + 1.

Identifier

A nonempty sequence of letters, digits, and symbols that does not take the form of a basic value, such as a number. For example, hello and a3+x are both identifiers, but 34 is not (it’s an integer). In Scheme, identifiers usually have associated values. Some identifiers, such as define and if are treated as keywords and are (a) not bound to values and (b) result in a different evaluation strategy than we typically use.

Value

An entity that can be manipulated by the program. Alternately, something that cannot be further evaluated. Examples include numbers, strings, lists, and images.

Basic value

A value that does not contain other values. Examples include numbers, strings, the empty list, and images.

Compound value

A value that contains other values. Examples include strings, nonempty lists, and vectors. Images built with operations like overlay and above are also considered compound values.

Expression

Initially, either (a) a value or (b) the application of a function to a sequence of expressions. That application is written with an open parenthesis, the function (often represented by an identifier), the sequence of expressions (often called arguments) separated by spaces, and a close parenthesis. For example (+ 2 3) or (string-length (string-append "hello" "scheme")). Eventually, we’ll also see some expressions that start with keywords.

Non-trivial expression

Any expression that is not a basic value. (+ 2 3) is a nontrivial expression. 2 is a trivial expression.

Immediate subexpression

Any in the sequence of expressions in a function application. In (+ 2 (* 3 4) (- 5 6)), 2, (* 3 4), and (- 5 6) are the immediate subexpressions. Of those, (* 3 4) and (- 5 6) are the nontrivial immediate subexpressions.

Subexpression

An immediate subexpression or any subexpression of an immediate subexpression. (If we think about family trees, immediate subexpressions are like children and subexpressions are like descendants.) In (+ 2 (* 3 (+ 4 5)) (- 7 7)), 2, (* 3 (+ 4 5)), 3, (+ 4 5), 4, 5, (- 7 7), 7, and 7 are the subexpressions and (* 3 (+ 4 5)), (+ 4 5), and (- 7 7) are the nontrivial subexpressions.

Statement

Either a Scheme expression or something that looks remarkably like an application (open paren, keyword, arguments, close paren), except that it starts with one of the statement keywords, such as define. The latter kind of statements usually affect the state of the program (e.g., which value is bound to an identifier).