Figure 
shows the terms of
.
Variables are terms, although since they are not closed they are not executable.
Variables are written as identifiers, with
distinct identifiers indicating distinct variables.
Nonnegative integers are written
in standard decimal notation. There is
no way to write a negative
integer in
; the best one can do is to write a noncanonical
term, such as -5, which evaluates to a negative integer.
Atom constants are written as character strings enclosed in
double quotes, with distinct strings indicating distinct atom constants.
The free occurrences of a variable x
in a term t are the occurrences
of x which either are t or are free in the immediate subterms of t,
excepting those occurrences of x which become bound
in t. In figure
the variables written below the terms indicate which variable
occurrences become bound; some examples are explained below.
Parentheses may be used freely around terms and often must be used to resolve
ambiguous notations correctly. Figure gives the
relative precedences and
associativities
of
operators.
The closed terms above the dotted line in figure are the
canonical terms, while the closed terms below it
are the noncanonical terms. Note that
carets appear below most of the noncanonical forms; these indicate the
principal argument places of those
terms. This notion is used in the
evaluation procedure below. Certain terms are
designated as redices , and each redex has a
unique contractum .
Figure shows all redices and their contracta.
The evaluation procedure is as follows. Given a (closed) term t,
