Common Lisp the Language, 2nd Edition

1.2.3. Evaluation, Expansion, and Equivalence

Execution of code in Lisp is called evaluation because executing a piece of code normally results in a data object called the value produced by the code. The symbol => is used in examples to indicate evaluation. For example,

(+ 4 5) => 9

means ``the result of evaluating the code (+ 4 5) is (or would be, or would have been) 9.''

The symbol -> is used in examples to indicate macro expansion. For example,

(push x v) -> (setf v (cons x v))

means ``the result of expanding the macro-call form (push x v) is (setf v (cons x v)).'' This implies that the two pieces of code do the same thing; the second piece of code is the definition of what the first does.

The symbol == is used in examples to indicate code equivalence. For example,

(gcd x (gcd y z)) == (gcd (gcd x y) z)

means ``the value and effects of evaluating the form (gcd x (gcd y z)) are always the same as the value and effects of (gcd (gcd x y) z) for any values of the variables x, y, and z.'' This implies that the two pieces of code do the same thing; however, neither directly defines the other in the way macro expansion does.