ANSI Common Lisp 17 Sequences 17.2 Rules about Test Functions
17.2.1 Satisfying a Two-Argument TestWhen an object O is being considered iteratively against each element Ei of a sequence S by an operator F listed in the next figure, it is sometimes useful to control the way in which the presence of O is tested in S is tested by F. This control is offered on the basis of a function designated with either a :test or :test-not argument.
The object O might not be compared directly to Ei. If a :key argument is provided, it is a designator for a function of one argument to be called with each Ei as an argument, and yielding an object Zi to be used for comparison. (If there is no :key argument, Zi is Ei.)
The function designated by the :key argument is never called on O itself. However, if the function operates on multiple sequences (e.g., as happens in set-difference), O will be the result of calling the :key function on an element of the other sequence.
A :test argument, if supplied to F, is a designator for a function of two arguments, O and Zi. An Ei is said (or, sometimes, an O and an Ei are said) to satisfy the test if this :test function returns a generalized boolean representing true.
A :test-not argument, if supplied to F, is designator for a function of two arguments, O and Zi. An Ei is said (or, sometimes, an O and an Ei are said) to satisfy the test if this :test-not function returns a generalized boolean representing false.
If neither a :test nor a :test-not argument is supplied, it is as if a :test argument of #'eql was supplied.