## 17.2 Rules about Test Functions

### 17.2.1 Satisfying a Two-Argument Test

When an object O is being considered iteratively against each element Ei of a sequence S by an operator F listed in Figure 17–2, 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.

The consequences are unspecified if both a :test and a :test-not argument are supplied in the same call to F.

#### 17.2.1.1 Examples of Satisfying a Two-Argument Test

``` (remove "FOO" '(foo bar "FOO" "BAR" "foo" "bar") :test #'equal)
→ (foo bar "BAR" "foo" "bar")
(remove "FOO" '(foo bar "FOO" "BAR" "foo" "bar") :test #'equalp)
→ (foo bar "BAR" "bar")
(remove "FOO" '(foo bar "FOO" "BAR" "foo" "bar") :test #'string-equal)
→ (bar "BAR" "bar")
(remove "FOO" '(foo bar "FOO" "BAR" "foo" "bar") :test #'string=)
→ (BAR "BAR" "foo" "bar")

(remove 1 '(1 1.0 #C(1.0 0.0) 2 2.0 #C(2.0 0.0)) :test-not #'eql)
→ (1)
(remove 1 '(1 1.0 #C(1.0 0.0) 2 2.0 #C(2.0 0.0)) :test-not #'=)
→ (1 1.0 #C(1.0 0.0))
(remove 1 '(1 1.0 #C(1.0 0.0) 2 2.0 #C(2.0 0.0)) :test (complement #'=))
→ (1 1.0 #C(1.0 0.0))

(count 1 '((one 1) (uno 1) (two 2) (dos 2)) :key #'cadr) → 2

(count 2.0 '(1 2 3) :test #'eql :key #'float) → 1

(count "FOO" (list (make-pathname :name "FOO" :type "X")
(make-pathname :name "FOO" :type "Y"))
:key #'pathname-name
:test #'equal)
→ 2```

### 17.2.2 Satisfying a One-Argument Test

When using one of the functions in Figure 17–3, the elements E of a sequence S are filtered not on the basis of the presence or absence of an object O under a two argument predicate, as with the functions described in Section 17.2.1 (Satisfying a Two-Argument Test), but rather on the basis of a one argument predicate.

The element Ei might not be considered directly. 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.)

Functions defined in this specification and having a name that ends in “`-if`” accept a first argument that is a designator for a function of one argument, Zi. An Ei is said to satisfy the test if this :test function returns a generalized boolean representing true.

Functions defined in this specification and having a name that ends in “`-if-not`” accept a first argument that is a designator for a function of one argument, Zi. An Ei is said to satisfy the test if this :test function returns a generalized boolean representing false.

#### 17.2.2.1 Examples of Satisfying a One-Argument Test

``` (count-if #'zerop '(1 #C(0.0 0.0) 0 0.0d0 0.0s0 3)) → 4

(remove-if-not #'symbolp '(0 1 2 3 4 5 6 7 8 9 A B C D E F))
→ (A B C D E F)
(remove-if (complement #'symbolp) '(0 1 2 3 4 5 6 7 8 9 A B C D E F))
→ (A B C D E F)

(count-if #'zerop '("foo" "" "bar" "" "" "baz" "quux") :key #'length)
→ 3```