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equal (Function)

— Function: equal x y generalized-boolean
Arguments and Values:

x—an object.

y—an object.

generalized-boolean—a generalized boolean.


Returns true if x and y are structurally similar (isomorphic) objects. Objects are treated as follows by equal.

Symbols, Numbers, and Characters

equal is true of two objects if they are symbols that are eq, if they are numbers that are eql, or if they are characters that are eql.


For conses, equal is defined recursively as the two cars being equal and the two cdrs being equal.


Two arrays are equal only if they are eq, with one exception: strings and bit vectors are compared element-by-element (using eql). If either x or y has a fill pointer, the fill pointer limits the number of elements examined by equal. Uppercase and lowercase letters in strings are considered by equal to be different.


Two pathnames are equal if and only if all the corresponding components (host, device, and so on) are equivalent. Whether or not uppercase and lowercase letters are considered equivalent in strings appearing in components is implementation-dependent. pathnames that are equal should be functionally equivalent.

Other (Structures, hash-tables, instances, ...)

Two other objects are equal only if they are eq.

equal does not descend any objects other than the ones explicitly specified above. The next figure summarizes the information given in the previous list. In addition, the figure specifies the priority of the behavior of equal, with upper entries taking priority over lower ones.

Type Behavior
number uses eql
character uses eql
cons descends
bit vector descends
string descends
pathname “functionally equivalent”
structure uses eq
Other array uses eq
hash table uses eq
Other object uses eq

Figure 5.12: Summary and priorities of behavior of equal

Any two objects that are eql are also equal.

equal may fail to terminate if x or y is circular.

 (equal 'a 'b)  false
 (equal 'a 'a)  true
 (equal 3 3)  true
 (equal 3 3.0)  false
 (equal 3.0 3.0)  true
 (equal #c(3 -4) #c(3 -4))  true
 (equal #c(3 -4.0) #c(3 -4))  false
 (equal (cons 'a 'b) (cons 'a 'c))  false
 (equal (cons 'a 'b) (cons 'a 'b))  true
 (equal #\A #\A)  true
 (equal #\A #\a)  false
 (equal "Foo" "Foo")  true
 (equal "Foo" (copy-seq "Foo"))  true
 (equal "FOO" "foo")  false
 (equal "This-string" "This-string")  true
 (equal "This-string" "this-string")  false
See Also:

eq, eql (Function), equalp, =, string=, string-equal, char=, char-equal, tree-equal


Object equality is not a concept for which there is a uniquely determined correct algorithm. The appropriateness of an equality predicate can be judged only in the context of the needs of some particular program. Although these functions take any type of argument and their names sound very generic, equal and equalp are not appropriate for every application.

A rough rule of thumb is that two objects are equal if and only if their printed representations are the same.