Equality Predicates

Here we describe functions that test for equality between two objects. Other functions test equality of contents between objects of specific types, e.g., strings. For these predicates, see the appropriate chapter describing the data type. 
 — Function: eq object1 object2

This function returns t if object1 and object2 are the same object, and nil otherwise. 

If object1 and object2 are integers with the same value, they are considered to be the same object (i.e., eq returns t). If object1 and object2 are symbols with the same name, they are normally the same object—but see Creating Symbols for exceptions. For other types (e.g., lists, vectors, strings), two arguments with the same contents or elements are not necessarily eq to each other: they are eq only if they are the same object, meaning that a change in the contents of one will be reflected by the same change in the contents of the other. 
          (eq 'foo 'foo)
               ⇒ t
          
          (eq 456 456)
               ⇒ t
          
          (eq "asdf" "asdf")
               ⇒ nil
          
          (eq "" "")
               ⇒ t
          ;; This exception occurs because Emacs Lisp
          ;; makes just one multibyte empty string, to save space.
          
          (eq '(1 (2 (3))) '(1 (2 (3))))
               ⇒ nil
          
          (setq foo '(1 (2 (3))))
               ⇒ (1 (2 (3)))
          (eq foo foo)
               ⇒ t
          (eq foo '(1 (2 (3))))
               ⇒ nil
          
          (eq [(1 2) 3] [(1 2) 3])
               ⇒ nil
          
          (eq (point-marker) (point-marker))
               ⇒ nil

The make-symbol function returns an uninterned symbol, distinct from the symbol that is used if you write the name in a Lisp expression. Distinct symbols with the same name are not eq. See Creating Symbols. 
          (eq (make-symbol "foo") 'foo)
               ⇒ nil
 — Function: equal object1 object2

This function returns t if object1 and object2 have equal components, and nil otherwise. Whereas eq tests if its arguments are the same object, equal looks inside nonidentical arguments to see if their elements or contents are the same. So, if two objects are eq, they are equal, but the converse is not always true. 
          (equal 'foo 'foo)
               ⇒ t
          
          (equal 456 456)
               ⇒ t
          
          (equal "asdf" "asdf")
               ⇒ t
          (eq "asdf" "asdf")
               ⇒ nil
          
          (equal '(1 (2 (3))) '(1 (2 (3))))
               ⇒ t
          (eq '(1 (2 (3))) '(1 (2 (3))))
               ⇒ nil
          
          (equal [(1 2) 3] [(1 2) 3])
               ⇒ t
          (eq [(1 2) 3] [(1 2) 3])
               ⇒ nil
          
          (equal (point-marker) (point-marker))
               ⇒ t
          
          (eq (point-marker) (point-marker))
               ⇒ nil

Comparison of strings is case-sensitive, but does not take account of text properties—it compares only the characters in the strings. See Text Properties. Use equal-including-properties to also compare text properties. For technical reasons, a unibyte string and a multibyte string are equal if and only if they contain the same sequence of character codes and all these codes are either in the range 0 through 127 (ASCII) or 160 through 255 (eight-bit-graphic). (see Text Representations). 
          (equal "asdf" "ASDF")
               ⇒ nil

However, two distinct buffers are never considered equal, even if their textual contents are the same. 

The test for equality is implemented recursively; for example, given two cons cells x and y, (equal x y) returns t if and only if both the expressions below return t: 
     (equal (car x) (car y))
     (equal (cdr x) (cdr y))

Because of this recursive method, circular lists may therefore cause infinite recursion (leading to an error). 
 — Function: equal-including-properties object1 object2

This function behaves like equal in all cases but also requires that for two strings to be equal, they have the same text properties. 
          (equal "asdf" (propertize "asdf" '(asdf t)))
               ⇒ t
          (equal-including-properties "asdf"
                                      (propertize "asdf" '(asdf t)))
               ⇒ nil