— Function: eql a b

This function is almost the same as eq, except that if a and b are numbers of the same type, it compares them for numeric equality (as if by equal instead of eq). This makes a difference only for versions of Emacs that are compiled with floating-point support. Emacs floats are allocated objects just like cons cells, which means that (eq 3.0 3.0) will not necessarily be true—if the two 3.0s were allocated separately, the pointers will be different even though the numbers are the same. But (eql 3.0 3.0) will always be true.

The types of the arguments must match, so (eql 3 3.0) is still false.

Note that Emacs integers are “direct” rather than allocated, which basically means (eq 3 3) will always be true. Thus eq and eql behave differently only if floating-point numbers are involved, and are indistinguishable on Emacs versions that don't support floats.

There is a slight inconsistency with Common Lisp in the treatment of positive and negative zeros. Some machines, notably those with IEEE standard arithmetic, represent +0 and -0 as distinct values. Normally this doesn't matter because the standard specifies that (= 0.0 -0.0) should always be true, and this is indeed what Emacs Lisp and Common Lisp do. But the Common Lisp standard states that (eql 0.0 -0.0) and (equal 0.0 -0.0) should be false on IEEE-like machines; Emacs Lisp does not do this, and in fact the only known way to distinguish between the two zeros in Emacs Lisp is to format them and check for a minus sign.

— Function: equalp a b

This function is a more flexible version of equal. In particular, it compares strings case-insensitively, and it compares numbers without regard to type (so that (equalp 3 3.0) is true). Vectors and conses are compared recursively. All other objects are compared as if by equal.

This function differs from Common Lisp equalp in several respects. First, Common Lisp's equalp also compares characters case-insensitively, which would be impractical in this package since Emacs does not distinguish between integers and characters. In keeping with the idea that strings are less vector-like in Emacs Lisp, this package's equalp also will not compare strings against vectors of integers.