Re: doc eq? eqv? equal?

[Kevin Ryde]

New words about eq? etc.

I dropped the bit in eqv about "left slightly open to interpretation",
which doesn't really seem right in my reading of the r5rs.  My reading
is that literals and indistinguishable procedures may or may not be
eqv, but that's the limit of the flexibility, at least as far as the
standard types go.



3.1.2 Equality
--------------

There are three kinds of core equality predicates in Scheme, described
below.  The same kinds of comparison arise in other functions, like
`memq' and friends (*note List Searching::).

   For all three tests, objects of different types are never equal.  So
for instance a list and a vector are not `equal?', even if their
contents are the same.  Exact and inexact numbers are considered
different types too, and are hence not equal even if their values are
the same.

   `eq?' tests just for the same object (essentially a pointer
comparison).  This is fast, and can be used when searching for a
particular object, or when working with symbols or keywords (which are
always unique objects).

   `eqv?' extends `eq?' to look into the value of numbers and
characters.  It can for instance be used somewhat like `=' (*note
Comparison::) but without an error if one operand isn't a number.

   `equal?' goes further, it looks (recursively) into the contents of
lists, vectors, etc.  This is good for instance on lists that have been
read or calculated in various places and are the same, just not made up
of the same pairs.  Such lists look the same (when printed), and
`equal?' will consider them the same.


 -- Scheme Procedure: eq? x y
 -- C Function: scm_eq_p (x, y)
     Return `#t' if X and Y are the same object, except for numbers and
     characters.  For example,

          (define x (vector 1 2 3))
          (define y (vector 1 2 3))

          (eq? x x)  => #t
          (eq? x y)  => #f

     Numbers and characters are not equal to any other object, but the
     problem is they're not necessarily `eq?' to themselves either.
     This is even so when the number comes directly from a variable,

          (let ((n (+ 2 3)))
            (eq? n n))       => *unspecified*

     Generally `eqv?' below should be used when wanting to compare
     numbers or characters.  `=' (*note Comparison::) or `char=?'
     (*note Characters::) can be used too.

     It's worth noting that end-of-list `()', `#t', `#f', a symbol of a
     given name, and a keyword of a given name, are unique objects.
     There's just one of each, so for instance no matter how `()'
     arises in a program, it's the same object and can be compared with
     `eq?',

          (define x (cdr '(123)))
          (define y (cdr '(456)))
          (eq? x y) => #t

          (define x (string->symbol "foo"))
          (eq? x 'foo) => #t

 -- C Function: int scm_is_eq (SCM x, SCM y)
     Return `1' when X and Y are equal in the sense of `eq?', otherwise
     return `0'.

     The `==' operator should not be used on `SCM' values, an `SCM' is
     a C type which cannot necessarily be compared using `==' (*note
     The SCM Type::).


 -- Scheme Procedure: eqv? x y
 -- C Function: scm_eqv_p (x, y)
     Return `#t' if X and Y are the same object, or for characters and
     numbers the same value.

     On objects except characters and numbers, `eqv?' is the same as
     `eq?' above, it's true if X and Y are the same object.

     If X and Y are numbers or characters, `eqv?' compares their type
     and value.  An exact number is not `eqv?' to an inexact number
     (even if their value is the same).

          (eqv? 3 (+ 1 2)) => #t
          (eqv? 1 1.0)     => #f


 -- Scheme Procedure: equal? x y
 -- C Function: scm_equal_p (x, y)
     Return `#t' if X and Y are the same type, and their contents or
     value are equal.

     For a pair, string, vector or array, `equal?' compares the
     contents, and does so using using the same `equal?' recursively,
     so a deep structure can be traversed.

          (equal? (list 1 2 3) (list 1 2 3))   => #t
          (equal? (list 1 2 3) (vector 1 2 3)) => #f

     For other objects, `equal?' compares as per `eqv?' above, which
     means characters and numbers are compared by type and value (and
     like `eqv?', exact and inexact numbers are not `equal?', even if
     their value is the same).

          (equal? 3 (+ 1 2)) => #t
          (equal? 1 1.0)     => #f

     Hash tables are currently only compared as per `eq?', so two
     different tables are not `equal?', even if their contents are the
     same.

     `equal?' does not support circular data structures, it may go into
     an infinite loop if asked to compare two circular lists or similar.

     New application-defined object types (*note Defining New Types
     (Smobs)::) have an `equalp' handler which is called by `equal?'.
     This lets an application traverse the contents or control what is
     considered `equal?' for two objects of such a type.  If there's no
     such handler, the default is to just compare as per `eq?'.