ARRAYS-EXAMPLE.html -- ACL2 Version 6.3

### ARRAYS-EXAMPLE

an example illustrating ACL2 arrays

    Major Section:  ARRAYS

The example below illustrates the use of ACL2 arrays. It is not, of course, a substitute for the detailed explanations provided elsewhere (see arrays, including subtopics).

    ACL2 !>(defun defarray (name size initial-element)
             (compress1 name
                        (cons (list :HEADER
                                    :DIMENSIONS (list size)
                                    :MAXIMUM-LENGTH (1+ size)
                                    :DEFAULT initial-element
                                    :NAME name)
                              nil)))

    Since DEFARRAY is non-recursive, its admission is trivial.  We observe
    that the type of DEFARRAY is described by the theorem
    (AND (CONSP (DEFARRAY NAME SIZE INITIAL-ELEMENT))
         (TRUE-LISTP (DEFARRAY NAME SIZE INITIAL-ELEMENT))).
    We used the :type-prescription rule COMPRESS1.

    Summary
    Form:  ( DEFUN DEFARRAY ...)
    Rules: ((:TYPE-PRESCRIPTION COMPRESS1))
    Warnings:  None
    Time:  0.02 seconds (prove: 0.00, print: 0.02, other: 0.00)
     DEFARRAY
    ACL2 !>(assign my-ar (defarray 'a1 5 17))
     ((:HEADER :DIMENSIONS (5)
               :MAXIMUM-LENGTH 6 :DEFAULT 17 :NAME A1))
    ACL2 !>(aref1 'a1 (@ my-ar) 3)
    17
    ACL2 !>(aref1 'a1 (@ my-ar) 8)

    ACL2 Error in TOP-LEVEL:  The guard for the function symbol AREF1,
    which is
    (AND (ARRAY1P NAME L) (INTEGERP N) (>= N 0) (< N (CAR (DIMENSIONS NAME L)))),
    is violated by the arguments in the call (AREF1 'A1 '(#) 8).

    ACL2 !>(assign my-ar (aset1 'a1 (@ my-ar) 3 'xxx))
     ((3 . XXX)
      (:HEADER :DIMENSIONS (5)
               :MAXIMUM-LENGTH 6 :DEFAULT 17 :NAME A1))
    ACL2 !>(aref1 'a1 (@ my-ar) 3)
    XXX
    ACL2 !>(aset1 'a1 (@ my-ar) 3 'yyy) ; BAD: (@ my-ar) now points to
                                        ;      an old copy of the array!
    ((3 . YYY)
     (3 . XXX)
     (:HEADER :DIMENSIONS (5)
              :MAXIMUM-LENGTH 6 :DEFAULT 17 :NAME A1))
    ACL2 !>(aref1 'a1 (@ my-ar) 3) ; Because of "BAD" above, the array
                                   ; access is done using assoc rather
                                   ; than Lisp aref, hence is slower;
                                   ; but the answer is still correct,
                                   ; reflecting the value in (@ my-ar),
                                   ; which was not changed above.

    **********************************************************
    Slow Array Access!  A call of AREF1 on an array named
    A1 is being executed slowly.  See :DOC slow-array-warning
    **********************************************************

    XXX
    ACL2 !>