a warning issued when arrays are used inefficiently
Major Section:  ARRAYS

If you use ACL2 arrays you may sometimes see a slow array warning. We here explain what that warning means and some likely ``mistakes'' it may signify.

The discussion in the documentation for arrays defines what we mean by the semantic value of a name. As noted there, behind the scenes ACL2 maintains the invariant that with some names there is associated a pair consisting of an ACL2 array alist, called the semantic value of the name, and an equivalent raw lisp array. Access to ACL2 array elements, as in (aref1 name alist i), is executed in constant time when the array alist is the semantic value of the name, because we can just use the corresponding raw lisp array to obtain the answer. Aset1 and compress1 modify the raw lisp array appropriately to maintain the invariant.

If aref1 is called on a name and alist, and the alist is not the then-current semantic value of the name, the correct result is computed but it requires linear time because the alist must be searched. When this happens, aref1 prints a slow array warning message to the comment window. Aset1 behaves similarly because the array it returns will cause the slow array warning every time it is used.

From the purely logical perspective there is nothing ``wrong'' about such use of arrays and it may be spurious to print a warning message. But because arrays are generally used to achieve efficiency, the slow array warning often means the user's intentions are not being realized. Sometimes merely performance expectations are not met; but the message may mean that the functional behavior of the program is different than intended.

Here are some ``mistakes'' that might cause this behavior. In the following we suppose the message was printed by aset1 about an array named name. Suppose the alist supplied aset1 is alist.

(1) Compress1 was never called on name and alist. That is, perhaps you created an alist that is an array1p and then proceeded to access it with aref1 but never gave ACL2 the chance to create a raw lisp array for it. After creating an alist that is intended for use as an array, you must do (compress1 name alist) and pass the resulting alist' as the array.

(2) Name is misspelled. Perhaps the array was compressed under the name 'delta-1 but accessed under 'delta1?

(3) An aset1 was done to modify alist, producing a new array, alist', but you subsequently used alist as an array. Inspect all (aset1 name ...) occurrences and make sure that the alist modified is never used subsequently (either in that function or any other). It is good practice to adopt the following syntactic style. Suppose the alist you are manipulating is the value of the local variable alist. Suppose at some point in a function definition you wish to modify alist with aset1. Then write

(let ((alist (aset1 name alist i val))) ...)
and make sure that the subsequent function body is entirely within the scope of the let. Any uses of alist subsequently will refer to the new alist and it is impossible to refer to the old alist. Note that if you write
 (foo (let ((alist (aset1 name alist i val))) ...)  ; arg 1
      (bar alist))                                  ; arg 2
you have broken the rules, because in arg 1 you have modified alist but in arg 2 you refer to the old value. An appropriate rewriting is to lift the let out:
 (let ((alist (aset1 name alist alist i val)))
   (foo ...                                         ; arg 1
        (bar alist)))                               ; arg 2
Of course, this may not mean the same thing.

(4) A function which takes alist as an argument and modifies it with aset1 fails to return the modified version. This is really the same as (3) above, but focuses on function interfaces. If a function takes an array alist as an argument and the function uses aset1 (or a subfunction uses aset1, etc.), then the function probably ``ought'' to return the result produced by aset1. The reasoning is as follows. If the array is passed into the function, then the caller is holding the array. After the function modifies it, the caller's version of the array is obsolete. If the caller is going to make further use of the array, it must obtain the latest version, i.e., that produced by the function.