Major Section: PROGRAMMING

Example Form: (mv-let (x y z) ; local variables (mv 1 2 3) ; multi-valued expression (declare (ignore y)) ; optional declarations (cons x z)) ; bodyThe form above binds the three ``local variables,''

`x`

, `y`

, and `z`

,
to the three results returned by the multi-valued expression and
then evaluates the body. The result is `'(1 . 3)`

. The second local,
`y`

, is declared `ignore`

d. The multi-valued expression can be any ACL2
expression that returns `k`

results, where `k`

is the number of local
variables listed. Often however it is simply the application of a
`k`

-valued function. `Mv-let`

is the standard way to invoke a
multi-valued function when the caller must manipulate the vector of
results returned.

General Form: (mv-let (var1 ... vark) term body) or (mv-let (var1 ... vark) term (declare ...) ... (declare ...) body)where the

`vari`

are distinct variables, `term`

is a term that returns
`k`

results and mentions only variables bound in the environment
containing the `mv-let`

expression, and `body`

is a term mentioning only
the `vari`

and variables bound in the environment containing the
`mv-let`

. Each `vari`

must occur in `body`

unless it is declared `ignore`

d
in one of the optional `declare`

forms, unless this requirement is
turned off; see set-ignore-ok. The value of the `mv-let`

term is
the result of evaluating `body`

in an environment in which the `vari`

are bound, in order, to the `k`

results obtained by evaluating
`term`

in the environment containing the `mv-let`

.
Here is an extended example that illustrates both the definition of
a multi-valued function and the use of `mv-let`

to call it. Consider
a simple binary tree whose interior nodes are `cons`

es and whose
leaves are non-`cons`

es. Suppose we often need to know the number, `n`

,
of interior nodes of such a tree; the list, `syms`

, of symbols that
occur as leaves; and the list, `ints`

, of integers that occur as
leaves. (Observe that there may be leaves that are neither symbols
nor integers.) Using a multi-valued function we can collect all
three results in one pass.

Here is the first of two definitions of the desired function. This definition is ``primitive recursive'' in that it has only one argument and that argument is reduced in size on every recursion.

(defun count-and-collect (x)This use of multiple values to ``do several things at once'' is very common in ACL2. However, the function above is inefficient because it appends; We return three results, (mv n syms ints) as described above.

(cond ((atom x)

; X is a leaf. Thus, there are 0 interior nodes, and depending on ; whether x is a symbol, an integer, or something else, we return ; the list containing x in as the appropriate result.

(cond ((symbolp x) (mv 0 (list x) nil)) ((integerp x)(mv 0 nil (list x))) (t (mv 0 nil nil)))) (t

; X is an interior node. First we process the car, binding n1, syms1, and ; ints1 to the answers.

(mv-let (n1 syms1 ints1) (count-and-collect (car x))

; Next we process the cdr, binding n2, syms2, and ints2.

(mv-let (n2 syms2 ints2) (count-and-collect (car x))

; Finally, we compute the answer for x from those obtained for its car ; and cdr, remembering to increment the node count by one for x itself.

(mv (1+ (+ n1 n2)) (append syms1 syms2) (append ints1 ints2)))))))

`syms1`

to `syms2`

and `ints1`

to `ints2`

, copying the
list structures of `syms1`

and `ints1`

in the process. By adding
``accumulators'' to the function, we can make the code more
efficient.
(defun count-and-collect1 (x n syms ints) (cond ((atom x) (cond ((symbolp x) (mv n (cons x syms) ints)) ((integerp x) (mv n syms (cons x ints))) (t (mv n syms ints)))) (t (mv-let (n2 syms2 ints2) (count-and-collect1 (cdr x) (1+ n) syms ints) (count-and-collect1 (car x) n2 syms2 ints2)))))We claim that

`(count-and-collect x)`

returns the same triple of
results as `(count-and-collect1 x 0 nil nil)`

. The reader is urged to
study this claim until convinced that it is true and that the latter
method of computing the results is more efficient. One might try
proving the theorem
(defthm count-and-collect-theorem (equal (count-and-collect1 x 0 nil nil) (count-and-collect x))).Hint: the inductive proof requires attacking a more general theorem.

ACL2 does not support the Common Lisp construct
`multiple-value-bind`

, whose logical meaning seems difficult to
characterize. `Mv-let`

is the ACL2 analogue of that construct.