Книга: Practical Common Lisp

Local Flow of Control

Local Flow of Control

The next four special operators I'll discuss also create and use names in the lexical environment but for the purposes of altering the flow of control rather than defining new functions and macros. I've mentioned all four of these special operators in passing because they provide the underlying mechanisms used by other language features. They're BLOCK, RETURN-FROM, TAGBODY, and GO. The first two, BLOCK and RETURN-FROM, are used together to write code that returns immediately from a section of code—I discussed RETURN-FROM in Chapter 5 as a way to return immediately from a function, but it's more general than that. The other two, TAGBODY and GO, provide a quite low-level goto construct that's the basis for all the higher-level looping constructs you've already seen.

The basic skeleton of a BLOCK form is this:

(block name
form*)

The name is a symbol, and the forms are Lisp forms. The forms are evaluated in order, and the value of the last form is returned as the value of the BLOCK unless a RETURN-FROM is used to return from the block early. A RETURN-FROM form, as you saw in Chapter 5, consists of the name of the block to return from and, optionally, a form that provides a value to return. When a RETURN-FROM is evaluated, it causes the named BLOCK to return immediately. If RETURN-FROM is called with a return value form, the BLOCK will return the resulting value; otherwise, the BLOCK evaluates to NIL.

A BLOCK name can be any symbol, which includes NIL. Many of the standard control construct macros, such as DO, DOTIMES, and DOLIST, generate an expansion consisting of a BLOCK named NIL. This allows you to use the RETURN macro, which is a bit of syntactic sugar for (return-from nil ...), to break out of such loops. Thus, the following loop will print at most ten random numbers, stopping as soon as it gets a number greater than 50:

(dotimes (i 10)
(let ((answer (random 100)))
(print answer)
(if (> answer 50) (return))))

Function-defining macros such as DEFUN, FLET, and LABELS, on the other hand, wrap their bodies in a BLOCK with the same name as the function. That's why you can use RETURN-FROM to return from a function.

TAGBODY and GO have a similar relationship to each other as BLOCK and RETURN-FROM: a TAGBODY form defines a context in which names are defined that can be used by GO. The skeleton of a TAGBODY is as follows:

(tagbody
tag-or-compound-form*)

where each tag-or-compound-form is either a symbol, called a tag, or a nonempty list form. The list forms are evaluated in order and the tags ignored, except as I'll discuss in a moment. After the last form of the TAGBODY is evaluated, the TAGBODY returns NIL. Anywhere within the lexical scope of the TAGBODY you can use the GO special operator to jump immediately to any of the tags, and evaluation will resume with the form following the tag. For instance, you can write a trivial infinite loop with TAGBODY and GO like this:

(tagbody
top
(print 'hello)
(go top))

Note that while the tag names must appear at the top level of the TAGBODY, not nested within other forms, the GO special operator can appear anywhere within the scope of the TAGBODY. This means you could write a loop that loops a random number of times like this:

(tagbody
top
(print 'hello)
(when (plusp (random 10)) (go top)))

An even sillier example of TAGBODY, which shows you can have multiple tags in a single TAGBODY, looks like this:

(tagbody
a (print 'a) (if (zerop (random 2)) (go c))
b (print 'b) (if (zerop (random 2)) (go a))
c (print 'c) (if (zerop (random 2)) (go b)))

This form will jump around randomly printing as, bs, and cs until eventually the last RANDOM expression returns 1 and the control falls off the end of the TAGBODY.

TAGBODY is rarely used directly since it's almost always easier to write iterative constructs in terms of the existing looping macros. It's handy, however, for translating algorithms written in other languages into Common Lisp, either automatically or manually. An example of an automatic translation tool is the FORTRAN-to-Common Lisp translator, f2cl, that translates FORTRAN source code into Common Lisp in order to make various FORTRAN libraries available to Common Lisp programmers. Since many FORTRAN libraries were written before the structured programming revolution, they're full of gotos. The f2cl compiler can simply translate those gotos to GOs within appropriate TAGBODYs.[210]

Similarly, TAGBODY and GO can be handy when translating algorithms described in prose or by flowcharts—for instance, in Donald Knuth's classic series The Art of Computer Programming, he describes algorithms using a "recipe" format: step 1, do this; step 2, do that; step 3, go back to step 2; and so on. For example, on page 142 of The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Third Edition (Addison-Wesley, 1998), he describes Algorithm S, which you'll use in Chapter 27, in this form:

Algorithm S (Selection sampling technique). To select n records at random from a set of N, where 0 < n <= N.

S1. [Initialize.] Set t <— 0, m <— 0. (During this algorithm, m represents the number of records selected so far, and t is the total number of input records that we have dealt with.)

S2. [Generate U.] Generate a random number U, uniformly distributed between zero and one.

S3. [Test.] If (N - t)U >= n - m, go to step S5.

S4. [Select.] Select the next record for the sample, and increase m and t by 1. If m < n, go to step S2; otherwise the sample is complete and the algorithm terminates.

S5. [Skip.] Skip the next record (do not include it in the sample), increase t by 1, and go back to step S2.

This description can be easily translated into a Common Lisp function, after renaming a few variables, as follows:

(defun algorithm-s (n max) ; max is N in Knuth's algorithm
(let (seen ; t in Knuth's algorithm
selected ; m in Knuth's algorithm
u ; U in Knuth's algorithm
(records ())) ; the list where we save the records selected
(tagbody
s1
(setf seen 0)
(setf selected 0)
s2
(setf u (random 1.0))
s3
(when (>= (* (- max seen) u) (- n selected)) (go s5))
s4
(push seen records)
(incf selected)
(incf seen)
(if (< selected n)
(go s2)
(return-from algorithm-s (nreverse records)))
s5
(incf seen)
(go s2))))

It's not the prettiest code, but it's easy to verify that it's a faithful translation of Knuth's algorithm. But, this code, unlike Knuth's prose description, can be run and tested. Then you can start refactoring, checking after each change that the function still works.[211]

After pushing the pieces around a bit, you might end up with something like this:

(defun algorithm-s (n max)
(loop for seen from 0
when (< (* (- max seen) (random 1.0)) n)
collect seen and do (decf n)
until (zerop n)))

While it may not be immediately obvious that this code correctly implements Algorithm S, if you got here via a series of functions that all behave identically to the original literal translation of Knuth's recipe, you'd have good reason to believe it's correct.

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