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18. Destructuring

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Destructuring is a generalization of assignment. The operators setq and setf do assignments to individual variables. Destructuring combines assignment with access: instead of giving a single variable as the first argument, we give a pattern of variables, which are each assigned the value occurring in the corresponding position in some structure.



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18.1 Destructuring on Lists

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As of CLTL2, Common Lisp includes a new macro called destructuring-bind. This macro was briefly introduced in Chapter 7. Here we consider it in more detail. Suppose that lst is a list of three elements, and we want to bind x to the first, y to the second, and z to the third. In raw CLTL1 Common Lisp, we would have had to say:

 
(let ((x (first lst))
      (y (second lst))
      (z (third lst)))
  ...)

With the new macro we can say instead

 
(destructuring-bind (x y z) lst
  ...)

which is not only shorter, but clearer as well. Readers grasp visual cues much faster than textual ones. In the latter form we are shown the relationship between x, y, and z; in the former, we have to infer it.

If such a simple case is made clearer by the use of destructuring, imagine the improvement in more complex ones. The first argument to destructuring-bind can be an arbitrarily complex tree. Imagine

 
(destructuring-bind ((first last) (month day year) . notes)
    birthday
  ...)

written using let and the list access functions. Which raises another point: destructuring makes it easier to write programs as well as easier to read them.

Destructuring did exist in CLTL1 Common Lisp. If the patterns in the examples above look familiar, it's because they have the same form as macro parameter lists. In fact, destructuring-bind is the code used to take apart macro argument lists, now sold separately. You can put anything in the pattern that you would put in a macro parameter list, with one unimportant exception (the &environment keyword).

Establishing bindings en masse is an attractive idea. The following sections describe several variations upon this theme.



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18.2 Other Structures

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There is no reason to limit destructuring to lists. Any complex object is a candidate for it. This section shows how to write macros like destructuring-bind for other kinds of objects.

The natural next step is to handle sequences generally. Figure 18.1 contains a macro called dbind, which resembles destructuring-bind, but works for any kind of sequence. The second argument can be a list, a vector, or any combination thereof:

 
> (dbind (a b c) #(1 2 3)
(list a b c))
(1 2 3)
> (dbind (a (b c) d) '( 1 #(2 3) 4)
(list a b c d))
(1 2 3 4)
> (dbind (a (b . c) &rest d) '(1 "fribble" 2 3 4)
(list a b c d))
(1 #\f "ribble" (2 3 4))

 
(defmacro dbind (pat seq &body body)
  (let ((gseq (gensym)))
    `(let ((,gseq ,seq))
       ,(dbind-ex (destruc pat gseq #'atom) body))))

(defun destruc (pat seq &optional (atom? #'atom) (n 0))
  (if (null pat)
      nil
    (let ((rest (cond ((funcall atom? pat) pat)
		      ((eq (car pat) '&rest) (cadr pat))
		      ((eq (car pat) '&body) (cadr pat))
		      (t nil))))
      (if rest
	  `((,rest (subseq ,seq ,n)))
	(let ((p (car pat))
	      (rec (destruc (cdr pat) seq atom? (1+ n))))
	  (if (funcall atom? p)
	      (cons `(,p (elt ,seq ,n))
		    rec)
	    (let ((var (gensym)))
	      (cons (cons `(,var (elt ,seq ,n))
			  (destruc p var atom?))
		    rec))))))))

(defun dbind-ex (binds body)
  (if (null binds)
      `(progn ,@body)
    `(let ,(mapcar #'(lambda (b)
		       (if (consp (car b))
			   (car b)
			 b))
		   binds)
       ,(dbind-ex (mapcan #'(lambda (b)
			      (if (consp (car b))
				  (cdr b)))
			  binds)
		  body))))

Figure 18.1: General sequence destructuring operator.

The #( read-macro is for representing vectors, and #\ for representing characters. Since "abc" = #(#\a #\b #\c), the first element of "fribble" is the character #\f. For the sake of simplicity, dbind supports only the &rest and &body keywords.

Compared to most of the macros seen so far, dbind is big. It's worth studying the implementation of this macro, not only to understand how it works, but also because it embodies a general lesson about Lisp programming. As section 3.4 mentioned, Lisp programs may intentionally be written in a way that will make them easy to test. In most code, we have to balance this desire against the need for speed. Fortunately, as Section 7.8 explained, speed is not so important in expander code. When writing code that generates macroexpansions, we can make life easier for ourselves. The expansion of dbind is generated by two functions, destruc and dbind-ex. Perhaps they both could be combined into one function which would do everything in a single pass. But why bother? As two separate functions, they will be easier to test. Why trade this advantage for speed we don't need?

The first function, destruc, traverses the pattern and associates each variable with the location of the corresponding object at runtime:

 
> (destruc '(a b c) 'seq #'atom)
((A (ELT SEQ 0)) (B (ELT SEQ 1)) (C (ELT SEQ 2)))

The optional third argument is the predicate used to distinguish pattern structure from pattern content.

To make access more efficient, a new variable (a gensym) will be bound to each subsequence:

 
> (destruc '(a (b . c) &rest d) 'seq)
((A (ELT SEQ 0))
((#:G2 (ELT SEQ 1)) (B (ELT #:G2 0)) (C (SUBSEQ #:G2 1)))
(D (SUBSEQ SEQ 2)))

The output of destruc is sent to dbind-ex, which generates the bulk of the macroexpansion. It translates the tree produced by destruc into a nested series of lets:

 
> (dbind-ex (destruc '(a (b . c) &rest d) 'seq) '(body))
(LET ((A (ELT SEQ 0))
(#:G4 (ELT SEQ 1))
(D (SUBSEQ SEQ 2)))
(LET ((B (ELT #:G4 0))
(C (SUBSEQ #:G4 1)))
(PROGN BODY)))

 
(defmacro with-matrix (pats ar &body body)
  (let ((gar (gensym)))
    `(let ((,gar ,ar))
       (let ,(let ((row -1))
	       (mapcan
		#'(lambda (pat)
		    (incf row)
		    (setq col -1)
		    (mapcar #'(lambda (p)
				`(,p (aref ,gar
					   ,row
					   ,(incf col))))
			    pat))
		pats))
	 ,@body))))

(defmacro with-array (pat ar &body body)
  (let ((gar (gensym)))
    `(let ((,gar ,ar))
       (let ,(mapcar #'(lambda (p)
			 `(,(car p) (aref ,gar ,@(cdr p))))
		     pat)
	 ,@body))))

Figure 18.2: Destructuring on arrays.

Note that dbind, like destructuring-bind, assumes that it will find all the list structure it is looking for. Left-over variables are not simply bound to nil, as with multiple-value-bind. If the sequence given at runtime does not have all the expected elements, destructuring operators generate an error: > (dbind (a b c) (list 1 2)) >>Error: 2 is not a valid index for the sequence (1 2)

What other objects have internal structure? There are arrays generally, which differ from vectors in having more than one dimension. If we define a destructuring macro for arrays, how do we represent the pattern? For two-dimensional arrays, it is still practical to use a list. Figure 18.2 contains a macro, with-matrix, for destructuring on two-dimensional arrays.

 
(defmacro with-struct ((name . fields) struct &body body)
  (let ((gs (gensym)))
    `(let ((,gs ,struct))
       (let ,(mapcar #'(lambda (f)
			 `(,f (,(symb name f) ,gs)))
		     fields)
	 ,@body))))

Figure 18.3: Destructuring on structures.

 
> (setq ar (make-array '(3 3)))
#<Simple-Array T (3 3) C2D39E>
> (for (r 0 2)
(for (c 0 2)
(setf (aref ar r c) (+ (* r 10) c))))
NIL
> (with-matrix ((a b c)
(d e f)
(g h i)) ar
(list a b c d e f g h i))
(0 1 2 10 11 12 20 21 22)

For large arrays or those with dimension 3 or higher, we want a different kind of approach. We are not likely to want to bind variables to each element of a large array. It will be more practical to make the pattern a sparse representation of the array--containing variables for only a few elements, plus coordinates to identify them. The second macro in Figure 18.2 is built on this principle. Here we use it to get the diagonal of our previous array:

 
> (with-array ((a 0 0) (d 1 1) (i 2 2)) ar
(values a d i))
0
11
22

With this new macro we have begun to move away from patterns whose elements must occur in a fixed order. We can make a similar sort of macro to bind variables to fields in structures built by defstruct. Such a macro is defined in Figure 18.3. The first argument in the pattern is taken to be the prefix associated with the structure, and the rest are field names. To build access calls, this macro uses symb (page 58).

 
> (defstruct visitor name title firm)
VISITOR
> (setq theo (make-visitor :name "Theodebert"
:title 'king
:firm 'franks))
#S(VISITOR NAME "Theodebert" TITLE KING FIRM FRANKS)
> (with-struct (visitor- name firm title) theo
(list name firm title))
("Theodebert" FRANKS KING)

18.3 Reference

CLOS brings with it a macro for destructuring on instances. Suppose tree is a class with three slots, species, age, and height, and that my-tree is an instance of tree. Within

 
(with-slots (species age height) my-tree
	    ...)

we can refer to the slots of my-tree as if they were ordinary variables. Within the body of the with-slots, the symbol height refers to the height slot. It is not simply bound to the value stored there, but refers to the slot, so that if we write:

 
(setq height 72)

then the height slot of my-tree will be given the value 72. This macro works by defining height as a symbol-macro (Section 7.11) which expands into a slot reference. In fact, it was to support macros like with-slots that symbol-macrolet was added to Common Lisp.

Whether or not with-slots is really a destructuring macro, it has the same role pragmatically as destructuring-bind. As conventional destructuring is to call-by-value, this new kind is to call-by-name. Whatever we call it, it looks to be useful. What other macros can we define on the same principle?

We can create a call-by-name version of any destructuring macro by making it expand into a symbol-macrolet rather than a let. Figure 18.4 shows a version of dbind modified to behave like with-slots. We can use with-places as we do dbind:

 
> (with-places (a b c) #(1 2 3)
(list a b c))
(1 2 3)

 
(defmacro with-places (pat seq &body body)
  (let ((gseq (gensym)))
    `(let ((,gseq ,seq))
       ,(wplac-ex (destruc pat gseq #'atom) body))))

(defun wplac-ex (binds body)
  (if (null binds)
      `(progn ,@body)
    `(symbol-macrolet ,(mapcar #'(lambda (b)
				   (if (consp (car b))
				       (car b)
				     b))
			       binds)
       ,(wplac-ex (mapcan #'(lambda (b)
			      (if (consp (car b))
				  (cdr b)))
			  binds)
		  body))))

Figure 18.4: Reference destructuring on sequences.

But the new macro also gives us the option to setf positions in sequences, as we do slots in with-slots:

 
> (let ((lst '(1 (2 3) 4)))
(with-places (a (b . c) d) lst
(setf a 'uno)
(setf c '(tre)))
lst)
(UNO (2 TRE) 4)

As in a with-slots, the variables now refer to the corresponding locations in the structure. There is one important difference, however: you must use setf rather than setq to set these pseudo-variables. The with-slots macro must invoke a code-walker (page 273) to transform setqs into setfs within its body. Here, writing a code-walker would be a lot of code for a small refinement.

If with-places is more general than dbind, why not just use it all the time?

While dbind associates a variable with a value, with-places associates it with a set of instructions for finding a value. Every reference requires a lookup. Where dbind would bind c to the value of (elt x 2), with-places will make c a symbol-macro that expands into (elt x 2). So if c is evaluated n times in the body, that will entail n calls to elt. Unless you actually want to setf the variables created by destructuring, dbind will be faster.

The definition of with-places is only slightly changed from that of dbind (Figure 18.1). Within wplac-ex (formerly dbind-ex) the let has become a symbol-macrolet. By similar alterations, we could make a call-by-name version of any normal destructuring macro. 18.4 Matching

As destructuring is a generalization of assignment, pattern-matching is a generalization of destructuring. The term "pattern-matching" has many senses. In this context, it means comparing two structures, possibly containing variables, to see if there is some way of assigning values to the variables which makes the two equal. For example, if ?x and ?y are variables, then the two lists

 
(p ?x ?y c ?x)

(p a b c a)

match when ?x = a and ?y = b. And the lists

 
(p ?x b ?y a)

(p ?y b c a)

match when ?x = ?y = c.

Suppose a program works by exchanging messages with some outside source. To respond to a message, the program has to tell what kind of message it is, and also to extract its specific content. With a matching operator we can combine the two steps.

To be able to write such an operator we have to invent some way of distinguishing variables. We can't just say that all symbols are variables, because we will want symbols to occur as arguments within patterns. Here we will say that a pattern variable is a symbol beginning with a question mark. If it becomes inconvenient, this convention could be changed simply by redefining the predicate var?.

 
(defun match (x y &optional binds)
  (acond2
   ((or (eql x y) (eql x '_) (eql y '_)) (values binds t))
   ((binding x binds) (match it y binds))
   ((binding y binds) (match x it binds))
   ((varsym? x) (values (cons (cons x y) binds) t))
   ((varsym? y) (values (cons (cons y x) binds) t))
   ((and (consp x) (consp y) (match (car x) (car y) binds))
    (match (cdr x) (cdr y) it))
   (t (values nil nil))))

(defun varsym? (x)
  (and (symbolp x) (eq (char (symbol-name x) 0) #\?)))

(defun binding (x binds)
  (labels ((recbind (x binds)
		    (aif (assoc x binds)
			 (or (recbind (cdr it) binds)
			     it))))
    (let ((b (recbind x binds)))
      (values (cdr b) b))))

Figure 18.5: Matching function.

Figure 18.5 contains a pattern-matching function similar to ones that appear in several introductions to Lisp. We give match two lists, and if they can be made # to match, we will get back a list showing how:

 
> (match '(p a b c a) '(p ?x ?y c ?x))
((?Y . B) (?X . A))
T
> (match '(p ?x b ?y a) '(p ?y b c a))
((?Y . C) (?X . ?Y))
T
> (match '(a b c) '(a a a))
NIL
NIL

As match compares its arguments element by element, it builds up assignments of values to variables, called bindings, in the parameter binds. If the match is successful, match returns the bindings generated, otherwise it returns nil. Since not all successful matches generate any bindings, match, like gethash, returns a second value to indicate whether the match succeeded or failed:

 
> (match '(p ?x) '(p ?x))
NIL
T

 
(defmacro if-match (pat seq then &optional else)
  `(aif2 (match ',pat ,seq)
	 (let ,(mapcar #'(lambda (v)
			   `(,v (binding ',v it)))
		       (vars-in then #'atom))
	   ,then)
	 ,else))

(defun vars-in (expr &optional (atom? #'atom))
  (if (funcall atom? expr)
      (if (var? expr) (list expr))
    (union (vars-in (car expr) atom?)
	   (vars-in (cdr expr) atom?))))

(defun var? (x)
  (and (symbolp x) (eq (char (symbol-name x) 0) #\?)))

Figure 18.6: Slow matching operator.

When match returns nil and t as above, it indicates a successful match which yielded no bindings.

Like Prolog, match treats (underscore) as a wild-card. It matches everything, and has no effect on the bindings:

 
> (match '(a ?x b) '(_ 1 _))
((?X . 1))
T

Given match, it is easy to write a pattern-matching version of dbind. Figure 18.6 contains a macro called if-match. Like dbind, its first two arguments are a pattern and a sequence, and it establishes bindings by comparing the pattern with the sequence. However, instead of a body it has two more arguments: a then clause to be evaluated, with new bindings, if the match succeeds; and an else clause to be evaluated if the match fails. Here is a simple function which uses if-match:

 
(defun abab (seq)
  (if-match (?x ?y ?x ?y) seq
	    (values ?x ?y)
	    nil))

If the match succeeds, it will establish values for ?x and ?y, which will be returned:

 
> (abab '(hi ho hi ho))
HI
HO

The function vars-in returns all the pattern variables in an expression. It calls var? to test if something is a variable. At the moment, var? is identical to varsym? (Figure 18.5), which is used to detect variables in binding lists. We have two distinct functions in case we want to use different representations for the two kinds of variables.

As defined in Figure 18.6, if-match is short, but not very efficient. It does too much work at runtime. We traverse both sequences at runtime, even though the first is known at compile-time. Worse still, during the process of matching, we cons up lists to hold the variable bindings. If we take advantage of information known at compile-time, we can write a version of if-match which performs no unnecessary comparisons, and doesn't cons at all.

If one of the sequences is known at compile-time, and only that one contains variables, then we can go about things differently. In a call to match, either argument could contain variables. By restricting variables to the first argument of if-match, we make it possible to tell at compile-time which variables will be involved in the match. Then instead of creating lists of variable bindings, we could keep the values of variables in the variables themselves.

The new version of if-match appears in Figure 18.7 and 18.8. When we can predict what code would be evaluated at runtime, we can simply generate it at compile-time. Here, instead of expanding into a call to match, we generate code which performs just the right comparisons.

If we are going to use the variable ?x to contain the binding of ?x, how do we represent a variable for which no binding has yet been established by the match? Here we will indicate that a pattern variable is unbound by binding it to a gensym. So if-match begins by generating code which will bind all the variables in the pattern to gensyms. In this case, instead of expanding into a with-gensyms, it's safe to make the gensyms once at compile-time and insert them directly into the expansion.

The rest of the expansion is generated by pat-match. This macro takes the same arguments as if-match; the only difference is that it establishes no new bindings for pattern variables. In some situations this is an advantage, and Chapter 19 will use pat-match as an operator in its own right.

In the new matching operator, the distinction between pattern content and pattern structure will be defined by the function simple?. If we want to be able to use quoted literals in patterns, the destructuring code (and vars-in) have to be told not to go inside lists whose first element is quote. With the new matching operator, we will be able to use lists as pattern elements, simply by quoting them.

 
(defmacro if-match (pat seq then &optional else)
  `(let ,(mapcar #'(lambda (v) `(,v ',(gensym)))
		 (vars-in pat #'simple?))
     (pat-match ,pat ,seq ,then ,else)))

(defmacro pat-match (pat seq then else)
  (if (simple? pat)
      (match1 `((,pat ,seq)) then else)
    (with-gensyms (gseq gelse)
		  `(labels ((,gelse () ,else))
		     ,(gen-match (cons (list gseq seq)
				       (destruc pat gseq #'simple?))
				 then
				 `(,gelse))))))

(defun simple? (x) (or (atom x) (eq (car x) 'quote)))

(defun gen-match (refs then else)
  (if (null refs)
      then
    (let ((then (gen-match (cdr refs) then else)))
      (if (simple? (caar refs))
	  (match1 refs then else)
	(gen-match (car refs) then else)))))

Figure 18.7: Fast matching operator.

Like dbind, pat-match calls destruc to get a list of the calls that will take apart its argument at runtime. This list is passed on to gen-match, which recursively generates matching code for nested patterns, and thence to match1, which generates match code for each leaf of the pattern tree.

Most of the code which will appear in the expansion of an if-match comes from match1, which is shown in Figure 18.8. This function considers four cases. If the pattern argument is a gensym, then it is one of the invisible variables created by destruc to hold sublists, and all we need to do at runtime is test that it has the right length. If the pattern element is a wildcard ( ), no code need be generated. If the pattern element is a variable, match1 generates code to match it against, or set it to, the corresponding part of the sequence given at runtime. Otherwise, the pattern element is taken to be a literal value, and match1 generates code to compare it with the corresponding part of the sequence.

 
(defun match1 (refs then else)
  (dbind ((pat expr) . rest) refs
	 (cond ((gensym? pat)
		`(let ((,pat ,expr))
		   (if (and (typep ,pat 'sequence)
			    ,(length-test pat rest))
		       ,then
		     ,else)))
	       ((eq pat '_) then)
	       ((var? pat)
		(let ((ge (gensym)))
		  `(let ((,ge ,expr))
		     (if (or (gensym? ,pat) (equal ,pat ,ge))
			 (let ((,pat ,ge)) ,then)
		       ,else))))
	       (t `(if (equal ,pat ,expr) ,then ,else)))))

(defun gensym? (s)
  (and (symbolp s) (not (symbol-package s))))

(defun length-test (pat rest)
  (let ((fin (caadar (last rest))))
    (if (or (consp fin) (eq fin 'elt))
	`(= (length ,pat) ,(length rest))
      `(> (length ,pat) ,(- (length rest) 2)))))

Figure 18.8: Fast matching operator (continued).

Let's look at examples of how some parts of the expansion are generated. Suppose we begin with

 
(if-match (?x 'a) seq
	  (print ?x)
	  nil)

The pattern will be passed to destruc, with some gensym (call it g for legibility) to represent the sequence:

 
(destruc '(?x 'a) 'g #'simple?)

yielding:

 
((?x (elt g 0)) ((quote a) (elt g 1)))

On the front of this list we cons (g seq):

 
((g seq) (?x (elt g 0)) ((quote a) (elt g 1)))

and send the whole thing to gen-match. Like the naive implementation of length (page 22), gen-match first recurses all the way to the end of the list, and then builds its return value on the way back up. When it has run out of elements, gen-match returns its then argument, which will be ?x. On the way back up the recursion, this return value will be passed as the then argument to match1. Now we will have a call like:

 
(match1 '(((quote a) (elt g 1))) '(print ?x) '#else function#)

yielding:

 
(if (equal (quote a) (elt g 1))
    (print ?x)
  #else function#)

This will in turn become the then argument to another call to match1, the value of which will become the then argument of the last call to match1. The full expansion of this if-match is shown in Figure 18.9.

In this expansion gensyms are used in two completely unrelated ways. The variables used to hold parts of the tree at runtime have gensymed names, in order to avoid capture. And the variable ?x is initially bound to a gensym, to indicate that it hasn't yet been assigned a value by matching.

In the new if-match, the pattern elements are now evaluated instead of being implicitly quoted. This means that Lisp variables can be used in patterns, as well as quoted expressions:

 
> (let ((n 3))
(if-match (?x n 'n '(a b)) '(1 3 n (a b))
?x))
1

 
(if-match (?x 'a) seq
	  (print ?x))

expands into:

 
(let ((?x '#:g1))
  (labels ((#:g3 nil nil))
    (let ((#:g2 seq))
      (if (and (typep #:g2 'sequence)
	       (= (length #:g2) 2))
	  (let ((#:g5 (elt #:g2 0)))
	    (if (or (gensym? x) (equal ?x #:g5))
		(let ((?x #:g5))
		  (if (equal 'a (elt #:g2 1))
		      (print ?x)
		    (#:g3)))
	      (#:g3)))
	(#:g3)))))

Figure 18.9: Expansion of an if-match.

Two further improvements appear because the new version calls destruc (Figure 18.1). The pattern can now contain &rest or &body keywords (match doesn't bother with those). And because destruc uses the generic sequence operators elt and subseq, the new if-match will work for any kind of sequence. If abab is defined with the new version, it can be used also on vectors and strings:

 
> (abab "abab")
#\a
#\b
> (abab #(1 2 1 2))
1
2

In fact, patterns can be as complex as patterns to dbind:

 
> (if-match (?x (1 . ?y) . ?x) '((a b) #(1 2 3) a b)
(values ?x ?y))
(A B)
#(2 3)

Notice that, in the second return value, the elements of the vector are displayed. To have vectors printed this way, set *print-array* to t.

In this chapter we are beginning to cross the line into a new kind of programming. We began with simple macros for destructuring. In the final version of if-match we have something that looks more like its own language. The remaining chapters describe a whole class of programs which operate on the same philosophy.


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