Note: This appendix is a Texinfo conversion of Jonathan Amsterdam's Working Paper 324, MIT AI Lab entitled “Don't Loop, Iterate.”
Above all the wonders of Lisp's pantheon stand its metalinguistic tools; by their grace have Lisp's acolytes been liberated from the rigid asceticism of lesser faiths. Thanks to Macro and kin, the jolly, complacent Lisp hacker can gaze through a fragrant cloud of setfs and defstructs at the emaciated unfortunates below, scraping out their meager code in inflexible notation, and sneer superciliously. It's a good feeling.
But all's not joy in Consville. For—I beg your pardon, but—there
really is no good way to iterate in Lisp. Now, some are happy
to map their way about, whether for real with
friends, or with the make-believe of Series; others are so satisfied
do it's a wonder they're not C hackers.1 Still others have gotten by with
loop, but are
getting tired of looking up the syntax in the manual over and over
again. And in the elegant schemes of some, only tail recursion and
lambdas figure. But that still leaves a sizeable majority of
folk—well, me, at least—who would simply like to iterate,
thank you, but in a way that provides nice abstractions, is
extensible, and looks like honest-to-God Lisp.
In what follows I describe a macro package, called
provides the power and convenient abstractions of
loop but in a
more syntactically palatable way.
iter also has many features
loop lacks, like generators and better support for nested
iterate generates inline code, so it's more efficient than
using the higher-order function approach. And
iterate is also
extensible—it's easy to add new clauses to its vocabulary in order
to express new patterns of iteration in a convenient way.
A Common Lisp programmer who wonders what's lacking with present-day
iteration features would do well to consider
setf. Of course,
setf doesn't iterate, but it has some other nice properties.
It's easy to use, for one thing. It's extensible—you can define new
setf methods very easily, so that
setf will work with
setf is also efficient, turning into code that's as
good as anyone could write by hand. Arguably,
setf provides a
nice abstraction: it allows you to view value-returning forms, like
(car ...) or
(get ...) as locations that can be
stored into. Finally and most obviously,
like Lisp; it's got a syntax right out of
iterate attempts to provide all of these properties. Here is a simple
iterate that returns all the elements of
are greater than three:
(iterate (for el in num-list) (when (> el 3) (collect el)))
iterate form consists of the symbol
iterate followed by some Lisp
forms. Any legal Lisp form is allowed, as well as certain forms that
iterate treats specially, called clauses.
collect are the two clauses in the above example. An
iterate clause can appear anywhere a Lisp form can appear;
walks its body, looking inside every form, processing
when it finds them. It even expands macros, so you can write macros
iterate clauses. Almost all clauses use the syntax of
function keyword-argument lists: alternating keywords and arguments.
iterate keywords don't require a preceding colon, but you can use one
if you like.
iterate provides many convenient iteration abstractions, most of them
loop users. Iteration-driving clauses (those
for) can iterate over numbers, lists, arrays,
hashtables, packages and files. There are clauses for collecting
values into a list, summing and counting, maximizing, finding maximal
elements, and various other things. Here are a few examples, for
To sum a list of numbers:
(iterate (for i in list) (sum i))
To find the length of the shortest element in a list:
(iterate (for el in list) (minimize (length el)))
To find the shortest element in a list:
(iterate (for el in list) (finding el minimizing (length el)))
t only if every other element of a list is odd:
(iterate (for els on list by #'cddr) (always (oddp (car els))))
To split an association list into two separate lists (this example
iterate's ability to do destructuring):
(iterate (for (key . item) in alist) (collect key into keys) (collect item into items) (finally (return (values keys items))))
As with any aspect of coding, how to iterate is a matter of taste. I
do not wish to dictate taste or even to suggest that
iterate is a
“better” way to iterate than other methods. I would, however, like
to examine the options, and explain why I prefer
iterate to its
do form has long been a Lisp iteration staple. It provides
for binding of iteration variables, an end-test, and a body of
arbitrary code. It can be a bit cumbersome for simple applications,
but the most common special cases—iterating over the integers from
zero and over the members of a list—appear more conveniently as
do's major problem is that it provides no abstraction. For
example, collection is typically handled by binding a variable to
nil, pushing elements onto the variable, and
the result before returning it. Such a common iteration pattern
should be easier to write. (It is, using
Another problem with
do, for me at least, is that it's hard to
read. The crucial end-test is buried between the bindings and the
body, marked off only by an extra set of parens (and some
indentation). It is also unclear, until after a moment of
recollection, whether the end-test has the sense of a “while” or an
Despite its flaws,
do is superior to the iteration facilities
of every other major programming language except CLU. Perhaps that is
the reason many Lisp programmers don't mind using it.
Tail-recursive implementations of loops, like those found in Scheme code [SchemeBook], are parsimonious and illuminating. They have the advantage of looking like recursion, hence unifying the notation for two different types of processes. For example, if only tail-recursion is used, a loop that operates on list elements from front to back looks very much like a recursion that operates on them from back to front.
However, using tail-recursion exclusively can lead to cumbersome code and a proliferation of functions, especially when one would like to embed a loop inside a function. Tail-recursion also provides no abstraction for iteration; in Scheme, that is typically done with higher-order functions.
Lisp's age-old mapping functions, recently revamped for Common Lisp [CLM], are another favorite for iteration. They provide a pleasing abstraction, and it's easy to write new higher-order functions to express common iteration patterns. Common Lisp already comes with many such useful functions, for removing, searching, and performing reductions on lists. Another Common Lisp advantage is that these functions work on any sequence—vectors as well as lists.
One problem with higher-order functions is that they are inefficient,
requiring multiple calls on their argument function. While the the
mapcar, can be open-coded, that
cannot be so easily done for user-written functions. Also, using
higher-order functions often results in the creation of intermediate
sequences that could be avoided if the iteration were written out
The second problem with higher-order functions is very much a matter of personal taste. While higher-order functions are theoretically elegant, they are often cumbersome to read and write. The unpleasant sharp-quote required by Common Lisp is particularly annoying here, and even in Scheme, I find the presence of a lambda with its argument list visually distracting.
Another problem is that it's difficult to express iteration of
sequences of integers without creating such sequences explicitly as
lists or arrays. One could resort to tail-recursion or
dotimes—but then it becomes very messy to express double
iterations where one driver is over integers. Multiple iteration is
iterate, as illustrated by the following example, which creates
an alist of list elements and their positions:
(iterate (for el in list) (for i from 0) (collect (cons el i)))
For really heavy-duty iteration jobs, nothing less than a coroutine-like mechanism will do. Such mechanisms hide the state of the iteration behind a convenient abstraction. A generator is a procedure that returns the next element in the iteration each time it is called. A stream (in the terminology of [SchemeBook]) is a data structure which represents the iteration, but which computes the next element only on demand. Generators and streams support a similar style of programming. Here, for example, is how you might enumerate the leaves of a tree (represented as a Lisp list with atoms at the leaves) using streams:
(defun tree-leaves (tree) (if (atom tree) (stream-cons tree empty-stream) (stream-append (tree-leaves (car tree)) (tree-leaves (cdr tree)))))
tree-leaves looks like an ordinary recursion, it will
only do enough work to find the first leaf before returning. The
stream it returns can be accessed with
stream-car, which will
yield the (already computed) first leaf of the tree, or with
stream-cdr, which will initiate computation of the next leaf.
Such a computation would be cumbersome to write using
iterate, or any
of the other standard iteration constructs; in fact, it is not even
technically speaking an iteration, if we confine that term to
processes that take constant space and linear time. Streams, then,
are definitely more powerful than standard iteration machinery.
Unfortunately, streams are very expensive, since they must somehow save the state of the computation. Generators are typically cheaper, but are less powerful and still require at least a function call. So these powerful tools should be used only when necessary, and that is not very often; most of the time, ordinary iteration suffices.
There is one aspect of generators that
iterate can capture, and that
is the ability to produce elements on demand. Say we wish to create
an alist that pairs the non-null elements of a list with the positive
integers. We saw above that it is easy to iterate over a list and a
series of numbers simultaneously, but here we would like to do
something a little different: we want to iterate over the list of
elements, but only draw a number when we need one (namely, when a list
element is non-null). The solution employs the
keyword in place of
for and the special clause
(iterate (for el in list) (generate i from 1) (if el (collect (cons el (next i)))))
next with any driver variable changes how that driver
works. Instead of supplying its values one at a time on each
iteration, the driver computes a value only when a
is executed. This ability to obtain values on demand greatly
iterate's power. Here,
el is set to the next element
of the list on each iteration, as usual; but
i is set only when
(next i) is executed.
Richard C. Waters has developed a very elegant notation called Series which allows iteration to be expressed as sequence-mapping somewhat in the style of APL, but which compiles to efficient looping code [Series].
My reasons for not using Series are, again, matters of taste. Like
many elegant notations, Series can be somewhat cryptic. Understanding
what a Series expression does can require some effort until one has
mastered the idiom. And if you wish to share your code with others,
they will have to learn Series as well.
iterate suffers from this
problem to some extent, but since the iteration metaphor it proposes
is much more familiar to most programmers than that of Series, it is
considerably easier to learn and read.
Oh, don't be silly.
loop is the iteration construct most similar to
loop is a macro written originally for MacLisp and
in widespread use [Loop]. It has been adopted as part of Common Lisp.
loop provides high-level iteration with abstractions for
collecting, summing, maximizing and so on. Recall our first
(iterate (for el in num-list) (when (> el 3) (collect el)))
Expressed with \looP, it would read
(loop for el in list when (> el 3) collect el)
The similarity between the two macros should immediately be apparent.
iterate's clauses were borrowed from
loop has a paucity of parens. Though
touted as more readable than heavily-parenthesized code,
Pascalish syntax creates several problems. First, many
dyed-in-the-wool Lisp hackers simply find it ugly. Second, it
requires learning the syntax of a whole new sublanguage. Third, the
absence of parens makes it hard to parse, both by machine and, more
importantly, by human. Fourth, one often has to consult the manual to
recall lesser-used aspects of the strange syntax. Fifth, there is no
good interface with the rest of Lisp, so
loop clauses cannot
appear inside Lisp forms and macros cannot expand to pieces of
loop. And Sixth, pretty-printers and indenters that don't know
loop will invariably display it wrongly. This is
particularly a problem with program-editor indenters. A reasonably
clever indenter, like that of Gnu Emacs, can indent nearly any normal
Lisp form correctly, and can be easily customized for most new forms.
But it can't at present handle
loop. The syntax of
designed to keep parens to a minimum, but conform close enough to Lisp
so as not to confuse code-display tools. Gnu Emacs indents
reasonably with no modifications.
Indenting is a mere annoyance;
loop's lack of extensibility is
a more serious problem. The original
loop was completely
extensible, but the Symbolics version only provides for the definition
of new iteration-driving clauses, and the Common Lisp specification
does not have any extension mechanism. But extensibility is a boon.
Consider first the problem of adding the elements of a list together,
which can be accomplished with
(iterate (for el in list) (sum el))
(loop for el in list sum el)
But now, say that you wished to compute the sum of the square roots of
the elements. You could of course write, in either
(iterate (for el in list) (sum (sqrt el)))
But perhaps you find yourself writing such loops often enough to make
it worthwhile to create a new abstraction. There is nothing you can
loop, but in
iterate you could simply write a macro:
(defmacro (sum-of-sqrts expr &optional into-var) `(sum (sqrt ,expr) into ,into-var))
sum-of-sqrts is a perfectly ordinary Lisp macro. Since
expands all macros and processes the results,
will behave exactly as if we'd written
(sum (sqrt el)).
There's also a way to define macros that use
iterate's clause syntax.
A Common Lisp implementation of
iterate has existed for well over a
year. It runs under Lucid for HP 300's, Sun 3's and SPARCstations,
and on Symbolics Lisp machines.
Iteration is a matter of taste. I find
iterate more palatable than
other iteration constructs: it's more readable, more efficient than
most, provides nice abstractions, and can be extended.
If you're new to Lisp iteration, start with
iterate—look before you
loop. If you're already using
loop and like the power
that it offers, but have had enough of its syntax and inflexibility,
then my advice to you is, don't
Thanks to David Clemens for many helpful suggestions and for the
egregious pun near the end. Conversations with Richard Waters
prompted me to add many improvements to
iterate. Alan Bawden, Sundar
Narasimhan, and Jerry Roylance also provided useful comments. David
Clemens and Oren Etzioni shared with me the joys of beta-testing.
 Hey, don't get mad—I'll be much more polite later, when the real paper starts.