\input texinfo   @c -*- Mode: Texinfo; Mode: auto-fill -*-
@c %**start of header
@setfilename iterate.info
@settitle The Iterate Manual and Paper
@exampleindent 2

@c @documentencoding utf-8

@macro iter {}
@code{iterate}
@end macro

@macro mathx {tex, non-tex}
@iftex
@math{\tex\}
@end iftex
@ifnottex
@emph{\non-tex\}
@end ifnottex
@end macro

@macro impnote {text}
@quotation Implementor's note
@emph{\text\}
@end quotation
@end macro

@c Set ROMANCOMMENTS to get comments in roman font.
@ifset ROMANCOMMENTS
@alias lispcmt = r
@end ifset
@ifclear ROMANCOMMENTS
@alias lispcmt = asis
@end ifclear

@c Index for iterate clauses.
@defindex it

@macro clauseu {name1}
@itindex \name1\
@c
@end macro

@macro claused {name1, name2}
@itindex \name1\@dots{}\name2\
@c
@end macro

@macro clauset {name1, name2, name3}
@itindex \name1\@dots{}\name2\@dots{}\name3\
@c
@end macro

@macro k {what}
@code{\what\}
@end macro

@iftex
@alias v = asis
@alias cl = code
@end iftex

@ifnottex
@alias v = var
@alias cl = strong
@end ifnottex

@c Show variables, clauses, and concepts in the same index.
@syncodeindex it cp
@syncodeindex vr cp

@copying
Copyright @copyright{} 1989 Jonathan Amsterdam <jba at ai.mit.edu> @*
@c Copyright @copyright{} 2006 Lu@'{@dotless{i}}s Oliveira
@c  <loliveira at common-lisp.net> @*

@quotation
The present manual is a conversion of Jonathan Amsterdam's ``The
Iterate Manual'', @acronym{MIT} @acronym{AI} Memo No.@: 1236.  Said memo
mentioned the following contract information:

@emph{This report describes research done at the Artificial
Intelligence Laboratory of the Massachusetts Institute of Technology.
Support for the laboratory's artificial intelligence research is
provided in part by the Advanced Research Projects Agency of the
Department of Defense under Office of Naval Research contract
N00014-85-K-0124.}

The appendix includes Jonathan Amsterdam's Working Paper 324,
MIT AI Lab entitled ``Don't Loop, Iterate.''
@end quotation
@end copying
@c %**end of header

@titlepage
@title The Iterate Manual and Paper
@c @subtitle Version X.X
@c @author Jonathan Amsterdam

@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage

@contents

@ifnottex
@node Top
@top iterate
@insertcopying
@end ifnottex

@menu
* Introduction::                
* Clauses::                     
* Other Features::              
* Types and Declarations::      
* Problems with Code Movement::  
* Differences Between Iterate and Loop::  
* Rolling Your Own::            
* Non-portable Extensions to Iterate (Contribs)::  
* Obtaining Iterate::           
* Acknowledgements::            
* Don't Loop Iterate::                 
* Comprehensive Index::         
@end menu

@c ===================================================================
@node Introduction
@chapter Introduction

This manual describes @iter{}, a powerful iteration facility for
Common Lisp.  @iter{} provides abstractions for many common iteration
patterns and allows for the definition of additional patterns.
@iter{} is a macro that expands into ordinary Lisp at compile-time, so
it is more efficient than higher-order functions like @code{map} and
@code{reduce}.  While it is similar to @code{loop}, @iter{} offers a
more Lisp-like syntax and enhanced extensibility.  (For a more
complete comparison of @iter{} with other iteration constructs, see
@acronym{MIT} @acronym{AI} Lab Working Paper No.@: 324, @emph{Don't
Loop, Iterate.} also included in this manual in @ref{Don't Loop
Iterate}.)

An @iter{} form consists of the symbol @code{iter}@footnote{You can
also use @code{iterate}, but @code{iter} is preferred because it
avoids potential conflicts with possible future additions to Common
Lisp, and because it saves horizontal space when writing code.}
followed by one or more forms, some of which may be @iter{}
@emph{clauses}.  Here is a simple example of @iter{} which collects
the numbers from 1 to 10 into a list, and returns the list.  The
return value is shown following the arrow.

@lisp
(iter (for i from 1 to 10)
      (collect i))          @result{} (1 2 3 4 5 6 7 8 9 10)
@end lisp

This form contains two clauses: a @code{for} clause that steps the
variable @code{i} over the integers from 1 to 10, and a @code{collect}
clause that accumulates its argument into a list.  With a few
exceptions, all @iter{} clauses have the same format: alternating
symbols (called @emph{keywords}) and expressions (called
@emph{arguments}).  The syntax and terminology are those of Common
Lisp's keyword lambda lists.  One difference is that @iter{}'s keywords
do not have to begin with a colon---though they may, except for the
first symbol of a clause.  So you can also write @code{(for i :from 1
:to 10)} if you prefer.

Any Lisp form can appear in the body of an @iter{}, where it will have
its usual meaning.  @iter{} walks the entire body, expanding macros,
and recognizing clauses at any level.  This example collects all the
odd numbers in a list:

@lisp
(iter (for el in list)
      (if (and (numberp el) (oddp el))
          (collect el)))
@end lisp

There are clauses for iterating over numbers, lists, arrays and other
objects, and for collecting, summing, counting, maximizing and other
useful operations.  @iter{} also supports the creation of new variable
bindings, stepping over multiple sequences at once, destructuring, and
compiler declarations of variable types.  The following example
illustrates some of these features:

@lisp
(iter (for (key . item) in alist)
      (for i from 0)
      (declare (fixnum i))
      (collect (cons i key)))
@end lisp

This loop takes the keys of an alist and returns a new alist
associating the keys with their positions in the original list.  The
compiler declaration for @code{i} will appear in the generated code in
the appropriate place.

@c ===================================================================
@node Clauses
@chapter Clauses

Most of @iter{}'s clauses will be familiar to @code{loop} programmers.
(@code{loop} is an iteration macro that has been incorporated into
Common Lisp.  See Guy Steele's @emph{Common Lisp, 2nd Edition}.)  In
nearly all cases they behave the same as their @code{loop}
counterparts, so a @code{loop} user can switch to @iter{} with little
pain (and much gain).

All clauses with the standard keyword-argument syntax consist of two
parts: a @emph{required} part, containing keywords that must be present and
in the right order; and an @emph{optional} part, containing keywords that
may be omitted and, if present, may occur in any order.  In the
descriptions below, the parts are separated by the Lisp lambda-list
keyword @code{&optional}.

@menu
* Drivers::                     
* Variable Binding and Setting::  
* Gathering Clauses::           
* Control Flow::                
* Predicates::                  
* Code Placement::              
@end menu

@c ===================================================================
@node Drivers
@section Drivers

An iteration-driving clause conceptually causes the iteration to go
forward.  Driver clauses in @iter{} allow iteration over numbers,
lists, vectors, hashtables, packages, files and streams.
Iteration-driving clauses must appear at the top level of an @iter{}
form; they cannot be nested inside another clause.  The driver
variable is updated at the point where the driver clause occurs.
Before the clause is executed for the first time, the value of the
variable is undefined.

@c Also, regardless of where the driver clause appears in the body,
@c the driver variable is stepped at the top of the loop; hence it is
@c stylistically preferable, though not required, to place driver
@c clauses at the beginning of the @iter{}.

Multiple drivers may appear in a single @iter{} form, in which case all
of the driver variables are updated each time through the loop, in the
order in which the clauses appear.  The first driver to terminate will
terminate the entire loop.

In all cases, the value of the driver variable on exit from the loop,
including within the epilogue code (see the @code{finally} clause), is
undefined.

All the parameters of a driver clause are evaluated once, before the
loop begins.  Hence it is not possible to change the bounds or other
properties of an iteration by side-effect from within the loop.

With one exception, driver clauses begin with the word @code{for} (or
the synonym @code{as}) and mention an iteration variable, which is
given a binding within the @iter{} form.  The exception is
@code{repeat}, which just executes a loop a specified number of times:

@clauseu{repeat}
@deffn Clause repeat @v{n}

Repeat the loop @var{n} times.  For example:

@lisp
(iter (repeat 100)
      (print "I will not talk in class."))
@end lisp

If @mathx{n \leq 0, n <= 0}, then loop will never be executed.  If @var{n} is
not an integer, the actual number of executions will be @mathx{\lceil n
\rceil, ceil(n)}.
@end deffn

@menu
* Numerical Iteration::         
* Sequence Iteration::          
* Generalized Drivers::         
* Generators::                  
* Previous Values of Driver Variables::  
@end menu

@c ===================================================================
@node Numerical Iteration
@subsection Numerical Iteration

@clauseu{for}
@deffn Clause for @v{var} @k{&sequence}

The general form for iterating over a sequence of numbers requires a
variable and, optionally, one or more keywords that provide the bounds
and step size of the iteration.  The @code{&sequence} lambda-list
keyword is a shorthand for these sequence keywords.  They are:
@code{from}, @code{upfrom}, @code{downfrom}, @code{to}, @code{downto},
@code{above}, @code{below} and @code{by}.  @code{from} provides the
starting value for @var{var} and defaults to zero.  @code{to} provides
a final value and implies that the successive values of @var{var} will
be increasing; @code{downto} implies that they will be decreasing.
The loop terminates when @var{var} passes the final value
(i.e.@: becomes smaller or larger than it, depending on the direction of
iteration); in other words, the loop body will never be executed for
values of @var{var} past the final value.  @code{below} and
@code{above} are similar to @code{to} and @code{downto}, except that
the loop terminates when @var{var} equals or passes the final value.

If no final value is specified, the variable will be stepped forever.
Using @code{from} or @code{upfrom} will result in increasing values,
while @code{downfrom} will give decreasing values.

On each iteration, @var{var} is incremented or decremented by the
value of the sequence keyword @code{by}, which defaults to 1.  It
should always be a positive number, even for downward iterations.

In the following examples, the sequence of numbers generated is shown
next to the clause.

@lisp
(for i upfrom 0) @result{} 0 1 2 @dots{}
(for i from 5) @result{} 5 6 7 @dots{}    ; either from or upfrom is okay
(for i downfrom 0) @result{} 0 -1 -2 @dots{}
(for i from 1 to 3) @result{} 1 2 3
(for i from 1 below 3) @result{} 1 2
(for i from 1 to 3 by 2) @result{} 1 3
(for i from 1 below 3 by 2) @result{} 1
(for i from 5 downto 3) @result{} 5 4 3
@end lisp
@end deffn

@c ===================================================================
@node Sequence Iteration
@subsection Sequence Iteration

There are a number of clauses for iterating over sequences.  In all of
them, the argument following @code{for} may be a list instead of a
symbol, in which case destructuring is performed.  See
@ref{Destructuring}.

@claused{for, in}
@deffn Clause for @v{var} @cl{in} @v{list} @k{&optional} @k{by} @v{step-function}

@var{var} is set to successive elements of list. @var{step-function},
which defaults to @code{cdr}, is used to obtain the next sublist.

This clause uses @code{endp} to test for the end of a list, hence
should signal an error when processing an improper list whose final
@code{cdr} is not @code{nil}---like @code{loop}.  Prior to 2007,
@iter{} would default to @code{atom} and silently exit.

@vindex *list-end-test*
@quotation Compatibility Note
The original implementation used the variable
@code{iterate::*list-end-test*}, defaulting to @code{atom}.  Years
later, it was deemed unacceptable for the semantics @emph{not} to be
lexically apparent from the iteration form so this variable was
removed.  If your application depends on the original behaviour, the
ancient @code{for @v{var} in} is equivalent to
@code{for (@v{var}) on}.
@end quotation
@end deffn

@claused{for, on}
@deffn Clause for @v{var} @cl{on} @v{list} @k{&optional} @k{by} @v{step-function}

@var{var} is set to successive sublists of list.  @var{step-function}
(default @code{cdr}) is used as in @code{for@dots{} in}.

This clause uses @code{atom} to test for the end of a list, so it can
be used with dotted lists---like @code{loop}.
@end deffn

@c These two clauses use @code{atom} to test for the end of a list.
@c Hence, given a list whose final @code{cdr} is not @code{nil}, they
@c will silently ignore the last @code{cdr}.  Other choices are
@c @code{endp}, which would signal an error, and @code{null}, which would
@c probably result in an error somewhere else.  If you wish to use an
@c end-test other than @code{atom}, set the variable
@c @code{iterate::*list-end-test*} to the name of the desired function.

@claused{for, in-vector}
@deffn Clause for @v{var} @cl{in-vector} @v{vector} @k{&sequence}

@var{var} takes on successive elements from @var{vector}.  The vector's
fill-pointer is observed.  Here and in subsequent clauses, the
@code{&sequence} keywords include @code{with-index}, which takes a
symbol as argument and uses it for the index variable instead of an
internally generated symbol.  The other @code{&sequence} keywords
behave as in numerical iteration, except that the default iteration
bounds are the bounds of the vector.  E.g.@: in @code{(for i in-vector v
downto 3)}, @code{i} will start off being bound to the last element in
@code{v}, and will be set to preceding elements down to and including
the element with index 3.
@end deffn

@claused{for, in-sequence}
@deffn Clause for @v{var} @cl{in-sequence} @v{seq} @k{&sequence}

This uses Common Lisp's generalized sequence functions, @code{elt} and
@code{length}, to obtain elements and determine the length of
@var{seq}.  Hence it will work for any sequence, including lists, and
will observe the fill-pointers of vectors.
@end deffn

@claused{for, in-string}
@deffn Clause for @v{var} @cl{in-string} @v{string} @k{&sequence}

@var{var} is set to successive characters of @var{string}.
@end deffn

@claused{for, index-of-vector}
@claused{for, index-of-sequence}
@claused{for, index-of-string}
@deffn Clause for @v{var} @cl{index-of-vector} @v{vector} @k{&sequence}
@deffnx Clause for @v{var} @cl{index-of-sequence} @v{sequence} @k{&sequence}
@deffnx Clause for @v{var} @cl{index-of-string} @v{string} @k{&sequence}

@var{var} is set to successive indices of the sequence.  These clauses
avoid the overhead of accessing the sequence elements for those
applications where they do not need to be examined, or are examined
rarely.  They admit all the optional keywords of the other sequence
drivers except the (redundant) @code{with-index} keyword.
@end deffn

@claused{for, in-hashtable}
@deffn Clause for (@v{key} @v{value}) @cl{in-hashtable} @v{table}

@var{key} and @var{value}, which must appear as shown in a list and
may be destructuring templates, are set to the keys and values of
@var{table}.  If @var{key} is @code{nil}, then the hashtable's keys
will be ignored; similarly for @var{value}.  The order in which
elements of @var{table} will be retrieved is unpredictable.
@end deffn

@claused{for, in-package}
@deffn Clause for @v{var} @cl{in-package} @v{package} @
                  @k{&optional} @k{external-only} @v{ext}

Iterates over all the symbols in @var{package}, or over only the
external symbols if @var{ext} is specified and non-@code{nil}.
@var{ext} is not evaluated.  The same symbol may appear more than
once.
@end deffn

@claused{for, in-packages}
@deffn Clause for @v{var} @cl{in-packages} @
                  @k{&optional} @k{having-access} @v{symbol-types}

Iterates over all the symbols from the list of packages denoted by the
descriptor @var{packages} and having accessibility (or visibility)
given by @var{symbol-types}.  This defaults to the list
@code{(:external :internal :inherited)} and is not evaluated.
@var{var} must be a list of up to three variables: in each iteration,
these will be set to a symbol, its access-type and package (as per
@code{with-package-iterator} in ANSI CL).  The same symbol may appear
more than once.
@end deffn

@claused{for, in-file}
@deffn Clause for @v{var} @cl{in-file} @v{name} @
                  @k{&optional} @k{using} @v{reader}

Opens the file @var{name} (which may be a string or pathname) for
input, and iterates over its contents.  @var{reader} defaults to
@code{read}, so by default @emph{var} will be bound to the successive
forms in the file.  The @iter{} body is wrapped in an
@code{unwind-protect} to ensure that the file is closed no matter how
the @iter{} is exited.
@end deffn

@claused{for, in-stream}
@deffn Clause for @v{var} @cl{in-stream} @v{stream} @k{&optional} @k{using} @
              @v{reader}

Like @code{for@dots{} in-file}, except that @var{stream} should be an
existing stream object that supports input operations.
@end deffn

@c ===================================================================
@node Generalized Drivers
@subsection Generalized Drivers

These are primarily useful for writing drivers that can also be used
as generators (see @ref{Generators}).

@clauseu{terminate}
@claused{for, next}
@deffn Clause for @v{var} @cl{next} @v{expr}

@var{var} is set to @var{expr} each time through the loop.
Destructuring is performed.  When the clause is used as a generator,
@var{expr} is the code that is executed when @code{(next @emph{var})}
is encountered (see @ref{Generators}).  @var{expr} should compute the
first value for @var{var}, as well as all subsequent values, and is
responsible for terminating the loop.  For compatibility with future
versions of @iter{}, this termination should be done with
@code{terminate}, which can be considered a synonym for @code{finish}
(see @ref{Control Flow}).

As an example, the following clauses are equivalent to @code{(for i
from 1 to 10)}:

@lisp
(initially (setq i 0))
(for i next (if (> i 10) (terminate) (incf i)))
@end lisp
@end deffn

@claused{for, do-next}
@deffn Clause for @v{var} @k{do-next} @v{form}

@var{form} is evaluated each time through the loop.  Its value is
@var{not} set to @var{var}; that is @var{form}'s job.  @var{var} is
only present so that @iter{} knows it is a driver variable. @*
@code{(for @var{var} next @var{expr})} is equivalent to @code{(for
@var{var} do-next (dsetq @var{var} @var{expr}))}.  (See
@ref{Destructuring} for an explanation of @code{dsetq}.)
@end deffn

@c ===================================================================
@node Generators
@subsection Generators

In all of the above clauses, the driver variable is updated on each
iteration.  Sometimes it is desirable to have greater control over
updating.  For instance, consider the problem of associating numbers,
in increasing order and with no gaps, with the non-@code{nil} elements
of a list.  One obvious first pass at writing this is:

@lisp
(iter (for el in list)
      (for i upfrom 1)
      (if el (collect (cons el i))))
@end lisp

But on the list @code{(a b nil c)} this produces @code{((a . 1) (b
. 2) (c .  4))} instead of the desired @code{((a . 1) (b . 2) (c
. 3))}.  The problem is that @code{i} is incremented each time through
the loop, even when @code{el} is @code{nil}.

The problem could be solved elegantly if we could step @code{i} only
when we wished to.  This can be accomplished for any @iter{} driver by
writing @code{generate} (or its synonym @code{generating}) instead of
@code{for}.  Doing so produces a @emph{generator}---a driver whose
values are yielded explicitly.  To obtain the next value of a
generator variable @var{v}, write @code{(next @var{v})}.  The value of
a @code{next} form is the next value of @emph{v}, as determined by its
associated driver clause.  @code{next} also has the side-effect of
updating @var{v} to that value.  If there is no next value,
@code{next} will terminate the loop, just as with a normal driver.

Using generators, we can now write our example like this:

@lisp
(iter (for el in list)
      (generate i upfrom 1)
      (if el (collect (cons el (next i)))))
@end lisp

Now @code{i} is updated only when @code{(next i)} is executed, and
this occurs only when @code{el} is non-@code{nil}.

To better understand the relationship between ordinary drivers and
generators, observe that we can rewrite an ordinary driver using its
generator form immediately followed by @code{next}, as this example
shows:

@lisp
(iter (generating i from 1 to 10)
      (next i)
      @dots{})
@end lisp

Provided that the loop body contains no @code{(next i)} forms, this
will behave just as if we had written @code{(for i from 1 to 10)}.

We can still refer to a driver variable @var{v} without using
@code{next}; in this case, its value is that given to it by the last
evaluation of @code{(next @var{v})}.  Before @code{(next @var{v})} has
been called the first time, the value of @var{v} is undefined.

This semantics is more flexible than one in which @var{v} begins the
loop bound to its first value and calls of @code{next} supply
subsequent values, because it means the loop will not terminate too
soon if the generator's sequence is empty.  For instance, consider the
following code, which tags non-@code{nil} elements of a list using a
list of tags, and also counts the null elements.  (We assume there are
at least as many tags as non-@code{nil} elements.)

@lisp
(let* ((counter 0)
       (tagged-list (iter (for el in list)
                          (generating tag in tag-list) 
                          (if (null el)
                              (incf counter)
                              (collect (cons el (next tag)))))))
  @dots{})
@end lisp

It may be that there are just as many tags as non-null elements of
@code{list}.  If all the elements of @code{list} are null, we still
want the counting to proceed, even though @code{tag-list} is
@code{nil}.  If @code{tag} had to be assigned its first value before
the loop begins, we would have had to terminate the loop before the
first iteration, since when @code{tag-list} is @code{nil}, @code{tag}
has no first value.  With the existing semantics, however, @code{(next
tag)} will never execute, so the iteration will cover all the elements
of @code{list}.
        
When the ``variable'' of a driver clause is actually a destructuring
template containing several variables, all the variables are eligible
for use with @code{next}.  As before, @code{(next @var{v})} evaluates
to @var{v}'s next value; but the effect is to update all of the
template's variables.  For instance, the following code will return
the list @code{(a 2 c)}.

@lisp
(iter (generating (key . item) in '((a . 1) (b . 2) (c . 3)))
      (collect (next key))
      (collect (next item)))
@end lisp

Only driver clauses with variables can be made into generators.  This
includes all clauses mentioned so far except for @code{repeat}.  It
does @emph{not} include @code{for@dots{} previous}, @code{for@dots{}
=}, @code{for@dots{} initially@dots{} then} or @code{for@dots{}
first@dots{} then} (see below).

@c ===================================================================
@node Previous Values of Driver Variables
@subsection Previous Values of Driver Variables

Often one would like to access the value of a variable on a previous
iteration.  @iter{} provides a special clause for accomplishing this.

@claused{for, previous}
@deffn Clause for @v{pvar} @cl{previous} @v{var} @
                  @k{&optional} @k{initially} @v{init} @k{back} @v{n}

Sets @var{pvar} to the previous value of @var{var}, which should be a
driver variable, a variable from another @code{for@dots{} previous}
clause, or a variable established by a @code{for@dots{} =},
@code{for@dots{}  initially@dots{} then} or @code{for@dots{}
first@dots{} then} clause (see @ref{Variable Binding and Setting}).
Initially, @var{pvar} is given the value @var{init} (which defaults to
@code{nil}).  The @var{init} expression will be moved outside the loop
body, so it should not depend on anything computed within the loop.
@var{pvar} retains the value of @var{init} until @var{var} is set to
its second value, at which point @var{pvar} is set to @var{var}'s
first value; and so on.

The argument @var{n} to @code{back} must be a constant, positive
integer, and defaults to 1.  It determines how many iterations back
@var{pvar} should track @var{var}.  For example, when @var{n} is 2,
then @var{pvar} will be assigned @var{var}'s first value when
@var{var} is set to its third value.

A @code{for@dots{} previous} clause may occur after or before its
associated driver clause.  @code{for@dots{} previous} works with
generators as well as ordinary drivers.

Example:

@lisp
(iter (for el in '(1 2 3 4))
      (for p-el previous el)
      (for pp-el previous p-el initially 0)
      (collect pp-el))
@end lisp

This evaluates to @code{(0 0 1 2)}.  It could have been written more
economically as

@lisp
(iter (for el in '(1 2 3 4))
      (for pp-el previous el back 2 initially 0)
      (collect pp-el))
@end lisp
@end deffn

@c ===================================================================
@node Variable Binding and Setting
@section Variable Binding and Setting

Several clauses exist for establishing new variable bindings or for
setting variables in the loop.  They all support destructuring.

@clauseu{with}
@deffn Clause with @v{var} @k{&optional} @k{=} @v{value}

Causes @var{var} to be bound to value before the loop body is entered.
If @var{value} is not supplied, @var{var} assumes a default binding,
which will be @code{nil} in the absence of declarations.  Also, if
@var{value} is not supplied, no destructuring is performed; instead,
@var{var} may be a list of symbols, all of which are given default
bindings.  If @var{value} is supplied, @var{var} is bound to it, with
destructuring.

Because @code{with} creates bindings whose scope includes the entire
@iter{} form, it is good style to put all @code{with} clauses at the
beginning.

Successive occurrences of @code{with} result in sequential bindings
(as with @code{let*}).  There is no way to obtain parallel bindings;
see @ref{Parallel Binding and Stepping} for a rationale.
@end deffn

@claused{for, =}
@deffn Clause for @v{var} @cl{=} @v{expr}

On each iteration, @var{expr} is evaluated and @var{var} is set to its
value.

This clause may appear to do the same thing as @code{for@dots{} next}.
In fact, they are quite different.  @code{for@dots{} =} provides only
three services: it sets up a binding for @var{var}, sets it to
@var{expr} on each iteration, and makes it possible to use
@code{for@dots{}  previous} with @var{var}.  @code{for@dots{} next}
provides these services in addition to the ability to turn the driver
into a generator.

@c Also, the code which sets @var{var} appears in the loop body in the
@c same place as the @code{for@dots{} =} clause; the code for
@c @code{for@dots{} next} appears at the top of the loop, as with
@c other drivers (except when being used as a generator).
@end deffn

@clauset{for, initially, then}
@deffn Clause for @v{var} @cl{initially} @v{init-expr} @cl{then} @v{then-expr}

Before the loop begins, @var{var} is set to @var{init-expr;} on all
iterations after the first it is set to @var{then-expr.} This clause
must occur at top-level.  @var{init-expr} will be moved outside the
loop body and @var{then-expr} will be moved to the end of the loop
body, so they are subject to code motion problems (see @ref{Problems
with Code Movement}).

This clause may appear to be similar to @code{for@dots{} next}, but in
fact they differ significantly.  @code{for@dots{} initially@dots{}
then} is typically used to give @var{var} its first value before the
loop begins, and subsequent values on following iterations.  This is
incompatible with generators, whose first value and subsequent values
must all be computed by @code{(next @var{var})}.  Also, the update of
@var{var} in @code{for@dots{} initially@dots{} then} does not occur at
the location of the clause.

Use @code{for@dots{} initially@dots{} then} for one-shot computations
where its idiom is more convenient, but use @code{for@dots{} next} for
extending @iter{} with new drivers (see @ref{Rolling Your Own}).
@end deffn

@clauset{for, first, then}
@deffn Clause for @v{var} @cl{first} @v{first-expr} @cl{then} @v{then-expr}

The first time through the loop, @var{var} is set to @var{first-expr};
on subsequent iterations, it is set to @var{then-expr}.  This differs
from @code{for@dots{} initially} in that @var{var} is set to
@var{first-expr} inside the loop body, so @var{first-expr} may depend
on the results of other clauses.  For instance,

@lisp
(iter (for num in list)
      (for i first num then (1+ i))
      ...)
@end lisp

will set @code{i} to the first element of @code{list} on the first
iteration, whereas

@lisp
(iter (for num in list)
      (for i initially num then (1+ i))
      ...)
@end lisp

is probably erroneous; @code{i} will be bound to @code{num}'s default
binding (usually @code{nil}) for the first iteration.
@end deffn

@quotation Compatibility Note
@code{loop}'s @code{for@dots{} =} works like @iter{}'s, but
@code{loop} used the syntax @code{for@dots{} =@dots{} then} to mean
@code{for@dots{} initially@dots{} then}.  It was felt that these two
operations were sufficiently different to warrant different keywords.

Also, the @code{for} in the above three clauses is misleading, since
none is true driver (e.g.@: none has a corresponding @code{generate}
form).  @code{setting} would have been a better choice, but @code{for}
was used to retain some compatibility with @code{loop}.
@end quotation

@c ===================================================================
@node Gathering Clauses
@section Gathering Clauses

Many of @iter{}'s clauses accumulate values into a variable, or set a
variable under certain conditions.  At the end of the loop, this
variable contains the desired result.  All these clauses have an
optional @code{into} keyword, whose argument should be a symbol.  If
the @code{into} keyword is not supplied, the accumulation variable
will be internally generated and its value will be returned at the end
of the loop; if a variable is specified, that variable is used for the
accumulation, and is not returned as a result---it is up to the user
to return it explicitly, in the loop's epilogue code (see
@code{finally}).  It is safe to examine the accumulation variable
during the loop, but it should not be modified.

These clauses all begin with a verb.  When the verb does not conflict
with an existing Common Lisp function, then it may be used in either
its infinitival or present-participle form (e.g.@: @code{sum},
@code{summing}).  However, when there is a conflict with Common Lisp,
only the present-participle form may be used (e.g.@: @code{unioning}).
This is to prevent @iter{} clauses from clashing with Common Lisp
functions.

@c although these clauses are described as ``producing a value,'' it
@c is a mistake to think of the lisp list representing the clause as a
@c value-producing form in the usual way.  clauses may legally be
@c written where a value is expected, e.g.@: @code{(setq x (sum i))},
@c but the lisp value of a clause in such a context is undefined.

@menu
* Reductions::                  
* Accumulations::               
* Finders::                     
* Aggregated Boolean Tests::    
@end menu

@c ===================================================================
@node Reductions
@subsection Reductions

@emph{Reduction} is an extremely common iteration pattern in which the
results of successive applications of a binary operation are
accumulated.  For example, a loop that computes the sum of the
elements of a list is performing a reduction with the addition
operation.  This could be written in Common Lisp as @code{(reduce #'+
list)} or with @iter{} as

@lisp
(iter (for el in list)
      (sum el))
@end lisp

@clauseu{sum}
@deffn Clause sum @v{expr} @k{&optional} @k{into} @v{var}
                                         @k{result-type} @v{type}

Each time through the loop, @var{expr} is evaluated and added to a
variable, which is bound initially to zero.  If @var{expr} has a type,
it is @emph{not} used as the type of the sum variable.  Unless
@var{type} is supplied or @var{var} has a declared type, @var{var} will
always have type @code{number}. To get the result variable to be of a
more specific type, either supply @var{type}, as in:

@lisp
(iter (for el in number-list)
      (sum el result-type fixnum))
@end lisp

or use an explicit variable, as in:

@lisp
(iter (for el in number-list)
      (sum el into x)
      (declare (fixnum x))
      (finally (return x)))
@end lisp
@end deffn

@clauseu{multiply}
@deffn Clause multiply @v{expr} @k{&optional} @k{into} @v{var}
                                              @k{result-type} @v{type}

Like @code{sum}, but the initial value of the result variable is
@math{1}, and the variable is updated by multiplying @var{expr} into
it.
@end deffn

@clauseu{counting}
@deffn Clause counting @v{expr} @k{&optional} @k{into} @v{var}
                                              @k{result-type} @v{type}

@var{expr} is evaluated on each iteration.  If it is non-@code{nil},
the accumulation variable, initially zero, is incremented.
@end deffn

@clauseu{maximize}
@clauseu{minimize}
@deffn Clause maximize @v{expr} @k{&optional} @k{into} @v{var}
@deffnx Clause minimize @v{expr} @k{&optional} @k{into} @v{var}

@var{expr} is evaluated on each iteration and its extremum (maximum or
minimum) is stored in the accumulation variable.  If @var{expr} is
never evaluated, then the result is @code{nil} (if the accumulation
variable is untyped) or @math{0} (if it has a numeric type).
@end deffn

@clauseu{reducing}
@deffn Clause reducing @v{expr} @k{by} @v{func} @k{&optional}
                       @k{initial-value} @v{init-val} @k{into} @v{var}
                       @k{result-type} @v{type}

This is a general way to perform reductions.  @var{func} should be a
function of two arguments, the first of which will be the value
computed so far and the second of which will be the value of
@var{expr}.  It should return the new value.  @code{reducing} is
roughly equivalent to the Common Lisp @code{(reduce @var{func}
@var{sequence} :key @var{expr-function})}, where @var{expr-function}
is used to derive values from the successive elements of
@var{sequence}.

If the @code{reducing} clause is never executed, the result is
undefined.

It is not necessary to provide an initial value, but better code can
be generated if one is supplied.  Regardless of its location in the
@iter{} body, @var{init-val} will be evaluated before the loop is
entered, so it should not depend on any value computed inside the
@iter{} form.

@c if a @var{var} is not specified, you can get @iter{} to declare the
@c type of the internal variable by putting a @code{the} expression
@c around @var{func}.  see @ref{Types}.
@end deffn

@c @impnote{in principle, |maximize| and |minimize| can be thought of
@c as reductions where the initial value is the smallest (or largest)
@c value that the accumulation variable can assume.  because lisp's
@c bignums can represent arbitrary integers, these clauses cannot be
@c implemented as reductions in general.  if, however, the type of
@c ~expr~ or ~var~ can be determined to be a fixnum or a float,
@c @iter{} will implement the clause as a true reduction, using one of
@c the constants |most-negative-fixnum|, |@c most-positive-fixnum|,
@c |most-negative-short-float|, etc.@: as appropriate.}

@c ===================================================================
@node Accumulations
@subsection Accumulations

All the predefined accumulation clauses add values to a sequence.  If
the sequence is a list, they all have the property that the partial
list is kept in the correct order and available for inspection at any
point in the loop.

@clauseu{collect}
@deffn Clause collect @v{exptr} @k{&optional}
                      @k{into} @v{var} @k{at} @v{place} @k{result-type} @v{type}

Produces a sequence of the values of @var{exptr} on each
iteration.  @var{place} indicates where the next value of @var{exptr}
is added to the list and may be one of the symbols @code{start},
@code{beginning} (a synonym for @code{start}) or @code{end}.  The
symbol may be quoted, but need not be.  The default is @code{end}.
For example,

@lisp
(iter (for i from 1 to 5)
      (collect i))
@end lisp

produces @code{(1 2 3 4 5)}, whereas

@lisp
(iter (for i from 1 to 5)
      (collect i at beginning))
@end lisp

produces @code{(5 4 3 2 1)} (and is likely to be faster in most Common
Lisp implementations).

If @var{type} is provided, it should be a subtype of @code{sequence}.
The default is @code{list}.  Specifying a type other than @code{list}
will result in @code{collect} returning a sequence of that type.
@emph{However}, the type of the sequence being constructed when inside
the loop body is undefined when a non-@code{list} type is specified.
(As with @var{place}, quoting @var{type} is optional.)
@end deffn

@clauseu{adjoining}
@deffn Clause adjoining @v{exptr} @k{&optional} @k{into} @v{var} @
                        @k{test} @v{test} @k{at} @v{place} @
                        @k{result-type} @v{type}

Like @code{collect}, but only adds the value of @var{exptr} if it is
not already present.  @var{test}, which defaults to @code{#'eql}, is
the test to be used with @code{member}.
@end deffn

@clauseu{appending}
@clauseu{nconcing}
@clauseu{unioning}
@clauseu{nunioning}
@deffn Clause appending @v{expr} @k{&optional} @k{into} @v{var} @k{at} @v{place}
@deffnx Clause nconcing @v{expr} @k{&optional} @k{into} @v{var} @k{at} @v{place}
@deffnx Clause unioning @v{expr} @k{&optional} @k{into} @v{var} @
                        @k{test} @v{test} @k{at} @v{place}
@deffnx Clause nunioning @v{expr} @k{&optional} @k{into} @v{var} @
                         @k{test} @v{test} @k{at} @v{place}

These are like @code{collect}, but behave like the Common Lisp
functions @code{append}, @code{nconc}, @code{union} or @code{nunion}.
As in Common Lisp, they work only on lists.  Also as in Common Lisp,
@code{unioning} and @code{nunioning} assume that the value of
@var{expr} contains no duplicates.
@end deffn

@clauseu{accumulate}
@deffn Clause accumulate @v{expr} @k{by} @v{func} @k{&optional} @
                         @k{initial-value} @v{init-val} @k{into} @v{var}

This is a general-purpose accumulation clause.  @var{func} should be a
function of two arguments, the value of @var{expr} and the value
accumulated so far in the iteration, and it should return the updated
value.  If no initial value is supplied, @code{nil} is used.

@c If a @var{var} is not specified, you can get @iter{} to declare the
@c type of the internal variable by putting a @code{the} expression
@c around @var{func}.  see section \ref{types}.

The differences between @code{accumulate} and @code{reducing} are
slight.  One difference is that the functions take their arguments in
a different order.  Another is that in the absence of @var{init-val},
@code{accumulate} will use @code{nil}, whereas @code{reducing} will
generate different code that avoids any dependence on the initial
value.  The reason for having both clauses is that one usually thinks
of reductions (like @code{sum}) and accumulations (like
@code{collect}) as different beasts.
@end deffn

@c ===================================================================
@node Finders
@subsection Finders

A @emph{finder} is a clause whose value is an expression that meets
some condition.

@claused{finding, such-that}
@deffn Clause finding @var{expr} @cl{such-that} @v{test} @k{&optionally} @
                      @k{into} @v{var} @k{on-failure} @v{failure-value}

If @var{test} (which is an expression) ever evaluates to
non-@code{nil}, the loop is terminated, the epilogue code is run and
the value of @var{expr} is returned.  Otherwise, @code{nil} (or
@var{failure-value}, if provided) is returned.  If @var{var} is
provided, it will have either the non-@code{nil} value of @var{expr}
or @var{failure-value} when the epilogue code is run.

As a special case, if the @var{test} expression is a sharp-quoted
function, then it is applied to @var{expr} instead of being simply
evaluated.  E.g.@: @code{(finding x such-that #'evenp)} is equivalent to
@code{(finding x such-that (evenp x))}.

@c \cpar although @var{test} need have nothing to do with ~@c expr~ as in
@c |(finding j such-that (> i 3))|, it usually 
@c will: |(finding (length el) such-that (oddp (length el)))|.  to
@c avoid performing the |length| computation twice, you could write
@c |(finding (length el) such-that \#'oddp)| or |(finding (length
@c el) such-that 'oddp)|; for these cases, @iter{} generates code that
@c executes @var{expr} only once.  the code for |\#'oddp|
@c is slightly different from that for {\lisp 'oddp}; see the discussion
@c under {\lisp for\dots in} and {\lisp for\dots on}.

@code{On-failure} is a misnomer.  Because it is always evaluated, it
behaves more like the default third argument to the @code{gethash}
function.  As a result, @code{on-failure (error "Not found")} makes no
sense.  Instead, the clauses @code{leave} or @code{thereis} can be used
in conjunction with @code{finally} as follows:

@lisp
(iter (for x in '(1 2 3))
      (if (evenp x) (leave x))
      (finally (error "not found")))
@end lisp

This clause may appear multiple times when all defaults are
identical.  It can also be used together with either
@code{always}/@code{never} or @code{thereis} if their defaults
match.  More specifically, @code{on-failure nil} is compatible with
@code{thereis}, while @code{on-failure t} is compatible with
@code{always} and @code{never} clauses.

@lisp
(iter (for i in '(7 -4 2 -3))
      (if (plusp i)
        (finding i such-that (evenp i))
        (finding (- i) such-that (oddp i))))
@end lisp
@end deffn

@claused{finding, maximizing}
@claused{finding, minimizing}
@deffn Clause finding @v{expr} @cl{maximizing} @v{m-expr} @
                      @k{&optional} @k{into} @v{var}
@deffnx Clause finding @v{expr} @cl{minimizing} @v{m-expr} @
                       @k{&optional} @k{into} @v{var}

Computes the extremum (maximum or minimum) value of @var{m-expr} over
all iterations, and returns the value of @var{expr} corresponding to
the extremum.  @var{expr} is evaluated inside the loop at the time the
new extremum is established.  If @var{m-expr} is never evaluated (due
to, for example, being embedded in a conditional clause), then the
returned value depends on the type, if any, of @var{expr} (or
@var{var}, if one is supplied).  If there is no type, the returned
value will be @code{nil}; if the type is numeric, the returned value
will be zero.

For these two clauses, @var{var} may be a list of two symbols; in that
case, the first is used to record @var{expr} and the second,
@var{m-expr}.

As with @code{finding@dots{} such-that}, if @var{m-expr} is a
sharp-quoted function, then it is called on @var{expr} instead of
being evaluated.
@end deffn

@c ===================================================================
@node Aggregated Boolean Tests
@subsection Aggregated Boolean Tests

@clauseu{always}
@deffn Clause always @v{expr}

If @var{expr} ever evaluates to @code{nil}, then @code{nil} is
immediately returned; the epilogue code is not executed.  If
@var{expr} never evaluates to @code{nil}, the epilogue code is
executed and the last value of @var{expr} (or @code{t} if @var{expr}
was never evaluated) is returned (whereas @code{loop} would constantly
return @code{t}).

@c mention last evaluated clause when multiple always clauses?
@end deffn

@clauseu{never}
@deffn Clause never @v{expr}

Like @code{(always (not @var{expr}))}, except it does not influence
the last value returned by a possible other @code{always} clause.  That
is,

@lisp
(iter (repeat 2)
      (always 2)
      (never nil)) @result{} 2 ; not t
@end lisp
@end deffn

@clauseu{thereis}
@deffn Clause thereis @v{expr}

If @var{expr} is ever non-@code{nil}, its value is immediately
returned without running epilogue code.  Otherwise, the epilogue code
is performed and @code{nil} is returned.

This clause cannot be used together with @code{always} or
@code{never}, because their defaults are opposed (similarly,
@code{(loop always 3 thereis nil)} refuses to compile in some
implementations of @code{loop}).
@end deffn

@c ===================================================================
@node Control Flow
@section Control Flow

Several clauses can be used to alter the usual flow of control in a
loop.

@quotation Note
The clauses of this and subsequent sections don't adhere to
@iter{}'s usual syntax, but instead use standard Common Lisp syntax.
Hence the format for describing syntax subsequently is like the
standard format used in the Common Lisp manual, not like the
descriptions of clauses above.
@end quotation

@clauseu{finish}
@deffn Clause finish

Stops the loop and runs the epilogue code.
@end deffn

@c for example:
@c 
@c @lisp
@c (iter (with answer = nil)
@c          (initially (make-a-mess))
@c          (for i from 1 to 10)
@c          (when (correct? i)
@c            (setq answer i)
@c            (finish))
@c          (finally (cleanup)))
@c @end lisp
@c 
@c this code will execute |cleanup| whether or not the test |(correct?
@c i)| ever succeeds.
@c the (more elegant) formulation,
@c @lisp
@c (iter (initially (make-a-mess))
@c          (for i from 1 to 10)
@c          (finding i such-that (correct? i))
@c          (finally (cleanup)))
@c @end lisp
@c would not execute |cleanup| if |(correct? i)| succeeded; it
@c would do an immediate return.

@clauseu{leave}
@deffn Clause leave @k{&optional} @v{value}

Immediately returns @var{value} (default @code{nil}) from the current
@iter{} form, skipping the epilogue code.  Equivalent to using
@code{return-from}.
@end deffn

@clauseu{next-iteration}
@deffn Clause next-iteration

Skips the remainder of the loop body and begins the next iteration of
the loop.
@end deffn

@clauseu{while}
@deffn Clause while @v{expr}

If @var{expr} ever evaluates to @code{nil}, the loop is terminated and
the epilogue code executed.  Equivalent to @code{(if (not @var{expr})
(finish))}.
@end deffn

@clauseu{until}
@deffn Clause until @v{expr}

Equivalent to @code{(if @var{expr} (finish))}.
@end deffn

@clauseu{if-first-time}
@deffn Clause if-first-time @v{then} @k{&optional} @v{else}

If this clause is being executed for the first time in this invocation
of the @iter{} form, then the @var{then} code is evaluated; otherwise
the @var{else} code is evaluated.

@code{(for @var{var} first @var{expr1} then @var{expr2})} is almost
equivalent to

@lisp
(if-first-time (dsetq @var{var} @var{expr1})
               (dsetq @var{var} @var{expr2}))
@end lisp

The only difference is that the @code{for} version makes @var{var}
available for use with @code{for@dots{} previous}.
@end deffn

@c ===================================================================
@node Predicates
@section Predicates

@quotation Compatibility Note
The clauses in this section were added in the twenty-first century and
not part of Jonathan Amsterdam's original design.
@end quotation

@clauseu{first-iteration-p}
@deffn Clause first-iteration-p

Returns @code{t} in the first iteration of the loop, otherwise @code{nil}.
@end deffn

@clauseu{first-time-p}
@deffn Clause first-time-p

Returns @code{t} the first time the expression is evaluated, and then
@code{nil} forever.  This clause comes handy when printing (optional)
elements separated by a comma:

@lisp
(iter (for el in '(nil 1 2 nil 3))
      (when el
        (unless (first-time-p)
          (princ ", "))
        (princ el)))
@print{} 1, 2, 3
@end lisp
@end deffn

@c ===================================================================
@node Code Placement
@section Code Placement

When fine control is desired over where code appears in a loop
generated by @iter{}, the following special clauses may be useful.
They are all subject to code-motion problems (see @ref{Problems with
Code Movement}).

@clauseu{initially}
@deffn Clause initially @k{&rest} @var{forms}

The lisp @var{forms} are placed in the prologue section of the loop,
where they are executed once, before the loop body is entered.
@end deffn

@clauseu{after-each}
@deffn Clause after-each @k{&rest} @v{forms}

The @var{forms} are placed at the end of the loop body, where they
are executed after each iteration.  Unlike the other clauses in this
section, @var{forms} may contain @iter{} clauses.
@end deffn

@clauseu{else}
@deffn Clause else @k{&rest} @v{forms}

The lisp @var{forms} are placed in the epilogue section of the loop,
where they are executed if this @code{else} clause is never met during
execution of the loop and the loop terminates normally.
@end deffn

@clauseu{finally}
@deffn Clause finally @k{&rest} @v{forms}

The lisp @var{forms} are placed in the epilogue section of the loop,
where they are executed after the loop has terminated normally.
@end deffn

@clauseu{finally-protected}
@deffn finally-protected @k{&rest} @v{forms}

The lisp @var{forms} are placed in the second form of an
@code{unwind-protect} outside the loop.  They are always executed
after the loop has terminated, regardless of how the termination
occurred.
@end deffn

@c ===================================================================
@node Other Features
@chapter Other Features

@section Multiple Accumulations

It is permitted to have more than one clause accumulate into the same
variable, as in the following:

@lisp
(iter (for i from 1 to 10)
      (collect i into nums)
      (collect (sqrt i) into nums)
      (finally (return nums)))
@end lisp

Clauses can only accumulate into the same variable if they are
compatible.  @code{collect}, @code{adjoining}, @code{appending},
@code{nconcing}, @code{unioning} and @code{nunioning} are compatible
with each other; @code{sum}, @code{multiply} and @code{counting} are
compatible; @code{always} and @code{never} are compatible;
@code{finding}@dots{} @code{such-that} is compatible with either
@code{thereis} or @code{always} and @code{never} when their defaults
match; and @code{maximize} and @code{minimize} clauses are compatible
only with other @code{maximize} and @code{minimize} clauses,
respectively.

@c note that the same variable ~cannot~ be both an accumulation
@c variable and an ordinary variable; there can be only one variable
@c with a given name within an @iter{} form.

@menu
* Named Blocks::                
* Destructuring::               
* On-line Help::                
* Parallel Binding and Stepping::  
@end menu

@c ===================================================================
@node Named Blocks
@section Named Blocks

Like Common Lisp @code{block}s, @iter{} forms can be given names.  The
name should be a single symbol, and it must be the first form in the
@iter{}.  The generated code behaves exactly like a named block; in
particular, @code{(return-from @var{name})} can be used to exit it:

@lisp
(iter fred
      (for i from 1 to 10)
      (iter barney
            (for j from i to 10)
            (if (> (* i j) 17)
                (return-from fred j))))
@end lisp

An @iter{} form that is not given a name is implicitly named
@code{nil}.

Sometimes one would like to write an expression in an inner @iter{}
form, but have it processed by an outer @iter{} form.  This is
possible with the @code{in} clause.

@clauseu{in}
@deffn Clause in @v{name} @k{&rest} @v{forms}

Evaluates @var{forms} as if they were part of the @iter{} form named
@var{name}.  In other words, @iter{} clauses are processed by the
@iter{} form named @var{name}, and not by any @iter{} forms that occur
inside @var{name}.

As an example, consider the problem of collecting a list of the
elements in a two-dimensional array.  The naive solution,
@lisp
(iter (for i below (array-dimension ar 0))
      (iter (for j below (array-dimension ar 1))
            (collect (aref ar i j))))
@end lisp
is wrong because the list created by the inner @iter{} is simply
ignored by the outer one.  But using @code{in} we can write:
@lisp
(iter outer (for i below (array-dimension ar 0))
      (iter (for j below (array-dimension ar 1))
            (in outer (collect (aref ar i j)))))
@end lisp
which has the desired result.
@end deffn

@c ===================================================================
@node Destructuring
@section Destructuring

In many places within @iter{} clauses where a variable is expected, a
list can be written instead.  In these cases, the value to be assigned
is @emph{destructured} according to the pattern described by the list.
As a simple example, the clause
@lisp
(for (key . item) in alist)
@end lisp
will result in @code{key} being set to the @code{car} of each element
in @code{alist}, and @code{item} being set to the @code{cdr}.  The
pattern list may be nested to arbitrary depth, and (as the example
shows) need not be terminated with @code{nil}; the only requirement is
that each leaf be a bindable symbol (or @code{nil}, in which case no
binding is generated for that piece of the structure).

Sometimes, you might like to do the equivalent of a
@code{multiple-value-setq} in a clause.  This ``multiple-value
destructuring'' can be expressed by writing @code{(values @var{pat_1}
@var{pat_2} @dots{})} for a destructuring pattern, as in

@lisp
(for (values (a . b) c d) = (three-valued-function ...))
@end lisp

Note that the @var{pat_i} can themselves be destructuring patterns
(though not multiple-value destructuring patterns).  You can't do
multiple-value destructuring in a @code{with} clause; instead wrap the
whole @iter{} form in a @code{multiple-value-bind}.

@quotation Rationale
There are subtle interactions between variable declarations and
evaluation order that make the correct implementation of
multiple-value destructuring in a @code{with} somewhat tricky.
@end quotation

The destructuring feature of @iter{} is available as a separate
mechanism, using the @code{dsetq} macro:

@itindex dsetq
@defmac dsetq @v{template} @v{expr}

Performs destructuring of @var{expr} using @var{template}.  May be
used outside of an @iter{} form.  Yields the primary value of
@var{expr}.
@end defmac

@c ===================================================================
@node On-line Help
@section On-line Help

There is a limited facility for on-line help, in the form of the
@code{display-iterate-clauses} function.

@itindex display-iterate-clauses
@defun display-iterate-clauses @k{&optional} @v{clause-spec}

Displays a list of @iter{} clauses.  If @var{clause-spec} is not
provided, all clauses are shown; if it is a symbol, all clauses
beginning with that symbol are shown; and if it is a list of symbols,
all clauses for which @var{clause-spec} is a prefix are shown.
@end defun

@c ===================================================================
@node Parallel Binding and Stepping
@section Parallel Binding and Stepping

The parallel binding and stepping of variables is a feature that
@iter{} does @emph{not} have.  This section attempts to provide a
rationale.

We say that two variables are bound @emph{in parallel} if neither
binding shadows the other.  This is the usual semantics of @code{let}
(as opposed to @code{let*}).  Similarly, we can say that iteration
variables are stepped in parallel if neither variable is updated
before the other, conceptually speaking; in other words, if the code
to update each variable can reference the old values of both
variables.

@code{loop} allows parallel binding of variables and parallel stepping
of driver variables.  My view is that if you are depending on the
serial/parallel distinction, you are doing something obscure.  If you
need to bind variables in parallel using @code{with}, then you must be
using a variable name that shadows a name in the existing lexical
environment.  Don't do that.  The most common use for parallel
stepping is to track the values of variables on the previous
iteration, but in fact this does not require parallel stepping at all;
the following will work:

@lisp
(iter (for current in list)
      (for prev previous current)
      @dots{})
@end lisp

@c ===================================================================
@node Types and Declarations
@chapter Types and Declarations

@section Discussion

Sometimes efficiency dictates that the types of variables be declared.
This type information needs to be communicated to @iter{} so it can
bind variables to appropriate values.  Furthermore, @iter{} must often
generate internal variables invisible to the user; there needs to be a
way for these to be declared.

As an example, consider this code, which will return the number of
odd elements in @code{number-list}:

@lisp
(iter (for el in number-list)
      (count (oddp el)))
@end lisp

In processing this form, @iter{} will create an internal variable, let
us call it @code{list17}, to hold the successive @code{cdr}s of
@code{number-list}, and will bind the variable to @code{number-list}.
It will also generate a default binding for @code{el}; only inside the
body of the loop will @code{el} be set to the @code{car} of
@code{list17}.  Finally, @iter{} will generate a variable, call it
@code{result}, to hold the result of the count, and will bind it to
zero.

When dealing with type declarations, @iter{} observes one simple rule:
@emph{it will never generate a declaration unless requested to do so}.
The reason is that such declarations might mask errors in compiled
code by avoiding error-checks; the resulting problems would be doubly
hard to track down because the declarations would be hidden from the
programmer.  Of course, a compiler might omit error-checks even in the
absence of declarations, though this behavior can usually be avoided,
e.g.@: by saying @code{(declaim (optimize (safety 3)))}.

So, the above @iter{} form will generate code with no declarations.
But say we wish to declare the types of @code{el} and the internal
variables @code{list17} and @code{result}.  How is this done?

Declaring the type of @code{el} is easy, since the programmer knows
the variable's name:

@lisp
(iter (for el in number-list)
      (declare (fixnum el))
      (counting (oddp el)))
@end lisp

@iter{} can read variable type declarations like this one.  Before
processing any clauses, it scans the entire top-level form for type
declarations and records the types, so that variable bindings can be
performed correctly.  In this case, @code{el} will be bound to zero
instead of @code{nil}.  Also, @iter{} collects all the top-level
declarations and puts them at the begining of the generated code, so
it is not necessary to place all declarations at the beginning of an
@iter{} form; instead, they can be written near the variables whose
types they declare.

Since @iter{} is not part of the compiler, it will not know
about declarations that occur outside an @iter{} form; these
declarations must be repeated inside the form.

Here is another way we could have declared the type of @code{el}:

@lisp
(iter (for (the fixnum el) in number-list)
      (counting (oddp el)))
@end lisp

@itindex the
@iter{} extends the Common Lisp @code{the} form to apply to variables
as well as value-producing forms; anywhere a variable is allowed---in
a @code{with} clause, as the iteration variable in a driver clause, as
the @code{into} argument of an accumulation clause, even inside a
destructuring template---you can write @code{(the @var{type}
@var{symbol})} instead.

There is one crucial difference between using a @code{the} form and
actually declaring the variable: explicit declarations are always
placed in the generated code, but type information from a @code{the}
form is not turned into an actual declaration unless you tell @iter{}
to do so using @code{iterate:declare-variables}.  See below.

Declaring the types of internal variables is harder than declaring the
types of explicitly mentioned variables, since their names are
unknown.  You do it by declaring @code{iterate:declare-variables}
somewhere inside the top level of the @iter{} form.  (This will also
generate declarations for variables declared using @code{the}.)
@iter{} does not provide much selectivity here: it's all or none.  And
unfortunately, since @iter{} is not privy to compiler information but
instead reads declarations itself, it will not hear if you
@code{(declaim (iterate:declare-variables))}.  Instead, set the
variable @code{iterate::*always-declare-variables*} to @code{t} at
compile-time, using @code{eval-when}.

To determine the appropriate types for internal variables, @iter{}
uses three sources of information:

@itemize
@item
Often, the particular clause dictates a certain type for a
variable; @iter{} will use this information when available.  In the
current example, the variable @code{list17} will be given the type
@code{list}, since that is the only type that makes sense; and the
variable @code{result} will be given the type @code{fixnum}, on the
assumption that you will not be counting high enough to need bignums.
You can override this assumption on @code{count}, @code{sum} and
@code{multiply} clauses (and their synonyms, @code{counting},
@code{summing} and @code{multiplying}) using the optional
@code{result-type} argument:

@lisp
(iter (declare (iterate:declare-variables))
      (for el in number-list)
      (count (oddp el) result-type integer))
@end lisp

Alterately, you can override it on any form which takes an optional
@code{into var} argument by declaring the type of @code{var} and
explicitly returning it:

@lisp
(iter (declare (iterate:declare-variables))
      (for el in number-list)
      (count (oddp el) into my-result)
      (declare (integer my-result))
      (finally (return my-result)))
@end lisp

Other examples of the type assumptions that @iter{} makes are: type
@code{list} for @code{into} variables of collection clauses; type
@code{list} for expressions that are to be destructured; type
@code{vector} for the variable holding the vector in a
@code{for@dots{} in-vector} clause, and similarly for @code{string}
and the @code{for@dots{} in-string} clause; and the
implementation-dependent type @code{(type-of array-dimension-limit)}
for the index and limit variables generated by sequence iteration
drivers like @code{for@dots{} in-vector} and @code{for@dots{}
in-string} (but not @code{for@dots{} in-sequence}, because it may be
used to iterate over a list).

@item
Sometimes, @iter{} will examine expressions and try to determine their
types in a simple-minded way.  If the expression is self-evaluating
(like a number, for instance), @iter{} knows that the expression's
type is the same as the type of the value it denotes, so it can use
that type.  If the expression is of the form @code{(the @var{type}
@var{expr})}, @iter{} is smart enough to extract @var{type} and use
it.  However, the current version of @iter{} does not examine
declarations of function result types or do any type inference.  It
will not determine, for example, that the type of @code{(+ 3 4)} is
@code{fixnum}, or even @code{number}.

@item
In some cases, the type of an internal variable should match the type
of some other variable.  For instance, @iter{} generates an internal
variable for @code{(f x)} in the clause @code{(for i from 1 to (f
x))}, and in the absence of other information will give it the same
type as @code{i}.  If, however, the expression had been written
@code{(the fixnum (f x))}, then @iter{} would have given the internal
variable the type @code{fixnum} regardless of @code{i}'s type.  The
type incompatibility errors that could arise in this situation are not
checked for.
@end itemize

Note that if you do declare @code{iterate:declare-variables}, then
@iter{} may declare user variables as well as internal ones if they do
not already have declarations, though only for variables that it
binds.  For instance, in this code:

@lisp
(iter (declare (iterate:declare-variables))
      (for i from 1 to 10)
      (collect i into var))
@end lisp

the variable @code{var} will be declared to be of type @code{list}.

@section Summary

@itindex declare-variables
@itindex *always-declare-variables*
@iter{} understands standard Common Lisp variable type declarations
that occur within an @iter{} form and will pass them through to the
generated code.  If the declaration @code{(iterate:declare-variables)}
appears at the top level of an @iter{} form, or if
@code{iterate::*always-declare-variables*} is non-@code{nil}, then
@iter{} will use the type information gleaned from user declarations,
self-evaluating expressions and @code{the} expressions, combined with
reasonable assumptions, to determine variable types and declare them.

@c ===================================================================
@node Problems with Code Movement
@chapter Problems with Code Movement

Some @iter{} clauses, or parts of clauses, result in code being moved
from the location of the clause to other parts of the loop.  Drivers
behave this way, as do code-placement clauses like @code{initially}
and @code{finally}.  When using these clauses, there is a danger of
writing an expression that makes sense in its apparent location but
will be invalid or have a different meaning in another location.  For
example:

@lisp
(iter (for i from 1 to 10)
      (let ((x 3))
        (initially (setq x 4))))
@end lisp

While it may appear that the @code{x} of @code{(initially (setq x 4))}
is the same as the @code{x} of @code{(let ((x 3)) @dots{}}, in fact
they are not: @code{initially} moves its code outside the loop body,
so @code{x} would refer to a global variable.  Here is another example
of the same problem:

@lisp
(iter (for i from 1 to 10)
      (let ((x 3))
        (collect i into x)))
@end lisp

If this code were executed, @code{collect} would create a binding for
its @code{x} at the top level of the @iter{} form that the @code{let}
will shadow.

Happily, @iter{} is smart enough to catch these errors; it walks all
problematical code to ensure that free variables are not bound inside
the loop body, and checks all variables it binds for the same problem.

However, some errors cannot be caught:

@lisp
(iter (with x = 3)
      (for el in list)
      (setq x 1)
      (reducing el by #'+ initial-value x))
@end lisp

@code{reducing} moves its @code{initial-value} argument to the
initialization part of the loop in order to produce more efficient
code.  Since @iter{} does not perform data-flow analysis, it cannot
determine that @code{x} is changed inside the loop; all it can
establish is that @code{x} is not bound internally.  Hence this code
will not signal an error and will use @math{3} as the initial value of
the reduction.

The following list summarizes all cases that are subject to these code
motion and variable-shadowing problems.

@itemize
@item
Any variable for which @iter{} creates a binding, including those used
in @code{with} and the @code{into} keyword of many clauses.

@item
The special clauses which place code: @code{initially},
@code{after-each}, @code{else}, @code{finally} and
@code{finally-protected}.

@item
The variables of a @code{next} or @code{do-next} form.

@item
The @code{initially} arguments of @code{for@dots{} initially@dots{}
then} and @code{for@dots{} previous}.

@item
The @code{then} argument of @code{for@dots{} initially@dots{} then}.

@item
The @code{initial-value} arguments of @code{reducing} and
@code{accumulate}.

@item
The @code{on-failure} argument of @code{finding@dots{} such-that}.
@end itemize

@c ===================================================================
@node Differences Between Iterate and Loop
@chapter Differences Between @code{Iterate} and @code{Loop}

@code{loop} contains a great deal of complexity which @iter{} tries to
avoid.  Hence many esoteric features of @code{loop} don't exist in
@iter{}.  Other features have been carried over, but in a cleaned-up
form.  And of course, many new features have been added; they are not
mentioned in this list.

@itemize
@item
@iter{}'s syntax is more Lisp-like than @code{loop}'s, having a higher
density of parens.

@item
The current implementation of @iter{}, unlike the standardised version
of @code{loop}, is extensible (see @ref{Rolling Your Own}).

@item
@code{loop} puts the updates of all driver variables at the top of the
loop; @iter{} leaves them where the driver clauses appear.  In
particular, @iter{} allows to place drivers after @code{while} clauses.

@item
While for the most part @iter{} clauses that resemble @code{loop}
clauses behave similarly, there are some differences.  For instance,
there is no @code{for@dots{} =@dots{} then} in @iter{}; instead use
@code{for@dots{} initially@dots{} then}.

@item
@code{loop} binds the variable @code{it} at certain times to allow
pseudo-English expressions like @code{when @var{expr} return it}.  In
@iter{}, you must bind @var{expr} to a variable yourself.  Note that
@code{when @var{expr} return it} is like @code{thereis @var{expr}}
except that the latter is an accumulation clause and therefore
competes with other accumulations (remember ``Multiple Accumulations''
in @ref{Other Features}).

@c repeat different behaviour of |always| clause here?

@item
@code{loop} has a special @code{return} clause, illustrated in the
previous item.  @iter{} doesn't need one, since an ordinary Lisp
@code{return} has the same effect.

@item
@code{loop} allows for parallel binding and stepping of iteration
variables.  @iter{} does not.  (See @ref{Parallel Binding and
Stepping}.)

@item
@code{loop} and @iter{} handle variable type declarations very
differently.  @code{loop} provides a special syntax for declaring
variable types, and does not examine declarations.  Moreover, the
standard implementation of @code{loop} will generate declarations when
none are requested.  @iter{} parses standard Common Lisp type
declarations, and will never declare a variable itself unless
declarations are specifically requested.
@end itemize

@c ===================================================================
@node Rolling Your Own
@chapter Rolling Your Own

@section Introduction

@iter{} is extensible---you can write new clauses that embody new
iteration patterns.  You might want to write a new driver clause for a
data structure of your own, or you might want to write a clause that
collects or manipulates elements in a way not provided by @iter{}.

This section describes how to write clauses for @iter{}.  Writing a
clause is like writing a macro.  In fact, writing a clause @emph{is}
writing a macro: since @iter{} code-walks its body and macroexpands,
you can add new abstractions to @iter{} with good old @code{defmacro}.

Actually, there are two extensions you can make to @iter{} that are
even easier than writing a macro.  They are adding a synonym for an
existing clause and defining a driver clause for an indexable
sequence.  These can be done with @code{defsynonym} and
@code{defclause-sequence}, respectively.  See @ref{Extensibility
Aids}.

The rest of this section explains how to write macros that expand into
@iter{} clauses.  Here's how you could add a simplified version of
@iter{}'s @code{multiply} clause, if @iter{} didn't already have one:

@lisp
(defmacro multiply (expr)
  `(reducing ,expr by #'* initial-value 1))
@end lisp

If you found yourself summing the square of an expression often, you
might want to write a macro for that.  A first cut might be

@lisp
(defmacro sum-of-squares (expr)
  `(sum (* ,expr ,expr)))
@end lisp

but if you are an experienced macro writer, you will realize that this
code will evaluate @var{expr} twice, which is probably a bad idea.  A
better version would use a temporary:

@lisp
(defmacro sum-of-squares (expr)
  (let ((temp (gensym)))
    `(let ((,temp ,expr))
       (sum (* ,temp ,temp)))))
@end lisp

Although this may seem complex, it is just the sort of thing you'd
have to go through to write any macro, which illustrates the point of
this section: if you can write macros, you can extend @iter{}.

Our macros don't use @iter{}'s keyword-argument syntax.  We could just
use keywords with @code{defmacro}, but we would still not be using
@iter{}'s clause indexing mechanism.  Unlike Lisp, which uses just the
first symbol of a form to determine what function to call, @iter{}
individuates clauses by the list of required keywords.  For instance,
@code{for@dots{} in} and @code{for@dots{} in-vector} are different
clauses implemented by distinct Lisp functions.

To buy into this indexing scheme, as well as the keyword-argument
syntax, use @code{defmacro-clause}:

@itindex defmacro-clause
@defmac defmacro-clause @v{arglist} @k{&body} @v{body}

Defines a new @iter{} clause.  @var{arglist} is a list of symbols
which are alternating keywords and arguments.  @code{&optional} may be
used, and the list may be terminated by @code{&sequence}.  @var{body}
is an ordinary macro body, as with @code{defmacro}.  If the first form
of @var{body} is a string, it is considered a documentation string and
will be shown by
@code{display-iterate-clauses}.  @code{defmacro-clause} will signal an
error if defining the clause would result in an ambiguity.  E.g.@: you
cannot define the clause @code{for@dots{} from} because there would be
no way to distinguish it from a use of the @code{for} clause with
optional keyword @code{from}.
@end defmac

Here is @code{multiply} using @code{defmacro-clause}.  The keywords
are capitalized for readability.

@lisp
(defmacro-clause (MULTIPLY expr &optional INTO var)
  `(reducing ,expr by #'* into ,var initial-value 1))
@end lisp

You don't have to worry about the case when @code{var} is not
supplied; for any clause with an @code{into} keyword, saying
@code{into nil} is equivalent to omitting the @code{into} entirely.

As another, more extended example, consider the fairly common
iteration pattern that involves finding the sequence element that
maximizes (or minimizes) some function.  @iter{} provides this as
@code{finding@dots{} maximizing}, but it's instructive to see how to
write it.  Here, in pseudocode, is how you might write such a loop for
maximizing a function F:

@example
@r{set variable MAX-VAL to NIL;}
@r{set variable WINNER to NIL;}
@r{for each element EL in the sequence}
    @r{if MAX-VAL is NIL or F(EL) > MAX-VAL then}
        @r{set MAX-VAL to F(EL);}
        @r{set WINNER to EL;}
    @r{end if;}
@r{end for;}
@r{return WINNER.}
@end example

Here is the macro:

@lisp
(defmacro-clause (FINDING expr MAXIMIZING func &optional INTO var)
  "Simple FINDING... MAXIMIZING implementation"
  (let ((max-val (gensym "MAX-VAL"))
        (temp1 (gensym "EL"))
        (temp2 (gensym "VAL"))
        (winner (or var iterate::*result-var*)))
    `(progn 
       (with ,max-val = nil)
       (with ,winner = nil)
       (let* ((,temp1 ,expr)
              (,temp2 (funcall ,func ,temp1)))
         (when (or (null ,max-val) (> ,temp2 ,max-val))
           (setq ,winner ,temp1 ,max-val ,temp2))))))
@end lisp

@c This example differs from the built-in finder:
@c - The built-in one specifies the clause's value (el so far)
@c   (trivial to implement: add ,winner at end of progn)
@c - The built-in one accepts an (el max-val) tuple var spec.
@c - Influence of (the type var) on type declarations

Note that if no @code{into} variable is supplied, we use
@code{iterate::*result-var*}, which contains the internal variable
into which all clauses place their results.  If this variable is bound
by some clause, then @iter{} will return its value automatically;
otherwise, @code{nil} will be returned.

@c The original example had four flaws:
@c - ,expr and ,func occured twice in expansion
@c - (finally (leave ,winner)) breaks because FINALLY does not walk
@c   its forms, so LEAVE does not work inside FINALLY.
@c - Do not use (finally (return ,winner)) either, as that would
@c   always return winner, even in case of ... INTO nil.
@c - Value of clause as form undefined, unlike all built-in clauses

@menu
* Writing Drivers::             
* Extensibility Aids::          
* Subtleties::                  
@end menu

@c ===================================================================
@node Writing Drivers
@section Writing Drivers

In principle, drivers can be implemented just as easily as other
@iter{} clauses.  In practice, they are a little harder to get right.
As an example, consider writing a driver that iterates over all the
elements of a vector, ignoring its fill-pointer.  @code{for@dots{}
in-vector} won't work for this, because it observes the fill-pointer.
It's necessary to use @code{array-dimension} instead of @code{length}
to obtain the size of the vector.  Here is one approach:

@lisp
(defmacro-clause (FOR var IN-WHOLE-VECTOR v)
  "All the elements of a vector (disregards fill-pointer)"
  (let ((vect (gensym))
        (index (gensym)))
    `(progn
       (with ,vect = ,v)
       (for ,index from 0 below (array-dimension ,vect 0))
       (for ,var = (aref ,vect ,index)))))
@end lisp

Note that we immediately put @code{v} in a variable, in case it is an
expression.  Again, this is just good Lisp macrology.  It also has a
subtle effect on the semantics of the driver: @code{v} is evaluated
only once, at the beginning of the loop, so changes to @code{v} in the
loop have no effect on the driver.  Similarly, the bounds for
numerical iteration e.g.@: the above @code{array-dimension} are also
evaluated once only.  This is how all of @iter{}'s drivers work.

There is an important point concerning the @code{progn} in this code.
We need the @code{progn}, of course, because we are returning several
forms, one of which is a driver.  But @iter{} drivers must occur at
top-level.  Is this code in error?  No, because @emph{top-level} is
defined in @iter{} to include forms inside a @code{progn}.  This is
just the definition of top-level that Common Lisp uses, and for the
same reason: to allow macros to return multiple forms at top-level.

While our @code{for@dots{} in-whole-vector} clause will work, it is
not ideal.  In particular, it does not support generating.  Do do so,
we need to use @code{for@dots{} next} or @code{for@dots{} do-next}.
The job is simplified by the @code{defmacro-driver} macro.

@itindex defmacro-driver
@defmac defmacro-driver @v{arglist} @k{&body} @v{body}

Defines a driver clause in both the @code{for} and @code{generate}
forms, and provides a parameter @code{generate} which @var{body} can
examine to determine how it was invoked.  @var{arglist} is as in
@code{defmacro-clause}, and should begin with the symbol @code{for}.
@end defmac

With @code{defmacro-driver}, our driver looks like this:

@lisp
(defmacro-driver (FOR var IN-WHOLE-VECTOR v)
  "All the elements of a vector (disregards fill-pointer)"
   (let ((vect (gensym))
         (end (gensym))
         (index (gensym))
         (kwd (if generate 'generate 'for)))
     `(progn
        (with ,vect = ,v)
        (with ,end = (array-dimension ,vect 0))
        (with ,index = -1)
        (,kwd ,var next (progn (incf ,index)
                               (if (>= ,index ,end) (terminate))
                               (aref ,vect ,index))))))
@end lisp

We are still missing one thing: the @code{&sequence} keywords.
We can get them easily enough, by writing

@lisp
(defmacro-driver (FOR var IN-WHOLE-VECTOR v &sequence) 
  @dots{})
@end lisp

We can now refer to parameters @code{from}, @code{to}, @code{by},
etc.@: which contain either the values for the corresponding keyword, or
@code{nil} if the keyword was not supplied.  Implementing the right
code for these keywords is cumbersome but not difficult; it is left as
an exercise.  But before you begin, see @code{defclause-sequence}
below for an easier way.

@c ===================================================================
@node Extensibility Aids
@section Extensibility Aids

This section documents assorted features that may be of use in
extending @iter{}.

@itindex *result-var*
@defvr {Unexported Variable} *result-var*

Holds the variable that is used to return a value as a result of the
@iter{} form.  You may examine this and use it in a @code{with}
clause, but you should not change it.
@end defvr

@itindex defsynonym
@defmac defsynonym @v{syn} @v{word}

Makes @var{syn} a synonym for the existing @iter{} keyword @var{word}.
Only the first word in each clause can have synonyms.
@end defmac

@itindex defclause-sequence
@defmac defclause-sequence @v{element-name} @v{index-name} @k{&key} @
                           @v{access-fn} @v{size-fn} @v{sequence-type} @
                           @v{element-type} @v{element-doc-string} @
                           @v{index-doc-string}
  
Provides a simple way to define sequence clauses.  Generates two
clauses, one for iterating over the sequence's elements, the other for
iterating over its indices.  The first symbol of both clauses will
have print-name @code{for}.  @var{element-name} and @var{index-name}
should be symbols.  @var{element-name} is the second keyword of the
element iterator (typically of the form
@code{in-@var{sequence-type}}), and @var{index-name} is the second
keyword of the index-iterator (typically of the form
@code{index-of-@var{sequence-type}}).  Either name may be @code{nil},
in which case the corresponding clause is not defined.  If both
symbols are supplied, they should be in the same package.  The
@code{for} that begins the clauses will be in this package.

@var{access-fn} is the function to be used to access elements of the
sequence in the element iterator.  The function should take two
arguments, a sequence and an index, and return the appropriate
element.  @var{size-fn} should denote a function of one argument, a
sequence, that returns its size.  Both @var{access-fn} and
@var{size-fn} are required for the element iterator, but only
@var{size-fn} is needed for the index iterator.

The @var{sequence-type} and @var{element-type} keywords are used to
suggest types for the variables used to hold the sequence and the
sequence elements, respectively.  The usual rules about @iter{}'s
treatment of variable type declarations apply (see @ref{Types and
Declarations}).

@var{element-doc-string} and @var{index-doc-string} are the
documentation strings, for use with @code{display-iterate-clauses}.

The generated element-iterator performs destructuring on the element
variable.
@end defmac

As an example, the above @code{for@dots{} in-whole-vector} example
could have been written:

@lisp
(defclause-sequence IN-WHOLE-VECTOR INDEX-OF-WHOLE-VECTOR
  :access-fn 'aref
  :size-fn (lambda (v) (array-dimension v 0))
  :sequence-type 'vector
  :element-type t
  :element-doc-string "Elements of a vector, disregarding fill-pointer"
  :index-doc-string  "Indices of vector, disregarding fill-pointer")
@end lisp

@c ===================================================================
@node Subtleties
@section Subtleties

There are some subtleties to be aware of when writing @iter{} clauses.
First, the code returned by your macros may be @code{nconc}'ed into a
list, so you should always returned freshly consed lists, rather than
constants.  Second, @iter{} matches clauses by using @code{eq} on the
first symbol and @code{string=} on the subsequent ones, so the package
of the first symbol of a clause is relevant.  All of the clauses in
this manual have their first word in the @iter{} package.  You can use
the package system in the usual way to shadow @iter{} clauses without
replacing them.

@c say more here, about the badness that only the first word of a
@c clause is packagey.

@c ===================================================================
@node Non-portable Extensions to Iterate (Contribs)
@chapter Non-portable Extensions to Iterate (Contribs)

Currently, there is only one non-portable extension to iterate in the
distribution: @code{iterate-pg}.  If you have made an extension that
depends on non-portable features, feel free to send them to
the @iter{} project team for inclusion in the iterate distribution.

@section An SQL Query Driver for Iterate

The pg package by Eric Marsden (see @url{http://cliki.net/pg})
provides an interface to the PostgreSQL database.  Using the
@code{in-relation} driver, it is possible to handle the results of SQL
queries with @iter{}.

This usage example should give you an idea of how to use it:

@lisp
(pg:with-pg-connection (c "somedb" "someuser")
  (iter (for (impl version date) in-relation "select * from version"
                                 on-connection *dbconn*)
        (collect version)))
@end lisp

The distribution now contains an @file{iterate.asd} system definition
file for the @iter{} package.
To use the extension via @acronym{ASDF, Another System Definition
Facility}, simply make your system depend on the @code{iterate-pg}
system instead of the @code{iterate} system.  To load it manually,
use:

@lisp
(asdf:oos 'asdf:load-op :iterate-pg)
@end lisp

@c ===================================================================
@node Obtaining Iterate
@chapter Obtaining @code{Iterate}

@iter{} has been successfully ported to most implementations that
purport to conform to ANSI CL.  Since 2006, source and project
information is available from
@url{http://common-lisp.net/project/iterate/}.  The mailing list for
all purposes is @email{iterate-devel@@common-lisp.net}, but you need
to subscribe to it before posting.

The source file was split into two files in 2003: @file{package.lisp}
contains the package definition, @file{iterate.lisp} the main code.
Other files in the distribution contain user contributions, test cases
and documentation.

@iter{} resides in the @code{iterate} package (nickname @code{iter}).
Just say @code{(use-package :iterate)} to make all the necessary
symbols available.  If a symbol is not exported, it appears in this
manual with an ``@code{iterate::}'' prefix.

The regression test suite in @file{iterate-test.lisp}, based on
@acronym{MIT}'s @code{RT} package, contains many examples.

@quotation Note
The rest of this chapter serves history.
@end quotation

@iter{} currently runs on Lisp Machines, and on HP's, Sun3's and
Sparcstations under Lucid.  @iter{} source and binaries are available
at the @acronym{MIT} @acronym{AI} Lab in the subdirectories of
@file{/src/local/lisplib/}.
The source file, @code{iterate.lisp}, is also available for anonymous
FTP in the directory @file{/com/ftp/pub/} on the machine
@code{TRIX.AI.MIT.EDU} (Internet number 128.52.32.6).  If you are
unable to obtain @code{iterate} in one of these ways, send mail to
@email{jba@@ai.mit.edu} and I will send you the source file.

Send bug reports to @email{bug-iterate@@ai.mit.edu}.  The
@code{info-iterate} mailing list will have notices of changes and
problems; to have yourself added, send mail to
@email{info-iterate-request@@ai.mit.edu}.

@c ===================================================================
@node Acknowledgements
@chapter Acknowledgements

Richard Waters provided invaluable criticism which spurred me to
improve @iter{} greatly.  As early users, David Clemens, Oren Etzioni
and Jeff Siskind helped ferret out many bugs.

Thanks to Andreas Fuch, J@"org H@"ohle and Attila Lendvai, who more
than a decade after the original release, ported the code to ANSI CL
and fixed long-standing bugs.

@c ===================================================================
@node Don't Loop Iterate
@appendix Don't Loop, Iterate

@quotation Note
This appendix is a Texinfo conversion performed by Lu@'{@dotless{i}}s
Oliveira of Jonathan Amsterdam's Working Paper 324, MIT AI Lab
entitled ``Don't Loop, Iterate.''
@end quotation

@section Introduction

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 @emph{iterate} in Lisp.  Now, some are happy
to map their way about, whether for real with @code{mapcar} and
friends, or with the make-believe of Series; others are so satisfied
with @code{do} it's a wonder they're not C hackers.@footnote{Hey,
don't get mad---I'll be much more polite later, when the real paper
starts.}  Still others have gotten by with @code{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 @emph{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 @iter{}, that
provides the power and convenient abstractions of @code{loop} but in a
more syntactically palatable way.  @code{iter} also has many features
that @code{loop} lacks, like generators and better support for nested
loops.  @iter{} generates inline code, so it's more efficient than
using the higher-order function approach.  And @iter{} 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.

@c \iter\ is fully documented in AI Lab Memo No.@: 1236, \iman.

@section More about @iter{}

A Common Lisp programmer who wonders what's lacking with present-day
iteration features would do well to consider @code{setf}.  Of course,
@code{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
@code{setf} methods very easily, so that @code{setf} will work with
new forms.  @code{setf} is also efficient, turning into code that's as
good as anyone could write by hand.  Arguably, @code{setf} provides a
nice abstraction: it allows you to view value-returning forms, like
@code{(car @dots{})} or @code{(get @dots{})} as locations that can be
stored into.  Finally and most obviously, @code{setf} @emph{looks}
like Lisp; it's got a syntax right out of @code{setq}.

@iter{} attempts to provide all of these properties.  Here is a simple
use of @iter{} that returns all the elements of @code{num-list} that
are greater than three:

@lisp
(iterate (for el in num-list)
         (when (> el 3)
           (collect el)))
@end lisp

An @iter{} form consists of the symbol @iter{} followed by some Lisp
forms.  Any legal Lisp form is allowed, as well as certain forms that
@iter{} treats specially, called @emph{clauses}.  @code{for@dots{}in}
and @code{collect} are the two clauses in the above example.  An
@iter{} clause can appear anywhere a Lisp form can appear; @iter{}
walks its body, looking inside every form, processing @iter{} clauses
when it finds them.  It even expands macros, so you can write macros
that contain @iter{} clauses.  Almost all clauses use the syntax of
function keyword-argument lists: alternating keywords and arguments.
@iter{} keywords don't require a preceding colon, but you can use one
if you like.

@iter{} provides many convenient iteration abstractions, most of them
familiar to @code{loop} users.  Iteration-driving clauses (those
beginning with @code{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
extra flavor.

To sum a list of numbers:

@lisp
(iterate (for i in list)
         (sum i))
@end lisp

To find the length of the shortest element in a list:

@lisp
(iterate (for el in list)
         (minimize (length el)))
@end lisp

To find the shortest element in a list:

@lisp
(iterate (for el in list)
         (finding el minimizing (length el)))
@end lisp

To return @code{t} only if every other element of a list is odd:

@lisp
(iterate (for els on list by #'cddr)
         (always (oddp (car els))))
@end lisp

To split an association list into two separate lists (this example
uses @iter{}'s ability to do destructuring):

@lisp
(iterate (for (key . item) in alist)
         (collect key into keys)
         (collect item into items)
         (finally (return (values keys items))))
@end lisp

@section Comparisons With Other Iteration Methods

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 @iter{} is a
``better'' way to iterate than other methods.  I would, however, like
to examine the options, and explain why I prefer @iter{} to its
competitors.

@subsection @code{do}, @code{dotimes} and @code{dolist}

The @code{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
@code{dotimes} and @code{dolist}.

@code{do}'s major problem is that it provides no abstraction.  For
example, collection is typically handled by binding a variable to
@code{nil}, pushing elements onto the variable, and @code{nreverse}ing
the result before returning it.  Such a common iteration pattern
should be easier to write.  (It is, using @code{mapcar}---but see
below.)

Another problem with @code{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
``until.''

Despite its flaws, @code{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.

@subsection Tail Recursion
@c FIXME: removed citation due to laziness

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.

@subsection High-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
built-ins, like @code{map} and @code{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
explicitly.

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
@code{dotimes}---but then it becomes very messy to express double
iterations where one driver is over integers.  Multiple iteration is
easy in @iter{}, as illustrated by the following example, which creates
an alist of list elements and their positions:

@lisp
(iterate (for el in list)
         (for i from 0)
         (collect (cons el i)))
@end lisp

@subsection Streams and Generators

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 @emph{generator} is
a procedure that returns the next element in the iteration each time
it is called.  A @emph{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:

@lisp
(defun tree-leaves (tree)
  (if (atom tree)
      (stream-cons tree empty-stream)
      (stream-append (tree-leaves (car tree)) 
                     (tree-leaves (cdr tree)))))
@end lisp

Although @code{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 @code{stream-car}, which will
yield the (already computed) first leaf of the tree, or with
@code{stream-cdr}, which will initiate computation of the next leaf.

Such a computation would be cumbersome to write using @iter{}, 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 @iter{} 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 @iter{} @code{generate}
keyword in place of @code{for} and the special clause @code{next}:

@lisp
(iterate (for el in list)
         (generate i from 1)
         (if el
             (collect (cons el (next i)))))
@end lisp

Using @code{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 @code{next} clause
is executed.  This ability to obtain values on demand greatly
increases @iter{}'s power.  Here, @code{el} is set to the next element
of the list on each iteration, as usual; but @code{i} is set only when
@code{(next i)} is executed.

@subsection Series

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.  @iter{} 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.

@subsection @code{Prog} and @code{Go}

Oh, don't be silly.

@subsection @code{Loop}

@code{loop} is the iteration construct most similar to @iter{} in
appearance.  @code{loop} is a macro written originally for MacLisp and
in widespread use [Loop].  It has been adopted as part of Common Lisp.
@code{loop} provides high-level iteration with abstractions for
collecting, summing, maximizing and so on.  Recall our first @iter{}
example:

@lisp
(iterate (for el in num-list)
         (when (> el 3)
           (collect el)))
@end lisp

Expressed with @code{loop}, it would read

@lisp
(loop for el in list
      when (> el 3)
        collect el)
@end lisp

The similarity between the two macros should immediately be apparent.
Most of @iter{}'s clauses were borrowed from @code{loop}.  But
compared to @iter{}, @code{loop} has a paucity of parens.  Though
touted as more readable than heavily-parenthesized code, @code{loop}'s
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 @code{loop} clauses cannot
appear inside Lisp forms and macros cannot expand to pieces of
@code{loop}.  And Sixth, pretty-printers and indenters that don't know
about @code{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 @code{loop}.  The syntax of @iter{} was
designed to keep parens to a minimum, but conform close enough to Lisp
so as not to confuse code-display tools.  Gnu Emacs indents @iter{}
reasonably with no modifications.

Indenting is a mere annoyance; @code{loop}'s lack of extensibility is
a more serious problem.  The original @code{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 @iter{} by

@lisp
(iterate (for el in list)
         (sum el))
@end lisp

and in @code{loop} with

@lisp
(loop for el in list
      sum el)
@end lisp

But now, say that you wished to compute the sum of the square roots of
the elements.  You could of course write, in either @code{loop} or
@iter{},

@lisp
(iterate (for el in list)
         (sum (sqrt el)))
@end lisp

But perhaps you find yourself writing such loops often enough to make
it worthwhile to create a new abstraction.  There is nothing you can
do in @code{loop}, but in @iter{} you could simply write a macro:

@lisp
(defmacro (sum-of-sqrts expr &optional into-var)
  `(sum (sqrt ,expr) into ,into-var))
@end lisp

@code{sum-of-sqrts} is a perfectly ordinary Lisp macro.  Since @iter{}
expands all macros and processes the results, @code{(sum-of-sqrts el)}
will behave exactly as if we'd written @code{(sum (sqrt el))}.

There's also a way to define macros that use @iter{}'s clause syntax.
@c removed citation again

@c Just to beat a dead horse, I'd like to point out that there's no
@c way to define {\lisp for...maximizing} in \looP.\footnote{In fact,
@c it was in part the frustration of knowing that \looP\ could
@c generate code to maximize a value, but could not be easily altered
@c to supply the element associated with that maximum, that prompted
@c me to write \iter.}

@section Implementation

A Common Lisp implementation of @iter{} 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.
@c See \iman\ for details.

@section Conclusion

Iteration is a matter of taste.  I find @iter{} 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 @iter{}---look before you
@code{loop}.  If you're already using @code{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 @code{loop}---@iter{}.

@section Acknowledgments

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 @iter{}.  Alan Bawden, Sundar
Narasimhan, and Jerry Roylance also provided useful comments.  David
Clemens and Oren Etzioni shared with me the joys of beta-testing.

@section Bibliography

@itemize
@item
[SchemeBook] Abelson, Harold and Gerald Jay Sussman.  @emph{Structure
and Interpretation of Computer Programs.} Cambridge, MA: The MIT
Press, 1985.

@item
[Loop] ``The loop Iteration Macro.'' In @emph{Symbolics Common
Lisp---Language Concepts}, manual 2A of the Symbolics documentation,
pp.@: 541--567.

@item
[CLM] Steele, Guy L@.  @emph{Common Lisp: The Language}.  Bedford, MA:
Digital Press, 1984.

@item
[Series] Waters, Richard C@.  @emph{Optimization of Series Expressions:
Part I: User's Manual for the Series Macro Package}.  MIT AI Lab Memo
No.@: 1082.
@end itemize

@c ===================================================================
@node Comprehensive Index
@unnumbered Index
@printindex cp

@bye