/ 
CPS-0.02
River stage two • 3 direct dependents • 10 total dependents
/ CPS

NAME

CPS - flow control structures in Continuation-Passing Style

OVERVIEW

The functions in this module implement or assist the writing of programs, or parts of them, in Continuation Passing Style (CPS). Briefly, CPS is a style of writing code where the normal call/return mechanism is replaced by explicit "continuations", values passed in to functions which they should invoke, to implement return behaviour. For more detail on CPS, see the SEE ALSO section.

What this module implements is not in fact true CPS, as Perl does not natively support the idea of a real continuation (such as is created by a co-routine). Furthermore, for CPS to be efficient in languages that natively support it, their runtimes typically implement a lot of optimisation of CPS code, which the Perl interpreter would be unable to perform. Instead, CODE references are passed around to stand in their place. While not particularly useful for most regular cases, this becomes very useful whenever some form of asynchronous or event-based programming is being used. Continuations passed in to the body function of a control structure can be stored in the event handlers of the asynchronous or event-driven framework, so that when they are invoked later, the code continues, eventually arriving at its final answer at some point in the future.

In order for these examples to make sense, a fictional and simple asynchronisation framework has been invented. The exact details of operation should not be important, as it simply stands to illustrate the point. I hope its general intention should be obvious. :)

read_stdin_line( \&on_line ); # wait on a line from STDIN, then pass it
                              # to the handler function

SYNOPSIS

use CPS qw( kwhile );

kwhile( sub {
   my ( $knext, $klast ) = @_;

   print "Enter a number, or q to quit: ";

   read_stdin_line( sub {
      my ( $first ) = @_;
      chomp $first;

      return $klast->() if $first eq "q";

      print "Enter a second number: ";

      read_stdin_line( sub {
         my ( $second ) = @_;

         print "The sum is " . ( $first + $second ) . "\n";

         $knext->();
      } );
   } );
},
sub { exit }
);

FUNCTIONS

In all of the following functions, the \&body function can provide results by invoking its continuation / one of its continuations, either synchronously or asynchronously at some point later (via some event handling or other mechanism); the next invocation of \&body will not take place until the previous one exits if it is done synchronously.

They all take the prefix k before the name of the regular perl keyword or function they aim to replace. It is common in CPS code in other languages, such as Scheme or Haskell, to store a continuation in a variable called k. This convention is followed here.

kwhile( \&body, $k )

CPS version of perl's while loop. Repeatedly calls the body code until it indicates the end of the loop, then invoke $k.

$body->( $knext, $klast )
   $knext->()
   $klast->()

$k->()

If $knext is invoked, the body will be called again. If $klast is invoked, the continuation $k is invoked.

kforeach( \@items, \&body, $k )

CPS version of perl's foreach loop. Calls the body code once for each element in @items, until either the items are exhausted or the body invokes its $klast continuation, then invoke $k.

$body->( $item, $knext, $klast )
   $knext->()
   $klast->()

$k->()

kmap( \@items, \&body, $k )

CPS version of perl's map statement. Calls the body code once for each element in @items, capturing the list of values the body passes into its continuation. When the items are exhausted, $k is invoked and passed a list of all the collected values.

$body->( $item, $kret )
   $kret->( @items_out )

$k->( @all_items_out )

kgrep( \@items, \&body, $k )

CPS version of perl's grep statement. Calls the body code once for each element in @items, capturing those elements where the body's continuation was invoked with a true value. When the items are exhausted, $k is invoked and passed a list of the subset of @items which were selected.

$body->( $item, $kret )
   $kret->( $select )

$k->( @chosen_items )

kfoldl( \@items, \&body, $k )

CPS version of List::Util::reduce, which collapses (or "folds") a list of values down to a single scalar, by successively accumulating values together.

If @items is empty, invokes $k immediately, passing in undef.

If @items contains a single value, invokes $k immediately, passing in just that single value.

Otherwise, initialises an accumulator variable with the first value in @items, then for each additional item, invokes the body passing in the accumulator and the next item, storing back into the accumulator the value that body passed to its continuation. When the @items are exhausted, it invokes $k, passing in the final value of the accumulator.

$body->( $acc, $item, $kret )
   $kret->( $new_acc )

$k->( $final_acc )

Technically, this is not a true Scheme/Haskell-style foldl, as it does not take an initial value. (It is what Haskell calls foldl1.) However, if such an initial value is required, this can be provided by

kfoldl( [ $initial, @items ], \&body, $k )

kfoldr( \@items, \&body, $k )

A right-associative version of kfoldl(). Where kfoldl() starts with the first two elements in @items and works forward, kfoldr() starts with the last two and works backward.

$body->( $item, $acc, $kret )
   $kret->( $new_acc )

$k->( $final_acc )

As before, an initial value can be provided by modifying the @items array, though note it has to be last this time:

kfoldr( [ @items, $initial ], \&body, $k )

kgenerate( $seed, \&body, $k )

An inverse operation to kfoldl(); turns a single scalar into a list of items. Repeatedly calls the body code, capturing the values it generates, until it indicates the end of the loop, then invoke $k with the collected values.

$body->( $seed, $kmore, $kdone )
   $kmore->( $new_seed, @items )
   $kdone->( @items )

$k->( @all_items )

With each iteration, the body is invoked and passed the current $seed value and two continuations, $kmore and $kdone. If $kmore is invoked, the passed items, if any, are appended to the eventual result list. The body is then re-invoked with the new $seed value. If $klast is invoked, the passed items, if any, are appended to the return list, then the entire list is passed to $k.

CPS UTILITIES

These function names do not begin with k because they are not themselves CPS primatives, but may be useful in CPS-oriented code.

$kfunc = liftk { BLOCK }

$kfunc = liftk( \&func )

Returns a new CODE reference to a CPS-wrapped version of the code block or passed CODE reference. When $kfunc is invoked, the function &func is called in list context, being passed all the arguments given to $kfunc apart from the last, expected to be its continuation. When &func returns, the result is passed into the continuation.

$kfunc->( @func_args, $k )
   $k->( @func_ret )

The following are equivalent

print func( 1, 2, 3 );

my $kfunc = liftk( \&func );
$kfunc->( 1, 2, 3, sub { print @_ } );

Note that the returned wrapper function only has one continuation slot in its arguments. It therefore cannot be used as the body for kwhile(), kforeach() or kgenerate(), because these pass two continuations. There does not exist a "natural" way to lift a normal call/return function into a CPS function which requires more than one continuation, because there is no way to distinguish the different named returns.

EXAMPLES

The following aren't necessarily examples of code which would be found in real programs, but instead, demonstrations of how to use the above functions as ways of controlling program flow.

Without dragging in large amount of detail on an asynchronous or event-driven framework, it is difficult to give a useful example of behaviour that CPS allows that couldn't be done just as easily without. Nevertheless, I hope the following examples will be useful to demonstrate use of the above functions, in a way which hints at their use in a real program.

Implementing join() using kfoldl()

use CPS qw( kfoldl );

my @words = qw( My message here );

kfoldl(
   \@words,
   sub {
      my ( $left, $right, $k ) = @_;

      $k->( "$left $right" );
   },
   sub {
      my ( $str ) = @_;

      print "Joined up words: $str\n";
   }
);

Implementing split() using kgenerate()

The following program illustrates the way that kgenerate() can split a string, in a reverse way to the way kfoldl() can join it.

use CPS qw( kgenerate );

my $str = "My message here";

kgenerate(
   $str,
   sub {
      my ( $s, $kmore, $kdone ) = @_;

      if( $s =~ s/^(.*?) // ) {
         return $kmore->( $s, $1 );
      }
      else {
         return $kdone->( $s );
      }
   },
   sub {
      my @words = @_;
      print "Words in message:\n";
      print "$_\n" for @words;
   }
);

Generating Prime Numbers

While the design of kgenerate() is symmetric to kfoldl(), the seed value doesn't have to be successively broken apart into pieces. Another valid use for it may be storing intermediate values in computation, such as in this example, storing a list of known primes, to help generate the next one:

use CPS qw( kgenerate );

kgenerate(
   [ 2, 3 ],
   sub {
      my ( $vals, $kmore, $kdone ) = @_;

      return $kdone->() if @$vals >= 50;

      PRIME: for( my $n = $vals->[-1] + 2; ; $n += 2 ) {
         $n % $_ == 0 and next PRIME for @$vals;

         push @$vals, $n;
         return $kmore->( $vals, $n );
      }
   },
   sub {
      my @primes = ( 2, 3, @_ );
      print "Primes are @primes\n";
   }
);

Forward-reading Program Flow

One side benefit of the CPS control-flow methods which is unassociated with asynchronous operation, is that the flow of data reads in a more natural left-to-right direction, instead of the right-to-left flow in functional style. Compare

sub square { $_ * $_ }
sub add { $a + $b }

print reduce( \&add, map( square, primes(10) ) );

(because map is a language builtin but reduce is a function with (&) prototype, it has a different way to pass in the named functions)

with

my $ksquare = liftk { $_[0] * $_[0] };
my $kadd = liftk { $_[0] + $_[1] };

kprimes 10, sub {
   kmap \@_, $ksquare, sub {
      kfoldl \@_, $kadd, sub {
         print $_[0];
      }
   }
};

This translates roughly to a functional vs imperative way to describe the problem:

Print the sum of the squares of the first 10 primes.

Take the first 10 primes. Square them. Sum them. Print.

Admittedly the closure creation somewhat clouds the point in this small example, but in a larger example, the real problem-solving logic would be larger, and stand out more clearly against the background boilerplate.

SEE ALSO

AUTHOR

Paul Evans <leonerd@leonerd.org.uk>