I'll provide some examples, but in order to appreciate them you must
understand the library of tiny FP functions that form the core
vocabulary of FP programming. I have enclosed a small subset of that
vocabulary below, mostly drawn directly from the Haskell Prelude.
I have tried to select examples that can be shown using only this
subset.
Keep in mind that the following code is probably too small, too simple,
and too limited to be useful for drawing general conclusions. The best
you can hope for is to get a taste. To draw inferences about the
whole cuisine from this tiny sampling would be a mistake.
First some library functions:
package ToolBox;
use AutoCurry ':all';
use List::Util qw( min );
# zips
sub zip {
my $len = min( map scalar @$_, @_ );
map [ do { my $i=$_; map $_>[$i], @_ } ], 0..$len1;
}
sub zip_with {
my $f = shift;
map $f>(@$_), zip(@_);
}
# folds & scans
sub foldl {
my $f = shift;
my $z = shift;
$z = $f>($z, $_) for @_;
$z;
}
# (other folds and scans omitted)
# functional glue: curry and compose
sub _compose2 {
my ($f, $g) = @_;
sub { $f>($g>(@_)) }
}
sub compose {
foldl( \&_compose2, @_ );
}
sub pipeline {
compose( reverse @_ );
}
# a partiallyapplicable map
sub map_c(&@) {
my $f = shift;
my $args = \@_;
sub {
map $f>($_), @$args, @_;
}
}
Now let us write code using the above vocabulary. First, the
preliminaries:
use ToolBox;
use Data::Dumper;
# a convenience function for examining our output
sub say(@) {
local $Data::Dumper::Terse = 1;
local $Data::Dumper::Indent = 0;
my @d = map Dumper($_), @_;
print "@d$/";
}
Let us start with some simple functions to show the general idea:
# some simple binary operators
sub plus { $_[0] + $_[1] }
sub times { $_[0] * $_[1] }
# build nary operators from them
*sum = foldl_c( \&plus, 0 );
*product = foldl_c( \×, 1 );
# test them out
say sum(1..10); # 55
say product(1..10); # 3628800
Now let us build further to create a function to compute vector dot
products:
*dot_product = compose( \&sum, zip_with_c( \&product ));
say dot_product( [1,1,1], [1,2,3] ); # 6
So far, we have computed only with numbers. Let us now turn to data.
One common programming task is to compute the combinations that can be
generated by taking one element from a set of sets. (I selected this
problem because various implementations can be found on Perl Monks for
comparison.) Here's my implementation:
*combos = foldr_c( \&outer_prod, [[]] );
sub outer_prod {
my ($xs, $ys) = @_;
[ map do { my $x=$_; map [$x, @$_], @$ys }, @$xs ];
}
say combos( ['a','b'], [1,2,3] );
# [['a',1],['a',2],['a',3],['b',1],['b',2],['b',3]]
Building further, let's compute
power sets. One
common method of computing the power set of a set
S is the
following:
 Replace each element e of S with the set {{e},{}}:
[1,2] ==> [ [[1],[]], [[2],[]] ]
 Compute the combinations that can be formed from the sets:
==> [ [[1],[2]], [[1],[]], [[],[2]], [[],[]]] ]
 Compute the union of the sets within each combination:
==> [ [1,2], [1], [2], [] ]
This method translates directly into the following code:
*powerset = pipeline(
map_c { [ [$_], [] ] }, # step 1
\&combos, # step 2
map_c { map [ map @$_, @$_ ], @$_ } # step 3
);
say powerset( 1, 2 );
# [1,2] [1] [2] []
say powerset(qw( a b c ));
# ['a','b','c'] ['a','b'] ['a','c'] ['a']
# ['b','c'] ['b'] ['c'] []
Each step in the original method maps directly to a stage in the
composition pipeline, the output of each stage becoming the input of
the next.
This ends my example.
You are welcome to code your own versions of these functions for
comparison. Because these functions are so simple, the comparisons
might not yield much insight. A more useful exercise might be for you
to write FP and nonFP code to solve more complex problems and then
compare the coding experiences instead of the code itself.
Cheers,
Tom
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