The document discusses hyper-multiplying Ethiopians and the use of functional programming concepts in Perl 6 (now Raku) for implementing Ethiopian multiplication. It covers different coding styles, including imperative, functional, and declarative programming, demonstrating how to write algorithms with reduced complexity and higher maintainability. Additionally, it introduces features of Perl 6 such as hyperoperators and provides examples of using these to improve code readability and performance.

1. Hyper-Multiplying Ethiopians:
Lambdas, Lazyness, & Perl6
Steven Lembark
Workhorse Computing
lembark@wrkhors.com
Hyper-Multiplying Ethiopians:
Lambdas, Lazyness, & Perl6

2. Welcome to Perl6
Rakudo­Star distro.
Rosetta Code.
Ethiopic Multiplication:
What it is.
More than one way to do it.

3. Rakudo Star: Perl6 in a tarball
Pretty much what you are used to:
Snag a tarball or pull from GitHub.
perl Configure;
make all test install;

4. Acquiring Rakudo-Star
Call it “Rakudo” from now on.
http://rakudo.org/

5. Acquiring Rakudo-Star
Quareterly updates are in ./downloads/star
wget .../rakudo-star-2016.01.tar.gz;
gzip -dc < *.tar.gz | tar xf -;
cd rakudo-star-2016.01;
less README;

6. Acquiring Rakudo-Star
Quarterly updates are in ./downloads/star
wget .../rakudo-star-2013.10.tar.gz;
gzip -dc < *.tar.gz | tar xf -;
cd rakudo-star-2013.10;
perl Configure.pl –prefix=/opt/perl6
--backends=moar --gen-nqp --gen-moar &&
make all test install;

7. Information on Perl6
rakudo.org has links to everything else Perl6­ish.
Rakudo's own doc's page is at:
<http://rakudo.org/documentation>
Also the Perl Maven: Gabor Szabo
<http://perl6maven.com/>
For example:
./parsing-command-line-arguments-perl6

8. Rosetta Code
Wonderful site, if you care about languages.
Various algorithms, variety of languages.
Perl6 versions largely coded by Larry Wall.

9. Ethiopian Multiplication
.../wiki/Ethiopian_Multiplication
Developed in the time of roman numerals:
MCMXIV * XXXIIV = ??
Using integer math:
Halve the first number to 1, double the second.
Sum doubled numbers for odd halved ones.

10. Maybe an example will help...
17 x 34 write down two numbers...

11. Maybe an example will help...
17 x 34
8 halve the first number to 1
4 using integer math...
2
1

12. Maybe an example will help...
17 x 34
8 68
4 136 double the second number...
2 272
1 544

13. Maybe an example will help...
17 34
8 68
4 136
2 272
1 544 sum the doubles with odd halves...

14. Maybe an example will help...
17 34
8 68
4 136
2 272
1 544
578 Viola!, the product

15. Plan 1: Imperative programming
Loop over the halved value.
Doubling the other.
Summing as you go.

16. What it looks like in Perl5
sub halve { int((shift) / 2) }
sub double { (shift) * 2 }
sub iseven { ((shift) & 1) == 0 }
sub ethiopicmult
{
my ($plier, $plicand) = @_;
my $r = 0;
while ($plier >= 1)
{
$r += $plicand unless iseven $plier;
$plier = halve $plier;
$plicand = double $plicand;
}
return $r;
}

17. Perl6
More ways to do it:
Parameter types.
Local functions.

18. Stand-alone subs
sub halve (Int $n is rw) { $n div= 2 } # integer divide
sub double (Int $n is rw) { $n *= 2 }
sub even (Int $n --> Bool) { $n %% 2 } # return, is-divisible
sub ethiopicmult
(
Int $a is copy, Int $b is copy --> Int
)
{
my $r = 0;
while $a
{
even $a or $r += $b;
halve $a;
double $b;
}
return $r;
}

19. Embedded subs
sub ethiopicmult
(
Int $a is copy, Int $b is copy --> Int
)
{
sub halve (Int $n is rw) { $n div= 2 }; # subs are
sub double (Int $n is rw) { $n *= 2 }; # lexically
sub even (Int $n --> Bool) { $n %% 2 }; # scoped
my $r = 0;
while $a
{
even $a or $r += $b;
halve $a;
double $b;
}
return $r;
}

20. Self-contained with lexical subs
sub ethiopicmult
(
Int $a is copy, Int $b is copy --> Int
)
{
my &halve = * div= 2; # placeholders save
my &double = * *= 2; # syntax.
my &even = * %% 2;
my $r = 0;
loop # a.k.a. for(;;)
{
even $a or $r += $b;
halve $a or return $r;
double $b;
}
}

21. Self-contained with lexical subs
sub ethiopicmult
(
Int $a is copy, Int $b is copy --> Int
)
{
state &halve = * div= 2; # “state” avoids
state &double = * *= 2; # re-compiling.
state &even = * %% 2;
my $r = 0;
loop
{
even $a or $r += $b;
halve $a or return $r;
double $b;
}
}

22. Even more than...
Functional Programming:
Yet Another Way to Avoid Spaghetti Code.
Neither “structured programming” nor “objects”.
Manage state and side effects.

23. The Evil State
State is hard to maintain.
Coding errors: losing, failed, multiple updates...
Avoiding it reduces errors.

24. Unintended Consequences
sub loop
{
double $b;
even $a or $r += $b;
halve $a or return $r;
double $b;
}

25. “Functional” programming
e.g., Haskell, Scheme, Scala, Clojure, Perl6
Declarative: describe the answer not steps.
(e.g., order of execution in Haskell is derived).

26. Ideal: pure functional code
Fully deterministic function calls.
Avoid state & side­effects.
No surprises.
Easy to test, with full validation.

27. Catch: it doesn't work
Examples?
time()
random()
readline()
fetchrow_array()
Result: Be realistic.

28. Looking at it in Perl6
Replace steps with declarations.
Say “how” not “what”.

29. Declarative definition
sum a list ...

30. Declarative definition
sum a list ...
selecting the doubled values whose halved
entry is odd ...

31. Declarative definition
sum a list ...
selecting the doubled values whose halved
entry is odd ...
from a list of pairs ...

32. Declarative definition
sum a list ...
selecting the doubled values whose halved
entry is odd ...
from a list of pairs ...
halving the first value to one,
doubling the second one each time.

33. Iterators & maps & zips, oh my!
sub ethiopicmult
( Int $a is copy, Int $b is copy --> Int )
{
state &halve = * div= 2;
state &double = * *= 2;
state &odd = * % 2;
[+] # list operator [] iterates '+'.
map # map pulls two values each time.
{
$^col_2 if odd $^col_1 # parameters extract in lexical order.
},
zip # new list from the list arguments
(
$a, &halve ... 1 ; # semi-colon separates lists
$b, &double ... * # indefinite lazy list
);
}

34. Iterators & maps & zips, oh my!
sub ethiopicmult
( Int $a is copy, Int $b is copy --> Int )
{
state &halve = * div= 2;
state &double = * *= 2;
[+]
map -> $half, $dbl # named parameters
{
$dbl if $half % 2
},
zip
(
$a, &halve ... 1 ;
$b, &double ... *
);
}

35. Inline list generators replace subs
sub ethiopicmult
( Int $a is copy, Int $b is copy --> Int )
{
# what you see is all you get
[+]
map -> $half, $dbl
{
$dbl if $half % 2
},
zip
(
$a, * div 2 ... 1 ; # implicit subs
$b, * * 2 ... *
)
}

36. Ternary Operator Makes 0 Explicit
sub ethiopicmult
{
my ($a,$b) = @_; # still works
[+]
map -> $half, $dbl
{
$half % 2
?? $dbl # wider ?? !! easier to see
!! 0 # or ()
},
zip
(
$a, &halve ... 1;
$b, &double ... *
)
}

37. Result
Minimal, declarative syntax.
Avoid order­of­execution errors.
Hopefully more descriptive, easier to maintain.

38. Result
Minimal, declarative syntax.
Avoid order­of­execution errors.
Hopefully more descriptive, easier to maintain.
But wait!
There's More!

39. What you are used to
Processing a list with map:
@result = map { $_->$method( @argz ) } @inputs;
Single­threaded.
Fixed order of input.
Fixed order of processing.

40. Perl6 adds “hyperoperators”
The “»” or “>>” parallel execution:
@result = @objects».&function( @args );
@objects blessed or class, literal or variable.
@result in the same order as @objects.
Order of execution is indeterminate.

41. Zipping pairs, not flat lists.
“zip” generates a flat list.
“Z=>” normally used for hashes:
my %hash =
( ( $a, * div 2 … 1 ) Z=> ( $b, * * 2 … * ) );
List of key:value pairs:
( ( 17, 34 ) ; ( ( 8, 68 ) ; … )

42. Processing pairs
Pair object has “key” and “value”:
sub odd_values( $pair )
{
$pair.key % 2 ?? $pair.value !! ()
}

43. Generating the list of odd values
[+]
( ( $a, * div 2 … 1 ) Z=> ( $b, * * 2 … * ) )
».odd_values
Selection of odd values is parallel.
Generation and sum are single­threaded.

44. Hyper-whybotherators?
“$a % 2” ??
Comparing DNA or proteins...
… complex financial simulation...
… playing conway's game of life?
without loops, forks, breaks, joins,
co routines, or queues?‑

45. What's this got to do with FP?
Hyperoperators lack repeatable sequence.
Side effects, state?
Fix: FP [­ish] functions for hyperoperators.

46. Reading on the ceiling
Catch: map­ish code reads “upside down”.
Wish you could read it going down the page?

47. Feeding on the floor
Feed operator:
( ( $a, * div 2 … 1 ) Z=> ( $b, * * 2 … * ) )
».odd_values ==> [+]
odd_values into [+] block­iterator.

48. The result
sub ethiopic_hyper_mult( $a, $b )
{
sub odd_values( $pair )
{ $pair.key % 2 ?? $pair.value !! () }
(( $a, * div 2 … 1 ) Z=> ( $b, * * 2 … * ) ))
>>.&odd_values ==> [+]
}

49. New things in Perl6
%% is “Divisible By" & "div" integer division.
my &subname = ... for lexically defined subs.
* for parameters.
$^foo for block parameters.
Parameterized lists with $start, OP, $end.
List operators with [ OP ].
Hyperopertors & friends.

50. Shameless Plug
Glacier Hashes are nice for FP.
Perl5 is nice for Glacier Hashes.
YAPC::NA 2016: FP code & benchmarks.
With tail recursion.
In Perl5.

51. References
Monads in Perl5:
http://web.archive.org/web/20080515195640/http://sle
epingsquirrel.org/monads/monads.html
Introduces the basic ideas of functional
programming with monads using Perl5 examples.

52. References
Readable descriptions of “Monad”:
https://stackoverflow.com/questions/44965/what-is-a-
monad
https://stackoverflow.com/questions/2704652/monad-
in-plain-english-for-the-oop-programmer-with-no-fp-
background

53. References
What databases mean to Functional Programming:
<https://stackoverflow.com/questions/8406261/most
­common­pattern­for­using­a­database­in­a­
functional­language­given­desire>
The most common pattern for dealing with side­
effects and impurity in functional languages is:
­ be pragmatic, not a purist ...

54. References
Realistic view of FP:
https://stackoverflow.com/questions/330371/are-
databases-and-functional-programming-at-odds
Functional languages do not have the goal to
remain stateless, they have the goal to make
management of state explicit.

55. References
Good overview of the vocabulary:
http://en.wikipedia.org/wiki/Functional_Programming

56. References
Academic description of Monads:
http://web.archive.org/web/20071128090030/http://hom
epages.inf.ed.ac.uk/wadler/papers/marktoberdorf/baas
tad.pdf