# Backus, Functional Programming, and Ruby

Discussion in 'Ruby' started by Jesse Merriman, Mar 25, 2007.

1. ### Jesse MerrimanGuest

Recently, John Backus, the father of Fortran, died. In 1977 he won the Turi=
ng=20
Award, and gave a lecture promoting functional programming. The lecture can=
=20
be accessed here:

and an interesting blog post about it is here:

=C2=A0=20
http://scienceblogs.com/goodmath/2007/03/backuss_idea_of_functional_pro_1.p=
hp

In section 5 of the lecture an example is given comparing calculation of th=
e=20
inner product of two vectors in an imperative style versus a functional=20
style. I thought it'd be fun to try to write it (functionally) in Ruby, and=
I=20
think it came out rather nifty, so I thought I'd post it here. The basic id=
ea=20
is to define an inner_product function as the compose of 3 other functions =
(a=20
sum insert, multiply mapping, and transpose), instead of doing it iterative=
ly=20
like this:

def inner_product(a, b)
sum =3D 0
(0...a.length).each do |i|
sum +=3D a * b
end
sum
end

Below is my more functional solution. Most of it is defining functions for=
=20
doing composes and such, and then almost at the end inner_product is define=
d=20
as Backus would've liked.

=2D--------------------------------------------------------------------
# Ruby implementation of John Backus' functional inner product example, from
# section 5.2 of his 1977 Turing Award Lecture, available here:

# Returns the transpose of a pair of vectors as a vector of pairs.
transpose =3D lambda do |pair_of_vec|
=C2=A0 pair_of_vec.first.zip(pair_of_vec.last)
end

# Returns a Proc that takes a vector of pairs and returns a vector of whate=
ver
# f returns.
apply_to_all =3D lambda do |f|
=C2=A0 lambda do |vec_of_pair|
=C2=A0 =C2=A0 vec_of_pair.map { |pair| f.call(pair.first, pair.last) }
=C2=A0 end
end

# Returns a Proc that takes a vector and returns a value of whatever f
# returns.
insert =3D lambda do |f|
=C2=A0 lambda do |vec|
=C2=A0 =C2=A0 # The reverse is taken so that, for example, when vec is [1,2=
,3,4], the
=C2=A0 =C2=A0 # result is: =C2=A01 <op> (2 <op> (3 <op> 4))
=C2=A0 =C2=A0 # instead of: ((1 <op> 2) <op> 3) <op> 4
=C2=A0 =C2=A0 # (Though its just a convention, and in many cases doesn't ma=
tter)
=C2=A0 =C2=A0 vec.reverse.inject { |memo, e| f.call(memo, e) }
=C2=A0 end
end

# Returns the composition of f and g as a Proc.
compose =3D lambda do |f,g|
=C2=A0 lambda { |*args| f.call(g.call(*args)) }
end

# Returns the composition of all given functions as a Proc.
compose_all =3D lambda do |*funcs|
=C2=A0 funcs.reverse.inject { |memo, f| compose.call(f, memo) }
end

# Convenience Procs.
add =C2=A0=3D lambda { |x,y| x+y }
mult =3D lambda { |x,y| x*y }

# Returns a value: the inner product of a pair of vectors.
inner_product =3D compose_all.call(
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 insert.call(=

# Test case from the lecture. Should print out 28.
puts inner_product.call([[1,2,3], [6,5,4]])
=2D--------------------------------------------------------------------

=2D-=20
Jesse Merriman

http://www.jessemerriman.com/

Jesse Merriman, Mar 25, 2007

2. ### Joel VanderWerfGuest

Jesse Merriman wrote:
...
Ruby has its own way of doing things, not that there is anything wrong
with defining new ways:

[[1,2,3], [6,5,4]].transpose.map{|x,y|x*y}.inject{|s,x|s+x}
=> 28

Joel VanderWerf, Mar 25, 2007

3. ### Jesse MerrimanGuest

Yep, I was just seeing how close I could make Ruby code look like Backus'
code; the goal was to define inner_product as a compose of the three other
functions without any named variables.

Jesse Merriman, Mar 25, 2007
4. ### Devin MullinsGuest

module Enumerable
def inner_product
transpose.map(&:*).inject(&:+)
end
end (Not to slight Backus. Functional programming and BNF are both totally
cool.)

Devin Mullins, Mar 25, 2007
5. ### Jesse MerrimanGuest

That looks good, but is it right?

irb(main):001:0> module Enumerable
irb(main):002:1> def inner_product
irb(main):003:2> transpose.map(&:*).inject(&:+)
irb(main):004:2> end
irb(main):005:1> end
=> nil
irb(main):006:0> [[0,1,2], [6,5,4]].inner_product
TypeError: wrong argument type Symbol (expected Proc)
from (irb):3:in `inner_product'
from (irb):6

\$ ruby --version
ruby 1.8.5 (2006-12-04 patchlevel 2) [i686-linux]

Jesse Merriman, Mar 26, 2007
6. Well ... let me throw a bit of historical perspective into the mix:

1. I read the article when it was published. At the time, I was working
as a mainly assembly language programmer in real-time operating systems.
I was quite familiar with functional programming styles, Lisp (1.5), the
lambda calculus and combinatory logic, and I was studying the formal
semantics of programming languages. The article resonated with me for
those reasons. However, I found it difficult to read in context with the
other computer science I was studying.

2. A few years later, functional languages, so-called single-assignment
languages and dataflow programming paradigms started to make an
appearance during the renaissance of high-performance scientific
computing that occurred during the Reagan years. Despite their

3. Maybe the time is *finally* ripe for the functional programming
least a few useful applications written in Haskell, Erlang and OCaml.
After all, FORTRAN I came out in 1957 and LISP I only three years or so
later. I date the start of Lisp from McCarthy's 1960 paper, but I'm not
sure when the first actual LISP interpreter was put into operation.
Maybe ... but it's been about 50 years and the Von
Neumann/FORTRAN/imperative paradigm has continued to dominate the
computing world. The Church/McCarthy/LISP/Functional paradigm has held
its own -- once there were Lisp machines, after all -- but it is a
distinct second place runner.

M. Edward (Ed) Borasky, Mar 26, 2007
7. ### Chris CarterGuest

He is assuming you have the famed "Symbol#to_proc" method, you can
find it with a quick google.

Chris Carter, Mar 26, 2007
8. ### Jesse MerrimanGuest

Ah, very nice. Very nice.

Jesse Merriman, Mar 26, 2007
9. ### Giles BowkettGuest

He is assuming you have the famed "Symbol#to_proc" method, you can
I think this technique is massively underutilized. Imagine what it
would be like if overriding to_proc was a standard technique for all
kinds of objects. Things could get really weird.

(In a good way.)

Giles Bowkett, Mar 26, 2007
10. ### SonOfLilitGuest

SonOfLilit, Mar 26, 2007
11. ### Giles BowkettGuest

Yep -- I've always been a fan of OSOP. (Oooh Shiny Oriented Programming.)

Giles Bowkett, Mar 26, 2007