Functional Programming and Ruby
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This document contains summaries of functional programming concepts like higher order functions, lazy evaluation, and memoization. It provides examples of higher order functions in Ruby like map and collect. It explains lazy evaluation through examples using infinite ranges and chaining enumerables. It also discusses memoization and provides an example of a memoized Fibonacci function in Ruby.
![foo :: Ord a => [a] -> [a]
foo [] = []
foo (p:xs) =
(foo lesser)
++ [p]
++ (foo greater)
where
lesser = filter (< p) xs
greater = filter (>= p) xs](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-1-320.jpg)
![quicksort :: Ord a => [a] -> [a]
quicksort [] = []
quicksort (p:xs) =
(quicksort lesser)
++ [p]
++ (quicksort greater)
where
lesser = filter (< p) xs
greater = filter (>= p) xs](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-9-320.jpg)
![[1..10]
=>[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
(1..10).to_a](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-15-320.jpg)
![[ x*x | x <- [1..10]]
(1..10).collect { |x| x*x }
=>[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
(1..10).map { |x| x*x }](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-16-320.jpg)
![map (x -> x*x) [1..10]
(1..10).map &lambda { |x| x*x }
=>[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
(1..10).map &(->(x) { x*x })](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-18-320.jpg)
![[ x+1 | x <- [ x*x | x <- [1..10]]]
=>[2, 5, 10, 17, 26, 37, 50, 65, 82, 101]](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-20-320.jpg)
![[1..10] f(x) =
x*x
g(x) =
x+1
[2..101]
f(1) = 1 g(1) = 2Step 1:
f(2) = 4 g(4) = 5Step 2:
f(3) = 9 g(9) = 10Step 3:
f(4) = 16 g(16) = 17Step 4:](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-21-320.jpg)
![(1..10).collect { |x| x*x }
.collect { |x| x+1 }
=>[2, 5, 10, 17, 26, 37, 50, 65, 82, 101]](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-22-320.jpg)
![x*x
[1..100]
yield
loop:
1 -> 10
collect_i
(1..10).collect { |x| x*x }
Enumerable#collect](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-26-320.jpg)
![Enumerable#collect
def collect(range, &block)
result = []
range.each do |x|
result << block.call(x)
end
result
end](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-27-320.jpg)
![[1..10] f(x) =
x*x
[1..100] g(x) =
x+1
[2..101]
Step 1:
Call f(x) 10 times
Step 2:
Call g(x) 10 times](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-29-320.jpg)
![[1..]
=>[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,1
05,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,
etc...](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-31-320.jpg)
![take 10 [1..]
=>[1,2,3,4,5,6,7,8,9,10]](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-32-320.jpg)
![take 10 [ x+1 | x <- [ x*x | x <- [1..]]]
=>[2,5,10,17,26,37,50,65,82,101]](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-33-320.jpg)
![(1..Float::INFINITY).lazy.collect { |x| x*x }
.collect { |x| x+1 }
.take(10).force
=>[2,5,10,17,26,37,50,65,82,101]](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-34-320.jpg)
![(1..Float::INFINITY).lazy.collect { |x| x*x }
.collect { |x| x+1 }
.first(10)
=>[2,5,10,17,26,37,50,65,82,101]](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-35-320.jpg)
![(1..Float::INFINITY).lazy.collect { |x| x*x }
.collect { |x| x+1 }.first(10)
yield to the blocks,
one at a time
Enumerator Enumerator
Stop
After 10
yield
pass
result
pass
result
x*x x+1
[2..101]
store
yield yield
loop](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-37-320.jpg)
![slow_fib 0 = 0
slow_fib 1 = 1
slow_fib n = slow_fib (n-2)
+ slow_fib (n-1)
map slow_fib [1..10]
=> [1,1,2,3,5,8,13,21,34,55]
http://www.haskell.org/haskellwiki/Memoization](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-40-320.jpg)
![memoized_fib = (map fib [0 ..] !!)
where fib 0 = 0
fib 1 = 1
fib n = memoized_fib (n-2)
+ memoized_fib (n-1)
Typical Haskell magic!
http://www.haskell.org/haskellwiki/Memoization](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-42-320.jpg)
![(map fib [0 ..] !!)
Infinite, lazy list of
return values
A curried function to
return the requested fib](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-43-320.jpg)
![[0 ..]
(0..Float::INFINITY)](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-44-320.jpg)
![map fib [0 ..]
(0..Float::INFINITY).lazy.map {|x| fib(x) }](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-45-320.jpg)
![(map fib [0 ..] !!)
cache =
(0..Float::INFINITY).lazy.map {|x| fib(x) }
nth_element_from_list =
lambda { |ary, n| ary[n]}
nth_fib =
nth_element_from_list.curry[cache]](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-46-320.jpg)
![map memoized_fib [1..10]
=> [1,1,2,3,5,8,13,21,34,55]
`block in <main>':
undefined method `[]'
for #<Enumerator::Lazy:
#<Enumerator::Lazy:
0..Infinity>:map>
(NoMethodError)](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-47-320.jpg)
![each
Range
Enumerable
#collect
(0..Float::INFINITY)
.lazy.map {|x| fib(x) }
nth_element_from_list =
lambda { |ary, n| ary[n]}](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-48-320.jpg)
![@cache = {}
@cache[1] = 1
@cache[2] = 1
def memoized_fib(n)
@cache[n] ||= memoized_fib(n-1)
+ memoized_fib(n-2)
end](https://image.slidesharecdn.com/functionalprogrammingandruby-180213192556/85/Functional-Programming-and-Ruby-49-320.jpg)
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Functional Programming and Ruby
- 1. foo :: Ord a => [a] -> [a] foo [] = [] foo (p:xs) = (foo lesser) ++ [p] ++ (foo greater) where lesser = filter (< p) xs greater = filter (>= p) xs
- 4. Ruby is a language designed in the following steps: * take a simple lisp language * add blocks, inspired by higher order functions * add methods found in Smalltalk * add functionality found in Perl So, Ruby was a Lisp originally, in theory. Let's call it MatzLisp from now on. ;-) matz.
- 9. quicksort :: Ord a => [a] -> [a] quicksort [] = [] quicksort (p:xs) = (quicksort lesser) ++ [p] ++ (quicksort greater) where lesser = filter (< p) xs greater = filter (>= p) xs
- 10. Haskell... is a polymorphically statically typed, lazy, purely functional language, quite different from most other programming languages. The language is named for Haskell Brooks Curry, ...
- 11. - What is “Functional Programming?” - Higher Order Functions - Lazy Evaluation - Memoization
- 15. [1..10] =>[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] (1..10).to_a
- 16. [ x*x | x <- [1..10]] (1..10).collect { |x| x*x } =>[1, 4, 9, 16, 25, 36, 49, 64, 81, 100] (1..10).map { |x| x*x }
- 18. map (x -> x*x) [1..10] (1..10).map &lambda { |x| x*x } =>[1, 4, 9, 16, 25, 36, 49, 64, 81, 100] (1..10).map &(->(x) { x*x })
- 20. [ x+1 | x <- [ x*x | x <- [1..10]]] =>[2, 5, 10, 17, 26, 37, 50, 65, 82, 101]
- 21. [1..10] f(x) = x*x g(x) = x+1 [2..101] f(1) = 1 g(1) = 2Step 1: f(2) = 4 g(4) = 5Step 2: f(3) = 9 g(9) = 10Step 3: f(4) = 16 g(16) = 17Step 4:
- 22. (1..10).collect { |x| x*x } .collect { |x| x+1 } =>[2, 5, 10, 17, 26, 37, 50, 65, 82, 101]
- 23. (1..10).collect { |x| x*x } each Range Enumerable #collect Enumerable#collect
- 26. x*x [1..100] yield loop: 1 -> 10 collect_i (1..10).collect { |x| x*x } Enumerable#collect
- 27. Enumerable#collect def collect(range, &block) result = [] range.each do |x| result << block.call(x) end result end
- 29. [1..10] f(x) = x*x [1..100] g(x) = x+1 [2..101] Step 1: Call f(x) 10 times Step 2: Call g(x) 10 times
- 30. Lazy Evaluation
- 33. take 10 [ x+1 | x <- [ x*x | x <- [1..]]] =>[2,5,10,17,26,37,50,65,82,101]
- 34. (1..Float::INFINITY).lazy.collect { |x| x*x } .collect { |x| x+1 } .take(10).force =>[2,5,10,17,26,37,50,65,82,101]
- 35. (1..Float::INFINITY).lazy.collect { |x| x*x } .collect { |x| x+1 } .first(10) =>[2,5,10,17,26,37,50,65,82,101]
- 37. (1..Float::INFINITY).lazy.collect { |x| x*x } .collect { |x| x+1 }.first(10) yield to the blocks, one at a time Enumerator Enumerator Stop After 10 yield pass result pass result x*x x+1 [2..101] store yield yield loop
- 39. Memoization
- 40. slow_fib 0 = 0 slow_fib 1 = 1 slow_fib n = slow_fib (n-2) + slow_fib (n-1) map slow_fib [1..10] => [1,1,2,3,5,8,13,21,34,55] http://www.haskell.org/haskellwiki/Memoization
- 42. memoized_fib = (map fib [0 ..] !!) where fib 0 = 0 fib 1 = 1 fib n = memoized_fib (n-2) + memoized_fib (n-1) Typical Haskell magic! http://www.haskell.org/haskellwiki/Memoization
- 43. (map fib [0 ..] !!) Infinite, lazy list of return values A curried function to return the requested fib
- 45. map fib [0 ..] (0..Float::INFINITY).lazy.map {|x| fib(x) }
- 46. (map fib [0 ..] !!) cache = (0..Float::INFINITY).lazy.map {|x| fib(x) } nth_element_from_list = lambda { |ary, n| ary[n]} nth_fib = nth_element_from_list.curry[cache]
- 47. map memoized_fib [1..10] => [1,1,2,3,5,8,13,21,34,55] `block in <main>': undefined method `[]' for #<Enumerator::Lazy: #<Enumerator::Lazy: 0..Infinity>:map> (NoMethodError)
- 48. each Range Enumerable #collect (0..Float::INFINITY) .lazy.map {|x| fib(x) } nth_element_from_list = lambda { |ary, n| ary[n]}
- 49. @cache = {} @cache[1] = 1 @cache[2] = 1 def memoized_fib(n) @cache[n] ||= memoized_fib(n-1) + memoized_fib(n-2) end
- 50. Ruby has many functional features, but is not a functional language
- 51. Learn by studying other languages... and acquire a different perspective on Ruby