SlideShare a Scribd company logo

All You Need is Fold in the Key of C#

Mike Harris, profile picture
Mike Harris

The document discusses the concept of 'fold' in functional programming, particularly in C#, highlighting its applications in various functions like 'and', 'or', 'length', 'reverse', 'map', 'filter', and 'zip'. It includes educational references, practical examples, and code snippets demonstrating the implementation of these concepts. Additionally, it features quotes from philosopher Paul Feyerabend, emphasizing the limitations of methodologies.

Software
1 of 134
Download to read offline
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
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
All You Need is Fold
 in the Key of C# Mike Harris
All You Need Is FOLD
All You Need Is FOLD
All you need is FOLD
FOLD
Fold is All You Need!
Tour • Backstage • Concert • Farewell
Backstage
f g Function
f g f(g) Function
Fold a1 a2 an b
Fold foldr :: (α → β → β) → β → ([α] → β)
 
 foldl :: (β → α→ β) → β → ([α] → β) SeedFunc a1 a2 an Fold b Given We Func Seed
f anf a2f Seed a1
f anf a2f(Seed, a1)
f anf(f(Seed, a1), a2)
b
Fold a1 a2 an b
— Paul Feyerabend
 Against Method 
 Chapter 16 “Fundamental conceptual change … presupposes new world-views and new languages capable of expressing them.”
Concert All You Need is Fold
Set List • And • Or • Length • Reverse • Map • Filter • Zip
Set List • And • Or • Length • Reverse • Map • Filter • Zip
And T/F T/F T/F T/F
And and :: [Bool] → Bool
 and = fold (∧) True TrueAnd f1 f2 fn Fold f Given We And True
And True And
public bool And(
 params bool[] facts)
 {
 return facts.Aggregate(
 true,
 (m, x) => m && x);
 } And True
var sut = new Folder(); sut.And(false, true, false);
And True False True False And
And True False True False M X result False And
And False True False M X result False And
And False False M X result False And
And True False True False result False And
public bool And(
 params bool[] facts)
 {
 return facts.Aggregate(
 true,
 (m, x) => m && x);
 } And True
Set List • And • Or • Length • Reverse • Map • Filter • Zip
Or T/F T/F T/F T/F
Or or :: [Bool] → Bool
 or = fold (∨) False FalseOr f1 f2 fn Fold f Given We Or False
Or False Or
public bool Or(
 params bool[] facts)
 {
 return facts.Aggregate(
 false,
 (m, x) => m || x);
 } Or False
var sut = new Folder(); sut.Or(false, true, false);
Or False False True False Or
Or False False True False M X result False Or
Or False True False M X result True Or
Or True False M X result True Or
Or False False True False result True Or
public bool Or(
 params bool[] facts)
 {
 return facts.Aggregate(
 false,
 (m, x) => m || x);
 } Or False
Set List • And • Or • Length • Reverse • Map • Filter • Zip
Length size
Length length :: [α] → Int
 length = fold (λx n → 1 + n) 0 0+ 1 x1 x2 xn Fold # Given We + 1 0
+ 1 0 Length
public int Length(ICollection<T> coll)
 {
 return coll.Aggregate(
 0,
 (m, _) => m + 1);
 } + 1 0
var sut = new Folder(); sut.Length("Mike".ToCharArray());
+ 1 0 M i k e Length
+ 1 0M result 1 M i k e Length
+ 1 1M result 2 i k e Length
+ 1 2M result 3 k e Length
+ 1 3M result 4 e Length
+ 1 0 result 4 M i k e Length
public int Length(ICollection<T> coll)
 {
 return coll.Aggregate(
 0,
 (m, _) => m + 1);
 } + 1 0
Set List • And • Or • Length • Reverse • Map • Filter • Zip
Reverse x1 x2 xn xn x2 x1
Reverse reverse :: [α] → [α]
 reverse = fold (λx m → m ++ [x]) [ ] [ ]Cons x1 x2 xn Fold [x] Given We Cons [ ]
Cons [ ] Reverse
public IEnumerable<T>
 Reverse(IEnumerable<T> coll)
 {
 return coll.Aggregate(
 new List<T>(),
 (m, x) => new List<T> {x}
 .Concat(m).ToList()););
 } Cons [ ]
var sut = new Folder(); sut.Reverse("Mike".ToCharArray());
Cons [ ] M i k e Reverse
Cons [ ] M i k M X result M e Reverse
Cons M i k e M X result iM Reverse
Cons iM k e M X result kiM Reverse
Cons kiM e M X result ekiM Reverse
Cons [ ] result ekiM M i k e Reverse
public IEnumerable<T>
 Reverse(IEnumerable<T> coll)
 {
 return coll.Aggregate(
 new List<T>(),
 (m, x) => new List<T> {x}
 .Concat(m).ToList()););
 } Cons [ ]
Set List • And • Or • Length • Reverse • Map • Filter • Zip
Map x1 x2 xn z1 z2 zn func
Map map :: (α → β) → ([α] → [β])
 map f = fold (λx xs → f x : xs) [ ] [ ]Conj x1 x2 xn Fold [z] Given We Conj [ ]
Conj [ ] func Map
public IEnumerable<U>
 Map<T, U>( IEnumerable<T> coll,
 Func<T, U> func)
 {
 return coll.Aggregate(
 new List<U>(),
 (m, x) => { 
 m.Add(func(x));
 return m;});
 } Conj [ ]
var sut = new Folder(); sut.Map(
 “Mike".ToCharArray(),
 s => s.ToUpper());
Conj [ ] M i k e upper Map
Conj [ ] M i k M X result M e upper Map
Conj M i k e M X result MIupper Map
Conj MI k e M X result MIKupper Map
Conj MIK e M X result MIKEupper Map
Conj [ ] M i k result e upper MIKE Map
public IEnumerable<U>
 Map<T, U>( IEnumerable<T> coll,
 Func<T, U> func)
 {
 return coll.Aggregate(
 new List<U>(),
 (m, x) => { 
 m.Add(func(x));
 return m;});
 } Conj [ ]
Set List • And • Or • Length • Reverse • Map • Filter • Zip
Filter x1 x2 xn x1 xn pred
Filter filter :: (α → Bool) → ([α] → [α])
 filter p = fold (λx xs → if p x then x : xs else xs) [ ] if Conj [ ] x1 x2 xn Fold [x] Given We [ ] if Conj
if [ ] pred Conj Filter
public IEnumerable<T>
 Filter<T>( IEnumerable<T> coll,
 Func<T, bool> pred)
 {
 return coll.Aggregate(
 new List<T>(),
 (m, x) => { 
 if(pred(x)) m.Add(x);
 return m;});
 } [ ]if Conj
var sut = new Folder(); sut.Filter(
 “Mike".ToCharArray(),
 s => s.All(char.IsLower));
if [ ] M i k e isLower Conj Filter
if [ ] M i k M X result [ ] e isLower Conj Filter
if [ ] i k e M X isLower result iConj Filter
if i k e M X isLower result ikConj Filter
if ik e M X isLower result ikeConj Filter
if [ ] isLower M i k e result ikeConj Filter
public IEnumerable<T>
 Filter<T>( IEnumerable<T> coll,
 Func<T, bool> pred)
 {
 return coll.Aggregate(
 new List<T>(),
 (m, x) => { 
 if(pred(x)) m.Add(x);
 return m;});
 } [ ]if Conj
Set List • And • Or • Length • Reverse • Map • Filter • Zip
Zip y1 y2 yj z1 z2 zk func x1 x2 xi
Zip zip2 :: (α → β → γ) → ([α] → [β] → [γ])
 zip2 f = fold (λx y xs ys → f x y : xs ys) [ ] [ ]Conj y1 y2 ym Fold [z] Given We Conj [ ] x1 x2 xn
Conj [ ] func Zip
public ICollection<TZ>
 Zip<TX, TY, TZ>( ICollection<TX> xs, ICollection<TY> ys,
 Func<TX, TY, TZ> func)
 {
 return xs.Zip(ys,(x, y) => new Tuple<TX, TY>(x, y))
 .Aggregate(
 new List<TZ>(), (m, p) => {
 m.Add(func.Invoke(p.Item1, p.Item2));
 return m; });
 } Conj [ ]
return xs.Zip(ys, (x, y) => new Tuple<TX, TY>(x, y))
 .Aggregate(
 new List<TZ>(), (m, p) => {
 m.Add(
 func.Invoke(p.Item1, p.Item2));
 return m; }); Conj [ ]
var sut = new Folder(); sut.Zip(
 new[] {1, 2}, new[] {10, 20},
 (x, y) => x + y);
Conj [ ] 1 2 + 10 20 Zip
Conj [ ] 1 2 + 10 20 M result 11 X Y Zip
Conj 11 2 + 20 M result 11 22 X Y Zip
Conj [ ] + result 11 22 1 2 10 20 Zip
public ICollection<TZ>
 Zip<TX, TY, TZ>( ICollection<TX> xs, ICollection<TY> ys,
 Func<TX, TY, TZ> func)
 {
 return xs.Zip(ys,(x, y) => new Tuple<TX, TY>(x, y))
 .Aggregate(
 new List<TZ>(), (m, p) => {
 m.Add(func.Invoke(p.Item1, p.Item2));
 return m; });
 } Conj [ ]
Encore Coin Changer
Change coin1 coin2 coinn c1 c2 cn amount
Coin Changer kata changeFor :: [α] → α → [α]
 changeFor a = fold (λa x xs → (a % x, a / x) : xs (a, [ ]) Conj Changer [ ] amount c1 c2 cn Fold Given We [c] 0 Conj Changer [ ] amount
Conj amount [ ] Changer Change
public class CoinChanger { public IEnumerable<int> Coins { get; set; } public IEnumerable<int> ChangeFor(int amount) { return Coins.Aggregate( new Tuple<int, List<int>>(amount, new List<int>()), (m, coin) => { m.Item2.Add(m.Item1/coin); return new Tuple<int, List<int>>(
 m.Item1%coin, m.Item2); }).Item2; }
 } Conj [ ] Changer amount
public IEnumerable<int> ChangeFor(int amount) { return Coins.Aggregate( new Tuple<int, List<int>>(amount, new List<int>()), (m, coin) => { m.Item2.Add(m.Item1/coin); return new Tuple<int, List<int>>(
 m.Item1%coin, m.Item2); }).Item2; } Conj [ ] Changer amount
var sut = new CoinChanger { Coins = new[] {25, 10, 5, 1} }; sut.ChangeFor(99);
Conj amount 25 10 5 1 [ ] Changer Change
Conj 99 25 10 5 1 [ ]M X result 24 3Changer Change
Conj 24 10 5 1 3M X result 4 3 2Changer Change
Conj 4 5 1 3 2M X result 4 3 2 0Changer Change
Conj 4 1 3 2 0M X result 0 3 2 0 4Changer Change
Conj result 0 3 2 0 4Changer amount [ ] 25 10 5 1 Change
public class CoinChanger { public IEnumerable<int> Coins { get; set; } public IEnumerable<int> ChangeFor(int amount) { return Coins.Aggregate( new Tuple<int, List<int>>(amount, new List<int>()), (m, coin) => { m.Item2.Add(m.Item1/coin); return new Tuple<int, List<int>>(
 m.Item1%coin, m.Item2); }).Item2; }
 } Conj [ ] Changer amount
— Paul Feyerabend
 Against Method 
 Chapter 18 “[A]ll methodologies, even the most obvious ones, have their limits”
All You Need is Fold in the Key of C#
All You Need is Fold in the Key of C#
All You Need is Fold in the Key of C#
Thank you! Mike Harris
 
 @MikeMKH
 http://comp-phil.blogspot.com/
 
 
 Remember, all you need is Fold!
Talks • Rich Hickey - “Reducers”, EuroClojure 2012.
 https://vimeo.com/45561411 • Rich Hickey - “Transducers”, StrangeLoop 2014.
 https://www.youtube.com/watch?v=6mTbuzafcII • Tomas Petricek - “History and Philosophy of Types”, StrangeLoop 2015.
 http://tpetricek.github.io/Talks/2015/philosophy-of-types/ #/
Books • Richard Bird and Phil Wadler - Introduction to Functional Programming. Prentice-Hall,1988.
 http://usi-pl.github.io/lc/sp-2015/doc/Bird_Wadler. %20Introduction%20to%20Functional%20Programming. 1ed.pdf • Paul Feyerabend - Against Method. Verso, 2010. • Michael Fogus - Functional JavaScript: Introducing Functional Programming with Underscore.js. O’Reilly, 2013.
 http://functionaljavascript.com/
Papers • Erik Meijer, Maarten Fokkinga, and Ross Paterson - “Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire”.
 http://eprints.eemcs.utwente.nl/7281/01/db- utwente-40501F46.pdf • Graham Hutton - “A tutorial on the universality and expressiveness of fold”.
 http://www.cs.nott.ac.uk/~gmh/fold.pdf
Blog Posts • Brian McNamara - “Catamorphisms, part one”
 https://lorgonblog.wordpress.com/2008/04/05/ catamorphisms-part-one/ • Edward Kmett - “Catamorphisms”
 https://www.fpcomplete.com/user/edwardk/recursion- schemes/catamorphisms
Websites • ClojureDocs - https://clojuredocs.org/ • HaskellWiki - https://wiki.haskell.org/Haskell • Inside F# - https://lorgonblog.wordpress.com/ • lodash - https://lodash.com/docs • MDN - https://developer.mozilla.org/en-US/ • ReactiveX - http://reactivex.io/
Images (in order used) • "Abbey Rd Studios" by Misterweiss at en.wikipedia - Transfered from en.wikipedia Transfer was stated to be made by User:Blast.. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Abbey_Rd_Studios.jpg#/media/ File:Abbey_Rd_Studios.jpg • "60s wallpaper" by Domincspics - Flickr. Licensed under CC BY 2.0 via Commons - https://commons.wikimedia.org/wiki/File: 60s_wallpaper.jpg#/media/File:60s_wallpaper.jpg • "70's Wallpaper" by Liz Sullivan - Own work. Licensed under CC BY-SA 4.0 via Wikimedia Commons - https:// commons.wikimedia.org/wiki/File:70%27s_Wallpaper.JPG#/media/File:70%27s_Wallpaper.JPG • "Flickr - ronsaunders47 - The Beatles-Sgt Pepper backdrop.". Licensed under CC BY-SA 2.0 via Wikimedia Commons - https:// commons.wikimedia.org/wiki/File:Flickr_-_ronsaunders47_-_The_Beatles-Sgt_Pepper_backdrop..jpg#/media/File:Flickr_- _ronsaunders47_-_The_Beatles-Sgt_Pepper_backdrop..jpg • "All you need is love graffiti Osijek" by Objavljeno - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons - https:// commons.wikimedia.org/wiki/File:All_you_need_is_love_graffiti_Osijek.JPG#/media/File:All_you_need_is_love_graffiti_Osijek.JPG • "Illumined Pleasure Salvador Dali" by Salvador Dalí - Own workMrArifnajafov (Photography from the original). Licensed under CC BY-SA 3.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:Illumined_Pleasure_Salvador_Dali.JPG#/media/ File:Illumined_Pleasure_Salvador_Dali.JPG • "3 Savile Row" by Original uploader was Misterweiss at en.wikipedia - Transfered from en.wikipedia Transfer was stated to be made by User:Vinhtantran.. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File: 3_Savile_Row.jpg#/media/File:3_Savile_Row.jpg • "Paul Feyerabend 2" by Grazia Borrini-Feyerabend. Licensed under Attribution via Commons - https://commons.wikimedia.org/ wiki/File:Paul_Feyerabend_2.jpg#/media/File:Paul_Feyerabend_2.jpg
Images (in order used) • "The Beatles on Green Hill in Almaty, Kazakhstan" by Ken and Nyetta - Flickr: The Beatles on Green Hill in Almaty. Licensed under CC BY 2.0 via Commons - https:// commons.wikimedia.org/wiki/File:The_Beatles_on_Green_Hill_in_Almaty,_Kazakhstan.jpg#/ media/File:The_Beatles_on_Green_Hill_in_Almaty,_Kazakhstan.jpg • "The Beatles in America" by United Press International, photographer unknown - This image is available from the United States Library of Congress's Prints and Photographs division under the digital ID cph.3c11094.This tag does not indicate the copyright status of the attached work. • "The Beatles rooftop concert" by Source. Licensed under Fair use via Wikipedia - https:// en.wikipedia.org/wiki/File:The_Beatles_rooftop_concert.jpg#/media/ File:The_Beatles_rooftop_concert.jpg • "Paul Feyerabend 2" by Grazia Borrini-Feyerabend. Licensed under Attribution via Commons - https://commons.wikimedia.org/wiki/File:Paul_Feyerabend_2.jpg#/media/ File:Paul_Feyerabend_2.jpg • Myself taken at StrangeLoop 2014 by my wife, Kelsey Harris

More Related Content

PDF
The Ring programming language version 1.10 book - Part 33 of 212
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.5.2 book - Part 24 of 181
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.10 book - Part 45 of 212
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.5.2 book - Part 35 of 181
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.5.4 book - Part 22 of 185
Mahmoud Samir Fayed
 
KEY
関数潮流(Function Tendency)
riue
 
PDF
Why The Free Monad isn't Free
Kelley Robinson
 
PPTX
Running Free with the Monads
kenbot
 
The Ring programming language version 1.10 book - Part 33 of 212
Mahmoud Samir Fayed
 
The Ring programming language version 1.5.2 book - Part 24 of 181
Mahmoud Samir Fayed
 
The Ring programming language version 1.10 book - Part 45 of 212
Mahmoud Samir Fayed
 
The Ring programming language version 1.5.2 book - Part 35 of 181
Mahmoud Samir Fayed
 
The Ring programming language version 1.5.4 book - Part 22 of 185
Mahmoud Samir Fayed
 
関数潮流(Function Tendency)
riue
 
Why The Free Monad isn't Free
Kelley Robinson
 
Running Free with the Monads
kenbot
 

What's hot (20)

PDF
The Ring programming language version 1.5.3 book - Part 30 of 184
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.9 book - Part 38 of 210
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.10 book - Part 43 of 212
Mahmoud Samir Fayed
 
PDF
All You Need is Fold
Mike Harris
 
PDF
The Ring programming language version 1.3 book - Part 25 of 88
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.7 book - Part 40 of 196
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.3 book - Part 16 of 88
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.8 book - Part 35 of 202
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.8 book - Part 94 of 202
Mahmoud Samir Fayed
 
PDF
Ray Tracing with ZIO
Pierangelo Cecchetto
 
PDF
The Ring programming language version 1.6 book - Part 44 of 189
Mahmoud Samir Fayed
 
PPTX
Introduction to Monads in Scala (2)
stasimus
 
PDF
The Ring programming language version 1.3 book - Part 27 of 88
Mahmoud Samir Fayed
 
DOCX
CLUSTERGRAM
Dr. Volkan OBAN
 
PDF
The Ring programming language version 1.3 book - Part 32 of 88
Mahmoud Samir Fayed
 
PDF
The Ring programming language version 1.5.3 book - Part 36 of 184
Mahmoud Samir Fayed
 
PDF
Ray tracing with ZIO-ZLayer
Pierangelo Cecchetto
 
PPTX
The Essence of the Iterator Pattern
Eric Torreborre
 
PDF
The Ring programming language version 1.5.3 book - Part 24 of 184
Mahmoud Samir Fayed
 
PPTX
Data made out of functions
kenbot
 
The Ring programming language version 1.5.3 book - Part 30 of 184
Mahmoud Samir Fayed
 
The Ring programming language version 1.9 book - Part 38 of 210
Mahmoud Samir Fayed
 
The Ring programming language version 1.10 book - Part 43 of 212
Mahmoud Samir Fayed
 
All You Need is Fold
Mike Harris
 
The Ring programming language version 1.3 book - Part 25 of 88
Mahmoud Samir Fayed
 
The Ring programming language version 1.7 book - Part 40 of 196
Mahmoud Samir Fayed
 
The Ring programming language version 1.3 book - Part 16 of 88
Mahmoud Samir Fayed
 
The Ring programming language version 1.8 book - Part 35 of 202
Mahmoud Samir Fayed
 
The Ring programming language version 1.8 book - Part 94 of 202
Mahmoud Samir Fayed
 
Ray Tracing with ZIO
Pierangelo Cecchetto
 
The Ring programming language version 1.6 book - Part 44 of 189
Mahmoud Samir Fayed
 
Introduction to Monads in Scala (2)
stasimus
 
The Ring programming language version 1.3 book - Part 27 of 88
Mahmoud Samir Fayed
 
CLUSTERGRAM
Dr. Volkan OBAN
 
The Ring programming language version 1.3 book - Part 32 of 88
Mahmoud Samir Fayed
 
The Ring programming language version 1.5.3 book - Part 36 of 184
Mahmoud Samir Fayed
 
Ray tracing with ZIO-ZLayer
Pierangelo Cecchetto
 
The Essence of the Iterator Pattern
Eric Torreborre
 
The Ring programming language version 1.5.3 book - Part 24 of 184
Mahmoud Samir Fayed
 
Data made out of functions
kenbot
 
Ad

Viewers also liked (20)

PDF
Testing the Next Generation
Mike Harris
 
PDF
There and Back Again
Mike Harris
 
PDF
Learn You a Functional JavaScript for Great Good
Mike Harris
 
PDF
Combinators - Lightning Talk
Mike Harris
 
PDF
P1 e1 internet
Carolina Bermejo Casero
 
DOC
Galeria
movsurmedios
 
PPTX
Audience feedback double page spread
victoria-hollie
 
PPTX
Getting to know kyla
klynch688
 
PDF
Libro1
padillaestefania
 
PPTX
The Opportunities for Australian B2B organisations
Think Bespoke
 
PPT
Ddfdd
MCDH
 
PDF
Bienes inmateriales
mariaceciliacorda
 
PDF
Prabhavathi Daffodils - bangalore5.com
Bangalore Property
 
PDF
Isolasi kloroplas
SMA Negeri 9 KERINCI
 
PDF
Scan, Focus, Act
easleyme
 
PDF
Pengamatan plasmolisis
SMA Negeri 9 KERINCI
 
PDF
C# 7
Mike Harris
 
PDF
Happy 70th Birthday
Denise Howell
 
DOCX
Sesiones diciembre 2015
Eduardo Redondo-Cerezo
 
DOC
Sesiones abril 2012
Eduardo Redondo-Cerezo
 
Testing the Next Generation
Mike Harris
 
There and Back Again
Mike Harris
 
Learn You a Functional JavaScript for Great Good
Mike Harris
 
Combinators - Lightning Talk
Mike Harris
 
P1 e1 internet
Carolina Bermejo Casero
 
Galeria
movsurmedios
 
Audience feedback double page spread
victoria-hollie
 
Getting to know kyla
klynch688
 
Libro1
padillaestefania
 
The Opportunities for Australian B2B organisations
Think Bespoke
 
Ddfdd
MCDH
 
Bienes inmateriales
mariaceciliacorda
 
Prabhavathi Daffodils - bangalore5.com
Bangalore Property
 
Isolasi kloroplas
SMA Negeri 9 KERINCI
 
Scan, Focus, Act
easleyme
 
Pengamatan plasmolisis
SMA Negeri 9 KERINCI
 
C# 7
Mike Harris
 
Happy 70th Birthday
Denise Howell
 
Sesiones diciembre 2015
Eduardo Redondo-Cerezo
 
Sesiones abril 2012
Eduardo Redondo-Cerezo
 
Ad

Similar to All You Need is Fold in the Key of C# (20)

PDF
The Essence of the Iterator Pattern (pdf)
Eric Torreborre
 
PDF
Modular Module Systems
league
 
PDF
The Ring programming language version 1.7 book - Part 28 of 196
Mahmoud Samir Fayed
 
PDF
Monadologie
league
 
PPTX
Laziness, trampolines, monoids and other functional amenities: this is not yo...
Codemotion
 
PDF
The Ring programming language version 1.5.4 book - Part 25 of 185
Mahmoud Samir Fayed
 
PPT
Introduction to MatLab programming
Damian T. Gordon
 
PDF
[2024] An Introduction to Functional Programming with Go [Y Combinator Remix]...
Eleanor McHugh
 
PDF
The Ring programming language version 1.10 book - Part 31 of 212
Mahmoud Samir Fayed
 
PPT
Introduction to MATLAB
Damian T. Gordon
 
PPTX
Initial value problems
Ali Jan Hasan
 
PPT
Learn Matlab
Abd El Kareem Ahmed
 
PPTX
(2015 06-16) Three Approaches to Monads
Lawrence Evans
 
PDF
The Ring programming language version 1.9 book - Part 45 of 210
Mahmoud Samir Fayed
 
PDF
Map, Reduce and Filter in Swift
Aleksandras Smirnovas
 
PDF
The Ring programming language version 1.8 book - Part 42 of 202
Mahmoud Samir Fayed
 
PDF
Actors for Behavioural Simulation
ClarkTony
 
PDF
Haskell 101
Roberto Pepato
 
PDF
TDC2016SP - Trilha Programação Funcional
tdc-globalcode
 
PPT
haskell5.ppt is a marketing document lol
dopointt
 
The Essence of the Iterator Pattern (pdf)
Eric Torreborre
 
Modular Module Systems
league
 
The Ring programming language version 1.7 book - Part 28 of 196
Mahmoud Samir Fayed
 
Monadologie
league
 
Laziness, trampolines, monoids and other functional amenities: this is not yo...
Codemotion
 
The Ring programming language version 1.5.4 book - Part 25 of 185
Mahmoud Samir Fayed
 
Introduction to MatLab programming
Damian T. Gordon
 
[2024] An Introduction to Functional Programming with Go [Y Combinator Remix]...
Eleanor McHugh
 
The Ring programming language version 1.10 book - Part 31 of 212
Mahmoud Samir Fayed
 
Introduction to MATLAB
Damian T. Gordon
 
Initial value problems
Ali Jan Hasan
 
Learn Matlab
Abd El Kareem Ahmed
 
(2015 06-16) Three Approaches to Monads
Lawrence Evans
 
The Ring programming language version 1.9 book - Part 45 of 210
Mahmoud Samir Fayed
 
Map, Reduce and Filter in Swift
Aleksandras Smirnovas
 
The Ring programming language version 1.8 book - Part 42 of 202
Mahmoud Samir Fayed
 
Actors for Behavioural Simulation
ClarkTony
 
Haskell 101
Roberto Pepato
 
TDC2016SP - Trilha Programação Funcional
tdc-globalcode
 
haskell5.ppt is a marketing document lol
dopointt
 

Recently uploaded (20)

PDF
Adobe Premiere Pro 2025 (v24.5.0.057) Crack free
ghrom2211g
 
PDF
Understanding Forklifts - TECH EHS Solution
TECH EHS Solution
 
PDF
How to Migrate SBCGlobal Email to Yahoo Easily
raymondjones7273
 
PPTX
CHAPTER 2 - PM Management and IT Context
KevinPutra14
 
PDF
Nekopoi APK 2025 free lastest update
umarali35kp
 
PPTX
Transform Your Business with a Software ERP System
Canada Software Company
 
PPTX
Agentic AI Use Case- Contract Lifecycle Management (CLM).pptx
mhxyzzp
 
PDF
top salesforce developer skills in 2025.pdf
CloudMetic
 
PDF
Design an Analysis of Algorithms II-SECS-1021-03
DilanEscobar1
 
PDF
Addressing The Cult of Project Management Tools-Why Disconnected Work is Hold...
OnePlan Solutions
 
PPTX
Introduction to Artificial Intelligence
lohedi9363
 
PDF
Internet Downloader Manager (IDM) Crack 6.42 Build 42 Updates Latest 2025
itskinga12
 
PDF
Why TechBuilder is the Future of Pickup and Delivery App Development (1).pdf
TechBuilder
 
PDF
Which alternative to Crystal Reports is best for small or large businesses.pdf
Varsha Nayak
 
PPTX
Reimagine Home Health with the Power of Agentic AI​
AutomationEdge Technologies
 
PDF
How to Choose the Right IT Partner for Your Business in Malaysia
Asian Business Services & Technologies
 
PDF
Flood Susceptibility Mapping Using Image-Based 2D-CNN Deep Learnin. Overview ...
lawrenceomai2
 
PDF
How Creative Agencies Leverage Project Management Software.pdf
Orangescrum
 
PDF
Design an Analysis of Algorithms I-SECS-1021-03
DilanEscobar1
 
PPTX
Agentic AI : A Practical Guide. Undersating, Implementing and Scaling Autono...
IT IDOL Technologies
 
Adobe Premiere Pro 2025 (v24.5.0.057) Crack free
ghrom2211g
 
Understanding Forklifts - TECH EHS Solution
TECH EHS Solution
 
How to Migrate SBCGlobal Email to Yahoo Easily
raymondjones7273
 
CHAPTER 2 - PM Management and IT Context
KevinPutra14
 
Nekopoi APK 2025 free lastest update
umarali35kp
 
Transform Your Business with a Software ERP System
Canada Software Company
 
Agentic AI Use Case- Contract Lifecycle Management (CLM).pptx
mhxyzzp
 
top salesforce developer skills in 2025.pdf
CloudMetic
 
Design an Analysis of Algorithms II-SECS-1021-03
DilanEscobar1
 
Addressing The Cult of Project Management Tools-Why Disconnected Work is Hold...
OnePlan Solutions
 
Introduction to Artificial Intelligence
lohedi9363
 
Internet Downloader Manager (IDM) Crack 6.42 Build 42 Updates Latest 2025
itskinga12
 
Why TechBuilder is the Future of Pickup and Delivery App Development (1).pdf
TechBuilder
 
Which alternative to Crystal Reports is best for small or large businesses.pdf
Varsha Nayak
 
Reimagine Home Health with the Power of Agentic AI​
AutomationEdge Technologies
 
How to Choose the Right IT Partner for Your Business in Malaysia
Asian Business Services & Technologies
 
Flood Susceptibility Mapping Using Image-Based 2D-CNN Deep Learnin. Overview ...
lawrenceomai2
 
How Creative Agencies Leverage Project Management Software.pdf
Orangescrum
 
Design an Analysis of Algorithms I-SECS-1021-03
DilanEscobar1
 
Agentic AI : A Practical Guide. Undersating, Implementing and Scaling Autono...
IT IDOL Technologies
 

All You Need is Fold in the Key of C#