Is Alice toepasbaar als introductie programmeertaal... (Els van Tol)
FRACTRAN - een tamelijk nutteloze...
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FRACTRAN FRACTRAN . . . een tamelijk nutteloze programmeertaal Hendrik Jan Hoogeboom Theoretische Informatica Universiteit Leiden 23.11’16 Leidsche Flesch Lunsch “And I thought Brainf*ck was weird” – R.H.
Transcript of FRACTRAN - een tamelijk nutteloze...
FRACTRAN
FRACTRAN. . . een tamelijk nutteloze programmeertaal
Hendrik Jan Hoogeboom
Theoretische Informatica
Universiteit Leiden 23.11’16
Leidsche Flesch Lunsch
“And I thought Brainf*ck was weird” – R.H.
FRACTRAN
“Hello world”
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)
FRACTRAN
searching for simple and powerful models
models for computability
Alan Turing (1912–1954)
“On Computable Numbers, with anApplication to the Entscheidungsproblem” (1937)
Emil Post (1897–1954)
“Finite Combinatory Processes - Formulation 1” (1936)
Marvin Minsky (1927–2016)
counter machine / register machine (1961)
pictures from turingarchive.org, Wikipedia, Bcjordan CC BY 3.0
FRACTRAN
John Horton Conway
Life, Death and the Monster - Numberphile (2014)
John Horton Conway (1937)
combinatorial game theory:surreal numbers, game of Life
geometric topology:knot polynomials
group theory: “A perfect group of order
8,315,553,613,086,720,000 . . .”
algorithmics: doomsday algorithm
theoretical physics:“ if experimenters have free will, then so do
elementary particles”
FRACTRAN
John Horton Conway
Life, Death and the Monster - Numberphile (2014)
John Horton Conway (1937)
combinatorial game theory:surreal numbers, game of Life
geometric topology:knot polynomials
group theory: “A perfect group of order
8,315,553,613,086,720,000 . . .”
algorithmics: doomsday algorithm
theoretical physics:“ if experimenters have free will, then so do
elementary particles”
FRACTRAN
John Horton Conway
Life, Death and the Monster - Numberphile (2014)
John Horton Conway (1937)
combinatorial game theory:surreal numbers, game of Life
geometric topology:knot polynomials
group theory: “A perfect group of order
8,315,553,613,086,720,000 . . .”
algorithmics: doomsday algorithm
theoretical physics:“ if experimenters have free will, then so do
elementary particles”
FRACTRAN
John Horton Conway
Life, Death and the Monster - Numberphile (2014)
John Horton Conway (1937)
combinatorial game theory:surreal numbers, game of Life
geometric topology:knot polynomials
group theory: “A perfect group of order
8,315,553,613,086,720,000 . . .”
algorithmics: doomsday algorithm
theoretical physics:“ if experimenters have free will, then so do
elementary particles”
FRACTRAN
John Horton Conway
Life, Death and the Monster - Numberphile (2014)
John Horton Conway (1937)
combinatorial game theory:surreal numbers, game of Life
geometric topology:knot polynomials
group theory: “A perfect group of order
8,315,553,613,086,720,000 . . .”
algorithmics: doomsday algorithm
theoretical physics:“ if experimenters have free will, then so do
elementary particles”
FRACTRAN
qualities of FRACTRAN
Only FRACTRAN has these star qualities!
Makes workday really easy!no complicated programming manual
Gets those functions really clean!configuration in a single integer, no other foreign concepts
Matches any machine on the marketeasy to write a FRACTRAN program to simulate othermachines
Astoundingly simple universal program!
FRACTRAN
computing with FRACTRAN
A Program for Primes
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)
FRACTRAN
computing with FRACTRAN
A Program for Primes
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132,116, 308, 364, 68, 4, 30, 225, 12375, 10875, 28875, 25375, 67375, 79625,14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 10780, 12740, 2380,2184, 408, 152, 92, 380, 230, 950, 575, 2375, 9625, 11375, 2125, 1950,1650, 1450, 3850, 4550, 850, 780, 660, 580, 1540, 1820, 340, 312, 264,232, 616, 728, 136, 8, 60, 450, 3375, 185625, 163125, 433125, 380625,1010625, 888125, 2358125, 2786875, 520625, 477750, 89250, 81900,15300, 14040, 11880, 10440, 27720, 24360, 64680, 56840, 150920,178360, 33320, 30576, 5712, 2128, 1288, 5320, 3220, 13300, 8050, 33250,20125, 83125, 336875, 398125, 74375, 68250, 12750, 11700, 9900, 8700,23100, 20300, 53900, 63700, . . .
FRACTRAN
computing with FRACTRAN
A Program for Primes
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132,116, 308, 364, 68, 4, 30, 225, 12375, 10875, 28875, 25375, 67375, 79625,14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 10780, 12740, 2380,2184, 408, 152, 92, 380, 230, 950, 575, 2375, 9625, 11375, 2125, 1950,1650, 1450, 3850, 4550, 850, 780, 660, 580, 1540, 1820, 340, 312, 264,232, 616, 728, 136, 8, 60, 450, 3375, 185625, 163125, 433125, 380625,1010625, 888125, 2358125, 2786875, 520625, 477750, 89250, 81900,15300, 14040, 11880, 10440, 27720, 24360, 64680, 56840, 150920,178360, 33320, 30576, 5712, 2128, 1288, 5320, 3220, 13300, 8050, 33250,20125, 83125, 336875, 398125, 74375, 68250, 12750, 11700, 9900, 8700,23100, 20300, 53900, 63700, . . .
FRACTRAN
computing with FRACTRAN
A Program for Primes
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132,116, 308, 364, 68, 4, 30, 225, 12375, 10875, 28875, 25375, 67375, 79625,14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 10780, 12740, 2380,2184, 408, 152, 92, 380, 230, 950, 575, 2375, 9625, 11375, 2125, 1950,1650, 1450, 3850, 4550, 850, 780, 660, 580, 1540, 1820, 340, 312, 264,232, 616, 728, 136, 8, 60, 450, 3375, 185625, 163125, 433125, 380625,1010625, 888125, 2358125, 2786875, 520625, 477750, 89250, 81900,15300, 14040, 11880, 10440, 27720, 24360, 64680, 56840, 150920,178360, 33320, 30576, 5712, 2128, 1288, 5320, 3220, 13300, 8050, 33250,20125, 83125, 336875, 398125, 74375, 68250, 12750, 11700, 9900, 8700,23100, 20300, 53900, 63700, . . .
FRACTRAN
computing with FRACTRAN
A Program for Primes
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132,116, 308, 364, 68, 4, 30, 225, 12375, 10875, 28875, 25375, 67375, 79625,14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 10780, 12740, 2380,2184, 408, 152, 92, 380, 230, 950, 575, 2375, 9625, 11375, 2125, 1950,1650, 1450, 3850, 4550, 850, 780, 660, 580, 1540, 1820, 340, 312, 264,232, 616, 728, 136, 8, 60, 450, 3375, 185625, 163125, 433125, 380625,1010625, 888125, 2358125, 2786875, 520625, 477750, 89250, 81900,15300, 14040, 11880, 10440, 27720, 24360, 64680, 56840, 150920,178360, 33320, 30576, 5712, 2128, 1288, 5320, 3220, 13300, 8050, 33250,20125, 83125, 336875, 398125, 74375, 68250, 12750, 11700, 9900, 8700,23100, 20300, 53900, 63700, . . .
FRACTRAN
computing with FRACTRAN
A Program for Primes
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132,116, 308, 364, 68, 4, 30, 225, 12375, 10875, 28875, 25375, 67375, 79625,14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 10780, 12740, 2380,2184, 408, 152, 92, 380, 230, 950, 575, 2375, 9625, 11375, 2125, 1950,1650, 1450, 3850, 4550, 850, 780, 660, 580, 1540, 1820, 340, 312, 264,232, 616, 728, 136, 8, 60, 450, 3375, 185625, 163125, 433125, 380625,1010625, 888125, 2358125, 2786875, 520625, 477750, 89250, 81900,15300, 14040, 11880, 10440, 27720, 24360, 64680, 56840, 150920,178360, 33320, 30576, 5712, 2128, 1288, 5320, 3220, 13300, 8050, 33250,20125, 83125, 336875, 398125, 74375, 68250, 12750, 11700, 9900, 8700,23100, 20300, 53900, 63700, . . . ,
FRACTRAN
computing with FRACTRAN
A Program for Primes
(17
91,78
85,19
51,23
38,29
33,77
29,95
23,77
19,1
17,11
13,13
11,15
14,15
2,55
1
)21, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132,116, 308, 364, 68, 4
20, 30, 225, 12375, 10875, 28875, 25375, 67375, 79625,
14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 10780, 12740, 2380,2184, 408, 152, 92, 380, 230, 950, 575, 2375, 9625, 11375, 2125, 1950,1650, 1450, 3850, 4550, 850, 780, 660, 580, 1540, 1820, 340, 312, 264,232, 616, 728, 136, 8
70, 60, 450, 3375, 185625, 163125, 433125, 380625,
1010625, 888125, 2358125, 2786875, 520625, 477750, 89250, 81900,15300, 14040, 11880, 10440, 27720, 24360, 64680, 56840, 150920,178360, 33320, 30576, 5712, 2128, 1288, 5320, 3220, 13300, 8050, 33250,20125, 83125, 336875, 398125, 74375, 68250, 12750, 11700, 9900, 8700,23100, 20300, 53900, 63700, . . . , 32
281, . . . , 128
708, . . . , 2048
2364, . . . , 8192
3877, . . .
FRACTRAN
qualities of FRACTRAN
Only FRACTRAN has these star qualities!
Makes workday really easy!no complicated programming manual
Gets those functions really clean!configuration in a single integer, no other foreign concepts
Matches any machine on the marketeasy to write a FRACTRAN program to simulate othermachines
Astoundingly simple universal program!
FRACTRAN
qualities of FRACTRAN
easy to write . . .(36546 ,
29161 ,
79575 ,
679451 ,
3159413 ,
83409 ,
473371 ,
638355 ,
434335 ,
89235 ,
17209 ,
79122 ,
31183 ,
41115 ,
51789 ,
11183 ,
30579 ,
2373 ,
7371 ,
6167 ,
3761 ,
1959 ,
8957 ,
4153 ,
83347 ,
5343
8641 ,
1338 ,
2337 ,
6731 ,
7129 ,
8319 ,
47517 ,
5913 ,
41291 ,
17 ,
111 ,
11024 ,
197 ,
891
)started at 2n the next power of 2 to appear is 2π(n) where
n = 0 1 2 3 4 5 6 7 8 9 10 11 12 . . .π(n) = 3 1 4 1 5 9 2 6 5 3 5 8 9 . . .
π
2=
2
1·23·43·45·65·67·87·89· . . . (Wallis)
FRACTRAN
A Program for Primes
Prime decomposition(17
7·13,2·3·135·17
,19
3·17,23
2·19,29
3·11,7·1129
,5·1923
,7·1119
,1
17,11
13,13
11,3·52·7
,3·52,5·111
)2
FRACTRAN
A Program for Primes
Prime decomposition(17
7·13,2·3·135·17
,19
3·17,23
2·19,29
3·11,7·1129
,5·1923
,7·1119
,1
17,11
13,13
11,3·52·7
,3·52,5·111
)2, 3·5
FRACTRAN
A Program for Primes
Prime decomposition(17
7·13,2·3·135·17
,19
3·17,23
2·19,29
3·11,7·1129
,5·1923
,7·1119
,1
17,11
13,13
11,3·52·7
,3·52,5·111
)2, 3·5, 3·52·11
FRACTRAN
A Program for Primes
Prime decomposition(17
7·13,2·3·135·17
,19
3·17,23
2·19,29
3·11,7·1129
,5·1923
,7·1119
,1
17,11
13,13
11,3·52·7
,3·52,5·111
)2, 3·5, 3·52·11, 52·29
FRACTRAN
A Program for Primes
Prime decomposition(17
7·13,2·3·135·17
,19
3·17,23
2·19,29
3·11,7·1129
,5·1923
,7·1119
,1
17,11
13,13
11,3·52·7
,3·52,5·111
)2, 3·5, 3·52·11, 52·29, 52·7·11
FRACTRAN
A Program for Primes
Prime decomposition(17
7·13,2·3·135·17
,19
3·17,23
2·19,29
3·11,7·1129
,5·1923
,7·1119
,1
17,11
13,13
11,3·52·7
,3·52,5·111
)2, 3·5, 3·52·11, 52·29, 52·7·11, 52·7·13
FRACTRAN
A Program for Primes
Prime decomposition(17
7·13,2·3·135·17
,19
3·17,23
2·19,29
3·11,7·1129
,5·1923
,7·1119
,1
17,11
13,13
11,3·52·7
,3·52,5·111
)2, 3·5, 3·52·11, 52·29, 52·7·11, 52·7·13, 52·17, 2·3·5·13, 2·3·5·11,2·5·29, 2·5·7·11, 2·5·7·13, 2·5·17, 22·3·13, 22·3·11, 22·29, 22·7·11,22·7·13, 22·17, 22, 2·3·5, 32·52, 32·53·11, 3·53·29, 3·537·11, . . .
FRACTRAN
Small program (2
3
)25·33 ; 26·32 ; 27·31 ; 28·30
2a·3b ; 2a+ b
FRACTRAN
Small program (2
3
)25·33 ; 26·32 ; 27·31 ; 28·30
2a·3b ; 2a+ b
while b>0 do
a++; b--;
od
// a += b;
// b = 0;
FRACTRAN
Small program (2) (5
2·3,1
2,1
3
)25·33
; 24·32·51 ; 23·31·52 ; 22·30·53 ; 21·53 ; 53
FRACTRAN
Small program (2) (5
2·3,1
2,1
3
)25·33 ; 24·32·51 ; 23·31·52 ; 22·30·53 ; 21·53 ; 53
FRACTRAN
Small program (2) (5
2·3,1
2,1
3
)25·33 ; 24·32·51 ; 23·31·52 ; 22·30·53 ; 21·53 ; 53
2a·3b ; 5min(a, b)
while a·b>0 do
a--; b--; c++
od
// a=0 || b=0
while a>0 do
a--;
od
// a=0
while b>0 do
b--;
od
FRACTRAN
Multiplication
Loops that multiply
multiplication a = b · c
registers a,b,c,d 2, 3, 5, 7states 11, 13, 17, 19, 23
value 2a·3b·5c·7d · s
// (repeat c times) a += b;
while c>0 do
while b>0 do
a++; b--;
d++
od
while d>0 do
d--; b++;
od
c--;
od
// ready: ’exit’
23
exit
15
FRACTRAN
Multiplication
Loops that multiply
multiplication a = b · c
registers a,b,c,d 2, 3, 5, 7states 11, 13, 17, 19, 23
value 2a·3b·5c·7d · s
// (repeat c times) a += b;
while c>0 do
while b>0 do
a++; b--;
d++
od
X while d>0 do
d--; b++;
od
c--;
od
// ready: ’exit’
X
2·73
15
37
exit
1719
FRACTRAN
Multiplication
Loops that multiply
multiplication a = b · c
registers a,b,c,d 2, 3, 5, 7states 11, 13, 17, 19, 23
value 2a·3b·5c·7d · s
// (repeat c times) a += b;
while c>0 do
while b>0 do
a++; b--;
d++
od
while d>0 do
d--; b++;
od
c--;
od
// ready: ’exit’
11
13
17
19
23
2·7·133·11
1113
1711
115·17
3·197·17
2317
1719
(. . . ,
3·197·17
,11
5·17,23
17, . . .
)d > 0 d = 0&c > 0 d = c = 0
17
15
FRACTRAN
Multiplication
multiplication & division (wikipedia)
multiplication(5·7·133·11 ,
1113 ,
111 ,
37 ,
112 ,
13
)
11
13
1
5·73
12
37
13
2a·3b ; 5a·b
division(7·132·3·11 ,
1113 ,
13·11 ,
5·1711 ,
3·197·17 ,
1719 ,
1117 .
13
)
11
13n=n-dd=0r=d
17d=rr=0q++
1
d=0
19
72·3
51
13start
13
37
2n·3d·11 ; 5q ·7r(n = q·d+ r, 0 ≤ r < d)
FRACTRAN
Final Program
(177·13 ,
2·3·135·17 ,
193·17 ,
232·19 ,
293·11 ,
7·1129 ,
5·1923 ,
7·1119 ,
117 ,
1113 ,
1311 ,
3·52·7 ,
3·52 ,
5·111
)
1311 17
1
19
29
23
d--
a++b++c--
a-- c++
b==0c==0c++
c==o
b--a==o
d--
b--
d++ b==0
d==0
b++c++a--d--
b++c++a--
R.K. Guy: Conway’s prime producing machine,Mathematics Magazine (1983)
FRACTRAN
Counter Machines
models for computability
Alan Turing (1912–1954)
“On Computable Numbers, with anApplication to the Entscheidungsproblem” (1937)
Emil Post (1897–1954)
“Finite Combinatory Processes - Formulation 1” (1936)
Marvin Minsky (1927–2016)
counter machine / register machine (1961)
#z: increment counter i, goto #x
#z: if counter i zero, goto #x,else decrement and goto #y
FRACTRAN
Counter Machines
models for computability
Alan Turing (1912–1954)
“On Computable Numbers, with anApplication to the Entscheidungsproblem” (1937)
Emil Post (1897–1954)
“Finite Combinatory Processes - Formulation 1” (1936)
Marvin Minsky (1927–2016)
counter machine / register machine (1961)
#z: increment counter i, goto #xi·xz
#z: if counter i zero, goto #x,
else decrement and goto #yy
i·z,x
z
FRACTRAN
Counter Machines
Only FRACTRAN has these star qualities!
Makes workday really easy!no complicated programming manual
Gets those functions really clean!configuration in a single integer, no other foreign concepts
Matches any machine on the marketeasy to write a FRACTRAN program to simulate othermachines
Astoundingly simple universal program!
FRACTRAN
Counter Machines
Only FRACTRAN has these star qualities!
Makes workday really easy!no complicated programming manual
Gets those functions really clean!configuration in a single integer, no other foreign concepts
Matches any machine on the marketeasy to write a FRACTRAN program to simulate othermachines
Astoundingly simple universal program!(583
559,629
551,437
527,82
517,615
329,371
129,
1
115,53
86,43
53,23
47,341
46,
41
43,47
41,29
37,37
31,299
29,47
23,161
15,527
19,159
7,1
17,1
13,1
3
)
FRACTRAN
Bibliography
J.H. Conway.Unpredictable Iterations.In: Proc. 1972 Number Theory Conference, Boulder Colorado,1972.
J.H. Conway.FRACTRAN: A simple universal programming language forarithmeticIn: Open Problems in Communication and Computation,Springer, 1983.
Julian Havil.Nonplussed!Princeton University Press, 2007
FRACTRAN
Bibliography
H.J. Hoogeboom.Carriers and Counters –P Systems with Carriers vs. (Blind) Counter Automata
Developments in Language Theory, LNCS 2450, 2003.(connection between counter automata and computational models)
