Data update
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Ingy döt Net
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10248 changed files with 63654 additions and 6775 deletions
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@ -1,3 +1,3 @@
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Y=. '('':''<@;(1;~":0)<@;<@((":0)&;))'(2 : 0 '')
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(1 : (m,'u'))(1 : (m,'''u u`:6('',(5!:5<''u''),'')`:6 y'''))(1 :'u u`:6')
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)
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Y=. {{x&(x`:6)`'' u y}} {{u`''&u}}
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fac=. 1:`{{(* x`:6@<:)y}}@.(0 < ])
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fib=. {{(-&1 +&(x`:6) -&2)y}}^:(1 < ])
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@ -1,6 +1 @@
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sr=. [ apply f.,&< NB. Self referring
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lv=. (((^:_1)b.)(`(<'0';_1)))(`:6) NB. Linear representation of a verb argument
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Y=. (&>)/lv(&sr) NB. Y with embedded states
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Y=. 'Y'f. NB. Fixing it...
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Y NB. ... To make it stateless (i.e., a combinator)
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((((&>)/)((((^:_1)b.)(`_1))(`:6)))(&([ 128!:2 ,&<)))
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XY=. (1 :'('':''<@;(1;~":0)<@;<@((":0)&;))u')(1 :'('':''<@;(1;~":0)<@;<@((":0)&;))((''u u`:6('',(5!:5<''u''),'')`:6 y''),(10{a.),'':'',(10{a.),''x(u u`:6('',(5!:5<''u''),'')`:6)y'')')(1 :'u u`:6')
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@ -1,20 +1,14 @@
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Y=:1 :0
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f=. u Defer
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(5!:1<'f') f y
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)
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Defer=: 1 :0
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:
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g=. x&(x`:6)
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(5!:1<'g') u y
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)
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almost_factorial=: 4 :0
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if. 0 >: y do. 1
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else. y * x`:6 y-1 end.
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)
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almost_fibonacci=: 4 :0
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if. 2 > y do. y
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else. (x`:6 y-1) + x`:6 y-2 end.
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)
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1 2 3 '([:`(>:@:])`(<:@:[ u 1:)`(<:@[ u [ u <:@:])@.(#.@,&*))'XY"0/ 1 2 3 4 5 NB. Ackermann function...
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3 4 5 6 7
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5 7 9 11 13
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13 29 61 125 253
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'1:`(<: u <:)@.* : (+ + 2 * u@:])'XY"0/~ i.7 NB. Ambivalent recursion...
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2 5 14 35 80 173 362
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3 6 15 36 81 174 363
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4 7 16 37 82 175 364
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5 8 17 38 83 176 365
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6 9 18 39 84 177 366
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7 10 19 40 85 178 367
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8 11 20 41 86 179 368
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NB. OEIS A097813 - main diagonal
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NB. OEIS A050488 = A097813 - 1 - adyacent upper off-diagonal
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@ -1,6 +1 @@
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almost_factorial Y 9
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362880
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almost_fibonacci Y 9
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34
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almost_fibonacci Y"0 i. 10
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0 1 1 2 3 5 8 13 21 34
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YX=. (1 :'('':''<@;(1;~":0)<@;<@((":0)&;))u')($:`)(`:6)
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@ -1,9 +0,0 @@
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Y=:2 :0(0 :0)
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NB. this block will be n in the second part
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:
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g=. x&(x`:6)
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(5!:1<'g') u y
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)
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f=. u (1 :n)
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(5!:1<'f') f y
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)
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@ -1,2 +0,0 @@
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almost_factorial f. Y 10
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3628800
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@ -1,4 +1,4 @@
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'if. * y do. y * u <: y else. 1 end.' Y 10 NB. Factorial
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3628800
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'(u@:<:@:<: + u@:<:)^:(1 < ])' Y 10 NB. Fibonacci
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55
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fac Y 9
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362880
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fib Y 9
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34
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@ -1,7 +1,4 @@
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arb=. ':'<@;(1;~":0)<@;<@((":0)&;) NB. AR of an explicit adverb from its body
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ara=. 1 :'arb u' NB. The verb arb as an adverb
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srt=. 1 :'arb ''u u`:6('' , (5!:5<''u'') , '')`:6 y''' NB. AR of the self-replication and transformation adverb
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gab=. 1 :'u u`:6' NB. The AR of the adverb and the adverb itself as a train
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Y=. ara srt gab NB. Train of adverbs
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Y=. ]:&>/]:^:_1 b.]:`(<'0';_1)`:6&([ 128!:2 ,&<)
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sr=. [ apply f. ,&< NB. Self referring
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fac=. 1:`(] * [ sr ] - 1:)@.(0 < ])
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fib=. (([ sr ] - 2:) + [ sr ] - 1:)^:(1 < ])
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@ -1 +1,4 @@
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XY=. (1 :'('':''<@;(1;~":0)<@;<@((":0)&;))u')(1 :'('':''<@;(1;~":0)<@;<@((":0)&;))((''u u`:6('',(5!:5<''u''),'')`:6 y''),(10{a.),'':'',(10{a.),''x(u u`:6('',(5!:5<''u''),'')`:6)y'')')(1 :'u u`:6')
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fac f. Y 10
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3628800
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fib f. Y 10
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55
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@ -1,14 +1,11 @@
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1 2 3 '([:`(>:@:])`(<:@:[ u 1:)`(<:@[ u [ u <:@:])@.(#.@,&*))'XY"0/ 1 2 3 4 5 NB. Ackermann function...
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3 4 5 6 7
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5 7 9 11 13
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13 29 61 125 253
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'1:`(<: u <:)@.* : (+ + 2 * u@:])'XY"0/~ i.7 NB. Ambivalent recursion...
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2 5 14 35 80 173 362
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3 6 15 36 81 174 363
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4 7 16 37 82 175 364
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5 8 17 38 83 176 365
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6 9 18 39 84 177 366
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7 10 19 40 85 178 367
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8 11 20 41 86 179 368
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NB. OEIS A097813 - main diagonal
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NB. OEIS A050488 = A097813 - 1 - adyacent upper off-diagonal
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fac f. Y NB. Factorial...
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'1:`(] * (([ 128!:2 ,&<) <:))@.(0 < ])&>/'&([ 128!:2 ,&<)
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fac f. NB. Factorial step...
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1:`(] * (([ 128!:2 ,&<) <:))@.(0 < ])
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fib f. Y NB. Fibonacci...
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'(([ ([ 128!:2 ,&<) ] - 2:) + [ ([ 128!:2 ,&<) ] - 1:)^:(1 < ])&>/'&([ 128!:2 ,&<)
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fib f. NB. Fibonacci step...
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(([ ([ 128!:2 ,&<) ] - 2:) + [ ([ 128!:2 ,&<) ] - 1:)^:(1 < ])
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@ -1 +1,6 @@
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YX=. (1 :'('':''<@;(1;~":0)<@;<@((":0)&;))u')($:`)(`:6)
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sr=. [ apply f. ,&< NB. Self referring
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lv=. ]:^:_1 b.]:`(<'0';_1)`:6 NB. Linear representation of a verb operand
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Y=. ]:&>/lv&sr NB. Y with embedded states
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Y=. 'Y' f. NB. Fixing it...
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Y NB. ... To make it stateless (i.e., a combinator)
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((]: & >) / ((((]: ^: (_1)) b. ]:) ` (<'0';_1)) `: 6)) & ([ 128!:2 ,&<)
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@ -1 +1,3 @@
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Y=. ((((&>)/)((((^:_1)b.)(`(<'0';_1)))(`:6)))(&([ 128!:2 ,&<)))
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Y=. '('':''<@;(1;~":0)<@;<@((":0)&;))'(2 : 0 '')
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(1 : (m,'u'))(1 : (m,'''u u`:6('',(5!:5<''u''),'')`:6 y'''))(1 :'u u`:6')
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)
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@ -1,11 +1,4 @@
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u=. [ NB. Function (left)
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n=. ] NB. Argument (right)
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sr=. [ apply f. ,&< NB. Self referring
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fac=. (1:`(n * u sr n - 1:)) @. (0 < n)
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fac f. Y 10
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'if. * y do. y * u <: y else. 1 end.' Y 10 NB. Factorial
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3628800
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Fib=. ((u sr n - 2:) + u sr n - 1:) ^: (1 < n)
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Fib f. Y 10
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'(u@:<:@:<: + u@:<:)^:(1 < ])' Y 10 NB. Fibonacci
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55
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@ -1,12 +1,7 @@
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fac f. Y NB. Factorial...
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'1:`(] * [ ([ 128!:2 ,&<) ] - 1:)@.(0 < ])&>/'&([ 128!:2 ,&<)
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arb=. ':'<@;(1;~":0)<@;<@((":0)&;) NB. AR of an explicit adverb from its body
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fac f. NB. Factorial step...
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1:`(] * [ ([ 128!:2 ,&<) ] - 1:)@.(0 < ])
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ara=. 1 :'arb u' NB. The verb arb as an adverb
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srt=. 1 :'arb ''u u`:6('' , (5!:5<''u'') , '')`:6 y''' NB. AR of the self-replication and transformation adverb
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gab=. 1 :'u u`:6' NB. The AR of the adverb and the adverb itself as a train
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Fib f. Y NB. Fibonacci...
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'(([ ([ 128!:2 ,&<) ] - 2:) + [ ([ 128!:2 ,&<) ] - 1:)^:(1 < ])&>/'&([ 128!:2 ,&<)
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Fib f. NB. Fibonacci step...
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(([ ([ 128!:2 ,&<) ] - 2:) + [ ([ 128!:2 ,&<) ] - 1:)^:(1 < ])
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Y=. ara srt gab NB. Train of adverbs
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14
Task/Y-combinator/Nu/y-combinator.nu
Normal file
14
Task/Y-combinator/Nu/y-combinator.nu
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@ -0,0 +1,14 @@
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def Y [f] {
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{|x| do $f {|y| do (do $x $x) $y } } | do $in $in
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}
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let factorial = Y {|rec|
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{|n| if $n < 2 { 1 } else { (do $rec ($n - 1)) * $n } }
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}
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let fibonacci = Y {|rec|
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{|n| if $n < 2 { $n } else { (do $rec ($n - 1)) + (do $rec ($n - 2)) } }
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}
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..9 | each { {fac: (do $factorial $in) fib: (do $fibonacci $in)} }
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> fac: {{$[y<2; 1; y*x y-1]} x}
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> (Y fac) 6
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720j
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> fib: {{$[y<2; 1; (x y-1) + (x y-2)]} x}
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> fib: {{$[y<2; y; (x y-1) + (x y-2)]} x}
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> (Y fib) each til 20
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1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
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0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181
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