Initial data commit

Task/Y-combinator/J/y-combinator-1.j

@@ -0,0 +1,3 @@
+Y=. '('':''<@;(1;~":0)<@;<@((":0)&;))'(2 : 0 '')
+  (1 : (m,'u'))(1 : (m,'''u u`:6('',(5!:5<''u''),'')`:6 y'''))(1 :'u u`:6')
+)

Task/Y-combinator/J/y-combinator-10.j

@@ -0,0 +1,6 @@
+   sr=. [ apply f.,&<                 NB. Self referring
+   lv=. (((^:_1)b.)(`(<'0';_1)))(`:6) NB. Linear representation of a verb argument
+   Y=. (&>)/lv(&sr)                   NB. Y with embedded states
+   Y=. 'Y'f.                          NB. Fixing it...
+   Y                                  NB. ... To make it stateless (i.e., a combinator)
+((((&>)/)((((^:_1)b.)(`_1))(`:6)))(&([ 128!:2 ,&<)))

Task/Y-combinator/J/y-combinator-11.j

@@ -0,0 +1,20 @@
+Y=:1 :0
+  f=. u Defer
+  (5!:1<'f') f y
+)
+
+Defer=: 1 :0
+:
+  g=. x&(x`:6)
+  (5!:1<'g') u y
+)
+
+almost_factorial=: 4 :0
+  if. 0 >: y do. 1
+  else. y * x`:6 y-1 end.
+)
+
+almost_fibonacci=: 4 :0
+  if. 2 > y do. y
+  else. (x`:6 y-1) + x`:6 y-2 end.
+)

Task/Y-combinator/J/y-combinator-12.j

@@ -0,0 +1,6 @@
+   almost_factorial Y 9
+362880
+   almost_fibonacci Y 9
+34
+   almost_fibonacci Y"0 i. 10
+0 1 1 2 3 5 8 13 21 34

Task/Y-combinator/J/y-combinator-13.j

@@ -0,0 +1,9 @@
+Y=:2 :0(0 :0)
+NB. this block will be n in the second part
+:
+  g=. x&(x`:6)
+  (5!:1<'g') u y
+)
+  f=. u (1 :n)
+  (5!:1<'f') f y
+)

Task/Y-combinator/J/y-combinator-14.j

@@ -0,0 +1,2 @@
+   almost_factorial f. Y 10
+3628800

Task/Y-combinator/J/y-combinator-2.j

@@ -0,0 +1,4 @@
+   'if. * y do. y * u <: y else. 1 end.' Y 10 NB. Factorial
+3628800
+          '(u@:<:@:<: + u@:<:)^:(1 < ])' Y 10 NB. Fibonacci
+55

Task/Y-combinator/J/y-combinator-3.j

@@ -0,0 +1,7 @@
+   arb=. ':'<@;(1;~":0)<@;<@((":0)&;)                     NB. AR of an explicit adverb from its body
+
+   ara=. 1 :'arb u'                                       NB. The verb arb as an adverb
+   srt=. 1 :'arb ''u u`:6('' , (5!:5<''u'') , '')`:6 y''' NB. AR of the self-replication and transformation adverb
+   gab=. 1 :'u u`:6'                                      NB. The AR of the adverb and the adverb itself as a train
+
+   Y=. ara srt gab                                        NB. Train of adverbs

Task/Y-combinator/J/y-combinator-4.j

@@ -0,0 +1 @@
+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')

Task/Y-combinator/J/y-combinator-5.j

@@ -0,0 +1,14 @@
+   1 2 3 '([:`(>:@:])`(<:@:[ u 1:)`(<:@[ u [ u <:@:])@.(#.@,&*))'XY"0/  1 2 3 4 5 NB. Ackermann function...
+ 3  4  5   6   7
+ 5  7  9  11  13
+13 29 61 125 253
+                               '1:`(<: u <:)@.* : (+ + 2 * u@:])'XY"0/~ i.7       NB. Ambivalent recursion...
+2  5 14 35 80 173 362
+3  6 15 36 81 174 363
+4  7 16 37 82 175 364
+5  8 17 38 83 176 365
+6  9 18 39 84 177 366
+7 10 19 40 85 178 367
+8 11 20 41 86 179 368
+   NB. OEIS A097813 - main diagonal
+   NB. OEIS A050488 = A097813 - 1 - adyacent upper off-diagonal

Task/Y-combinator/J/y-combinator-6.j

@@ -0,0 +1 @@
+YX=. (1 :'('':''<@;(1;~":0)<@;<@((":0)&;))u')($:`)(`:6)

Task/Y-combinator/J/y-combinator-7.j

@@ -0,0 +1 @@
+Y=. ((((&>)/)((((^:_1)b.)(`(<'0';_1)))(`:6)))(&([ 128!:2 ,&<)))

Task/Y-combinator/J/y-combinator-8.j

@@ -0,0 +1,11 @@
+   u=. [ NB. Function (left)
+   n=. ] NB. Argument (right)
+   sr=. [ apply f. ,&< NB. Self referring
+
+   fac=. (1:`(n * u sr n - 1:)) @. (0 < n)
+   fac f. Y 10
+3628800
+
+   Fib=. ((u sr n - 2:) + u sr n - 1:) ^: (1 < n)
+   Fib f. Y 10
+55

Task/Y-combinator/J/y-combinator-9.j

@@ -0,0 +1,12 @@
+   fac f. Y NB. Factorial...
+'1:`(] * [ ([ 128!:2 ,&<) ] - 1:)@.(0 < ])&>/'&([ 128!:2 ,&<)
+
+   fac f.   NB. Factorial step...
+1:`(] * [ ([ 128!:2 ,&<) ] - 1:)@.(0 < ])
+
+
+   Fib f. Y NB. Fibonacci...
+'(([ ([ 128!:2 ,&<) ] - 2:) + [ ([ 128!:2 ,&<) ] - 1:)^:(1 < ])&>/'&([ 128!:2 ,&<)
+
+   Fib f.   NB. Fibonacci step...
+(([ ([ 128!:2 ,&<) ] - 2:) + [ ([ 128!:2 ,&<) ] - 1:)^:(1 < ])