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f:monad

f/x

Applies the function f to x until a fixed point is reached: (f f x) ~ f x.

  %[;2]/50
0.0
  {1+%x}/1                      / golden ratio
1.618034
  _cos/1
0.7390851
  ,//(1;(2 3;(4 5;6);7 8);9)    / flatten
1 2 3 4 5 6 7 8 9

n f/x n:int

Applies the function f to x n times.

  4 (2+)/0
8
  (2+)(2+)(2+)(2+)0
8
  6 (10*)/1
1000000
  {x{x,+/-2#x}/!2} 5    / Fibonacci numbers
0 1 1 2 3 5 8

b f/x

Applies the f to x while the expression b is true.

  (1e6>)(2*)/1
1048576
  {|/x!'4 5 6 13}(1+)/1
780

f/x f:dyad

Applies the dyadic function f between the elements of x.

  +/1 2 3 4 5
15
  1+2+3+4+5
15
  -/1 2 3 4 5
-13
  1-2-3-4-5
-13
  {y-x}/1 2 3 4 5
3
  5-4-3-2-1
3

Applying a function using over on an empty list returns the identity element of the function:

  +/!0
0
  */!0
1

In the case of x f/y the x is the initial value, i.e.:

  2+/!6
17

f/[x0;x1;x1;...;xn] or {x+y+z}/[a;b;c] or {[a;b;c;d] ...}/[e;f;g;h]