Power (operator)
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⍣

Power (⍣
) is a primitive dyadic operator that performs bounded looping, unbounded looping, and function inverses in NARS2000, Dyalog APL, and related implementations like ngn/apl, dzaima/APL, and Extended Dyalog APL.
Description
A call to Power is of the form X(f⍣g)Y
, where
X
is an optional argument.f
is a function. IfX
is given, then it is bound tof
soX f⍣g Y
is equivalent toX∘f⍣g Y
.g
can be an array or a function.
Power repeatedly applies f
to Y
based on the type of operand g
:
 Function: Must be dyadic and must return a boolean singleton. The previous iteration value is provided as left argument to
f
, and the current iteration value is given as right argument.f
is repeatedly applied until this function returns 1.  Integer: Applies
f
g
times toY
. Ifg
is negative, then the inverse off
(if available) is applied.  Integer Array: In Extended Dyalog APL,
g
can be an integer array. Each integeri
ing
will be replaced by⊂(f⍣i)Y
.
Examples
Some basic examples:
1 (+⍣3) 5 ⍝ Fixed number of iterations
8
(2∘×⍣3) 5 ⍝ No X given
40
1 +∘÷⍣= 1 ⍝ iterate till fixed point
1.618033989
A wellknown use for Power is iterating until a fixed point is reached.
(∨.∧⍨∨⊢)⍣≡3 3⍴0 0 1 1 0 1 1 0 1 ⍝ Transitive closure of an adjacency matrix
1 0 1
1 0 1
1 0 1
Power is also used to access function inverses.
2(⊥⍣¯1)5
1 0 1