Here are a couple approaches:
First, make a list, then take the last thing in it.
fib_list=:3 : 0
z=.0 1
for. i.y-1 do.
z=.z,+/_2{. z
end.
if. y>0 do. z else. 0 end. NB. this only used to make fib_list 0 correct
)
fib_list 10
0 1 1 2 3 5 8 13 21 34 55
fib=:{:@fib_list
fib 10
55
fib 0
0
Or use matrix multiply
mp=:+/ . *
]W=:*i.2 2
0 1
1 1
W takes one fib pair to the next one
W mp 13 21
21 34
fib2=:3 : '{. W&mp^:y 0 1'
fib2 10
55
NB. It even works correctly for negative integers
fib2 _2
_1
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