Is there a way to create a fibonacci sequence in APL with a one-liner that doesn't require loops or flow control?

I've done it with a function using `→`

and a conditional test, but I feel there must be a more elegant, declarative way. An example that I've found that claims to do it on one line doesn't work on gnu-apl - it seems it's on the right track, using matrix math, but I'm having a hard time following along, and can't tweak it to work correctly.

I'm pursuing APL as my first real programming language (I love the symbols. I just do.) I'm now using Project Euler as a way to become better acquainted.

Answer:

I love APL's symbols too, as well as its array programming power. Other array languages may be more powerful, such as J, but they lack the beauty of APL's symbols and explicit syntax.

I just tried the example you link to in GNU APL and it works all right:

```
↑0 1↓↑+.×/5/⊂2 2⍴1 1 1 0
5
↑0 1↓↑+.×/6/⊂2 2⍴1 1 1 0
8
↑0 1↓↑+.×/7/⊂2 2⍴1 1 1 0
13
```

If you can't get it to work, make sure to:

- type (or copy and paste) the exact symbols shown in the example: in particular
`×`

is U+00D7 MULTIPLICATION SIGN, not an X;`⍴`

is U+2374 APL FUNCTIONAL SYMBOL RHO, not any other Greek Rho, and definitely not a P;`⊂`

is U+2282 SUBSET OF; and so on; - test some numbers other that 1 or 5, because they are the only numbers that are equal to their Fibonacci number;
- if you are not putting an actual number in place of N, make sure you define N in a proper way, such as
`N←7`

by itself in a previous line.

If you still can't get it to work, type the formula one step at a time, starting from the right:

```
2 2⍴1 1 1 0
1 1
1 0
⊂2 2⍴1 1 1 0
1 1
1 0
7/⊂2 2⍴1 1 1 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0 1 0 1 0 1 0 1 0 1 0 1 0
+.×/7/⊂2 2⍴1 1 1 0
21 13
13 8
↑+.×/7/⊂2 2⍴1 1 1 0
21 13
13 8
0 1↓↑+.×/7/⊂2 2⍴1 1 1 0
13
8
↑0 1↓↑+.×/7/⊂2 2⍴1 1 1 0
13
```

As for the question title, I think this matrix formula nails it (bravo @mappo!)

If I were golfing, I'd probably use a shorter variation, but that's all:

```
2⌷∊+.×/7/⊂∘.∨⍨1 0
13
```

There, from 24 to 17 chars. See if you can figure it out :-)

GNU APL is ok, although it lacks some modern features, but keep a copy of Dyalog APL Programmer's Guide & Language Reference handy, because it's one of the most comprehensive references about the language.

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