truth tables with /~ in J

Question

I was experimenting with generating truth tables in J:

    nand =: *:
    nand /~ 0 1
1 1
1 0
    bxor =: 22 b.  NB. Built-in bitwise XOR
    bxor /~ 0 1
0 1
1 0

Now I want to define my own logical xor, which I did like so:

    xor =: 3 : 0
]y                     NB. monadic case is just the identity
:
(x*.-.y)+.(y*.-.x)     NB. dyadic case is (x AND NOT y) OR (y AND NOT x)
)

This works as I expect when I call it directly.

    0 xor 0 1
0 1
    1 xor 0 1
1 0

But it doesn't generate a truth table:

    xor /~ 0 1
0 0

Why not?

I thought maybe the problem was that ]/~ 0 1 itself produced a 1 x 2 array, so I changed the monadic part to use nand (*:y) because it produces the 2x2 array:

    *:/~ 0 1
1 1
1 0


   xor =: 3 : 0
*:y                  NB. certainly wrong, but at least has 2x2 shape.
:
(x*.-.y)+.(y*.-.x)
)

But I still get the same behavior:

    xor /~ 0 1
0 0

Can someone help me understand the flaw in my thinking?

Answer 1

Your xor has infinite rank, while *:,~: have rank 0. You can verify that by using b.: v b. 0 like so:

~: b. 0
  _ 0 0 

*: b. 0
  0 0 0

xor b. 0
  _ _ _

What this means is that xor operates on the list 0 1 rather than on each individual atom 0, 1.

You will get the result you expect if you use xor with rank 0:

xor"0 /~ 0 1
0 1
1 0

Or if you define xor to be of rank 0.