Let’s not override pipe operator. This will create confusion. Also ^^ is really odd.

What about using full names as operators for bitwise ops?

I already know a good one:

• xor

  A xor B

We just need to find nice ones for other. I know some languages do that.

And let’s implement them as functions. So we don’t need to worry about precedence.

Or as alternative solution add a special "macro": bit which will be converting those expressions:

bit(A | B ^ ~C) 

And let’s implement them as functions. So we don’t need to worry about precedence.

Following the comments, I will also be adding the following built-in functions, along with their respective precedences.

// Bitwise ops
&, bitand     -    bitwise AND            integers
bor, bitor    -    bitwise OR             integers
xor, bitxor   -    bitwise XOR            integers
&^, bitnand   -    bit clear (AND NOT)    integers
~, bitnot     -    bit NOT                integer

// Bit Shift ops
<<, bitshl    -    left shift             integer << integer >= 0
>>, bitshr    -    right shift            integer >> integer >= 0
>>>, bitushr  -    unsigned right shift 

But let's drop operators