Create a Boolean parser

Question

What you need to do is create a Boolean parser.

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Boolean expressions, in case you haven't heard of them yet, have two inputs and one output. There are four 'gates' in boolean arithmetic, namely OR (represented by |), AND (represented by &), NOT (which are used a bit like brackets : / and \ note, I could have used !, but you can't use them as brackets, since !!!! is ambiguous (//\\ or /\/\)) and XOR (represented by ^). These gates operate on their inputs which are either true or false. We can list the possible inputs (A and B in this case) and the outputs (O) using a truth table as follows:

XOR
A|B|O
-----
0|0|0
0|1|1
1|0|1
1|1|0

OR
A|B|O
-----
0|0|0
0|1|1
1|0|1
1|1|1

AND
A|B|O
-----
0|0|0
0|1|0
1|0|0
1|1|1

NOT is only 1 input, and it goes from true to false and vice versa.

In Boolean expressions, they are used like this:

1^((0&1&1)&/(1&0&1)\)

Evaluating as follows:

1^(( 1 |1)&/(1&0&1)\)  |  0 OR 1 = 1, order of operations left to right - no brackets
1^(( 1   )&/(1&0&1)\)  |  1 OR 1 = 1
1^(  1    &/(1&0&1)\)  |  Remove brackets
1^(  1    &/( 0 &1)\)  |  1 AND 0 = 0
1^(  1    &/( 0   )\)  |  0 AND 1 = 0
1^(  1    &/  0    \)  |  Remove brackets
1^(  1    &   1     )  |  NOT 0 = 1
1^(  1              )  |  1 AND 1 = 1
1^   1                 |  Remove brackets
0                      |  1 XOR 1 = 0

so 0 is the result.

Task: create a program to do this!*

I/O examples

Input -> Output
1v(0.1) -> 1
1v(0.1./1\) -> 1
/0\v(0+1) -> 0
0v1v1 -> 0

Notes

• There is no order of precedence. We will treat 0.1v0+1 as (((0.1)v0)+1)

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Answer 1

GNU Sed 4.2.2, 102

Score includes +1 for -r option to sed:

y/+./oa/
:
s%/0\\%1%
s%/1\\|\b(0o0|(\w)v\2)%0%
s%\b(\wo\w|\wv\w|1a1)%1%
s/\b\wa\w/0/
s/\((\w)\)/\1/
t

Ideone.

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_{Incomplete Retina port.}