Mapping Boolean formulas to Python set expressions

Question

Say I have a Boolean formula that uses a known set of tokens, e.g.:

Boolean operators: and, or, not
Grouping operators: (, )

Given a Boolean formula using those tokens, e.g.:

F: (A or B) and not(A and C)

How can I convert this definition to a Python expression of set operators?

Fp = (x in A or x in B) and not(x in A and x in C)

For background on this question, see this thread and accepted answer.

Not sure why you accepted the linked answer which apparently didn't really solve the general problem. Anyway, you need to parse the boolean expression. You might find the [pyparsing](http://pyparsing.wikispaces.com/) module helpful. It comes with a number of examples to help you get going. — martineau, Mar 11 '14 at 17:50

score 1 · Answer 1 · answered Mar 11 '14 at 17:33

1

See the docs for set operations. You can do something like:

Fp = (A | B) - C

answered Mar 11 '14 at 17:33

Matt Woelk

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score 1 · Answer 2 · answered Mar 11 '14 at 17:37

1

Assuming your variables are one character in length:

s = "(A or B) and not(A and C)"
print re.sub("(?<![a-zA-Z])([A-Za-z])(?![A-Za-z])", "x in \\1", s)

answered Mar 11 '14 at 17:37

Sabuj Hassan

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score 1 · Answer 3 · answered Mar 11 '14 at 17:43

It looks like basically you are going to prepend x in to anything that is not one of your tokens. That looks like this, maybe:

tokens = ['and', 'or', 'not']
grouping = ['(', ')']

def resub(match):
    matchval = match.group(0)
    if matchval in tokens:
        return matchval
    return 'x in %s'%matchval

s = "(A or B) and not(A and C)"

re.sub('\w+', resub, s)
'(x in A or x in B) and not(x in A and x in C)'

It should work for symbols that are recognized as words; if you need something more specific (i.e. your variables have other characters in them), you'd need to define it yourself instead of using \w...

Hugh Bothwell · Answer 4 · 2014-03-11T17:58:21.310

This function will match against any Python identifier, will substitute for any desired target variable, and it's all wrapped up to be easy to use:

import re

def subst_in(s, varname, keywords={'and', 'or', 'not'}):
    repl = "{} in {{}}".format(varname)
    def fn(match):
        s = match.group(0)
        return s if s in keywords else repl.format(s)
    return re.sub("[a-z_][a-z0-9_]*", fn, s, flags=re.I)

f = "(A or B) and not(A and C)"
fp = subst_in(f, "x")

gives

'(x in A or x in B) and not(x in A and x in C)'

Edit: although frankly it should be

'x in B or (x in A and x not in C)'

Mapping Boolean formulas to Python set expressions

4 Answers4