r"""
Module designed for the creation and printing of truth tables that are
associated with a logical statement.
A logic table is essentially a 2-D array that is created by the statement class
and stored in the private global variable table, along with a list containing
the variable names to be used, in order.
The order in which the table is listed essentially amounts to counting in binary.
For instance, with the variables A, B, and C the truth table looks like:
A B C value
False False False ?
False False True ?
False True False ?
False True True ?
True False False ?
True False True ?
True True False ?
True True True ?
This is equivalent to counting in binary, where a table would appear thus;
2^2 2^1 2^0 value
0 0 0 0
0 0 1 1
0 1 0 2
0 1 1 3
1 0 0 4
1 0 1 5
1 1 0 6
1 1 1 7
Given that a table can be created corresponding to any range of acceptable
values for a given statement, it is easy to find the value of a statement
for arbitrary values of its variables.
EXAMPLES:
sage: import sage.logic.propcalc as propcalc
sage: s = propcalc.formula("a&b|~(c|a)")
sage: s.truthtable()
a b c value
False False False True
False False True False
False True False True
False True True False
True False False False
True False True False
True True False True
True True True True
sage: latex(s.truthtable(5,11))
\\\begin{tabular}{llll}c & b & a & value \\\hline True & False & True & False \\True & True & False & True \\True & True & True & True\end{tabular}
It is not an error to use nonsensical numeric inputs.
sage: s = propcalc.formula("a&b|~(c|a)")
sage: s.truthtable(5, 9)
a b c value
True False True False
True True False True
True True True True
sage: s.truthtable(9, 5)
a b c value
If one argument is provided, truthtable defaults to the end.
sage: s.truthtable(-1)
a b c value
False False False True
False False True False
False True False True
False True True False
True False False False
True False True False
True True False True
True True True True
If the second argument is negative, truthtable defaults to the end.
sage: s.truthtable(4, -2)
a b c value
True False False False
True False True False
True True False True
True True True True
NOTES:
For statements that contain a variable list that when printed is longer than
the \latex page, the columns of the table will run off the screen.
"""
__table = []
__vars_order = []
class Truthtable:
def __init__(self, t, vo):
r"""
This function initializes the data fields and is called when a
new table is created.
INPUT:
self -- the calling object.
t -- a 2-D array containing the table values
vo -- a list of the variables in the expression in order,
with each variable occurring only once.
OUTPUT:
Effectively returns an instance of this class.
EXAMPLES:
This example illustrates the creation of a table.
sage: import sage.logic.propcalc as propcalc
sage: s = propcalc.formula("a&b|~(c|a)")
sage: s.truthtable()
a b c value
False False False True
False False True False
False True False True
False True True False
True False False False
True False True False
True True False True
True True True True
There should be no errors.
"""
self.__table = t
self.__vars_order = vo
def _latex_(self):
r"""
Returns a string representation of the calling table object.
INPUT:
self -- the calling object.
OUTPUT:
Returns the \latex representation of this table.
EXAMPLES:
sage: import sage.logic.propcalc as propcalc
sage: s = propcalc.formula("man->monkey&human")
sage: latex(s.truthtable())
\\\begin{tabular}{llll}human & monkey & man & value \\\hline False & False & False & True \\False & False & True & True \\False & True & False & True \\False & True & True & True \\True & False & False & False \\True & False & True & False \\True & True & False & False \\True & True & True & True\end{tabular}
Strange parameters can lead to a table header with no body.
sage: latex(s.truthtable(2, 1))
\\\begin{tabular}{llll}human & monkey & man & value \\\hli\end{tabular}
"""
vars_len = []
rt = s = ""
self.__vars_order.reverse()
s = r'\\\begin{tabular}{'
s += 'l' * (len(self.__vars_order) + 1) + '}'
for var in self.__vars_order:
s += var + ' & '
rt += s + r'value \\' + r'\hline '
for row in self.__table:
s = ""
for i in row:
s += str(i) + ' & '
rt += s[:-3] + r' \\'
rt = rt[:-3] + r'\end{tabular}'
self.__vars_order.reverse()
return rt
def __repr__(self):
r"""
This function returns a string representation of the calling table object.
INPUT:
self -- the calling object: not used.
OUTPUT:
Returns a string representation of this table.
EXAMPLES:
sage: import sage.logic.propcalc as propcalc
sage: s = propcalc.formula("man->monkey&human")
sage: s.truthtable()
man monkey human value
False False False True
False False True True
False True False True
False True True True
True False False False
True False True False
True True False False
True True True True
Strange parameters can lead to the table header with no body.
sage: s.truthtable(2, 1)
man monkey human value
There should be no errors.
"""
vars_len = []
line = rt = s = ""
for var in self.__vars_order:
vars_len.append(len(var))
s = var + ' '
while(len(s) < len('False ')):
s += ' '
s += ' '
line += s
rt += line + 'value\n'
for row in self.__table:
line = s = ""
i = 0
for e in row:
if e == True:
j = 2
else:
j = 1
s = str(e) + ' ' * j
if(i < len(vars_len)):
while(len(s) <= vars_len[i]):
s += ' '
s += ' '
line += s
i += 1
rt += line + '\n'
return rt
def get_table_list(self):
r"""
This function returns a string representation of the calling table object.
INPUT:
self -- the calling object: not used.
OUTPUT:
Returns the list representation of this table.
EXAMPLES:
sage: import sage.logic.propcalc as propcalc
sage: s = propcalc.formula("man->monkey&human")
sage: s.truthtable().get_table_list()
[['man', 'monkey', 'human'], [False, False, False, True], [False, False, True, True], [False, True, False, True], [False, True, True, True], [True, False, False, False], [True, False, True, False], [True, True, False, False], [True, True, True, True]]
"""
t = self.__table[:]
t.insert(0, self.__vars_order)
return t
