# This section uses pyDatalog to illustrate datalog queries
#
# To install pyDatalog do the following:
#
# install python
# install pip (including prerequisites)
# type pip install pyDatalog
#
# To verify installation, start python IDLE, then type:
#
# from pyDatalog import pyDatalog
#
# If no package not found error, the package is installed correctly.

# ------------------- initialization ------------------
class NullDevice():
    def write(self, s):
        pass

import sys
stdoutbak = sys.stdout
sys.stdout = NullDevice()

from pyDatalog import pyDatalog

sys.stdout = stdoutbak

# Table terms
pyDatalog.create_terms("T,A,B")

# immediate significant
pyDatalog.create_terms("D")
#carry bit
pyDatalog.create_terms("C")
#result
pyDatalog.create_terms("R")


# variable terms
pyDatalog.create_terms("H,L,X,Z")


# ------------------- data insert ------------------

# insert into T, 8-length
for i in xrange(7,-1,-1):
    for j in xrange(i-1,-1,-1):
        + T (i,j)

#print T(H,Y)

# 1110100
+ A(2); + A(4); + A(5); + A(6);  
# 10100101: 
+ B(0); + B(2); + B(5); + B(7);

# print A(X)
# print B(X)


# ------------------- data insert ------------------

# immediate significant relation
D(H,L) <= T(H,L) & ~(T(H,Z) & T(Z,L))

#print D(H,L)

# carry bit
C(H) <= D(H,L) & A(L) & B(L) 
C(H) <= D(H,L) & C(L) & A(L) 
C(H) <= D(H,L) & C(L) & B(L)

#print C(H)

# final result
R(X) <= A(X) & B(X) & C(X)
R(X) <= A(X) & ~B(X) & ~C(X)
R(X) <= B(X) & ~A(X) & ~C(X)
R(X) <= C(X) & ~A(X) & ~B(X)

print R(X)