yap-6.3/CHR/chr/examples/examples-adder.bool

% Simple examples for boolean handler
/*
[eclipse 6]: and(X,Y,Z),(X=1;X=0;X=Y).

Z = Var_m333
X = 1
Y = Var_m333
 
Constraints:
(3) boolean(Var_m333)
     More? (;) 

Z = 0
X = 0
Y = Var_m333

Constraints:
(3) boolean(Var_m333)
     More? (;) 
 
Z = _m309
X = _m309
Y = _m309

Constraints:
(3) boolean(_m309)

yes.
*/


% alternative formulations

nand1(X1,Y1,Z):- and(X,Y,Z),neg(X1,X),neg(Y1,Y).
nand2(X1,Y1,Z):- or(X1,Y1,Z1),neg(Z1,Z).
test_nand(X,Y,Z1,Z2):- nand1(X,Y,Z1),nand2(X,Y,Z2),neg(Z1,Z2).

or1(X,Y,Z):- nand1(X,Y,Z1),neg(Z1,Z).
or2(X,Y,Z):- nand2(X,Y,Z1),neg(Z1,Z).
or3(A,B,C):- xor(A,B,D),and(A,B,E),xor(D,E,C).
test_or(A,B,C,D):- (or1(A,B,C);or2(A,B,C);or3(A,B,C)),or(A,B,D),neg(C,D).

xor1(A,B,C):- or(A,B,C1), and(A,B,C2), neg(C2,C3), and(C1,C3,C).
test_xor(A,B,C,D):- xor1(A,B,C),xor(A,B,D),neg(C,D).

and1(A,B,C):- neg(A,AN),neg(B,BN),or(AN,BN,CN),neg(CN,C).
test_and(A,B,C,D):-  and1(A,B,C),and(A,B,D),neg(C,D).

test(X,Y,Z):-  and(X,Y,Z),or(X,Y,Z),neg(X,Z).


% full-adder circuit boolean algebra example sept 1991, nov 1993

add(I1,I2,I3,O1,O2):-
	xor(I1,I2,X1),
	and(I1,I2,A1),
	xor(I3,X1,O1),
	and(I3,X1,A2),
	or(A1,A2,O2).
/*
add(L1,L2,L3):- add(L1,L2,L3,0).

add([],[],[C],C).
add([X|L1],[Y|L2],[Z|L3],C):-
	add(X,Y,C,Z,C1),
	add(L1,L2,L3,C1).
*/

add(L1,L2,[C|L3]):- add(L1,L2,L3,C).

add([],[],[],0).
add([X|L1],[Y|L2],[Z|L3],C):-
	add(L1,L2,L3,C1),
	add(X,Y,C1,Z,C).

/*
[eclipse 56]: add(L,L,R).

L = []
R = [0]     More? (;) 

L = [_g71]
R = [_g71, 0]     More? (;) 

L = [_g71, _g79]
R = [_g71, _g79, 0]     More? (;) 

L = [_g71, _g79, _g87]
R = [_g71, _g79, _g87, 0]     More? (;) 
 
L = [_g71, _g79, _g87, _g95]
R = [_g71, _g79, _g87, _g95, 0]     More? (;) 


[eclipse 59]: add([X,X,X],[Y,Y,Y],R), (X=1;X=0;X=Y;neg(X,Y)).

R = [_m5677, Var_m4777, Var_m2407, Var_m419]
X = 1
Y = Var_m395
 
Constraints:
(39) boolean(_m5251)
(33) boolean(Var_m1499)
(19) and(Var_m395, Var_m1499, 0)
(31) xor(Var_m395, Var_m1499, Var_m4777)
(34) and(Var_m395, Var_m1499, _m5251)
(16) xor(Var_m395, Var_m1499, Var_m2407)
(43) neg(Var_m395, Var_m419)
(38) boolean(Var_m395)
(37) or(Var_m395, _m5251, _m5677)
     More? (;) 

R = [0, Var_m395, Var_m395, Var_m395]
X = 0
Y = Var_m395
 
Constraints:
(33) boolean(Var_m395)
     More? (;) 

R = [_m371, _m371, _m371, 0]
X = _m371
Y = _m371

Constraints:
(3) boolean(_m371)
     More? (;) 

R = [_m5251, Var_m4777, Var_m2407, Var_m419]
X = _m371
Y = Var_m395

Constraints:
(1) xor(_m371, Var_m395, Var_m419)
(2) boolean(_m371)
(3) boolean(Var_m395)
(4) and(_m371, Var_m395, _m877)
(10) xor(_m371, Var_m395, Var_m1499)
(13) and(_m371, Var_m395, _m1973)
(16) xor(_m877, Var_m1499, Var_m2407)
(17) boolean(_m877)
(18) boolean(Var_m1499)
(19) and(_m877, Var_m1499, _m2881)
(22) or(_m1973, _m2881, _m3307)
(23) boolean(_m1973)
(24) boolean(_m2881)
(25) xor(_m371, Var_m395, Var_m3773)
(31) xor(_m3307, Var_m3773, Var_m4777)
(32) boolean(_m3307)
(33) boolean(Var_m3773)
(39) boolean(_m5251)
(34) and(_m3307, Var_m3773, _m5251)
(28) and(_m371, Var_m395, 0)

yes.


[eclipse 60]:  add([X,X,X],[Y,Y,Y],R), (X=1;X=0;X=Y;neg(X,Y)), labeling.

R = [0, 0, 0, 1]
X = 1
Y = 0     More? (;) 

R = [1, 1, 1, 0]
X = 1
Y = 1     More? (;) 

R = [0, 1, 1, 1]
X = 1
Y = 0     More? (;) 

R = [0, 0, 0, 0]
X = 0
Y = 0     More? (;) 

R = [0, 1, 1, 1]
X = 0
Y = 1     More? (;) 

R = [0, 0, 0, 0]
X = 0
Y = 0     More? (;) 

R = [1, 1, 1, 0]
X = 1
Y = 1     More? (;) 

R = [0, 0, 0, 0]
X = 0
Y = 0     More? (;) 

R = [0, 1, 1, 1]
X = 0
Y = 1     More? (;) 

R = [0, 1, 1, 1]
X = 1
Y = 0
yes.

[eclipse 66]: add(L,R,[X|L]).
 
R = []
X = 0
L = []     More? (;) 
 
R = [0]
X = 0
L = [_m295]

Constraints:
(2) boolean(_m295)
     More? (;) 

R = [0, 0]
X = 0
L = [_m1785, _m303]

Constraints:
(11) boolean(_m303)
(20) boolean(_m1785)
     More? (;) 

R = [0, 0, 0]
X = 0
L = [_m3275, _m1793, _m311]

Constraints:
(29) boolean(_m311)
(38) boolean(_m1793)
(47) boolean(_m3275)
     More? (;) 
yes.

*/