logical - Prolog - intern variables sum -

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i'm having trouble trying sum lists have.

i'm having: 

[[[_g8511,0,1,_g8520],[_g8526,1,0,0],[_g8541,_g8544,0,1]],  [[1,1,1,_g8568],[0,1,0,1],[0,_g8592,0,1]],  [[1,0,_g8613,_g8616],[0,1,_g8628,0],[0,_g8640,_g8643,1]]]

my problem try sum elements inside list. know how iterate through it, need either ignore intern variables, or make them 0.

i tried using sum_list(list, sum), figured can not handle intern variables. question how can either ignore elements not having value of 0 or 1, or how can make internal variables 0?

you use nonvar/1 predicate succeeds when argument not variable.

you write sum_list predicate:

sum_list(list,sum):-flatten(list,list2),sum_list2(list2,sum).  sum_list2([],0). sum_list2([h|t],sum):- var(h),sum_list2(t,sum). sum_list2([h|t],sum):- nonvar(h), sum_list2(t,sum1),sum sum1+h.

note in above solution since need sum , lists nested used flatten/2 predicate flatten nested list flat list. 

?- sum_list([[[_g8511,0,1,_g8520],[_g8526,1,0,0],[_g8541,_g8544,0,1]],[[1,1,1,_g8568],[0,1,0,1],[0,_g8592,0,1]],[[1,0,_g8613,_g8616],[0,1,_g8628,0],[0,_g8640,_g8643,1]]],sum). sum = 12 ; false.

another solution (deterministic) using foldl/4 be:

add(x,y,sum):- (nonvar(x)-> sum x+y;sum y).  sum(list,sum):- flatten(list,l2),foldl(add,l2,0,sum).

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