SWI-Prolog How to prove if 3 lists have the same sum?

Question

I have just started with Prolog and now I have my first problem, which I just can't solve:

I want to give the program 3 lists and as result I want to know if their sum is equal.

So something like this:

?- sum_equal([1,2,3],[4,1,1],[5,1,0]).
true

Until now I've got this:

partsum([],0).
partsum([Head|Tail],Solution) :- 
    partsum(Tail, Solution2), 
    Solution is Head+Solution2.

sum_equal([Head|Tail],[Head2|Tail2],[Head3|Tail3]):-
    sum1=partsum([Head|Tail],sum1),
    sum2=partsum([Head2|Tail2],sum2),
    sum3=partsum([Head3|Tail3],sum3),
    sum1=:=sum2,
    sum1=:=sum3.

But now I get the following message:

evaluable 'sum1' does not exist.

Thanks for your help.

score 2 · Answer 1 · edited May 23 '17 at 12:22

In this answer, we assume that all numbers used are integers, which allows us to use clpfd:

:- use_module(library(clpfd).

To define sum_equal/3 we proceed step by step—it's as easy as one, two, three!

Based on ...
- meta-predicate maplist/2, part of the Prolog prologue,
- the widely available predicate length/2,
- and the clpfd library predicate sum/3
... we define the following two auxiliary predicates:
```
sum_of_zs(S,Zs) :-
   length(Zs,_),                % ensure sufficient instantiation for sum/3
   sum(Zs,#=,S).

all_zs_have_the_same_sum(Zss,S) :-
   maplist(sum_of_zs(S),Zss).
```

sum_equal/3 is a mere specialization of all_zs_have_the_same_sum/2:

sum_equal(Xs,Ys,Zs) :-
   all_zs_have_the_same_sum([Xs,Ys,Zs],_).

We're done with coding. Let's put it to good use and run the sample query given by the OP:
```
?- sum_equal([1,2,3],[4,1,1],[5,1,0]).
true.
```

score 1 · Accepted Answer · answered Mar 29 '14 at 13:25

1

Just a couple of things I've noticed.

Prolog variables must start with a capital letter, so sum1 needs to be Sum1 etc.

In the lines like

sum1=partsum([Head|Tail],sum1),

the sum1= should not be there because partsum is returns with a value in sum1. so the lines should be similar to

partsum([Head|Tail],Sum1),

answered Mar 29 '14 at 13:25

Craunch

20
2

Thank you. Now it works. I thought you use only capital letters if you pass variables and here I give the name. But I think now I got it. – user3475727 Mar 29 '14 at 13:56

SWI-Prolog How to prove if 3 lists have the same sum?

2 Answers2