Prolog: compare list elements and sum

Question

New to prolog and trying to implement the following function that takes 3 lists:

• True if lists are the same length
• True if elements of third list is sum of the two lists

Example: fn([1,2,3],[4,5,6],[5,7,9]) returns true. Note that the sum is element-wise addition.

This is what I have so far:

fn([],[],[]).
fn([_|T1], [_|T2], [_|T3]) :-
    fn(T1,T2,T3),         % check they are same length
    fn(T1,T2,N1),         % check that T3=T1+T2
    N1 is T1+T2,
    N1 = T3.

From what I understand, the error is due to the base case (it has empty lists which causes error with evaluation of addition?)

Thanks for any help and explanations!

Answer 1

In addition to @GuyCoder's answer, I would point out that it is worthwhile to consider using one of the maplist predicates from library(apply) when modifying all elements of lists. You can use a predicate to describe the relation between three numbers...

:- use_module(library(apply)).   % for maplist/4

num_num_sum(X,Y,S) :-
   S is X+Y.

... and subsequently use maplist/4 to apply it to entire lists:

fn(X,Y,Z) :-
   maplist(num_num_sum,X,Y,Z).

This predicate yields the desired results if the first two lists are fully instantiated:

   ?- fn([1,2,3],[4,5,6],X).
X = [5,7,9]

However, due to the use of is/2 you get instantiation errors if the first two lists contain variables:

   ?- fn([1,A,3],[4,5,6],[5,7,9]).
     ERROR at  clause 1 of user:num_num_sum/3 !!
     INSTANTIATION ERROR- X is _+B: expected bound value
   ?- fn([1,2,3],[4,5,A],[5,7,9]).
     ERROR at  clause 1 of user:num_num_sum/3 !!
     INSTANTIATION ERROR- X is A+B: expected bound value

If you only want to use the predicate for lists of integers, you can use CLP(FD) to make it more versatile:

:- use_module(library(apply)).
:- use_module(library(clpfd)).   % <- use CLP(FD)

int_int_sum(X,Y,S) :-
   S #= X+Y.                     % use CLP(FD) constraint #=/2 instead of is/2

fnCLP(X,Y,Z) :-
   maplist(int_int_sum,X,Y,Z).

With this definition the previously problematic queries work as well:

   ?- fnCLP([1,A,3],[4,5,6],[5,7,9]).
A = 2
   ?- fnCLP([1,2,3],[4,5,A],[5,7,9]).
A = 6

Even the most general query yields results with this version:

   ?- fnCLP(X,Y,Z).
X = Y = Z = [] ? ;
X = [_A],
Y = [_B],
Z = [_C],
_A+_B#=_C ? ;
X = [_A,_B],
Y = [_C,_D],
Z = [_E,_F],
_A+_C#=_E,
_B+_D#=_F ? ;
.
.
.

Since the numbers in the above answers are not uniquely determined, you get residual goals instead of actual numbers. In order to get actual numbers in the answers, you have to restrict the range of two of the lists and label them subsequently (see documentation for details), e.g. to generate lists containing the numbers 3,4,5 in the first list and 6,7,8 in the second list, you can query:

                                             label the lists
                    restrict the domain         |        |
                       v           v            v        v
   ?- fnCLP(X,Y,Z), X ins 3..5, Y ins 6..8, label(X), label(Y).
X = Y = Z = [] ? ;
X = [3],
Y = [6],
Z = [9] ? ;
X = [3],
Y = [7],
Z = [10] ? ;
.
.
.
X = [3,4],
Y = [6,7],
Z = [9,11] ? ;
X = [3,4],
Y = [6,8],
Z = [9,12] ? ;
.
.
.

On an additional note: there are also clp libraries for booleans (CLP(B)), rationals and reals (CLP(Q,R)) that you might find interesting.

Answer 2

From what I understand, the error is due to the base case.

I don't see it that way.

The first problem I see is that you are trying to process list which leads to thinking about using DCGs, but since you are new I will avoid that route.

When processing list you typically process the head of the list then pass the tail back to the predicate using recursion.

e.g. for length of list you would have

ln([],N,N).
ln([_|T],N0,N) :-
   N1 is N0+1,
   ln(T,N1,N).

ln(L,N) :-
    ln(L,0,N).

The predicate ln/2 is used to set up the initial count of 0 and the predicate ln/3 does the work using recursion. Notice how the head of the list is taken off the front of the list and the tail of the list is passed recursively onto the predicate again. When the list is empty the predicate ln([],N,N). unifies, in this case think copies, the intermediate count from the second position into the third position, which it what is passed back with ln/2.

Now back to your problem.

The base case is fine

fn([],[],[]).

There are three list and for each one look at the list as [H|T]

fn([H1|T1],[H2|T2],[H3|T3])

and the call to do the recursion on the tail is

fn(T1,T2,T3) 

all that is left is to process the heads which is

H3 is H1 + H2

putting it all together gives us

fn([],[],[]).
fn([H1|T1], [H2|T2], [H3|T3]) :-
   H3 is H1 + H2,
   fn(T1,T2,T3).

and a quick few checks.

?- fn([],[],[]).
true.

?- fn([1],[1],[2]).
true.

?- fn([1,2],[3,4],[4,6]).
true.

?- fn([1,2],[3,4,5],[4,6,5]).
false.

With regards to the two conditions. When I look at exercises problems for logic programming they sometimes give a condition like True if lists are the same length or some other condition that returns true. I tend to ignore those at first and concentrate on getting the other part done first, in this case elements of third list is sum of the two lists then I check to see if the other conditions are correct. For most simple classroom exercises they are. I sometimes think teacher try to give out these extra conditions to confuse the student, but in reality the are there just to clarify how the code should work.