Define the predicate Prolog - prolog

Question

I'm reviewing some exercise for the coming test and having difficulty at this.
Given a list of integers L, define the predicate: add(L,S) which returns a list of integers S in which each element is the sum of all the elements in L up to the same position.
Example:
?- add([1,2,3,4,5],S).
S = [1,3,6,10,15].
So my question is what define the predicate means? It looks pretty general. I've read some threads but they did not provide much. Thanks!

Answer 1

This is a good exercise to familiarize yourself with two important Prolog concepts:
declarative integer arithmetic to reason about integers in all directions
meta-predicates to shorten your code.
We start with a very simple relation, relating an integer I and a sum of integers S0 to a new sum S:
sum_(I, S0, S) :- S #= S0 + I.
Depending on your Prolog system, you may need a directive like:
:- use_module(library(clpfd)).
to use declarative integer arithmetic.
Second, there is a powerful family of meta-predicates (see meta-predicate) called scanl/N, which are described in Richard O'Keefe's Prolog library proposal, and already implemented in some systems. In our case, we only need scanl/4.
Example query:
?- scanl(sum_, [1,2,3,4,5], 0, Sums).
Sums = [0, 1, 3, 6, 10, 15].
Done!
In fact, more than done, because we can use this in all directions, for example:
?- scanl(sum_, Is, 0, Sums).
Is = [],
Sums = [0] ;
Is = [_2540],
Sums = [0, _2540],
_2540 in inf..sup ;
Is = [_3008, _3014],
Sums = [0, _3008, _3044],
_3008+_3014#=_3044 ;
etc.
This is what we expect from a truly relational solution!
Note also the occurrence of 0 as the first element in the list of partial sums. It satisfies your textual description of the task, but not the example you posted. I leave aligning these as an exercise.

Answer 2

Define the predicate simply means write a predicate that does what the question requires.
In your question you have to write the definition of add/2 predicate( "/2" means that it has two arguments). You could write the definition below:
add(L,S):- add1(L,0,S).
add1([],_,[]).
add1([H|T],Sum,[H1|T1]):- H1 is Sum+H,NSum is Sum+H,add1(T,NSum,T1).
The above predicate gives you the desired output. A simple example:
?- add([1,2,3,4,5],S).
S = [1, 3, 6, 10, 15].
I think the above or something similar predicate is what someone would wait to see in a test.
Some additional information-issues
The problem with the predicate above is that if you query for example:
?- add(S,L).
S = L, L = [] ;
ERROR: is/2: Arguments are not sufficiently instantiated
As you see when you try to ask when your predicate succeeds it gives an obvious solutions and for further solutions it throws an error. This is not a very good-desired property. You could improve that by using module CLPFD:
:- use_module(library(clpfd)).
add(L,S):- add1(L,0,S).
add1([],_,[]).
add1([H|T],Sum,[H1|T1]):- H1 #= Sum+H,NSum #= Sum+H,add1(T,NSum,T1).
Now some querying:
?- add([1,2,3,4,5],S).
S = [1, 3, 6, 10, 15].
?- add(S,[1,3,6]).
S = [1, 2, 3].
?- add(S,L).
S = L, L = [] ;
S = L, L = [_G1007],
_G1007 in inf..sup ;
S = [_G1282, _G1285],
L = [_G1282, _G1297],
_G1282+_G1285#=_G1307,
_G1282+_G1285#=_G1297 ;
...and goes on..
As you can see now the predicate is in the position to give any information you ask! That's because now it has a more relational behavior instead of the functional behavior that it had before due to is/2 predicate. (These are some more information to improve the predicate's behavior. For the test you might not be allowed to use libraries etc... so you may write just a simple solution that at least answers the question).