Simple Prolog program: "Arguments are not sufficiently instantiated" error

I am writing a Prolog predicate that cuts first three elements off a numbered list and prints the result. An example of a numbered list:

[e(f,1),e(o,2),e(o,3),e(b,4),e(a,5),e(r,6)].

The original predicate for normal list looks like this:

strim([H|T],R) :-   
   append(P,R,[H|T]),  
   length(P,3).

So, since length predicate works perfectly for numbered lists as well, I only had to write predicate that appends one numbered list to another:

compose([],L,[L]).
compose([e(F,C)|T],e(A,_),[e(F,C)|L]) :-
   N is C+1,
   compose(T,e(A,N),L).

napp(X,[],X).
napp(L,[e(X,Y)|T],M):-
   compose(L,e(X,Y),L1),
   napp(L1,T,M).

I expected the predicate for numbered list to be a slightly modified version of predicate for normal list, so I wrote this:

numstrim([e(X,Y)|T],R) :-
   napp(P,R,[e(X,Y)|T]),
   length(P,3).

However, I'm getting this error:

ERROR: compose/3: Arguments are not sufficiently instantiated

Could somebody please explain what's causing the error and how to avoid it? I'm new to Prolog.

Solution

Instantiation errors are a common phenomenon in Prolog programs that use moded predicates: These are predicates that can only be used in special circumstances, requiring for example that some arguments are fully instantiated etc.

As a beginner, you are in my view well advised to use more general predicates instead, so that you can freely exchange the order of goals and do not have to take procedural limitations into account, at least not so early, and without the ability to freely experiment with your code.

For example, in your case, the following trivial change to compose/3 gives you a predicate that works in all directions:

compose([], L, [L]).
compose([e(F,C)|T], e(A,_), [e(F,C)|L]) :-
        N #= C+1,
        compose(T, e(A,N), L).

Here, I have simply replaced the moded predicate (is)/2 with the CLP(FD) constraint (#=)/2, which completeley subsumes the more low-level predicate over integers.

After this small change (depending on your Prolog system, you may have to import a library to use the more general arithmetic predicates), we get:

?- numstrim([e(f,1),e(o,2),e(o,3),e(b,4),e(a,5),e(r,6)], Es).
nontermination

So, we find out that the instantiation error has actually overshadowed a different problem that can only be understood procedurally, and which has now come to light.

To improve this, I now turn around the two goals of numstrim/2:

numstrim([e(X,Y)|T], R) :-
        length(P, 3),
        napp(P, R, [e(X,Y)|T]).

This is because length(P, 3) always terminates, and placing a goal that always terminates first can at most improve, never worsen, the termination properties of a pure and monotonic logic program.

So now we get:

?- numstrim([e(f,1),e(o,2),e(o,3),e(b,4),e(a,5),e(r,6)], Es).
Es = [e(b, _1442), e(a, _2678), e(r, _4286)] .

That is, at least we get an answer now!

However, the predicate still does not terminate universally, because we get:

?- numstrim([e(f,1),e(o,2),e(o,3),e(b,4),e(a,5),e(r,6)], Es), false.
nontermination

I leave fixing this as an exercise.