Question

I wrote a predicate to find sublists:

sublist([],[]).
sublist([X|T], [X|TS]) :- 
    sublist(T, TS).
sublist([_|T], X) :- 
    sublist(T, X).

But it is not correct because it will fail for this:

sublist([1,2,20,4,5,6],[1,2,4,20]).

How to change this predicate to answer true. For that question without making time complexity much bigger?

Answer 1

2015-05-13: Complete rewrite

It’s a bit unclear what you’re after here: Your predicate is called sublist but judging from your example query, it seems like you’re after a subset.

Anyway, here are definitions for both predicates:

sublist(?L1, +L2) (order and duplicates matter):

sublist([], L).
sublist([X|Xs], [X|Ys]) :- sublist(Xs, Ys).
sublist(Xs, [_|Ys]) :- sublist(Xs, Ys).

subset(?L1, +L2) (order and duplicates do not matter):

subset([], L).
subset([X|Xs], L) :- member(X, L), subset(Xs, L).

Note that these predicates may exist as built in predicates of your prolog implementation. You should not try to redefine those if this is the case.