implement a prolog predicate that removes all duplicate elements - prolog

Implement a Prolog Predicate that removes all duplicate elements from a list given in the first argument and returns the result in the second argument position.

Consider the possibilities. There's just a few cases:
The source list is the empty list ([]). That is a set (∅, the empty set) by definition. That give us this:
list_set( [] , [] ) .
The source list is not empty, and the head of the list is duplicated in the tail of the list. It this case, since the head can be found elsewhere in the list, it's a duplicate and can be discarded. That gives us this:
list_set( [X|Xs] , Ys ) :-
member(X,Xs),
list_set(Xs,Ys)
.
Finally, the source list is not empty, and the head of the list is *not duplicated in the tail of the list. In this case, since the head is unique, we can add the head to the result set. That gives us this:
list_set( [X|Xs] , [X|Ys] ) :-
\+ member(X,Xs),
list_set(Xs,Ys)
.
That's all there is to it.
Putting it all together you get:
list_set( [] , [] ) .
list_set( [X|Xs] , Ys ) :- member(X,Xs), list_set(Xs,Ys) .
list_set( [X|Xs] , [X|Ys] ) :- \+ member(X,Xs), list_set(Xs,Ys) .
You might notice the two tests using member/2. That can be optimized away by introducing a cut (!/0) to eliminate the choice point between clauses 2 and 3 of the above predicate. Having introduced that, we can eliminate the second member/2, because the only way to get to the third clause is if X is unique:
list_set( [] , [] ) .
list_set( [X|Xs] , Ys ) :- member(X,Xs), !, list_set(Xs,Ys) .
list_set( [X|Xs] , [X|Ys] ) :- list_set(Xs,Ys) .

Related

Removing duplicates from a list in prolog

I'm trying to implement a simple predicate, that would simply remove items that occur more than once in a list.
For instace, for,
unique([a,b,a,b,c,c,a], R)
should be R = [a,b,c]
unique([], []).
unique([X], [X]).
unique([H|T], [H|R]) :-
not_contains(H, R),
unique(T, R).
unique([H|T], R) :-
contains(H, R),
unique(T, R).
contains(_, []).
contains(X, [X|T]).
not_contains(_, []).
not_contains(X, [H|T]) :-
X \= H,
not_contains(X, T).
I am unsure what I'm doing wrong. If the item is not contained within R, add to it and repeat, and if is, don't add it and proceed with iteration.
A fun way to do it that I just thought of:
nub(L,R):- maplist( p(R), L), length(R,_), !.
p(R,E):- memberchk(E,R).
nub(L,R) makes a unique list R out of an input list L. It assumes R is a non-instantiated variable before the call is made, and L is a fully ground list.
This uses the result list as its own uniqueness accumulator while it is being built!
Testing:
6 ?- nub([a,b,a,b,c,c,a], R).
R = [a, b, c].
The easiest way to make a list unique is just use the built-in sort/2:
unique(Xs,Ys) :- sort(Xs,Ys).
so unique( [c,a,b,a] , Rs ) yields Rs = [a,b,c].
If you want to maintain order, you need to decide on the strategy you want to use — in case of duplicates, which duplicate "wins": First or last?
The "last wins" strategy is the simplest to implement:
unique( [] , [] ) . % the empty list is itself a unique set
unique( [X|Xs] , Ys ) :- % A non-empty list is unique if . . .
contains(X,Xs), % - X is contained within the source list's tail,
!, - and (eliminating the choice point)
unique( Xs, Ys ) . - omitting X, the remainder of the list is (recursively) unique
unique( [X|Xs] , Ys ) :- % Otherwise, the non-empty list is unique if . . .
unique( Xs,[X|Ys] ) . % - adding X to the results, the remainder of the list is (recursively) unique .
Here, unique( [a,b,a,c,a], Rs ) yields Rs = [b,c,a].
If you want to use the "first wins" strategy, you'll be wanting to use a helper predicate with an accumulator that grows the result list in reverse order, which is then reversed. That gives us something like this:
unique( Xs , Ys ) :- unique(Xs,[],Zs), reverse(Zs,Ys) .
unique( [] , Ys , Ys ) . % Source list exhausted? we're done.
unique( [X|Xs] , Ts , Ys ) :- % Otherwise . . .
contains(X,Ts) , % - if X is found in the accumulator,
!, % - eliminate the choice point, and
unique(Xs,Ts,Ys) . % - recurse down, discarding X
unique( [X|Xs] , Ts , Ys ) :- % Otherwise (X is unique) . . .
unique(Xs,[X|Ts],Ys) . % - recurse down, prepending X to the accumulator
And here, unique( [a,b,a,c,a], Rs ) yields Rs = [a,b,c].
You can avoid the use of reverse/2 here, by building the 2 lists (accumulator and final set) in parallel. A trade-off, though: memory for speed:
unique( Xs , Ys ) :- unique(Xs,[],Ys) .
unique( [] , _ , [] ) .
unique( [X|Xs] , Ts , Ys ) :- memberchk(X,Ts), !, unique( Xs, Ts , Ys ) .
unique( [X|Xs] , Ts , [X|Ys] ) :- unique( Xs, [X|Ts] , Ys ) .
You don't really need a contains/2 predicate: the in-built member/2 and memberchk/2 do exactly what you want. member/2 is non-deterministic and will succeed once for every time the item is found in the list; memberchk/2 is non-deterministic and will succeed at most once.
Since this is testing for uniqueness, memberchk/2 is what you'd want, giving you this:
contains(X,Ys) :- memberchk(X,Ys) .
Or you can roll you own (it's trivial):
contains( X , [X|Ys] ) :- ! .
contains( X , [_|Ys] ) :- contains(X,Ys) .
Or even simpler, just a one-liner:
contains( X , [Y|Ys] ) :- X = Y -> true ; contains(X,Ys) .

How do i remove reverse dulpicate list from a list in prolog?

I'm new to learn the prolog, I want to fulfill the predicate below.
removereverse([[1,5],[5,1],[2,3],[3,2]],List). ---> Input
what I want:
List = [[1,5],[2,3]].
mycode
removes([],[]).
removes([[N1,N2]|T],[[N1,N2]|New]):-
\+member([N1,N2],New),
removes(T,New).
Something like this?
First, lets define a predicate to tell us if a list is duplicated within a list-of-lists. This counts a list as a duplicate if either it or its reverse exists in the target list-of-lists:
duplicated(X,Ls) :- member(X,Ls).
duplicated(X,Ls) :- reverse(X,R), member(R,Ls).
Then we can say:
clean( [] , [] ) .
clean( [X|Xs] , Ys ) :- duplicated(X,Xs), !, clean(Xs,Ys) .
clean( [X|Xs] , [X|Ys] ) :- clean(Xs,Ys) .
That keeps the last "duplicate" found and discard those preceding them in the source list. To keep the first such "duplicate" instead, just change where the recursion occurs:
clean( [] , [] ) .
clean( [X|Xs] , Ys ) :- clean(Xs,Ys), duplicated(X,Xs), !.
clean( [X|Xs] , [X|Ys] ) :- clean(Xs,Ys).
Another approach uses a helper predicate:
This keeps the first:
clean( Xs, Ys ) :- clean(Xs,[],Y0), reverse(Y0,Ys).
clean( [] , Ys, Ys ) .
clean( [X|Xs] , Ts, Ys ) :- duplicated(X,Ts), !, clean(Xs, Ts ,Ys).
clean( [X|Xs] , Ts, Ys ) :- clean(Xs,[X|Ts],Ys).
To keep the last, simply change duplicate(X,Ts) to duplicate(X,Xs). The former checks to see if X exists in the accumulator Ts; the latter checks to see if X exists in the tail of the source list (Xs).

Prolog Split list into list of lists

i want to make one list split into list of lists, and skip the 'solid' and separate the list into sublist.
the input and output is below
split_s([A,B,C,solid,D,E,F],X).
X = [[A,B,C],[D,E,F]].
Can anyone help me?
Try something along the following lines. It helps if you decompose your problem. In this case, the heart of the problem is this:
find the longest prefix of a list that doesn't contain the atom solid.
Which you can do like this with a predicate like take_until( List , Separator , Prefix , Remainder ):
take_until( [] , _ , [] , [] ) . % if we hit the end of the source list, we're done.
take_until( [X|Xs] , X , [] , Xs ) . % if we hit the separator, we're done
take_until( [X|Xs] , S , [X|Ps] , Rs ) :- % otherwise...
X \= S , % - when the head of the list is NOT the separator
take_until( Xs , S , Ps , Rs ) % - we take it on to the sublist and keep going.
. %
Once you have that down, the rest is easy:
use the above predicate to extract the first such prefix, then
recurse down on what's left over.
Like this:
split( [] , [] ) . % splitting the empty list results in the empty list.
split( [X|Xs] , [Y|Ys] ) :- % splitting a non-empty list...
take_until( [X|Xs] , solid , Y , R ) , % - get the desired prefix
split(R, , Ys ) % - recurse down on what's left
. % Easy!
The following works for me:
split_s([],[[]]).
split_s([H|T],[[H|XH]|XR]) :- var(H),!,split_s(T,[XH|XR]).
split_s([solid|T],[[]|X]) :- !,split_s(T,X).
split_s([H|T],[[H|XH]|XR]) :- split_s(T,[XH|XR]).
EDIT: moved the cut in the 3rd clause in front of the split.
If you don't want empty lists, then try the following:
split_s([],[]).
split_s([H|T],[[H|XT]|XXT]) :- var(H),!,split_s([[H]|T],[[[H]|XT]|XXT]).
split_s([solid|T],X) :- !,split_s(T,X).
split_s([H],[[H]]) :- !.
split_s([H,M|T],[[H,M|XT]|XXT]) :- var(M),!,split_s([[M]|T],[[[M]|XT]|XXT]).
split_s([H,solid|T],[[H]|XT]) :- !,split_s(T,XT).
split_s([H|T],[[H|XH]|XR]) :- split_s(T,[XH|XR]).

How to double everything in a Prolog list (including sublists)

I have a Prolog function that must take in a list (which may include sublists) and return a list that has everything doubled.
For example,
?- doubleAll([1,2,[3,4],5,[6,7,[8],9],10), L).
L = [2,4,[6,8],10,[12,14,[16],18],20).
I was able to double everything when there were no sublists in the list, but when sublists are included I'm having some problems. Here is my code so far:
%L2 is the result of doubling everything in L1.
doubleEverything([],[]).
doubleEverything([H|T], [H2|T2]) :-
atomic(H), H2 is H*2, doubleEverything(T,T2).
doubleEverything([H|T], [H2|T2]) :-
not(atomic(H)), H2 is H*2, doubleEverything(T,T2), doubleEverything(H,T2).
Does anyone see how I can make this work?
Thanks!
Something like this would work:
double( [] , [] ) . % doubling the empty list is...the empty list.
double( [X|Xs] , [XX|XXs] ) :- % if the head of the list is a list,
is_list(X) , % we double it, then double the tail.
! ,
double(X,XX) ,
double(Xs,XXs)
.
double( [X|Xs] , [XX XXs] ) :- % doubling anything else is easy.
XX is X*2 ,
double(Xs,XXs)
.
is_list( X ) :- var(X) , ! , fail .
is_list( [] ) .
is_list( [_|_] ) .
not(atomic(H)), H2 is H*2, doesn't make sense.
Since atomic(H) (should be number(H), really) is already handled, simply recurse:
doubleEverything([H|T], [H2|T2]) :-
doubleEverything(H,H2), doubleEverything(T,T2).
Keep it simple, but remember to test what will happen if neither a number or a list is input...

SICStus Prolog Lists

Having trouble understanding how Prolog works. I'm tryig to write a rule that takes three lists of integers as input (representing sets) and puts the integers that belong to both the first and second list in the third list.
Example:
?-inter([10,20,30,40],[10,50,40,60], List3 )
List3 = [10, 40]
So far I have this, that can recognize if a list contains a certain letter:
mymember(X,[X|T]).
mymember(X,[H|T]) :- mymember(X,T).
There's actually an inbuilt library to sort that all out for you, known as ordsets.
inter(X, Y, Z) :-
list_to_ord_set(X, L1),
list_to_ord_set(Y, L2),
ord_intersection(L1, L2, Z).
Using your example input you get the following
| ?- inter([10,20,30,40],[10,50,40,60],X).
X = [10,40] ? ;
no
inter(Xs, Ys, Zs) will be true when each element in Zs also is in Xs and in Ys.
But Zs are unknown, then a more constructive approach is required.
Here it is: iterate on Xs and store in Zs each element that is in Ys.
An example of iteration is mymember/2, you can see that it requires a recursive predicate.
The other idiomatic part of the above statement is store in Zs, Prolog has a peculiar way to do such things, using pattern matching.
inter([X|Xs], Ys, [X|Zs]) :-
mymember(X, Ys), inter(Xs, Ys, Zs).
You will need to complete inter/3 with other 2 clauses: base recursion, i.e. when all Xs elements have been processed, and the case where X is not a member of Ys.
Try something like this, using the builtins member/2 and setof\3:
set_intersection( As , Bs , Xs ) :-
set_of( X , ( member(X,As) , member(X,Bs) ) , Xs )
.
One should note that this will fail if the lists As and Bs have no elements in common. An alternative would be use findall/3 rather than set_of/3. findall/3 will hand back and empty list rather than failure if the goal is not satisfied:
set_intersection( As , Bs , Xs ) :-
findall( X , ( member(X,As) , member(X,Bs) ) , Xs )
.
However findall/3 returns a bag (duplicates are allowed) rather than a set (no duplicates allowed), so if your two source lists aren't sets, you won't get a set out.
member/2 is a builtin predicate that unifies its first argument with an element of the list — the equivalent of
member(X,[X|_).
member(X,[_|Xs) :- member(X,Xs) .
And, finally, as #chac noted in his answer, you can recursively traverse the list.
set_intersection( [] , _ , [] ) . % the intersection of the empty set with anything is the empty set.
set_intersection( [A|As] , Bs , [A|Xs] ) :- % if the list is non-empty,
member(A,Bs) , % - and A is a member of the 2nd set
! , % - we cut off alternatives at this point (deterministic)
set_intersection( As , Bs , Xs ) % - and recurse down on the tail of the list.
.
set_intersection( [_|As] , Bs , Xs ) :- % if the list is non-empty, and A is NOT a embmer of the 2nd set
set_intersection( As , Bs , Xs ) % we just recurse down on the tail of the list.
.
#chac's technique builds the result list as he goes, something like:
[a|X]
[a,b|X]
[a,b,c|X]
The final unification, the special case of the empty list unifies the unbound tail of the list with [] making the list complete, so the final [a,b,c|X] becomes
[a,b,c]
A little prolog magic. An alternative that might be easier to understand is to use a worker predicate with an accumulator:
%
% set_intersection/3: the public interface predicate
%
set_intersection( As , Bs , Xs ) :-
set_intersection( As , Bc , [] , T ) % we seed our accumulator with the empty list here
.
%
% set_intersection/4: the private worker bee predicate
%
set_intersection( [] , _ , T , Xs ) :- % since our accumulator is essentially a stack
reverse(T,Xs) % we need to reverse the accumulator to
. % put things in the expected sequence
set_intersection( [A|As] , Bs , T , Xs ) :-
member( A, Bs ) ,
! ,
T1 = [A|T] ,
set_intersection( As , Bs , T1 , Xs )
.
set_intersection( [_|As] , Bs , T , Xs ) :-
set_intersection( As , Bs , T , Xs )
.

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