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HI I would like to know how a method that finds out if two members of a list in Prolog are adjacent as the catch is that the first and the last elements are checked if they are adjacent something like
(b,c,[b,a,d,c])
would give yes they are adjacent. I already have this code
adjacent(X, Y, [X,Y|_]).
adjacent(X, Y, [_|Tail]) :-
adjacent(X, Y, Tail).
but I do not know how to include the head of the list and the last elments as well being compared for being adjacent. If you are really good maybe you can tell me also how it is possible to make something like this
(c,b,[a,b,c,d])
to be true I mean the elements are adjacent no matter which exactly is first.
You can make use of last/2 predicate [swi-doc] to obtain the last element of the list. But you can not use this in the recursive call, since otherwise it will each element in the list pair with the last element as well.
The trick is to make a helper predicate for the recursive part, and then make the adjacent/3 predicate to call the recursive one you wrote yourself, or one where we match with the last element:
adjacent(X, Y, L) :-
adj(X, Y, L).
adjacent(X, Y, [Y|T]) :-
last(T, X).
adj(X, Y, [X,Y|_]).
adj(X, Y, [_|T]) :-
adj(X, Y, T).
Relations about lists can often be described with a Definite Clause Grammar dcg.
A first attempt might be:
adjacent(A, B, L) :-
phrase(adjacent(A, B), L). % interface to DCG
adjacent(A,B) -->
..., ( [A,B] | [B,A] ), ... .
... --> [] | [_], ... .
Yet, this leaves out cases like adjacent(a,d,[a,b,c,d]). One possibility would be to add another rule, or maybe simply extend the list to be considered.
adjacent(A, B, L) :-
L = [E,_|_],
append(L, [E], M),
phrase(adjacent(A, B), L).
I want to write predicate which can count all encountered number:
count(1, [1,0,0,1,0], X).
X = 2.
I tried to write it like:
count(_, [], 0).
count(Num, [H|T], X) :- count(Num, T, X1), Num = H, X is X1 + 1.
Why doesn't work it?
Why doesn't work it?
Prolog is a programming language that often can answer such question directly. Look how I tried out your definition starting with your failing query:
?- count(1, [1,0,0,1,0], X).
false.
?- count(1, Xs, X).
Xs = [], X = 0
; Xs = [1], X = 1
; Xs = [1,1], X = 2
; Xs = [1,1,1], X = 3
; ... .
?- Xs = [_,_,_], count(1, Xs, X).
Xs = [1,1,1], X = 3.
So first I realized that the query does not work at all, then I generalized the query. I replaced the big list by a variable Xs and said: Prolog, fill in the blanks for me! And Prolog did this and reveals us precisely the cases when it will succeed.
In fact, it only succeeds with lists of 1s only. That is odd. Your definition is too restricted - it correctly counts the 1s in lists where there are only ones, but all other lists are rejected. #coder showed you how to extend your definition.
Here is another one using library(reif) for
SICStus|SWI. Alternatively, see tfilter/3.
count(X, Xs, N) :-
tfilter(=(X), Xs, Ys),
length(Ys, N).
A definition more in the style of the other definitions:
count(_, [], 0).
count(E, [X|Xs], N0) :-
if_(E = X, C = 1, C = 0),
count(E, Xs, N1),
N0 is N1+C.
And now for some more general uses:
How does a four element list look like that has 3 times a 1 in it?
?- length(L, 4), count(1, L, 3).
L = [1,1,1,_A], dif(1,_A)
; L = [1,1,_A,1], dif(1,_A)
; L = [1,_A,1,1], dif(1,_A)
; L = [_A,1,1,1], dif(1,_A)
; false.
So the remaining element must be something different from 1.
That's the fine generality Prolog offers us.
The problem is that as stated by #lurker if condition (or better unification) fails then the predicate will fail. You could make another clause for this purpose, using dif/2 which is pure and defined in the iso:
count(_, [], 0).
count(Num, [H|T], X) :- dif(Num,H), count(Num, T, X).
count(Num, [H|T], X) :- Num = H, count(Num, T, X1), X is X1 + 1.
The above is not the most efficient solution since it leaves many choice points but it is a quick and correct solution.
You simply let the predicate fail at the unification Num = X. Basically, it's like you don't accept terms which are different from the only one you are counting.
I propose to you this simple solution which uses tail recursion and scans the list in linear time. Despite the length, it's very efficient and elegant, it exploits declarative programming techniques and the backtracking of the Prolog engine.
count(C, L, R) :-
count(C, L, 0, R).
count(_, [], Acc, Acc).
count(C, [C|Xr], Acc, R) :-
IncAcc is Acc + 1,
count(C, Xr, IncAcc, R).
count(C, [X|Xr], Acc, R) :-
dif(X, C),
count(C, Xr, Acc, R).
count/3 is the launcher predicate. It takes the term to count, the list and gives to you the result value.
The first count/4 is the basic case of the recursion.
The second count/4 is executed when the head of the list is unified with the term you are looking for.
The third count/4 is reached upon backtracking: If the term doesn’t match, the unification fails, you won't need to increment the accumulator.
Acc allows you to scan the entire list propagating the partial result of the recursive processing. At the end you simply have to return it.
I solved it myself:
count(_, [], 0).
count(Num, [H|T], X) :- Num \= H, count(Num, T, X).
count(Num, [H|T], X) :- Num = H, count(Num, T, X1), X is X1 + 1.
I have decided to add my solution to the list here.
Other solutions here use either explicit unification/failure to unify, or libraries/other functions, but mine uses cuts and implicit unification instead. Note my solution is similar to Ilario's solution but simplifies this using cuts.
count(_, [], 0) :- !.
count(Value, [Value|Tail],Occurrences) :- !,
count(Value,Tail,TailOcc),
Occurrences is TailOcc+1.
count(Value, [_|Tail], Occurrences) :- count(Value,Tail,Occurrences).
How does this work? And how did you code it?
It is often useful to equate solving a problem like this to solving a proof by induction, with a base case, and then a inductive step which shows how to reduce the problem down.
Line 1 - base case
Line 1 (count(_, [], 0) :- !.) handles the "base case".
As we are working on a list, and have to look at each element, the simplest case is zero elements ([]). Therefore, we want a list with zero elements to have no instances of the Value we are looking for.
Note I have replaced Value in the final code with _ - this is because we do not care what value we are looking for if there are no values in the list anyway! Therefore, to avoid a singleton variable we negate it here.
I also added a ! (a cut) after this - as there is only one correct value for the number of occurrences we do not want Prolog to backtrack and fail - therefore we tell Prolog we found the correct value by adding this cut.
Lines 2/3 - inductive step
Lines 2 and 3 handle the "inductive step". This should handle if we have one or more elements in the list we are given. In Prolog we can only directly look at the head of the list, therefore let us look at one element at a time. Therefore, we have two cases - either the value at the head of the list is the Value we are looking for, or it is not.
Line 2
Line 2 (count(Value, [Value|Tail],Occurrences) :- !, count(Value,Tail,TailOcc), Occurrences is TailOcc+1.) handles if the head of our list and the value we are looking for match. Therefore, we simply use the same variable name so Prolog will unify them.
A cut is used as the first step in our solution (which makes each case mutually exclusive, and makes our solution last-call-optimised, by telling Prolog not to try any other rules).
Then, we find out how many instances of our term there are in the rest of the list (call it TailOcc). We don't know how many terms there are in the list we have at the moment, but we know it is one more than there are in the rest of the list (as we have a match).
Once we know how many instances there are in the rest of the list (call this Tail), we can take this value and add 1 to it, then return this as the last value in our count function (call this Occurences).
Line 3
Line 3 (count(Value, [_|Tail], Occurrences) :- count(Value,Tail,Occurrences).) handles if the head of our list and the value we are looking for do not match.
As we used a cut in line 2, this line will only be tried if line 2 fails (i.e. there is no match).
We simply take the number of instances in the rest of the list (the tail) and return this same value without editing it.
I am trying to remove duplicate entries from a list in prolog. So a list [a,b,a,c,b,a] would return [a,b,c]. I can not use any built in functions. I searched here and found this code.
member(X,[X|_]) :- !.
member(X,[_|T]) :- member(X,T).
set([],[]).
set([H|T],[H|Out]) :- not(member(H,T)), set(T,Out).
set([H|T],Out) :- member(H,T), set(T,Out).
But that would take my list and return [c,b,a] not [a,b,c]
I have remove code that will take an element and a list and return a list with occurrences of that element in the list removed. So I tried to incorporate that into my remove duplicate method but I don't really understand prolog very well so it is not working. Logically I want to take a list cons the head with the recursive call on the new list minus all occurrences of the head. This is what the code would look like in sml.
fun remv(_,nil) = nil
| remv(a,x::xs) = if x=a then remv(a,xs) else x::remv(a,xs);
fun remvdub (nil) = nil
| remvdub(x::xs) = x::remvdub(remv(x,xs));
So this is what I tried in prolog
remv(_,[],[]).
remv(X,[X|T],Ans) :- remv(X,T,Ans).
remv(X,[H|T],[H|K]) :- remv(X,T,K).
remvdub([],[]).
remvdub([H|T],[H|Ans]) :- remvdub(Ans1,Ans), remv(H,T,Ans1).
What am I missing?
% An empty list is a set.
set([], []).
% Put the head in the result,
% remove all occurrences of the head from the tail,
% make a set out of that.
set([H|T], [H|T1]) :-
remv(H, T, T2),
set(T2, T1).
% Removing anything from an empty list yields an empty list.
remv(_, [], []).
% If the head is the element we want to remove,
% do not keep the head and
% remove the element from the tail to get the new list.
remv(X, [X|T], T1) :- remv(X, T, T1).
% If the head is NOT the element we want to remove,
% keep the head and
% remove the element from the tail to get the new tail.
remv(X, [H|T], [H|T1]) :-
X \= H,
remv(X, T, T1).
The snippet of Prolog code that you posted is logically correct. If you would like to keep the first, as opposed to the last, copy of each duplicated item, you can change your code as follows:
member(X,[X|_]) :- !.
member(X,[_|T]) :- member(X,T).
set(A,B) :- set(A, B, []).
set([],[],_).
set([H|T],[H|Out],Seen) :- not(member(H,Seen)), set(T,Out, [H|Seen]).
set([H|T],Out, Seen) :- member(H,Seen), set(T,Out,Seen).
The idea is to add a third parameter, which represents the list of items that you have seen so far, and check the membership against it, rather than checking the membership against the remaining list. Note that set/2 is added to hide this third argument from the users of your predicate.
Demo on ideone.
i have to get list difference between two integer list (both ordinate).
i white this:
difference(L,[],L) :- !.
difference([],_,[]) :- !.
difference([],[],W).
difference([H|T1],[D|T2],T3) :- difference(T1,[D|T2],[H|T3]).
difference([H|T1],[H|T2],T3) :- difference(T1,T2,T3).
but why i can't get my list difference?
if i write this:
difference([],[],W):- write(X).
and this example:
| ?- difference([1,4,4],[1,4],R).
[4|_27]
it makes right!
NB if i have duplicate number i have to show it!
I find your code rather odd. For instance, your third clause: what's W for? Seems like you mean to say:
difference([],[],_).
Second problem: in the fourth clause, there's nothing stopping H and D from being independent variables with the same binding. I suspect you mean something like this:
difference([H|T1],[D|T2],T3) :- H \= D, difference(T1,[D|T2],[H|T3]).
Fixing these things seems to fix the predicate to give a reasonable looking answer:
| ?- difference([1,4,4], [1,4], R).
R = [4]
I think your first several clauses are trying to handle different sorts of base cases, is that right? E.g.:
difference(L, [], L) % handles the case where the second list is exhausted
difference([], _, []) % handles the case where the first list is exhausted
difference([], [], W) % handles the case where the lists are exhausted at the same time
One problem with this is that L = [] is a legitimate binding, so the first and third clauses mean the same thing. You can probably safely remove the third one, because it would have matched and produced the same answer on the first. The second clause is more interesting, because it seems to say that regardless of whatever work we've done so far, if the first list is empty, the result is empty. I find that possibility a bit jarring--is it possible you actually want these two base cases? :
difference([], L, L).
difference(L, [], L).
I remain unconvinced, but until I have a better idea what you're trying to accomplish I may not be able to help more. For instance, what should happen with difference([1, 4], [1, 4, 4], R)? I posit you probably want R = [4], but your code will produce R = [].
Also, I find it unlikely that
difference([],[],W):- write(X).
is going to be a helpful debugging strategy, because Prolog will generate a new variable binding for X because there's nothing for it to refer to.
The final version I have with all my changes looks like this:
difference(L, [], L) :- !.
difference([], L, L) :- !.
difference([H|T1], [D|T2], T3) :- D \= H, difference(T1, [D|T2], [H|T3]).
difference([H|T1], [H|T2], T3) :- difference(T1, T2, T3).
Edit: does this implement your requirements?
not_in1(X, Left, Right) :- member(X, Left), \+ member(X, Right).
not_in(X, Left, Right) :- not_in1(X, Left, Right).
not_in(X, Left, Right) :- not_in1(X, Right, Left).
differences(Left, Right, Differences) :-
findall(X, not_in(X, Left, Right), Differences).
?- differences([1,2,3,4], [1,3,5], X).
X = [2,4,5]
If so, I'll try to get your original code to produce answers that match.
Edit 2: OK, so the problem with the solution above is that it is O(N^2). In the worst case (two totally distinct lists) it will have to compare every item from list 1 to every item of list 2. It's not exploiting the fact that both lists are ordered (I believe that's what you mean by 'ordinate').
The result looks a lot more like your original code, but your original code is not taking advantage of the fact that the items are ordered. This is why the fourth and fifth cases are confusing looking: you should recur down one of the lists or the other depending on which number is larger. The corrected code looks like this:
differences([], Result, Result).
differences(Result, [], Result).
differences([H|Ls], [H|Rs], Result) :- differences(Ls, Rs, Result).
differences([L|Ls], [R|Rs], [L|Result]) :-
L < R,
differences(Ls, [R|Rs], Result).
differences([L|Ls], [R|Rs], [R|Result]) :-
L > R,
differences([L|Ls], Rs, Result).
You can see this produces the same result as the O(N^2) method:
?- differences([1,2,3,4], [1,3,5], X).
X = [2,4,5]
You were right, you do need both base cases. This is so the remainder of either list becomes part of the result. Presumably these will be the largest values ([5] in the example).
Now I have three inductive cases: one for <, one for > and one for =. The equality case is intuitive: recur on both lists, discarding the head of both lists. The next case basically says if the left head is less than the right head, add it to the result and recur on the left's tail. The right is unchanged in that case. The other case is the mirror of this case.
Hope this helps!
[_, [ X , _ ],_] will match a list like [d, [X,a], s]. Is there a way to match it to any pattern where there is one or more anonymous variables? ie. [[X,a],s] and [[d,a],[p,z], [X,b]] would match?
I am trying to write a program to count the elements in a list ie. [a,a,a,b,a,b] => [[a,4],[b,2]] but I am stuck:
listcount(L, N) :- listcountA(LS, [], N).
listcountA([X|Tail], [? [X, B], ?], N) :- B is B+1, listcountA(Tail, [? [X,B] ?], N).
listcountA([X|Tail], AL, N) :- listcountA(Tail, [[X,0]|AL], N).
Thanks.
A variable match a term, and the anonimus variable is not exception. A list is just syntax sugar for a binary relation, between head and tail. So a variable can match the list, the head, or the tail, but not an unspecified sequence.
Some note I hope will help you:
listcount(L, N) :- listcountA(LS, [], N).
In Prolog, predicates are identified by name and num.of.arguments, so called functor and arity. So usually 'service' predicates with added arguments keep the same name.
listcountA([X|Tail], [? [X, B], ?], N) :- B is B+1, listcountA(Tail, [? [X,B] ?], N).
B is B+1 will never succeed, you must use a new variable. And there is no way to match inside a list, using a 'wildcard', as you seem to do. Instead write a predicate to find and update the counter.
A final note: usually pairs of elements are denoted using a binary relation, conveniently some (arbitrary) operator. For instance, most used is the dash.
So I would write
listcount(L, Counters) :-
listcount(L, [], Counters).
listcount([X | Tail], Counted, Counters) :-
update(X, Counted, Updated),
!, listcount(Tail, Updated, Counters).
listcount([], Counters, Counters).
update(X, [X - C | R], [X - S | R]) :-
S is C + 1.
update(X, [H | T], [H | R]) :-
update(X, T, R).
update(X, [], [X - 1]). % X just inserted
update/3 can be simplified using some library predicate, 'moving inside' the recursion. For instance, using select/3:
listcount([X | Tail], Counted, Counters) :-
( select(X - C, Counted, Without)
-> S is C + 1
; S = 1, Without = Counted
),
listcount(Tail, [X - S | Without], Counters).
listcount([], Counters, Counters).
I'll preface this post by saying that if you like this answer, consider awarding the correct answer to #chac as this answer is based on theirs.
Here is a version which also uses an accumulator and handles variables in the input list, giving you the output term structure you asked for directly:
listcount(L, C) :-
listcount(L, [], C).
listcount([], PL, PL).
listcount([X|Xs], Acc, L) :-
select([X0,C], Acc, RAcc),
X == X0, !,
NewC is C + 1,
listcount(Xs, [[X0, NewC]|RAcc], L).
listcount([X|Xs], Acc, L) :-
listcount(Xs, [[X, 1]|Acc], L).
Note that listcount/2 defers to the accumulator-based version, listcount/3 which maintains the counts in the accumulator, and does not assume an input ordering or ground input list (named/labelled variables will work fine).
[_, [X, _], _] will match only lists which have 3 elements, 1st and 3rd can be atoms or lists, second element must be list of length 2, but i suppore you know that. It won't match to 2 element list, its better to use head to tail recursion in order to find element and insert it into result list.
Heres a predicate sketch, wich i bet wont work if copy paste ;)
% find_and_inc(+element_to_search, +list_to_search, ?result_list)
find_and_inc(E, [], [[E, 1]]);
find_and_inc(E, [[E,C]|T1], [[E,C1]|T2]) :- C1 is C+1;
find_and_inc(E, [[K,C]|T1], [[K,C]|T2]) :- find_and_inc(E, T1, T2).