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Given the letters [a, b, c] generate the list containing all the words of length N, formed out of this letters.
For example:
?- generate(2, L).
should output:
L = [aa, ab, ac, ba, bb, bc, ca, cb, cc].
At first, this seemed like a pretty simple problem, but I've discovered that none of my implementations work.
This is the second implementation, the one that kind of works.
letter(X) :- member(X, [a, b, c]).
generateWord(0, []) :- !.
generateWord(N, [H|T]) :-
letter(H),
NextN is N - 1,
generateWord(NextN, T).
generateAtomicWord(N, Word) :-
generateWord(N, WList),
atomic_list_concat(WList, Word).
maxSolutions(N, R) :- R is N ** 3.
generate(N, CurrentList, ResultList) :-
maxSolutions(N, R),
length(CurrentList, L),
L =:= R,
append(CurrentList, [], ResultList), !.
generate(N, CurrentList, ResultList) :-
generateAtomicWord(N, NewWord),
\+ member(NewWord, CurrentList),
append(CurrentList, [NewWord], NewList),
generate(N, NewList, ResultList).
generate(N, ResultList) :-
generate(N, [], ResultList).
It kind of works because when given N = 3 the program outputs:
L = [aaa, aab, aac, aba, abb, abc, aca, acb, acc|...]
My first implementation is different, but I can't make it work on any case.
letter(X) :- member(X, [a, b, c]).
generateWord(0, []) :- !.
generateWord(N, [H|T]) :-
letter(H),
NextN is N - 1,
generateWord(NextN, T), !.
generateAtomicWord(N, Word) :-
generateWord(N, WList),
atomic_list_concat(WList, Word).
maxSolutions(N, R) :- R is N ** 3.
generate(N, [H]) :- generateAtomicWord(N, H).
generate(N, [H|T]) :-
generate(N, T),
length(T, TailLen),
maxSolutions(N, M),
(TailLen =:= M -> !;
generateAtomicWord(N, H),
\+ member(H, T)).
This one just outputs:
L = [aa]
and when requested for the rest of the solutions it cycles.
The problem must be solved without using predicates such as:
findall, findnsol, bagof, setof, etc...
that find all the solutions.
I've added the tag backtracking because it does resemble a backtracking problem, but I've no idea what a standard implementation might look like in Prolog.
It kind of works because when given N = 3 the program outputs:
L = [aaa, aab, aac, aba, abb, abc, aca, acb, acc|...]
That is not an error, that is the Prolog interpreter that displays the list in a shorter way. If you hit w when it shows the output, it will show the full list. For more information see this answer.
That being said, you make it too hard. You can first make a predicate that will unify a variable with all possible atoms:
letter(X) :- member(X, [a, b, c]).
word(0, []).
word(N, [C|W]) :-
N > 0,
N1 is N-1,
letter(C),
word(N1, W).
Now we can generate all possibilities with findall/3 [swi-doc], and use for example maplist/3 [swi-doc] with atomic_list_concat/2 to convert the list to a single atom:
words(N, L) :-
findall(W, word(N, W), Ws),
maplist(atomic_list_concat, Ws, L).
For example:
?- words(0, L).
L = [''].
?- words(1, L).
L = [a, b, c].
?- words(2, L).
L = [aa, ab, ac, ba, bb, bc, ca, cb, cc].
?- words(3, L).
L = [aaa, aab, aac, aba, abb, abc, aca, acb, acc|...].
We can generate a list of lists ourselves by updating a "difference" list until all possible words are generated:
wordlist(N, L) :-
wordlist(N, [], L, []).
wordlist(0, R, [W|T], T) :-
reverse(R, W),
!.
wordlist(N, C, L, T) :-
N > 0,
N1 is N-1,
wordfold([a,b,c], N1, C, L, T).
wordfold([], _, _, L, L).
wordfold([C|CS], N1, CT, L, T) :-
wordlist(N1, [C|CT], L, L2),
wordfold(CS, N1, CT, L2, T).
For example:
?- wordlist(0, L).
L = [[]].
?- wordlist(1, L).
L = [[a], [b], [c]].
?- wordlist(2, L).
L = [[a, a], [a, b], [a, c], [b, a], [b, b], [b, c], [c, a], [c|...], [...|...]].
You then still need to perform atomic_list_concat on it. I leave that as an exercise.
Imagine that we have a list: [1,2,2,3,4]. The problem can be splitted into two parts:
Reverse the list (we should receive [4,3,2,2,1])
Replace, e.g. all 2 with 100, so we should receive [4,3,100,100,1]
It's easy to reverse the list, here's a working code:
simple_reverse(List, Rev) :-
simple_reverse(List, Rev, []).
simple_reverse([], L, L).
simple_reverse([H|T], L, SoFar) :-
simple_reverse(T, L, [H|SoFar]).
But I have some troubles with replacing the elements. I have tried the following approach:
reverse(a, b, List, Rev) :-
reverse(a, b, List, Rev, []).
reverse(a, b, [], L, L).
reverse(a, b, [H|T], L, SoFar) :-
reverse(a, b, T, L, [H|SoFar]).
reverse(a, b, [a|T], L, SoFar) :-
reverse(a, b, T, L, [b|SoFar]).
What is the problem? By the way, I'm using https://swish.swi-prolog.org/ to run the code.
Instead of just a,b (which are atoms) you need to place variables in reverse/4 and reverse/5 predicates:
reverse(A, B, List, Rev) :-
reverse(A, B, List, Rev, []).
reverse(_, _, [], L, L).
reverse(A, B, [H|T], L, SoFar) :-
dif(A,H), %case where H is not A so we skip it
reverse(A, B, T, L, [H|SoFar]).
reverse(A, B, [A|T], L, SoFar) :-
reverse(A, B, T, L, [B|SoFar]).
You can use foldl in conjonction with library(lambda) :
:- use_module(library(lambda)).
my_reverse(L, A, B, R) :-
foldl([A,B] +\X^Y^Z^(dif(X, A) -> Z = [X |Y]; Z = [B|Y]), L, [],R).
example :
?- my_reverse([1,2,2,3,4], 2, 100, R).
R = [4, 3, 100, 100, 1].
It is folk knowledge that append(X,[Y],Z) finds the last element
Y of the list Z and the remaining list X.
But there is some advantage of having a customized predicate last/3,
namely it can react without leaving a choice point:
?- last([1,2,3],X,Y).
X = 3,
Y = [1,2]
?- append(Y,[X],[1,2,3]).
Y = [1,2],
X = 3 ;
No
Is there a way to realize a different implementation of
append/3 which would also not leave a choice point in the
above example?
P.S.: I am comparing:
/**
* append(L1, L2, L3):
* The predicate succeeds whenever L3 unifies with the concatenation of L1 and L2.
*/
% append(+List, +List, -List)
:- public append/3.
append([], X, X).
append([X|Y], Z, [X|T]) :- append(Y, Z, T).
And (à la Gertjan van Noord):
/**
* last(L, E, R):
* The predicate succeeds with E being the last element of the list L
* and R being the remainder of the list.
*/
% last(+List, -Elem, -List)
:- public last/3.
last([X|Y], Z, T) :- last2(Y, X, Z, T).
% last2(+List, +Elem, -Elem, -List)
:- private last2/4.
last2([], X, X, []).
last2([X|Y], U, Z, [U|T]) :- last2(Y, X, Z, T).
One way to do it is to use foldl/4 with the appropriate help predicate:
swap(A, B, B, A).
list_front_last([X|Xs], F, L) :-
is_list(Xs),
foldl(swap, Xs, F, X, L).
This should be it:
?- list_front_last([a,b,c,d], F, L).
F = [a, b, c],
L = d.
?- list_front_last([], F, L).
false.
?- list_front_last([c], F, L).
F = [],
L = c.
?- Ys = [y|Ys], list_front_last(Ys, F, L).
false.
Try to see if you can leave out the is_list/1 from the definition.
As I posted:
append2(Start, End, Both) :-
% Preventing unwanted choicepoint with append(X, [1], [1]).
is_list(Both),
is_list(End),
!,
append(Start, End, Both),
!.
append2(Start, End, Both) :-
append(Start, End, Both),
% Preventing unwanted choicepoint with append(X, Y, [1]).
(End == [] -> ! ; true).
Result in swi-prolog:
?- append2(Y, [X], [1,2,3]).
Y = [1, 2],
X = 3.
Im in rew to Prolog. I'm trying to write a zip function. The question goes like this.
zip(L1, L2, X): The list X is formed by “zipping” the first 2 arguments.
the result should be like this:
?- zip([a, b, c], [x, y, z], X).
L = [a, x, b, y, c, z]
?- zip([a, b], [x, y, z], X).
false
?- zip([a, b, c, d], X, [a, p, b, q, c, r, d, s]).
X = [p, q, r, s]
I have done this so far.
I can get the result for 1st 3rd but not the 2nd one. Can anybody can help me solving it for the 2nd one? thank you
zip([X],[Y],[X,Y]).
zip([], [], []).
zip([X|Xs], [Y|Ys], [X,Y|Zs]) :-
zip(Xs,Ys,Zs).
zip([X|Xs],[],[X|Xs]).
zip([Y|Ys],[],[Y|Ys]).
zip(Xs, [], Xs).
zip([], Ys, Ys).
How do I define this function where:
allsame(L): The list L contains identical elements.
I should get this.
?- allsame([b, b, b]).
true
?- allsame([c, c, c, Y, c, c, X, c]).
X = c, Y = c
You had it:
zip([], [], []).
zip([X|Xs], [Y|Ys], [X,Y|Zs]) :- zip(Xs,Ys,Zs).
This alone is enough to define the relation you're seeking. The extra clauses don't help.
Test:
?- zip([a, b, c], [x, y, z], X).
X = [a, x, b, y, c, z].
?- zip([a, b], [x, y, z], X).
false.
?- zip([a, b, c, d], X, [a, p, b, q, c, r, d, s]).
X = [p, q, r, s].
#m09 gave the correct answer. But I'd like to explain why what you have isn't correct:
(1) zip([X],[Y],[X,Y]).
This rule says that [X,Y] is what you get when you zip [X] with [Y]. That is correct, and will not lead to a problem. The rule is simply redundant with the rules below (which I'll explain...).
(2) zip([], [], []).
This rule says [] is what you get when you zip [] with [] which is correct and as simple a rule as you can have for zip.
(3) zip([X|Xs], [Y|Ys], [X,Y|Zs]) :-
zip(Xs,Ys,Zs).
This rule says that [X,Y|Zs] is what you get when you zip [X|Xs] with [Y|Ys] if Zs is what you get when you zip Xs with Ys. That is also logical and correct. Notice that zip([X], [Y], [X,Y]) is zip([X|[]], [Y|[]], [X,Y|[]]). so it can be derived from rules (2) and (3). It would match rule (3) first, zip([X|[]], [Y|[]], [X,Y|Zs]) :- zip([], [], Zs)., then Zs would become [] by rule (2)`.
(4) zip([X|Xs],[],[X|Xs]).
(5) zip([Y|Ys],[],[Y|Ys]).
Rule (4) says [X|Xs] is what you get when you zip [X|Xs] with []. Rule (5) says exactly the same thing, logically, only with a different variable name. These are incorrect, since that would mean, for example, zip([a,b,c], [], Z) would be true if Z = [a,b,c].
(6) zip(Xs, [], Xs).
This rule says that Xs is what you get when you zip Xs with []. Or stated another way, any input, zipped with [], would be that input value again. It wouldn't even have to be a list! This is clearly incorrect. Queries like zip(x, [], Z) would succeed with Z = x, and zip(friend(bill,mary), [], Z) would succeed with Z = friend(bill,mary).
(7) zip([], Ys, Ys).
This rule says that Ys is what you get when you zip [] with Ys. It is incorrect for the same reason (6) is incorrect. In fact, this rule, combined with (2) and (3) are why the query zip([a, b], [x, y, z], X). will yield a result rather than fail. Rules (2) and (3) will recurse to zip([b], [y,z], [b,y|T]) :- zip([], [z], T). and then zip([], [z], T) will finally succeed on rule (7) with T = [z], and ultimately yielding a final result to zip([a, b], [x, y, z], X) of X = [a, x, b, y, z].
/* substitute(X,Y,Xs,Ys) is true if the list Ys is the result of substituting Y for all occurrences of X in the list Xs.
This is what I have so far:
subs(_,_,[],[]).
subs(X,Y,[X|L1],[Y|L2]):- subs(X,Y,L1,L2).
subs(X,Y,[H|L1],[H|L2]):- X\=H, not(H=[_|_]), subs(X,Y,L1,L2).
subs(X,Y,[H|_],[L2]):- X\=H, H=[_|_], subs(X,Y,H,L2).
My code works except it omits the elements following the nested list. For example:
?- subs(a,b,[a,[a,c],a],Z).
Z = [b, [b, c]] .
What should I add to this program?
Here is how you could write it using (... -> ... ; ...):
subs(_, _, [], []).
subs(X, Y, [H1|T1], [H2|T2]) :-
(H1 == X ->
H2 = Y
; is_list(H1) ->
subs(X, Y, H1, H2),
subs(X, Y, T1, T2)
;
H1 = H2,
subs(X, Y, T1, T2)
).
The problem is that once you find a nested list, you forget about whatever is behind that nested list. Instead, after recursing with the nested nest, simply continue as before. Thus, you should change the last clause as follows:
subs(X,Y,[H|L1],[H2|L2]):- X\=H, H=[_|_], subs(X,Y,H,H2), subs(X, Y, L1, L2).
Aside from that, there are a couple of ways in which you can improve the code:
Use cuts (!/0) to stop backtracking. In this way you don't have to repeat yourself.
You can use is_list/1 to test whether an argument is a list.
It's okay to use more spaces. Really.
So, an alternative solution is (now using \+/1 instead of not/1):
subs(_, _, [], []).
subs(X, Y, [X|T1], [Y|T2]) :- subs(X, Y, T1, T2), !.
subs(X, Y, [H|T1], [H|T2]) :- \+ is_list(H), subs(X, Y, T1, T2), !.
subs(X, Y, [H1|T1], [H2|T2]) :- subs(X, Y, H1, H2), subs(X, Y, T1, T2).
Demonstration:
?- subs(a, b, [a, [a, [d, f, a]], a, b, a, [g]], Z).
Z = [b, [b, [d, f, b]], b, b, b, [g]].