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I'm new to Prolog and have a question:
Suppose I have a list of lists; [list1, list2, list3,..., list_n]
If list_j contains list_i, i.e. every variable in list_i occurs in list_j, then remove list_j.
For example, if the input is
[[a,b,c], [a,c], [a,d], [a,d,e]]
the output should be
[[a,c], [a,d]]
because [a,b,c] contains [a,c] and [a,d,e] contains [a,d].
How to implement this in SWI-Prolog? Any help is appreciated.
First of all, SWI already has a predicate to check whether a list is "contained" (in terms of set-inclusion) in another list: subset/2 (http://www.swi-prolog.org/pldoc/man?predicate=subset/2).
Now you can use that to check whether or not to remove a specific list from all lists:
remove(Lists, List) :-
member(List, Lists),
member(Sublist, Lists),
Sublist \= List,
subset(Sublist, List).
Read as: remove List from Lists if it is a member of Lists and there is also another (confirmed by \=) member of Lists (call it Sublist), which is a subset of List.
?- remove([[a,b,c], [a,c], [a,d], [a,d,e]], L).
L = [a, b, c] ;
L = [a, d, e] ;
Now you can use that to answer your original question:
remaining(Lists, Remaining) :-
bagof(List,
(
member(List, Lists),
\+ remove(Lists, List)
),
Remaining).
Let these lists be Remaining from Lists which are members of the original list of Lists and are not (\+) to be removed.
?- remaining([[a,b,c], [a,c], [a,d], [a,d,e]], Remaining).
Remaining = [[a, c], [a, d]].
Last time I learnt about =.. that can translate a list to term and opposite.
I have 3 predicates to do, first one is the one that translates a list to a term. I came up with sth like this:
list_to_term(List, Functor, Term) :-
Term =.. [Functor | List].
Is it okey? Enough? Or I miss something?
The other predicate is count(A,T,N) for element A, in term T with number N that is true if N is a count of elements A in term T... Can anyone help me with this one or how to start?
?- count(a,f(a),N).
N = 1
?- count(a,f(a,g(b,a),N).
N = 2.
?- count(a,f(a,g(X,a),N).
N = 2.
Looking at the answer of this post you can reuse the predicate flatten_term/2, a little bit modified to handle free variables, to sove your problem. Here is the code for a basic solution:
flatten_term(Term,[Term]):-
(atomic(Term);var(Term)),!.
flatten_term(Term,Flat):-
Term =.. TermList,
flatten_term_list(TermList,Flat),!.
flatten_term_list([],[]):-!.
flatten_term_list([H|T],List):-
flatten_term(H,HList),
flatten_term_list(T,TList),
append(HList,TList,List),!.
occurrences(_,[],N,N):-!.
occurrences(A,[H|T],N,Tot):-
A \== H,!,
occurrences(A,T,N,Tot).
occurrences(A,[H|T],N,Tot):-
A == H,!,
N1 is N+1,
occurrences(A,T,N1,Tot).
count(A,Term,N):-
flatten_term(Term,Flatten),
occurrences(A,Flatten,0,N).
?- count(a,f(a,g(X,a),d),T).
T = 2.
?- count(X,f(a,g(X,a),d),T).
T = 1
First of all you flatten the term using flatten_term/2. Then simply count the occurrences of the element you want to find using occurrences/4. You can, if you want, modify flatten_term/2 to avoid the usage of occurrences/4 and so scan the term (list) only one time... Something like: flatten_term(Term,Flatten,ElementToFind,Counter,Total).
Start by solving a more general problem of counting the terms in a list. Processing a term is processing a singleton list containing that term, after all:
count(A,T,N):- count(A, [T|Z],Z, 0,N).
count(_, [], [], C,N):- N is C, !.
count(A, [T|B],Z, C,N):- ?=(A,T), A=T, !, count(A, B,Z, C+1,N).
count(A, [T|B],Z, C,N):- ?=(A,T), T=..[_|S], !, append(S,Y,Z), count(A, B,Y, C,N).
count(A, [_|B],Z, C,N):- count(A, B,Z, C,N).
This opens up each head term in a list in succession and appends its argument terms to that list thus using it as a queue... thus processing the predicate's second argument T in a breadth-first manner.
This assumes A argument is an atom, and ?= is used to avoid instantiating the free variables we might encounter, and instead to skip over them, as your examples seem to indicate.
Is it okey? Enough? Or I miss something?
Prolog's =../2 predicate [swi-doc] can "pack" and "unpack" a list that contains the functor name and its arguments in a term and vice versa. So one can use this to construct a term, or to analyze a term. For example:
?- f(a,g(b,a)) =.. L.
L = [f, a, g(b, a)].
Here f is the functor name, and a and g(b, a) are the arguments. These arguments can be terms as well, and then we thus need to unpack these arguments further.
We can for example obtain all the subterms of a term with:
subterms(T, T) :-
\+ var(T).
subterms(T, ST) :-
\+ var(T),
T =.. [_|As],
member(A, As),
subterms(A, ST).
For example:
?- subterms(f(a,g(X,a)),N).
N = f(a, g(X, a)) ;
N = a ;
N = g(X, a) ;
N = a ;
false.
Now that we obtained all (sub)terms, we can slightly rewrite the predicate to count the number of elements that match:
subterm_query(Q, T) :-
Q == T.
subterm_query(Q, T) :-
\+ var(T),
T =.. [_|As],
member(A, As),
subterm_query(Q, A).
so we obtain if we query for a:
?- subterm_query(a, f(a,g(X,a))).
true ;
true ;
false.
If we can use the aggregate library, we can make use of the aggregate_all/3 predicate to count the number of times, the predicate was succesful:
?- aggregate_all(count, subterm_query(a, f(a,g(X,a))), Count).
Count = 2.
If not, you need to implement a mechanism that returns 1 for a match, and sums up recursively the matches of the child terms. I leave this as an exercise.
I am currently attempting to write a Prolog program which will add a given character to the end of a list. The list's I want to append are elements within a list. This is what I currently have.
extends(X, [], []).
extends(X, [[Head]|Lists], Y):-
append([X], [Head], Y),
extends(X, Lists, [Y]).
Here I'm attempting to concatenate X and Head, storing it in Y. However I want Y to be a list of lists, so when it repeats the process again the next concatenation will be stored also in Y. So at the end of the program Y would store the results of all the concatenations. I would want the result to look like as follows.
?- extends(a, [[b,c], [d,e,f], [x,y,z]], Y).
Y = [[b,c,a], [d,e,f,a], [x,y,z,a]].
Could anyone help me out with this?
You want to apply some operation to corresponding elements of two lists. That operation talks about lists itself. It's easy to get confused with the nested levels of lists, so let's try not to think in those terms. Instead, define first a predicate that does the extension of one list:
element_list_extended(Element, List, Extended) :-
append(List, [Element], Extended).
This behaves as follows, using cases from your example:
?- element_list_extended(a, [b, c], Extended).
Extended = [b, c, a].
?- element_list_extended(a, List, [x, y, z, a]).
List = [x, y, z] ;
false.
Looks good so far. All we need to do is to apply this operation to corresponding elements of two lists:
extends(_Element, [], []).
extends(Element, [Xs | Xss], [Ys | Yss]) :-
element_list_extended(Element, Xs, Ys),
extends(Element, Xss, Yss).
And this works:
?- extends(a, [[b,c], [d,e,f], [x,y,z]], Y).
Y = [[b, c, a], [d, e, f, a], [x, y, z, a]] ;
false.
The key to making it work was to decompose the problem into two parts and to solve those simpler parts separately.
Now, if we like, since the definition of element_list_extended/3 is a single clause containing a single goal, we might decide to do without it and inline its definition into extends/3:
extends(_Element, [], []).
extends(Element, [Xs | Xss], [Ys | Yss]) :-
append(Xs, [Element], Ys),
extends(Element, Xss, Yss).
As you can see, you were quite close! You just had some superfluous brackets because you got confused about list nesting. That's precisely where decomposing the problem helps.
(As the other answer said, SWI-Prolog has some useful libraries that allow you to express even this in even shorter code.)
extends(PostFix, ListIn, ListOut) :-
maplist({PostFix}/[In,Out]>>append(In,[PostFix],Out),ListIn, ListOut).
This is using library(yall) a maplist/3 and append/3.
In Prolog, let's say I have a list such as
[fun, joke1, joke2, fun, joke3, fun, joke4, joke5, joke6]
I'm trying to build a list of lists that will result to
[ [joke1, joke2], [joke4, joke5, joke6] ]
using fun as the delimiter and ignoring a built list of length 1, hence
[joke3]
is not inside that list.
I tried using split_string but it doesn't work for what I need to obtain. I've also tried recursion using append but that didn't work out as well. Hoping I can be pointed to the right direction.
Thanks!
Here is a solution which uses two predicates:
split_on_delimiter(L, D, S) :-
split_on_delimiter_(L, D, R),
findall(X, (member(X, R), length(X,Length), Length > 1), S).
split_on_delimiter_([], _, [[]]).
split_on_delimiter_([D|T], D, [[]|T2]) :-
split_on_delimiter_(T, D, T2).
split_on_delimiter_([H|T], D, [[H|T2]|T3]) :-
dif(H, D),
split_on_delimiter_(T, D, [T2|T3]).
split_on_delimiter_/3 is the predicate which really splits the list based on the delimiter D. split_on_delimiter/3 is the predicate that you would call and which will in turn call split_on_delimiter_/3.
To keep only the sublists of length more than 1, we use findall to find all sublists of the result of the split which have Length > 1.
split_on_delimiter_/3 itself is fairly simple:
First rule: spliting an empty list results in only one sublist: the empty list.
Second rule: when the first element of the list is the delimiter, the result is the empty list followed by the result of the recursive call.
Third rule: when the first element of the list is not the delimiter (dif(H, D)), then we put that element at the beginning of the first sublist and recursive call.
An example:
?- split_on_delimiter([fun, joke1, joke2, fun, joke3, fun, joke4, joke5, joke6], fun, Z).
Z = [[joke1, joke2], [joke4, joke5, joke6]] ;
false.
Note
split_on_delimiter_/3 has extraneous choice points (which is why you can press ; after the first result, because it thinks there can be more answers but there are none). You could solve this using ! or once.
A better solution to remove those choice points is using if_/3 and (=)/3 of module(reif) (though I doubt this is useful to you):
split_on_delimiter_(L, D, [L2|T2]) :-
if_(L = [],
[L2|T2] = [[]],
( L = [H|T],
if_(H = D,
( L2 = [],
split_on_delimiter_(T, D, T2)
),
( L2 = [H|T3],
split_on_delimiter_(T, D, [T3|T2])
)
)
)
).
I'm new in Prolog and trying to do some programming with Lists
I want to do this :
?- count_occurrences([a,b,c,a,b,c,d], X).
X = [[d, 1], [c, 2], [b, 2], [a, 2]].
and this is my code I know it's not complete but I'm trying:
count_occurrences([],[]).
count_occurrences([X|Y],A):-
occurrences([X|Y],X,N).
occurrences([],_,0).
occurrences([X|Y],X,N):- occurrences(Y,X,W), N is W + 1.
occurrences([X|Y],Z,N):- occurrences(Y,Z,N), X\=Z.
My code is wrong so i need some hits or help plz..
Here's my solution using bagof/3 and findall/3:
count_occurrences(List, Occ):-
findall([X,L], (bagof(true,member(X,List),Xs), length(Xs,L)), Occ).
An example
?- count_occurrences([a,b,c,b,e,d,a,b,a], Occ).
Occ = [[a, 3], [b, 3], [c, 1], [d, 1], [e, 1]].
How it works
bagof(true,member(X,List),Xs) is satisfied for each distinct element of the list X with Xs being a list with its length equal to the number of occurrences of X in List:
?- bagof(true,member(X,[a,b,c,b,e,d,a,b,a]),Xs).
X = a,
Xs = [true, true, true] ;
X = b,
Xs = [true, true, true] ;
X = c,
Xs = [true] ;
X = d,
Xs = [true] ;
X = e,
Xs = [true].
The outer findall/3 collects element X and the length of the associated list Xs in a list that represents the solution.
Edit I: the original answer was improved thanks to suggestions from CapelliC and Boris.
Edit II: setof/3 can be used instead of findall/3 if there are free variables in the given list. The problem with setof/3 is that for an empty list it will fail, hence a special clause must be introduced.
count_occurrences([],[]).
count_occurrences(List, Occ):-
setof([X,L], Xs^(bagof(a,member(X,List),Xs), length(Xs,L)), Occ).
Note that so far all proposals have difficulties with lists that contain also variables. Think of the case:
?- count_occurrences([a,X], D).
There should be two different answers.
X = a, D = [a-2]
; dif(X, a), D = [a-1,X-1].
The first answer means: the list [a,a] contains a twice, and thus D = [a-2]. The second answer covers all terms X that are different to a, for those, we have one occurrence of a and one occurrence of that other term. Note that this second answer includes an infinity of possible solutions including X = b or X = c or whatever else you wish.
And if an implementation is unable to produce these answers, an instantiation error should protect the programmer from further damage. Something along:
count_occurrences(Xs, D) :-
( ground(Xs) -> true ; throw(error(instantiation_error,_)) ),
... .
Ideally, a Prolog predicate is defined as a pure relation, like this one. But often, pure definitions are quite inefficient.
Here is a version that is pure and efficient. Efficient in the sense that it does not leave open any unnecessary choice points. I took #dasblinkenlight's definition as source of inspiration.
Ideally, such definitions use some form of if-then-else. However, the traditional (;)/2 written
( If_0 -> Then_0 ; Else_0 )
is an inherently non-monotonic construct. I will use a monotonic counterpart
if_( If_1, Then_0, Else_0)
instead. The major difference is the condition. The traditional control constructs relies upon the success or failure of If_0 which destroys all purity. If you write ( X = Y -> Then_0 ; Else_0 ) the variables X and Y are unified and at that very point in time the final decision is made whether to go for Then_0 or Else_0. What, if the variables are not sufficiently instantiated? Well, then we have bad luck and get some random result by insisting on Then_0 only.
Contrast this to if_( If_1, Then_0, Else_0). Here, the first argument must be some goal that will describe in its last argument whether Then_0 or Else_0 is the case. And should the goal be undecided, it can opt for both.
count_occurrences(Xs, D) :-
foldl(el_dict, Xs, [], D).
el_dict(K, [], [K-1]).
el_dict(K, [KV0|KVs0], [KV|KVs]) :-
KV0 = K0-V0,
if_( K = K0,
( KV = K-V1, V1 is V0+1, KVs0 = KVs ),
( KV = KV0, el_dict(K, KVs0, KVs ) ) ).
=(X, Y, R) :-
equal_truth(X, Y, R).
This definition requires the following auxiliary definitions:
if_/3, equal_truth/3, foldl/4.
If you use SWI-Prolog, you can do :
:- use_module(library(lambda)).
count_occurrences(L, R) :-
foldl(\X^Y^Z^(member([X,N], Y)
-> N1 is N+1,
select([X,N], Y, [X,N1], Z)
; Z = [[X,1] | Y]),
L, [], R).
One thing that should make solving the problem easier would be to design a helper predicate to increment the count.
Imagine a predicate that takes a list of pairs [SomeAtom,Count] and an atom whose count needs to be incremented, and produces a list that has the incremented count, or [SomeAtom,1] for the first occurrence of the atom. This predicate is easy to design:
increment([], E, [[E,1]]).
increment([[H,C]|T], H, [[H,CplusOne]|T]) :-
CplusOne is C + 1.
increment([[H,C]|T], E, [[H,C]|R]) :-
H \= E,
increment(T, E, R).
The first clause serves as the base case, when we add the first occurrence. The second clause serves as another base case when the head element matches the desired element. The last case is the recursive call for the situation when the head element does not match the desired element.
With this predicate in hand, writing count_occ becomes really easy:
count_occ([], []).
count_occ([H|T], R) :-
count_occ(T, Temp),
increment(Temp, H, R).
This is Prolog's run-of-the-mill recursive predicate, with a trivial base clause and a recursive call that processes the tail, and then uses increment to account for the head element of the list.
Demo.
You have gotten answers. Prolog is a language which often offers multiple "correct" ways to approach a problem. It is not clear from your answer if you insist on any sort of order in your answers. So, ignoring order, one way to do it would be:
Sort the list using a stable sort (one that does not drop duplicates)
Apply a run-length encoding on the sorted list
The main virtue of this approach is that it deconstructs your problem to two well-defined (and solved) sub-problems.
The first is easy: msort(List, Sorted)
The second one is a bit more involved, but still straight forward if you want the predicate to only work one way, that is, List --> Encoding. One possibility (quite explicit):
list_to_rle([], []).
list_to_rle([X|Xs], RLE) :-
list_to_rle_1(Xs, [[X, 1]], RLE).
list_to_rle_1([], RLE, RLE).
list_to_rle_1([X|Xs], [[Y, N]|Rest], RLE) :-
( dif(X, Y)
-> list_to_rle_1(Xs, [[X, 1],[Y, N]|Rest], RLE)
; succ(N, N1),
list_to_rle_1(Xs, [[X, N1]|Rest], RLE)
).
So now, from the top level:
?- msort([a,b,c,a,b,c,d], Sorted), list_to_rle(Sorted, RLE).
Sorted = [a, a, b, b, c, c, d],
RLE = [[d, 1], [c, 2], [b, 2], [a, 2]].
On a side note, it is almost always better to prefer "pairs", as in X-N, instead of lists with two elements exactly, as in [X, N]. Furthermore, you should keep the original order of the elements in the list, if you want to be correct. From this answer:
rle([], []).
rle([First|Rest],Encoded):-
rle_1(Rest, First, 1, Encoded).
rle_1([], Last, N, [Last-N]).
rle_1([H|T], Prev, N, Encoded) :-
( dif(H, Prev)
-> Encoded = [Prev-N|Rest],
rle_1(T, H, 1, Rest)
; succ(N, N1),
rle_1(T, H, N1, Encoded)
).
Why is it better?
we got rid of 4 pairs of unnecessary brackets in the code
we got rid of clutter in the reported solution
we got rid of a whole lot of unnecessary nested terms: compare .(a, .(1, [])) to -(a, 1)
we made the intention of the program clearer to the reader (this is the conventional way to represent pairs in Prolog)
From the top level:
?- msort([a,b,c,a,b,c,d], Sorted), rle(Sorted, RLE).
Sorted = [a, a, b, b, c, c, d],
RLE = [a-2, b-2, c-2, d-1].
The presented run-length encoder is very explicit in its definition, which has of course its pros and cons. See this answer for a much more succinct way of doing it.
refining joel76 answer:
count_occurrences(L, R) :-
foldl(\X^Y^Z^(select([X,N], Y, [X,N1], Z)
-> N1 is N+1
; Z = [[X,1] | Y]),
L, [], R).