I am having troubles counting the number of lists in a nested list.
count_lists([H|T],R):-
atomic(H),!,
count_lists(T,NR),
R is NR+1.
count_lists([[H|T]|Rest],R):-
!,
count_lists([H|T],R1),
count_lists(Rest,R2),
R is R1+R2.
count_lists([],0).
First of all, I try the basic case where an element in the list is atomic and thus, I should increment the counter by one. (Also, I tried removing the atomic predicate because I figured that because of it, my code will compute the number of elements in a nested list, but it still doesn't work)
Then, if the first element is a list itself, I go recursively on it and on the remaining list, adding the results.
And the third clause is states that the number of nested lists in an empty list is 0.
?count_lists([[1,5,2,4],[1,[4,2],[5]],[4,[7]],8,[11]],R).
should return 8 but instead, returns 12.
I know it's been a while since you asked this, but here is the answer I think you were looking for:
count_lists([],1).
count_lists([H|T],Rez):-atomic(H),!,count_lists(T,Part),Rez is Part.
count_lists([H|T],Rez):-count_lists(H,Part1),count_lists(T,Part2),Rez is Part1+Part2.
This way, you count only the number of lists and not the number of elements within.
you need to distinguish lists from other elements, i.e.
count_lists(E,R):-
is_list(E),!,count_elems(E,N),
R is N+1.
count_lists(_,0).
count_elems([H|T],R):-
count_lists(H,Hc),
count_elems(T,Tc),
R is Hc+Tc.
count_elems([],0).
but the code is contrived, using library we can get it done in 1 step:
count_lists(E, R):-
maplist(count_lists, E, Cs) -> sum_list(Cs, S), R is S+1 ; R = 0.
the code can be understood only WRT maplist/N behaviour
?- maplist(_,a).
false.
?- maplist(_,[]).
true.
?- maplist(_,[1]).
ERROR: apply:maplist_/2: Arguments are not sufficiently instantiated
In your solution you forget that e.g. [1,2,3] = [1,2,3| []] or [1,2,3] = [1| [2| [3| []]]]. Thus, you're "over-counting", thanks to your first clause. For example:
?- count_lists([1,2,3], N).
N = 3.
But there's another problem. In your second clause, if you've a nested list that nests other lists, you don't count it. Not clear from the title if that's intended or if it's a bug.
You shouldn't have complicated yourself.
count([],1).
count([L1|L2],Rez):- count(L1,Rez1),count(L2,Rez2),Rez is Rez1+Rez2.
You take out all the elements in a list recursively until you are left out with the empty list which values 1.
Related
I've been working on Prolog for a few weeks right now. I am now trying to write a function in it called matching:
Write a predicate called matching with three parameters, all lists.
The third list must contain the index of the positions in which
the first two lists contain the same value.
If I run
matching([10,71,83,9,24,5,2],[8,71,26,9],Positions).
The results are:
?- matching([10,71,83,9,24,5,2],[8,71,26,9],Positions).
Positions = [] ;
Positions = [] ;
Positions = [_2420] ;
Positions = [_2420] ;
Positions = [_2420, _2432];...
The correct answer would be that Positions is bound to [1,3]. I have no idea what is wrong with my code. Any hint is appreciated.
A hint? Each of your matchingHelper clauses contains a mistake!
OK, a little more than a hint:
Base cases
Prolog should be giving you a warning about singleton variables here. ListofIndex is a variable, but it is only used in one place. Essentially this means that there is absolutely no constraint on this, and thus can be anything.
The correct thing would be that if either of the input lists is empty, the output is also empty.
matchingHelper([], _, , []).
matchingHelper(, [], _, []).
Equal case
This one you almost have correct, but the way you deal with ListOfIndex is backwards. You construct a NewListOfIndex based on the predicate arguments, and use that in the recursive call. The problem is that the ListOfIndex is actually the output! So you should instead construct the ListOfIndex based on the output from the recursive call.
matchingHelper([X|Xs], [X|Ys], Index, [Index|ListofIndex]) :-
Index2 is Index + 1,
matchingHelper(Xs, Ys, Index2, ListofIndex).
Unequal case
Just 2 little issues with this one. First is that this clause should only apply if X and Y are different. Just using a different variable name does not enforce this. Because there is a previous clause which handles the equal case, the first result prolog finds would be correct, but it will continue to find other, incorrect solutions because of this.
The second issue is that you don't increment the index. If you ignore the first element, the current index has to be incremented to reflect the current position.
matchingHelper([X|Xs], [Y|Ys], Index, ListofIndex) :-
X \= Y,
Index2 is Index + 1,
matchingHelper(Xs, Ys, Index2, ListofIndex).
Here's a sample run:
?- matching([10,71,83,9,24,5,2],[8,71,26,9],Positions).
Positions = [1, 3]
false
Hello I want to make a program in Prolog, that given a list of numbers and a number, it appends all the concurences of position of the number in a second list.
For example for the list (5,10,4,5,6,5) and number =5 the new list should be
(1,4,6)
here is my code so far
positions(X, [X|_],1).
positions(X, [P|T], N) :- positions(X, T, N1), N is N1+1.
find(X, [H|T] ,Z) :-positions(X,[H|T],N) , append([],N,Z).
the positions returns the first concurrence of X in the list, but I don't know how to proceed. Can you help me?
If it's not an assignment, then you can benefit from using the built-ins findall/3 and nth1/3:
?- findall(Nth, nth1(Nth, [5,10,4,5,6,5], 5), Nths).
Nths = [1, 4, 6].
Taking just the nth1 phrase, and running that, you can see it is backtracking and finding multiple solutions, then we just use findall to collect them into a list.
?- nth1(Nth, [5,10,4,5,6,5], 5).
Nth = 1 ;
Nth = 4 ;
Nth = 6.
nth1/3, when using a variable for the first parameter, is saying 'give me a list index where where the 3rd parameter is found in the list of the second parameter.
You have some good ideas, but I would suggest a couple things:
1) In Prolog, it can be beneficial to give variables meaningful names
2) Use an accumulator and you will only need positions and append
3)Use a different base case
positions([Num|List],Num,[Index|SubResult],Index) :- Index2 is Index+1,
positions(List,Num,SubResult,Index2).
positions([NotNum|List],Num,Result,Index) :- NotNum \= Num,
Index2 is Index+1,
positions(List,Num,Result,Index2).
positions([],Num,[],Index).
In our first general case, we can see the numbers match, so we go find how many results are in our sublist, which we will call the SubResult and then push the current index on to our SubResult
The next general case, the numbers do not unify, and our Result IS the SubResult, so let's call them the same thing.
In our final case (the base case) we can see the list is empty, in this case we return an empty list as we cannot match against an empty list.
You can see that the above rules are order-independent, which is something very valuable in Prolog. This means you can arrange the rules in any order, and the semantics of your Prolog program remain unchanged. Using unification to achieve this will prevent future pain in debugging.
We can wrap our predicate in the following way
positions(Num, List, Positions) :- positions(List, Num, Positions, 1).
This will allow for queries of positions(5,[5,10,4,5,6,5],Positions).
I'm very new to Prolog and am trying to figure out exactly what is happening with this (function?) that takes out the 2nd to last element in a list.
remove([],[]).
remove([X],[X]).
remove([_,X],[X]).
remove([X|Xs], [X|Ys]) :-
Xs = [_,_|_],
remove(Xs,Ys).
I'm familiar with pattern matching, as I've done a little work in SML. The first one is clearly the base case, returning the empty list when we break it down. The second returns the same variable when there is only one left. The third looks as if it returns the last element, disregarding the 2nd to last? As for the inductive case, it will attach the head of the list to the new list if ...... (This is where I get completely lost). Could anyone explain what's happening in this function so I can have a better understanding of the language?
Elaborating on CapelliC's explanation:
remove([],[]).
An empty list is an empty list with the second-to-last element removed.
remove([X],[X]).
A single-element list is itself with the second-to-last element removed.
remove([_,X],[X]).
A two-element list with the second to last element removed is a list of one element consisting of the last element of the two-element list.
remove([X|Xs], [X|Ys]) :-
Xs = [_,_|_],
remove(Xs,Ys).
The second list is the first list with the second element removed, and share the same first element, IF:
The tail of the first list consists of at least two elements, AND
The tail of the second list is the tail of the first list with the second to last element removed
A set of clauses is a predicate, or procedure.
All first three are base cases, and the recursive one copies while there are at least 3 elements in the first list.
I would describe the behaviour like 'removes pre-last element'.
So, how to declaratively read
remove([X|Xs], [X|Ys]) :-
Xs = [_,_|_],
remove(Xs,Ys).
Most important is that you first realize what the :- actually means.
Head :- Body.
It means: Whenever Body holds, we can conclude that also Head holds. Note the rather unintuitive direction of the arrow. It goes right-to-left. And not left-to-right, as often written informally when you conclude something. However, the error points into the direction of what we get "out of it".
To better see this, you can enter Body as a query!
?- Xs = [_,_|_], remove(Xs,Ys).
Xs = [A, B], Ys = [B]
; Xs = [A, B, C], Ys = [A, C]
; ... .
So we get all answers, except those where Xs has less than two elements.
Please note that procedurally, things happen exactly in the other direction - and that is very confusing to beginners. Even more so, since Prolog uses two "non-traditional" features: chronological backtracking, and variables - I mean real variables, meaning all possible terms - not these compile time constructs you know from imperative and functional languages. In those languages variables are holders for runtime values. Concrete values. In Prolog, variables are there at runtime, too. For more to this, see Difference between logic programming and functional programming
There is also another issue, I am not sure you understood. Think of:
?- remove(Xs, [1,2]).
Xs = [1, A, 2]
; false.
What is removed here? Nothing! Quite the contrary, we are adding a further element into the list. For this reason, the name remove/2 is not ideal in Prolog - it reminds us of command oriented programming languages that enforce that some arguments are given and others are computed. You might at first believe that this does not matter much, after all it's only a name. But don't forget that when programming you often do not have the time to think through all of it. So a good relational name might be preferable.
To find one, start with just the types: list_list/2, and then refine list_removed/2 or list__without_2nd_last/2.
Annotated:
remove( [] , [] ) . % removing the 2nd last element from the empty list yields the empty list
remove( [X] , [X] ) . % removing the 2nd last element from a 1-element list yields the 1-element list.
remove( [_,X] , [X] ) . % removing the 2nd last element from a 2-element list yields the tail of the 2-element list
remove( [X|Xs] , [X|Ys] ) :- % for any other case...
Xs = [_,_|_], % * if the tail contains 2 or more elements, the list is 3 elements or more in length
remove(Xs,Ys). % we simply prepend the head of the list to the result and recurse down.
It should be noted that the last clause could re-written a tad more clearly (and a little more succinctly) as:
remove( [X1,X2,X3|Xs] , [X1|Ys] ) :- % for any other case (a list of length 3 or more)
remove([X2,X3|Xs],Ys). % we simply prepend the head of the list to the result and recurse down.
Or as
remove( [X1|[X2,X3|Xs]] , [X1|Ys] ) :- % for any other case (a list of length 3 or more)
remove([X2,X3|Xs],Ys). % we simply prepend the head of the list to the result and recurse down.
I need to write rules below:
Write the rules for a predicate take(L,N,L1), which succeeds if list L1 contains the
first N elements of list L, in the same order. The following queries show examples of using this predicate:
?- take([5,1,2,7], 3, L1).
L1 = [5,1,2]
?- take([5,1,2,7], 10, L1).
L1 = [5,1,2,7]
My idea is to delete the first number of two list any time until L1 is empty.
I am also thinking that I can use car([X|_], X) to delete the last number each time until the first list ==the second list. I already wrote the length(L,Len), but I don't know how to do next...
My code is:
take(L,X,[]).(I know it miss something, but I don't know how to do...)
take(H|L,N,H|L1):- take(L,X,L1), N is X-1.
=========================Update=================================================
Thank you 1638891!
Right now, the code is
take(L,0,[]).
take([H|L],N,[H|L1]):- take(L,X,L1), N is X+1.
But it doesn't work in the second case, which is
?- take([5,1,2,7], 10, L1).
L1 = [5,1,2,7]
I tried to add
take([],X,[])->!.
But it pop up "ERROR: is/2: Arguments are not sufficiently instantiated".
#user1638891 forgot to swap the subtraction, and to cover the case when you are requested more elements than available:
take(_,0,[]).
take([],_,[]).
take([H|L],N,[H|L1]) :- N > 0, X is N-1, take(L,X,L1).
You actually want to write X is N - 1.
take(L,0,[]).
take([H|L],N,[H|L1]):- take(L,X,L1), X is N-1.
As a general rule try to read your rules aloud. The first rule you wrote reads as "Empty list is the list with the first X elements in L." But it should have been "Empty list is the list with the first 0 elements in L" as a base case.
I'm reading 'the art of prolog' book and I found an exercise that reads 'Define the relation sum(ListOfIntegers,Sum) which holds if Sum is the sum of the ListOfIntegers, without using any auxiliary predicate' .I came up with this solution:
sum([],Sum).
sum([0|Xs], Sum):-sum(Xs, Sum).
sum([s(X)|Xs], Sum):-sum([X|Xs],s(Sum)).
Which does not work exactly as I would want it to.
?- sum([s(s(0)),s(0),s(s(s(0)))],X).
true ;
false.
I was expecting X to be
s(s(s(s(s(s(0))))))
I thought that the problem is that I have to 'initialize' Sum to 0 in the first 'iteration' but that would be very procedural and unfortunately I'm not quite apt in prolog to make that work.
Any ideas or suggestions?
Your first clause should read
sum([], 0).
With that change, the vacuous true return goes away and you're left with one problem: the third clause reverses the logic of summation. It should be
sum([s(X)|Xs], s(Sum)) :- sum([X|Xs], Sum).
because the number of s/1 terms in the left argument to sum/2 should be equal to the number of them in the right argument.
The best way to localize the problem is to first simplify your query:
?- sum([0],S).
true.
?- sum([],S).
true.
Even for those, you get as an answer that any S will do. Like
?- sum([],s(s(0))).
true.
Since [] can only be handled by your fact, an error must lie in that very fact.
You stated:
sum([], Sum).
Which means that the sum of [] is just anything. You probably meant 0.
Another error hides in the last rule... After fixing the first error, we get
?- sum([0],Sum).
Sum = 0.
?- sum([s(0)],Sum).
false.
Here, the last clause is responsible. It reads:
sum([s(X)|Xs], Sum):-sum([X|Xs],s(Sum)).
Recursive rules are relatively tricky to read in Prolog. The simplest way to understand them is to look at the :- and realize that this should be an arrow ← (thus a right-to-left arrow) meaning:
provided, that the goals on the right-hand side are truewe conclude what is found on the left-hand side
So, compared to informal writing, the arrows points into the opposite direction!
For our query, we can consider the following instantiation substituting Xs with [] and X with 0.
sum([s(0)| [] ], Sum) :- sum([0| []],s(Sum)).
So this rule now reads right-to-left: Provided, sum([0],s(Sum)) is true, ... However, we do know that only sum([0],0) holds, but not that goal. Therefore, this rule never applies! What you intended was rather the opposite:
sum([s(X)|Xs], s(Sum)):-sum([X|Xs],Sum).
I'm not really following your logic, what with all the seemingle extraneous s(X) structures floating about.
Wouldn't it be easier and simpler to do something like this?
First, define your solution in plain english, thus:
The sum of an empty list is 0.
The sum of a non-empty list is obtained by adding the head of the list to the sum of the tail of the list.
From that definition, the prolog follows directly:
sum( [] , 0 ) . % the sum of an empty list is 0.
sum( [X|Xs] , T ) :- % the sum of an non-empty list is obtained by:
sum( Xs , T1 ) , % - first computing the sum of the tail
T is X + T1 % - and then, adding that the to head of the list
. % Easy!