How do you write a Prolog procedure map(List, PredName, Result) that applies the predicate PredName(Arg, Res) to the elements of List, and returns the result in the list Result?
For example:
test(N,R) :- R is N*N.
?- map([3,5,-2], test, L).
L = [9,25,4] ;
no
This is usually called maplist/3 and is part of the Prolog prologue. Note the different argument order!
:- meta_predicate(maplist(2, ?, ?)).
maplist(_C_2, [], []).
maplist( C_2, [X|Xs], [Y|Ys]) :-
call(C_2, X, Y),
maplist( C_2, Xs, Ys).
The different argument order permits you to easily nest several maplist-goals.
?- maplist(maplist(test),[[1,2],[3,4]],Rss).
Rss = [[1,4],[9,16]].
maplist comes in different arities and corresponds to the following constructs in functional languages, but requires that all lists are of same length. Note that Prolog does not have the asymmetry between zip/zipWith and unzip. A goal maplist(C_3, Xs, Ys, Zs) subsumes both and even offers more general uses.
maplist/2 corresponds to all
maplist/3 corresponds to map
maplist/4 corresponds to zipWith but also unzip
maplist/5 corresponds to zipWith3 and unzip3
...
Related
All of these predicates are defined in pretty much the same way. The base case is defined for the empty list. For non-empty lists we unify in the head of the clause when a certain predicate holds, but do not unify if that predicate does not hold. These predicates look too similar for me to think it is a coincidence. Is there a name for this, or a defined abstraction?
intersect([],_,[]).
intersect(_,[],[]).
intersect([X|Xs],Ys,[X|Acc]) :-
member(X,Ys),
intersect(Xs,Ys,Acc).
intersect([X|Xs],Ys,Acc) :-
\+ member(X,Ys),
intersect(Xs,Ys,Acc).
without_duplicates([],[]).
without_duplicates([X|Xs],[X|Acc]) :-
\+ member(X,Acc),
without_duplicates(Xs,Acc).
without_duplicates([X|Xs],Acc) :-
member(X,Acc),
without_duplicates(Xs,Acc).
difference([],_,[]).
difference([X|Xs],Ys,[X|Acc]) :-
\+ member(X,Ys),
difference(Xs,Ys,Acc).
difference([X|Xs],Ys,Acc) :-
member(X,Ys),
difference(Xs,Ys,Acc).
delete(_,[],[]).
delete(E,[X|Xs],[X|Ans]) :-
E \= X,
delete(E,Xs,Ans).
delete(E,[X|Xs],Ans) :-
E = X,
delete(E,Xs,Ans).
There is an abstraction for "keep elements in list for which condition holds".
The names are inclide, exclude. There is a library for those in SWI-Prolog that you can use or copy. Your predicates intersect/3, difference/3, and delete/3 would look like this:
:- use_module(library(apply)).
intersect(L1, L2, L) :-
include(member_in(L1), L2, L).
difference(L1, L2, L) :-
exclude(member_in(L2), L1, L).
member_in(List, Member) :-
memberchk(Member, List).
delete(E, L1, L) :-
exclude(=(E), L1, L).
But please take a look at the implementation of include/3 and exclude/3, here:
https://www.swi-prolog.org/pldoc/doc/_SWI_/library/apply.pl?show=src#include/3
Also in SWI-Prolog, in another library, there are versions of those predicates called intersection/3, subtract/3, delete/3:
https://www.swi-prolog.org/pldoc/doc/_SWI_/library/lists.pl?show=src#intersection/3
https://www.swi-prolog.org/pldoc/doc/_SWI_/library/lists.pl?show=src#subtract/3
https://www.swi-prolog.org/pldoc/doc_for?object=delete/3
Those are similar in spirit to your solutions.
Your next predicate, without_duplicates, cannot be re-written like that with include/3 or exclude/3. Your implementation doesn't work, either. Try even something easy, like:
?- without_duplicates([a,b], L).
What happens?
But yeah, it is not the same as the others. To implement it correctly, depending on whether you need the original order or not.
If you don't need to keep the initial order, you can simply sort; this removes duplicates. Like this:
?- sort(List_with_duplicates, No_duplicates).
If you want to keep the original order, you need to pass the accumulated list to the recursive call.
without_duplicates([], []).
without_duplicates([H|T], [H|Result]) :-
without_duplicates_1(T, [H], Result).
without_duplicates_1([], _, []).
without_duplicates_1([H|T], Seen0, Result) :-
( memberchk(H, Seen0)
-> Seen = Seen0 , Result = Result0
; Seen = [H|Seen0], Result = [H|Result0]
),
without_duplicates_1(T, Seen, Result0).
You could get rid of one argument if you use a DCG:
without_duplicates([], []).
without_duplicates([H|T], [H|No_duplicates]) :-
phrase(no_dups(T, [H]), No_duplicates).
no_dups([], _) --> [].
no_dups([H|T], Seen) -->
{ memberchk(H, Seen) },
!,
no_dups(T, Seen).
no_dups([H|T], Seen) -->
[H],
no_dups(T, [H|Seen]).
Well, these are the "while loops" of Prolog on the one hand, and the inductive definitions of mathematical logic on the other hand (See also: Logic Programming, Functional Programming, and Inductive Definitions, Lawrence C. Paulson, Andrew W. Smith, 2001), so it's not surprising to find them multiple times in a program - syntactically similar, with slight deviations.
In this case, you just have a binary decision - whether something is the case or not - and you "branch" (or rather, decide to not fail the body and press on with the selected clause) on that. The "guard" (the test which supplements the head unification), in this case member(X,Ys) or \+ member(X,Ys) is a binary decision (it also is exhaustive, i.e. covers the whole space of possible X)
intersect([X|Xs],Ys,[X|Acc]) :- % if the head could unify with the goal
member(X,Ys), % then additionally check that ("guard")
(...action...). % and then do something
intersect([X|Xs],Ys,Acc) :- % if the head could unify with the goal
\+ member(X,Ys), % then additionally check that ("guard")
(...action...). % and then do something
Other applications may need the equivalent of a multiple-decision switch statement here, and so N>2 clauses may have to be written instead of 2.
foo(X) :-
member(X,Set1),
(...action...).
foo(X) :-
member(X,Set2),
(...action...).
foo(X) :-
member(X,Set3),
(...action...).
% inefficient pseudocode for the case where Set1, Set2, Set3
% do not cover the whole range of X. Such a predicate may or
% may not be necessary; the default behaviour would be "failure"
% of foo/1 if this clause does not exist:
foo(X) :-
\+ (member(X,Set1);member(X,Set2);member(X,Set3)),
(...action...).
Note:
Use memberchk/2 (which fails or succeeds-once) instead of member/2 (which fails or succeeds-and-then-tries-to-succeed-again-for-the-rest-of-the-set) to make the program deterministic in its decision whether member(X,L).
Similarly, "cut" after the clause guard to tell Prolog that if a guard of one clause succeeds, there is no point in trying the other clauses because they will all turn out false: member(X,Ys),!,...
Finally, use term comparison == and \== instead of unification = or unification failure \= for delete/3.
How do you write a Prolog procedure map(List, PredName, Result) that applies the predicate PredName(Arg, Res) to the elements of List, and returns the result in the list Result?
For example:
test(N,R) :- R is N*N.
?- map([3,5,-2], test, L).
L = [9,25,4] ;
no
This is usually called maplist/3 and is part of the Prolog prologue. Note the different argument order!
:- meta_predicate(maplist(2, ?, ?)).
maplist(_C_2, [], []).
maplist( C_2, [X|Xs], [Y|Ys]) :-
call(C_2, X, Y),
maplist( C_2, Xs, Ys).
The different argument order permits you to easily nest several maplist-goals.
?- maplist(maplist(test),[[1,2],[3,4]],Rss).
Rss = [[1,4],[9,16]].
maplist comes in different arities and corresponds to the following constructs in functional languages, but requires that all lists are of same length. Note that Prolog does not have the asymmetry between zip/zipWith and unzip. A goal maplist(C_3, Xs, Ys, Zs) subsumes both and even offers more general uses.
maplist/2 corresponds to all
maplist/3 corresponds to map
maplist/4 corresponds to zipWith but also unzip
maplist/5 corresponds to zipWith3 and unzip3
...
We all know the classic Prolog predicate for member:
member(X, [X|T]).
member(X, [Y|T]) :- member(X,Y).
I am struggling to come up with the extended member predicate which i searching for an element in a list of lists (of lists and so on...). For example:
member(4, [1,2,[3,4,[5]],[6,7,9]]).
TRUE
We can define such predicate by three rules. X is a member of a list L given L is a non-empty list with:
X is its first element;
X is a member of its first element (which is therefore a list as well); or
X is a member of the rest of the list (its "tail").
With these three conditions, we can write a predicate rmember/2 (recursive member) for example:
rmember(X, [X|_]). %% (1)
rmember(X, [H|_]) :- %% (2)
rmember(X, H).
rmember(X, [_|T]) :- %% (3)
rmember(X, T).
The first and third condition are also present in a simple member/2 predicate, only the second condition is "unique" to a recursive membercheck.
We can slightly improve the efficiency of the above, by making a predicate with three parameters, with the tail of the list the first one, the element to search the second one, and the head of the list the third one. This is a popular approach like for example SWI-Prolog's member/2 implementation [swi-doc].
The advantage of this is that we avoid unpacking the list multiple times. We can also restrict the pattern of the second case, such that this is only called for non-empty sublists:
rmember_(_, El, El).
rmember_(_, El, [H|T]) :-
rmember_(T, El, H).
rmember_([H|T], El, _) :-
rmember_(T, El, H).
we can then define rmember/2 in terms of _rmember/3:
rmember(X, [H|T]) :-
rmember_(T, X, H).
d_edge(a, b, 5).
e_edge(a, c, 6).
f_edge(b, c, 8).
% I will have a list of rules for the graph point
% from source to destination with weight.
list2pair([T], [A,B], [(T,A,B)]).
list2pair([T1|Tt], [A1,A2|T], Result) :-
list2pair(Tt, [A1|T], R1),
append([(T1,A1,A2)], R1, Result).
I want to come up with the result like
[d_edge(a,b), f_edge(b,c)]
my 1st arg will be the list of names [d_edge,f_edge]
my 2nd arg will be the list of vertexes [a,b,c].
My current code generates [(d_edge,a,b),(f_edge,b,c)].
Whenever I try to update the predicate from (T1,A1,A2) to T1(,A1,A2)
I get an error saying that it is not valid predicate.
I understand why I am getting the error. But I couldn't find a way around it.
First things first: T1(,A1,A2) is syntactically incorrect.
Here's how you could proceed using the built-in predicate (=..)/2 (a.k.a. "univ"):
list2pair([T], [A1,A2], [X]) :-
X =.. [T,A1,A2].
list2pair([T1|Tt], [A1,A2|T], [X|Xs]) :-
X =.. [T1,A1,A2],
list2pair(Tt, [A2|T], Xs).
Sample query using SICStus Prolog 4.3.2:
| ?- list2pair([d_edge,f_edge], [a,b,c], Xs).
Xs = [d_edge(a,b),f_edge(b,c)] ? ; % expected result
no
Note that the above only "constructs" these compound terms—it does not ensure that suitable facts d_edge/3, f_edge/3 etc really do exist.
I'm interested in formulae made up from lots of conjunctions (part of a larger problem). I want to write a program that takes something like this:
:- get_params(conj(conj(a,b),c),X)
and returns a list of all the parameters of the conjunctions i.e. X=[a,b,c]. At the moment I can do
:- get_params(conj(a,b),X) to get X=[a,b]
using simple Prolog pattern matching but how would you go about doing things such as
:- get_params(conj(conj(a,b),c),X) to get X=[a,b,c]
It seems really simple but I've been struggling all day!
Since you are describing a list, consider using DCG notation:
params(conj(A,B)) --> !, params(A), params(B).
params(X) --> [X].
Example:
?- phrase(params(conj(conj(a,b),c)), Ps).
Ps = [a, b, c].
Assuming that all conj functors are binary:
get_params(X, Y, L) :-
get_params(X, L1),
get_params(Y, L2),
append(L1, L2, L).
get_params(conj(X, Y), L) :-
get_params(X, Y, L), !.
get_params(A, [A]).