Editing Prolog (section)

== Higher-order programming ==
{{Main|Higher-order logic|Higher-order programming}}
A higher-order predicate is a predicate that takes one or more other predicates as arguments. Although support for higher-order programming takes Prolog outside the domain of first-order logic, which does not allow quantification over predicates,<ref>{{cite web|title=With regard to Prolog variables, variables only in the head are implicitly universally quantified, and those only in the body are implicitly existentially quantified|url=http://okmij.org/ftp/Prolog/quantification.txt|access-date=2013-05-04}}</ref> ISO Prolog now has some built-in higher-order predicates such as <code>call/1</code>, <code>call/2</code>, <code>call/3</code>, <code>findall/3</code>, <code>setof/3</code>, and <code>bagof/3</code>.<ref name="ISO 13211"/> Furthermore, since arbitrary Prolog goals can be constructed and evaluated at run-time, it is easy to write higher-order predicates like <code>maplist/2</code>, which applies an arbitrary predicate to each member of a given list, and <code>sublist/3</code>, which filters elements that satisfy a given predicate, also allowing for [[currying]].<ref name="Naish1996"/>

To convert solutions from temporal representation (answer substitutions on backtracking) to spatial representation (terms), Prolog has various all-solutions predicates that collect all answer substitutions of a given query in a list. This can be used for [[list comprehension]]. For example, [[perfect numbers]] equal the sum of their proper divisors:
<syntaxhighlight lang="prolog">
 perfect(N) :-
     between(1, inf, N), U is N // 2,
     findall(D, (between(1,U,D), N mod D =:= 0), Ds),
     sumlist(Ds, N).
</syntaxhighlight>
This can be used to enumerate perfect numbers, and to check if a number is perfect.

As another example, the predicate <code>maplist</code> applies a predicate <code>P</code> to all corresponding positions in a pair of lists:
<syntaxhighlight lang="prolog">
maplist(_, [], []).
maplist(P, [X|Xs], [Y|Ys]) :-
   call(P, X, Y),
   maplist(P, Xs, Ys).
</syntaxhighlight>

When <code>P</code> is a predicate that for all <code>X</code>, <code>P(X,Y)</code> unifies <code>Y</code> with a single unique value, <code>maplist(P, Xs, Ys)</code> is equivalent to applying the [[Map (higher-order function)|map]] function in [[functional programming]] as <code>Ys = map(Function, Xs)</code>.

Higher-order programming style in Prolog was pioneered in [[HiLog]] and [[λProlog]].