This library provides aggregating operators over the solutions of a predicate. The operations are a generalisation of the bagof/3, setof/3 and findall/3 built-in predicates. The defined aggregation operations are counting, computing the sum, minimum, maximum, a bag of solutions and a set of solutions. We first give a simple example, computing the country with the smallest area:
smallest_country(Name, Area) :-
aggregate(min(A, N), country(N, A), min(Area, Name)).
There are four aggregation predicates (aggregate/3, aggregate/4, aggregate_all/3 and aggregate/4), distinguished on two properties.
^Goal) and
providing multiple solutions for the remaining free variables in Goal.
The aggregate_all/3
predicate uses findall/3,
implicitly qualifying all free variables and providing exactly one
solution, while aggregate_all/4
uses sort/2 over
solutions that Discriminator (see below) generated using findall/3.
country(belgium, 11000000)
may succeed twice, we can use the following to avoid counting the
population of Belgium twice:
aggregate(sum(P), Name, country(Name, P), Total)
All aggregation predicates support the following operators below in
Template. In addition, they allow for an arbitrary named compound term,
where each of the arguments is a term from the list below. For example,
the term r(min(X), max(X)) computes both the minimum and
maximum binding for X.
sum(1).
min(Min, Witness), where Min is the minimal version
of Expr over all solutions, and Witness is any
other template applied to solutions that produced Min. If multiple
solutions provide the same minimum, Witness corresponds to
the first solution.
min(Expr, Witness), but producing the maximum result.
Acknowledgements
The development of this library was sponsored by SecuritEase, http://www.securitease.com
min(X),
max(X), min(X,Witness) or max(X,Witness)
and Goal has no solutions, i.e., the minumum and maximum of
an empty set is undefined.The implementation executes forall/2 if Goal does not contain any variables that are not shared with Generator.
Here is an example:
?- foreach(between(1,4,X), dif(X,Y)), Y = 5. Y = 5. ?- foreach(between(1,4,X), dif(X,Y)), Y = 3. false.
free_variables(Generator, Template, OldList, NewList)
finds this set using OldList as an accumulator.