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 builtin 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.
 aggregate vs. aggregate_all

The aggregate predicates use setof/3 (aggregate/4) or bagof/3
(aggregate/3), dealing with existential qualified variables
(Var^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.
 The Discriminator argument

The versions with 4 arguments deduplicate redundant solutions of
Goal. Solutions for which both the template variables and
Discriminator are identical will be treated as one solution. For
example, if we wish to compute the total population of all
countries, and for some reason
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.
 count
 Count number of solutions. Same as
sum(1)
.
 sum(Expr)
 Sum of Expr for all solutions.
 min(Expr)
 Minimum of Expr for all solutions.
 min(Expr, Witness)
 A term
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.
 max(Expr)
 Maximum of Expr for all solutions.
 max(Expr, Witness)
 As
min(Expr, Witness)
, but producing the maximum result.
 set(X)
 An ordered set with all solutions for X.
 bag(X)
 A list of all solutions for X.
Acknowledgements
The development of this library was sponsored by SecuritEase,
http://www.securitease.com
 Compatibility
  Quintus, SICStus 4. The forall/2 is a SWIProlog builtin and
term_variables/3 is a SWIProlog builtin with
different semantics.
 To be done
  Analysing the aggregation template and compiling a predicate
for the list aggregation can be done at compile time.
  aggregate_all/3 can be rewritten to run in constant space using
nonbacktrackable assignment on a term.
 aggregate(+Template, :Goal, Result) is nondet
 Aggregate bindings in Goal according to Template. The aggregate/3
version performs bagof/3 on Goal.
 aggregate(+Template, +Discriminator, :Goal, Result) is nondet
 Aggregate bindings in Goal according to Template. The aggregate/4
version performs setof/3 on Goal.
 aggregate_all(+Template, :Goal, Result) is semidet
 Aggregate bindings in Goal according to Template. The
aggregate_all/3 version performs findall/3 on Goal. Note that
this predicate fails if Template contains one or more of
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.
 aggregate_all(+Template, +Discriminator, :Goal, Result) is semidet
 Aggregate bindings in Goal according to Template. The
aggregate_all/4 version performs findall/3 followed by sort/2 on
Goal. See aggregate_all/3 to understand why this predicate can
fail.
 foreach(:Generator, :Goal)
 True if conjunction of results is true. Unlike forall/2, which
runs a failuredriven loop that proves Goal for each solution of
Generator, foreach/2 creates a conjunction. Each member of the
conjunction is a copy of Goal, where the variables it shares
with Generator are filled with the values from the corresponding
solution.
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.
 bug
  Goal is copied repeatedly, which may cause problems if
attributed variables are involved.
 free_variables(:Generator, +Template, +VarList0, VarList) is det
 Find free variables in bagof/setof template. In order to handle
variables properly, we have to find all the universally
quantified variables in the Generator. All variables as yet
unbound are universally quantified, unless
 they occur in the template
 they are bound by X^P, setof/3, or bagof/3
free_variables(Generator, Template, OldList, NewList)
finds this
set using OldList as an accumulator.
 author
  Richard O'Keefe
  Jan Wielemaker (made some SWIProlog enhancements)
 license
  Public domain (from DEC10 library).
 To be done
  Distinguish between controlstructures and data terms.
  Exploit our builtin term_variables/2 at some places?
 sandbox:safe_meta(+Goal, Called) is semidet[multifile]
 Declare the aggregate metacalls safe. This cannot be proven due
to the manipulations of the argument Goal.