- Compatibility
- Quintus, SICStus 4. The forall/2
is a SWI-Prolog built-in and
term_variables/3
is a SWI-Prolog built-in 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 non-backtrackable
assignment on a term.
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.
- 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
- [nondet]aggregate(+Template,
:Goal, -Result)
- Aggregate bindings in Goal according to Template.
The aggregate/3
version performs bagof/3
on Goal.
- [nondet]aggregate(+Template,
+Discriminator, :Goal, -Result)
- Aggregate bindings in Goal according to Template.
The aggregate/4
version performs setof/3
on Goal.
- [semidet]aggregate_all(+Template,
:Goal, -Result)
- 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.
- [semidet]aggregate_all(+Template,
+Discriminator, :Goal, -Result)
- 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 failure-driven 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.
- [det]free_variables(:Generator,
+Template, +VarList0, -VarList)
- 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 SWI-Prolog enhancements)
- license
- Public domain (from DEC10 library).
- To be done
- - Distinguish between control-structures and data terms.
- Exploit our built-in term_variables/2
at some places?
- [semidet,multifile]sandbox:safe_meta(+Goal,
-Called)
- Declare the aggregate meta-calls safe. This cannot be proven due to the
manipulations of the argument Goal.