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/* Part of SWI-Prolog
Author: Jan Wielemaker
E-mail: J.Wielemaker@vu.nl
WWW: http://www.swi-prolog.org
Copyright (c) 2008-2016, University of Amsterdam
VU University Amsterdam
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/
:- module(aggregate,
[ foreach/2, % :Generator, :Goal
aggregate/3, % +Templ, :Goal, -Result
aggregate/4, % +Templ, +Discrim, :Goal, -Result
aggregate_all/3, % +Templ, :Goal, -Result
aggregate_all/4, % +Templ, +Discrim, :Goal, -Result
free_variables/4 % :Generator, :Template, +Vars0, -Vars
]).
:- use_module(library(ordsets)).
:- use_module(library(pairs)).
:- use_module(library(error)).
:- use_module(library(lists)).
:- use_module(library(apply)).
:- meta_predicate
foreach(0,0),
aggregate(?,^,-),
aggregate(?,?,^,-),
aggregate_all(?,0,-),
aggregate_all(?,?,0,-).
/** <module> Aggregation operators on backtrackable predicates
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
|_
@compat 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|*.
@tbd Analysing the aggregation template and compiling a predicate
for the list aggregation can be done at compile time.
@tbd aggregate_all/3 can be rewritten to run in constant space using
non-backtrackable assignment on a term.
*/
/*******************************
* AGGREGATE *
*******************************/
%! aggregate(+Template, :Goal, -Result) is nondet.
%
% Aggregate bindings in Goal according to Template. The aggregate/3
% version performs bagof/3 on Goal.
aggregate(Template, Goal0, Result) :-
template_to_pattern(bag, Template, Pattern, Goal0, Goal, Aggregate),
bagof(Pattern, Goal, List),
aggregate_list(Aggregate, List, Result).
%! aggregate(+Template, +Discriminator, :Goal, -Result) is nondet.
%
% Aggregate bindings in Goal according to Template. The aggregate/4
% version performs setof/3 on Goal.
aggregate(Template, Discriminator, Goal0, Result) :-
template_to_pattern(bag, Template, Pattern, Goal0, Goal, Aggregate),
setof(Discriminator-Pattern, Goal, Pairs),
pairs_values(Pairs, List),
aggregate_list(Aggregate, List, Result).
%! 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(Var, _, _) :-
var(Var),
!,
instantiation_error(Var).
aggregate_all(count, Goal, Count) :-
!,
aggregate_all(sum(1), Goal, Count).
aggregate_all(sum(X), Goal, Sum) :-
!,
State = state(0),
( call(Goal),
arg(1, State, S0),
S is S0 + X,
nb_setarg(1, State, S),
fail
; arg(1, State, Sum)
).
aggregate_all(max(X), Goal, Max) :-
!,
State = state(X),
( call(Goal),
arg(1, State, M0),
M is max(M0,X),
nb_setarg(1, State, M),
fail
; arg(1, State, Max),
nonvar(Max)
).
aggregate_all(min(X), Goal, Min) :-
!,
State = state(X),
( call(Goal),
arg(1, State, M0),
M is min(M0,X),
nb_setarg(1, State, M),
fail
; arg(1, State, Min),
nonvar(Min)
).
aggregate_all(max(X,W), Goal, max(Max,Witness)) :-
!,
State = state(false, _Max, _Witness),
( call(Goal),
( State = state(true, Max0, _)
-> X > Max0,
nb_setarg(2, State, X),
nb_setarg(3, State, W)
; number(X)
-> nb_setarg(1, State, true),
nb_setarg(2, State, X),
nb_setarg(3, State, W)
; type_error(number, X)
),
fail
; State = state(true, Max, Witness)
).
aggregate_all(min(X,W), Goal, min(Min,Witness)) :-
!,
State = state(false, _Min, _Witness),
( call(Goal),
( State = state(true, Min0, _)
-> X < Min0,
nb_setarg(2, State, X),
nb_setarg(3, State, W)
; number(X)
-> nb_setarg(1, State, true),
nb_setarg(2, State, X),
nb_setarg(3, State, W)
; type_error(number, X)
),
fail
; State = state(true, Min, Witness)
).
aggregate_all(Template, Goal0, Result) :-
template_to_pattern(all, Template, Pattern, Goal0, Goal, Aggregate),
findall(Pattern, Goal, List),
aggregate_list(Aggregate, List, Result).
%! 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.
aggregate_all(Template, Discriminator, Goal0, Result) :-
template_to_pattern(all, Template, Pattern, Goal0, Goal, Aggregate),
findall(Discriminator-Pattern, Goal, Pairs0),
sort(Pairs0, Pairs),
pairs_values(Pairs, List),
aggregate_list(Aggregate, List, Result).
template_to_pattern(All, Template, Pattern, Goal0, Goal, Aggregate) :-
template_to_pattern(Template, Pattern, Post, Vars, Aggregate),
existential_vars(Goal0, Goal1, AllVars, Vars),
clean_body((Goal1, Post), Goal2),
( All == bag
-> add_existential_vars(AllVars, Goal2, Goal)
; Goal = Goal2
).
existential_vars(Var, Var) -->
{ var(Var) },
!.
existential_vars(Var^G0, G) -->
!,
[Var],
existential_vars(G0, G).
existential_vars(M:G0, M:G) -->
!,
existential_vars(G0, G).
existential_vars(G, G) -->
[].
add_existential_vars([], G, G).
add_existential_vars([H|T], G0, H^G1) :-
add_existential_vars(T, G0, G1).
%! clean_body(+Goal0, -Goal) is det.
%
% Remove redundant =true= from Goal0.
clean_body((Goal0,Goal1), Goal) :-
!,
clean_body(Goal0, GoalA),
clean_body(Goal1, GoalB),
( GoalA == true
-> Goal = GoalB
; GoalB == true
-> Goal = GoalA
; Goal = (GoalA,GoalB)
).
clean_body(Goal, Goal).
%! template_to_pattern(+Template, -Pattern, -Post, -Vars, -Aggregate)
%
% Determine which parts of the goal we must remember in the
% findall/3 pattern.
%
% @param Post is a body-term that evaluates expressions to reduce
% storage requirements.
% @param Vars is a list of intermediate variables that must be
% added to the existential variables for bagof/3.
% @param Aggregate defines the aggregation operation to execute.
template_to_pattern(Term, Pattern, Goal, Vars, Aggregate) :-
templ_to_pattern(Term, Pattern, Goal, Vars, Aggregate),
!.
template_to_pattern(Term, Pattern, Goal, Vars, term(MinNeeded, Functor, AggregateArgs)) :-
compound(Term),
!,
Term =.. [Functor|Args0],
templates_to_patterns(Args0, Args, Goal, Vars, AggregateArgs),
needs_one(AggregateArgs, MinNeeded),
Pattern =.. [Functor|Args].
template_to_pattern(Term, _, _, _, _) :-
invalid_template(Term).
templ_to_pattern(sum(X), X, true, [], sum) :- var(X), !.
templ_to_pattern(sum(X0), X, X is X0, [X0], sum) :- !.
templ_to_pattern(count, 1, true, [], count) :- !.
templ_to_pattern(min(X), X, true, [], min) :- var(X), !.
templ_to_pattern(min(X0), X, X is X0, [X0], min) :- !.
templ_to_pattern(min(X0, Witness), X-Witness, X is X0, [X0], min_witness) :- !.
templ_to_pattern(max(X0), X, X is X0, [X0], max) :- !.
templ_to_pattern(max(X0, Witness), X-Witness, X is X0, [X0], max_witness) :- !.
templ_to_pattern(set(X), X, true, [], set) :- !.
templ_to_pattern(bag(X), X, true, [], bag) :- !.
templates_to_patterns([], [], true, [], []).
templates_to_patterns([H0], [H], G, Vars, [A]) :-
!,
sub_template_to_pattern(H0, H, G, Vars, A).
templates_to_patterns([H0|T0], [H|T], (G0,G), Vars, [A0|A]) :-
sub_template_to_pattern(H0, H, G0, V0, A0),
append(V0, RV, Vars),
templates_to_patterns(T0, T, G, RV, A).
sub_template_to_pattern(Term, Pattern, Goal, Vars, Aggregate) :-
templ_to_pattern(Term, Pattern, Goal, Vars, Aggregate),
!.
sub_template_to_pattern(Term, _, _, _, _) :-
invalid_template(Term).
invalid_template(Term) :-
callable(Term),
!,
domain_error(aggregate_template, Term).
invalid_template(Term) :-
type_error(aggregate_template, Term).
%! needs_one(+Ops, -OneOrZero)
%
% If one of the operations in Ops needs at least one answer,
% unify OneOrZero to 1. Else 0.
needs_one(Ops, 1) :-
member(Op, Ops),
needs_one(Op),
!.
needs_one(_, 0).
needs_one(min).
needs_one(min_witness).
needs_one(max).
needs_one(max_witness).
%! aggregate_list(+Op, +List, -Answer) is semidet.
%
% Aggregate the answer from the list produced by findall/3,
% bagof/3 or setof/3. The latter two cases deal with compound
% answers.
%
% @tbd Compile code for incremental state update, which we will use
% for aggregate_all/3 as well. We should be using goal_expansion
% to generate these clauses.
aggregate_list(bag, List0, List) :-
!,
List = List0.
aggregate_list(set, List, Set) :-
!,
sort(List, Set).
aggregate_list(sum, List, Sum) :-
sum_list(List, Sum).
aggregate_list(count, List, Count) :-
length(List, Count).
aggregate_list(max, List, Sum) :-
max_list(List, Sum).
aggregate_list(max_witness, List, max(Max, Witness)) :-
max_pair(List, Max, Witness).
aggregate_list(min, List, Sum) :-
min_list(List, Sum).
aggregate_list(min_witness, List, min(Min, Witness)) :-
min_pair(List, Min, Witness).
aggregate_list(term(0, Functor, Ops), List, Result) :-
!,
maplist(state0, Ops, StateArgs, FinishArgs),
State0 =.. [Functor|StateArgs],
aggregate_term_list(List, Ops, State0, Result0),
finish_result(Ops, FinishArgs, Result0, Result).
aggregate_list(term(1, Functor, Ops), [H|List], Result) :-
H =.. [Functor|Args],
maplist(state1, Ops, Args, StateArgs, FinishArgs),
State0 =.. [Functor|StateArgs],
aggregate_term_list(List, Ops, State0, Result0),
finish_result(Ops, FinishArgs, Result0, Result).
aggregate_term_list([], _, State, State).
aggregate_term_list([H|T], Ops, State0, State) :-
step_term(Ops, H, State0, State1),
aggregate_term_list(T, Ops, State1, State).
%! min_pair(+Pairs, -Key, -Value) is det.
%! max_pair(+Pairs, -Key, -Value) is det.
%
% True if Key-Value has the smallest/largest key in Pairs. If
% multiple pairs share the smallest/largest key, the first pair is
% returned.
min_pair([M0-W0|T], M, W) :-
min_pair(T, M0, W0, M, W).
min_pair([], M, W, M, W).
min_pair([M0-W0|T], M1, W1, M, W) :-
( M0 < M1
-> min_pair(T, M0, W0, M, W)
; min_pair(T, M1, W1, M, W)
).
max_pair([M0-W0|T], M, W) :-
max_pair(T, M0, W0, M, W).
max_pair([], M, W, M, W).
max_pair([M0-W0|T], M1, W1, M, W) :-
( M0 > M1
-> max_pair(T, M0, W0, M, W)
; max_pair(T, M1, W1, M, W)
).
%! step(+AggregateAction, +New, +State0, -State1).
step(bag, X, [X|L], L).
step(set, X, [X|L], L).
step(count, _, X0, X1) :-
succ(X0, X1).
step(sum, X, X0, X1) :-
X1 is X0+X.
step(max, X, X0, X1) :-
X1 is max(X0, X).
step(min, X, X0, X1) :-
X1 is min(X0, X).
step(max_witness, X-W, X0-W0, X1-W1) :-
( X > X0
-> X1 = X, W1 = W
; X1 = X0, W1 = W0
).
step(min_witness, X-W, X0-W0, X1-W1) :-
( X < X0
-> X1 = X, W1 = W
; X1 = X0, W1 = W0
).
step(term(Ops), Row, Row0, Row1) :-
step_term(Ops, Row, Row0, Row1).
step_term(Ops, Row, Row0, Row1) :-
functor(Row, Name, Arity),
functor(Row1, Name, Arity),
step_list(Ops, 1, Row, Row0, Row1).
step_list([], _, _, _, _).
step_list([Op|OpT], Arg, Row, Row0, Row1) :-
arg(Arg, Row, X),
arg(Arg, Row0, X0),
arg(Arg, Row1, X1),
step(Op, X, X0, X1),
succ(Arg, Arg1),
step_list(OpT, Arg1, Row, Row0, Row1).
finish_result(Ops, Finish, R0, R) :-
functor(R0, Functor, Arity),
functor(R, Functor, Arity),
finish_result(Ops, Finish, 1, R0, R).
finish_result([], _, _, _, _).
finish_result([Op|OpT], [F|FT], I, R0, R) :-
arg(I, R0, A0),
arg(I, R, A),
finish_result1(Op, F, A0, A),
succ(I, I2),
finish_result(OpT, FT, I2, R0, R).
finish_result1(bag, Bag0, [], Bag) :-
!,
Bag = Bag0.
finish_result1(set, Bag, [], Set) :-
!,
sort(Bag, Set).
finish_result1(max_witness, _, M-W, R) :-
!,
R = max(M,W).
finish_result1(min_witness, _, M-W, R) :-
!,
R = min(M,W).
finish_result1(_, _, A, A).
%! state0(+Op, -State, -Finish)
state0(bag, L, L).
state0(set, L, L).
state0(count, 0, _).
state0(sum, 0, _).
%! state1(+Op, +First, -State, -Finish)
state1(bag, X, L, [X|L]) :- !.
state1(set, X, L, [X|L]) :- !.
state1(_, X, X, _).
/*******************************
* FOREACH *
*******************************/
%! 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.
foreach(Generator, Goal) :-
term_variables(Generator, GenVars0), sort(GenVars0, GenVars),
term_variables(Goal, GoalVars0), sort(GoalVars0, GoalVars),
ord_subtract(GoalVars, GenVars, SharedGoalVars),
( SharedGoalVars == []
-> \+ (Generator, \+Goal) % = forall(Generator, Goal)
; ord_intersection(GenVars, GoalVars, SharedVars),
Templ =.. [v|SharedVars],
SharedTempl =.. [v|SharedGoalVars],
findall(Templ, Generator, List),
prove_list(List, Templ, SharedTempl, Goal)
).
prove_list([], _, _, _).
prove_list([H|T], Templ, SharedTempl, Goal) :-
copy_term(Templ+SharedTempl+Goal,
H+SharedTempl+Copy),
Copy,
prove_list(T, Templ, SharedTempl, Goal).
%! 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
%
% 1. they occur in the template
% 2. 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
% @author Jan Wielemaker (made some SWI-Prolog enhancements)
% @license Public domain (from DEC10 library).
% @tbd Distinguish between control-structures and data terms.
% @tbd Exploit our built-in term_variables/2 at some places?
free_variables(Term, Bound, VarList, [Term|VarList]) :-
var(Term),
term_is_free_of(Bound, Term),
list_is_free_of(VarList, Term),
!.
free_variables(Term, _Bound, VarList, VarList) :-
var(Term),
!.
free_variables(Term, Bound, OldList, NewList) :-
explicit_binding(Term, Bound, NewTerm, NewBound),
!,
free_variables(NewTerm, NewBound, OldList, NewList).
free_variables(Term, Bound, OldList, NewList) :-
functor(Term, _, N),
free_variables(N, Term, Bound, OldList, NewList).
free_variables(0, _, _, VarList, VarList) :- !.
free_variables(N, Term, Bound, OldList, NewList) :-
arg(N, Term, Argument),
free_variables(Argument, Bound, OldList, MidList),
M is N-1,
!,
free_variables(M, Term, Bound, MidList, NewList).
% explicit_binding checks for goals known to existentially quantify
% one or more variables. In particular \+ is quite common.
explicit_binding(\+ _Goal, Bound, fail, Bound ) :- !.
explicit_binding(not(_Goal), Bound, fail, Bound ) :- !.
explicit_binding(Var^Goal, Bound, Goal, Bound+Var) :- !.
explicit_binding(setof(Var,Goal,Set), Bound, Goal-Set, Bound+Var) :- !.
explicit_binding(bagof(Var,Goal,Bag), Bound, Goal-Bag, Bound+Var) :- !.
%! term_is_free_of(+Term, +Var) is semidet.
%
% True if Var does not appear in Term. This has been rewritten
% from the DEC10 library source to exploit our non-deterministic
% arg/3.
term_is_free_of(Term, Var) :-
\+ var_in_term(Term, Var).
var_in_term(Term, Var) :-
Var == Term,
!.
var_in_term(Term, Var) :-
compound(Term),
arg(_, Term, Arg),
var_in_term(Arg, Var),
!.
%! list_is_free_of(+List, +Var) is semidet.
%
% True if Var is not in List.
list_is_free_of([Head|Tail], Var) :-
Head \== Var,
!,
list_is_free_of(Tail, Var).
list_is_free_of([], _).
% term_variables(+Term, +Vars0, -Vars) is det.
%
% True if Vars is the union of variables in Term and Vars0.
% We cannot have this as term_variables/3 is already defined
% as a difference-list version of term_variables/2.
%term_variables(Term, Vars0, Vars) :-
% term_variables(Term+Vars0, Vars).
%! sandbox:safe_meta(+Goal, -Called) is semidet.
%
% Declare the aggregate meta-calls safe. This cannot be proven due
% to the manipulations of the argument Goal.
:- multifile sandbox:safe_meta_predicate/1.
sandbox:safe_meta_predicate(aggregate:foreach/2).
sandbox:safe_meta_predicate(aggregate:aggregate/3).
sandbox:safe_meta_predicate(aggregate:aggregate/4).
sandbox:safe_meta_predicate(aggregate:aggregate_all/3).
sandbox:safe_meta_predicate(aggregate:aggregate_all/4).