/* Part of SWI-Prolog
Author: Jan Wielemaker
E-mail: J.Wielemaker@vu.nl
WWW: http://www.swi-prolog.org
Copyright (c) 2015-2017, VU University Amsterdam
All rights reserved.
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modification, are permitted provided that the following conditions
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2. Redistributions in binary form must reproduce the above copyright
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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,
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*/
:- module(solution_sequences,
[ distinct/1, % :Goal
distinct/2, % ?Witness, :Goal
reduced/1, % :Goal
reduced/3, % ?Witness, :Goal, +Options
limit/2, % +Limit, :Goal
offset/2, % +Offset, :Goal
call_nth/2, % :Goal, ?Nth
order_by/2, % +Spec, :Goal
group_by/4 % +By, +Template, :Goal, -Bag
]).
:- autoload(library(apply),[maplist/3]).
:- autoload(library(error),
[domain_error/2,must_be/2,instantiation_error/1]).
:- autoload(library(lists),[reverse/2,member/2]).
:- autoload(library(nb_set),
[empty_nb_set/1,add_nb_set/3,size_nb_set/2]).
:- autoload(library(option),[option/3]).
:- autoload(library(ordsets),[ord_subtract/3]).
/** Modify solution sequences
The meta predicates of this library modify the sequence of solutions of
a goal. The modifications and the predicate names are based on the
classical database operations DISTINCT, LIMIT, OFFSET, ORDER BY and
GROUP BY.
These predicates were introduced in the context of the
[SWISH](http://swish.swi-prolog.org) Prolog browser-based shell, which
can represent the solutions to a predicate as a table. Notably wrapping
a goal in distinct/1 avoids duplicates in the result table and using
order_by/2 produces a nicely ordered table.
However, the predicates from this library can also be used to stay
longer within the clean paradigm where non-deterministic predicates are
composed from simpler non-deterministic predicates by means of
conjunction and disjunction. While evaluating a conjunction, we might
want to eliminate duplicates of the first part of the conjunction. Below
we give both the classical solution for solving variations of (a(X),
b(X)) and the ones using this library side-by-side.
$ Avoid duplicates of earlier steps :
==
setof(X, a(X), Xs), distinct(a(X)),
member(X, Xs), b(X)
b(X).
==
Note that the distinct/1 based solution returns the first result
of distinct(a(X)) immediately after a/1 produces a result, while
the setof/3 based solution will first compute all results of a/1.
$ Only try b(X) only for the top-10 a(X) :
==
setof(X, a(X), Xs), limit(10, order_by([desc(X)], a(X))),
reverse(Xs, Desc), b(X)
first_max_n(10, Desc, Limit),
member(X, Limit),
b(X)
==
Here we see power of composing primitives from this library and
staying within the paradigm of pure non-deterministic relational
predicates.
@see all solution predicates findall/3, bagof/3 and setof/3.
@see library(aggregate)
*/
:- meta_predicate
distinct(0),
distinct(?, 0),
reduced(0),
reduced(?, 0, +),
limit(+, 0),
offset(+, 0),
call_nth(0, ?),
order_by(+, 0),
group_by(?, ?, 0, -).
:- noprofile((
distinct/1,
distinct/2,
reduced/1,
reduced/2,
limit/2,
offset/2,
call_nth/2,
order_by/2,
group_by/3)).
%! distinct(:Goal).
%! distinct(?Witness, :Goal).
%
% True if Goal is true and no previous solution of Goal bound
% Witness to the same value. As previous answers need to be
% copied, equivalence testing is based on _term variance_ (=@=/2).
% The variant distinct/1 is equivalent to distinct(Goal,Goal).
%
% If the answers are ground terms, the predicate behaves as the
% code below, but answers are returned as soon as they become
% available rather than first computing the complete answer set.
%
% ==
% distinct(Goal) :-
% findall(Goal, Goal, List),
% list_to_set(List, Set),
% member(Goal, Set).
% ==
distinct(Goal) :-
distinct(Goal, Goal).
distinct(Witness, Goal) :-
term_variables(Witness, Vars),
Witness1 =.. [v|Vars],
empty_nb_set(Set),
call(Goal),
add_nb_set(Witness1, Set, true).
%! reduced(:Goal).
%! reduced(?Witness, :Goal, +Options).
%
% Similar to distinct/1, but does not guarantee unique results in
% return for using a limited amount of memory. Both distinct/1 and
% reduced/1 create a table that block duplicate results. For
% distinct/1, this table may get arbitrary large. In contrast,
% reduced/1 discards the table and starts a new one of the table size
% exceeds a specified limit. This filter is useful for reducing the
% number of answers when processing large or infinite long tail
% distributions. Options:
%
% - size_limit(+Integer)
% Max number of elements kept in the table. Default is 10,000.
reduced(Goal) :-
reduced(Goal, Goal, []).
reduced(Witness, Goal, Options) :-
option(size_limit(SizeLimit), Options, 10_000),
term_variables(Witness, Vars),
Witness1 =.. [v|Vars],
empty_nb_set(Set),
State = state(Set),
call(Goal),
reduced_(State, Witness1, SizeLimit).
reduced_(State, Witness1, SizeLimit) :-
arg(1, State, Set),
add_nb_set(Witness1, Set, true),
size_nb_set(Set, Size),
( Size > SizeLimit
-> empty_nb_set(New),
nb_setarg(1, State, New)
; true
).
%! limit(+Count, :Goal)
%
% Limit the number of solutions. True if Goal is true, returning
% at most Count solutions. Solutions are returned as soon as they
% become available.
%
% @arg Count is either `infinite`, making this predicate equivalent to
% call/1 or an integer. If _|Count < 1|_ this predicate fails
% immediately.
limit(Count, Goal) :-
Count == infinite,
!,
call(Goal).
limit(Count, Goal) :-
Count > 0,
State = count(0),
call(Goal),
arg(1, State, N0),
N is N0+1,
( N =:= Count
-> !
; nb_setarg(1, State, N)
).
%! offset(+Count, :Goal)
%
% Ignore the first Count solutions. True if Goal is true and
% produces more than Count solutions. This predicate computes and
% ignores the first Count solutions.
offset(Count, Goal) :-
Count > 0,
!,
State = count(0),
call(Goal),
arg(1, State, N0),
( N0 >= Count
-> true
; N is N0+1,
nb_setarg(1, State, N),
fail
).
offset(Count, Goal) :-
Count =:= 0,
!,
call(Goal).
offset(Count, _) :-
domain_error(not_less_than_zero, Count).
%! call_nth(:Goal, ?Nth)
%
% True when Goal succeeded for the Nth time. If Nth is bound on entry,
% the predicate succeeds deterministically if there are at least Nth
% solutions for Goal.
call_nth(Goal, Nth) :-
integer(Nth),
!,
( Nth > 0
-> ( call_nth(Goal, Sofar),
Sofar =:= Nth
-> true
)
; domain_error(not_less_than_one, Nth)
).
call_nth(Goal, Nth) :-
var(Nth),
!,
State = count(0),
call(Goal),
arg(1, State, N0),
Nth is N0+1,
nb_setarg(1, State, Nth).
call_nth(_Goal, Bad) :-
must_be(integer, Bad).
%! order_by(+Spec, :Goal)
%
% Order solutions according to Spec. Spec is a list of terms, where
% each element is one of. The ordering of solutions of Goal that only
% differ in variables that are _not_ shared with Spec is not changed.
%
% - asc(Term)
% Order solution according to ascending Term
% - desc(Term)
% Order solution according to descending Term
%
% This predicate is based on findall/3 and (thus) variables in answers
% are _copied_.
order_by(Spec, Goal) :-
must_be(list, Spec),
non_empty_list(Spec),
maplist(order_witness, Spec, Witnesses0),
join_orders(Witnesses0, Witnesses),
non_witness_template(Goal, Witnesses, Others),
reverse(Witnesses, RevWitnesses),
maplist(x_vars, RevWitnesses, WitnessVars),
Template =.. [v,Others|WitnessVars],
findall(Template, Goal, Results),
order(RevWitnesses, 2, Results, OrderedResults),
member(Template, OrderedResults).
order([], _, Results, Results).
order([H|T], N, Results0, Results) :-
order1(H, N, Results0, Results1),
N2 is N + 1,
order(T, N2, Results1, Results).
order1(asc(_), N, Results0, Results) :-
sort(N, @=<, Results0, Results).
order1(desc(_), N, Results0, Results) :-
sort(N, @>=, Results0, Results).
non_empty_list([]) :-
!,
domain_error(non_empty_list, []).
non_empty_list(_).
order_witness(Var, _) :-
var(Var),
!,
instantiation_error(Var).
order_witness(asc(Term), asc(Witness)) :-
!,
witness(Term, Witness).
order_witness(desc(Term), desc(Witness)) :-
!,
witness(Term, Witness).
order_witness(Term, _) :-
domain_error(order_specifier, Term).
x_vars(asc(Vars), Vars).
x_vars(desc(Vars), Vars).
witness(Term, Witness) :-
term_variables(Term, Vars),
Witness =.. [v|Vars].
%! join_orders(+SpecIn, -SpecOut) is det.
%
% Merge subsequent asc and desc sequences. For example,
% [asc(v(A)), asc(v(B))] becomes [asc(v(A,B))].
join_orders([], []).
join_orders([asc(O1)|T0], [asc(O)|T]) :-
!,
ascs(T0, OL, T1),
join_witnesses(O1, OL, O),
join_orders(T1, T).
join_orders([desc(O1)|T0], [desc(O)|T]) :-
!,
descs(T0, OL, T1),
join_witnesses(O1, OL, O),
join_orders(T1, T).
ascs([asc(A)|T0], [A|AL], T) :-
!,
ascs(T0, AL, T).
ascs(L, [], L).
descs([desc(A)|T0], [A|AL], T) :-
!,
descs(T0, AL, T).
descs(L, [], L).
join_witnesses(O, [], O) :- !.
join_witnesses(O, OL, R) :-
term_variables([O|OL], VL),
R =.. [v|VL].
%! non_witness_template(+Goal, +Witness, -Template) is det.
%
% Create a template for the bindings that are not part of the
% witness variables.
non_witness_template(Goal, Witness, Template) :-
ordered_term_variables(Goal, AllVars),
ordered_term_variables(Witness, WitnessVars),
ord_subtract(AllVars, WitnessVars, TemplateVars),
Template =.. [t|TemplateVars].
ordered_term_variables(Term, Vars) :-
term_variables(Term, Vars0),
sort(Vars0, Vars).
%! group_by(+By, +Template, :Goal, -Bag) is nondet.
%
% Group bindings of Template that have the same value for By. This
% predicate is almost the same as bagof/3, but instead of
% specifying the existential variables we specify the free
% variables. It is provided for consistency and complete coverage
% of the common database vocabulary.
group_by(By, Template, Goal, Bag) :-
ordered_term_variables(Goal, GVars),
ordered_term_variables(By+Template, UVars),
ord_subtract(GVars, UVars, ExVars),
bagof(Template, ExVars^Goal, Bag).