/* Part of SWI-Prolog Author: Jan Wielemaker E-mail: J.Wielemaker@cs.vu.nl WWW: http://www.swi-prolog.org Copyright (C): 2015, VU University Amsterdam This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA As a special exception, if you link this library with other files, compiled with a Free Software compiler, to produce an executable, this library does not by itself cause the resulting executable to be covered by the GNU General Public License. This exception does not however invalidate any other reasons why the executable file might be covered by the GNU General Public License. */ :- module(solution_sequences, [ distinct/1, % :Goal distinct/2, % ?Witness, :Goal limit/2, % +Limit, :Goal offset/2, % +Offset, :Goal order_by/2, % +Spec, :Goal group_by/4 % +By, +Template, :Goal, -Bag ]). :- use_module(library(nb_set)). :- use_module(library(error)). :- use_module(library(apply)). :- use_module(library(lists)). :- use_module(library(ordsets)). /** 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), limit(+, 0), offset(+, 0), order_by(+, 0), group_by(?, ?, 0, -). %% distinct(:Goal). %% distinct(?Witness, :Goal). % % True if Goal is true and no previous solution of Goal bound % Witness to the same value. The variant distinct/1 is equivalent % to distinct(Goal,Goal). Semantically, distinct/1 is the same 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). %% 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. 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). %% 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 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).