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    1/*  Part of SWI-Prolog
    2
    3    Author:        Jan Wielemaker
    4    E-mail:        J.Wielemaker@vu.nl
    5    WWW:           http://www.swi-prolog.org
    6    Copyright (c)  2015-2017, VU University Amsterdam
    7    All rights reserved.
    8
    9    Redistribution and use in source and binary forms, with or without
   10    modification, are permitted provided that the following conditions
   11    are met:
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   13    1. Redistributions of source code must retain the above copyright
   14       notice, this list of conditions and the following disclaimer.
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   16    2. Redistributions in binary form must reproduce the above copyright
   17       notice, this list of conditions and the following disclaimer in
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   21    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   22    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   23    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
   24    FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
   25    COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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   33*/
   34
   35:- module(solution_sequences,
   36          [ distinct/1,                 % :Goal
   37            distinct/2,                 % ?Witness, :Goal
   38            reduced/1,                  % :Goal
   39            reduced/3,                  % ?Witness, :Goal, +Options
   40            limit/2,                    % +Limit, :Goal
   41            offset/2,                   % +Offset, :Goal
   42            call_nth/2,                 % :Goal, ?Nth
   43            order_by/2,                 % +Spec, :Goal
   44            group_by/4                  % +By, +Template, :Goal, -Bag
   45          ]).   46:- autoload(library(apply),[maplist/3]).   47:- autoload(library(error),
   48	    [domain_error/2,must_be/2,instantiation_error/1]).   49:- autoload(library(lists),[reverse/2,member/2]).   50:- autoload(library(nb_set),
   51	    [empty_nb_set/1,add_nb_set/3,size_nb_set/2]).   52:- autoload(library(option),[option/3]).   53:- 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 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 also
- all solution predicates findall/3, bagof/3 and setof/3.
- library(aggregate) */
  107:- meta_predicate
  108    distinct(0),
  109    distinct(?, 0),
  110    reduced(0),
  111    reduced(?, 0, +),
  112    limit(+, 0),
  113    offset(+, 0),
  114    call_nth(0, ?),
  115    order_by(+, 0),
  116    group_by(?, ?, 0, -).  117
  118:- noprofile((
  119       distinct/1,
  120       distinct/2,
  121       reduced/1,
  122       reduced/2,
  123       limit/2,
  124       offset/2,
  125       call_nth/2,
  126       order_by/2,
  127       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).
  149distinct(Goal) :-
  150    distinct(Goal, Goal).
  151distinct(Witness, Goal) :-
  152    term_variables(Witness, Vars),
  153    Witness1 =.. [v|Vars],
  154    empty_nb_set(Set),
  155    call(Goal),
  156    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.
  173reduced(Goal) :-
  174    reduced(Goal, Goal, []).
  175reduced(Witness, Goal, Options) :-
  176    option(size_limit(SizeLimit), Options, 10_000),
  177    term_variables(Witness, Vars),
  178    Witness1 =.. [v|Vars],
  179    empty_nb_set(Set),
  180    State = state(Set),
  181    call(Goal),
  182    reduced_(State, Witness1, SizeLimit).
  183
  184reduced_(State, Witness1, SizeLimit) :-
  185    arg(1, State, Set),
  186    add_nb_set(Witness1, Set, true),
  187    size_nb_set(Set, Size),
  188    (   Size > SizeLimit
  189    ->  empty_nb_set(New),
  190        nb_setarg(1, State, New)
  191    ;   true
  192    ).
 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.
Arguments:
Count- is either infinite, making this predicate equivalent to call/1 or an integer. If Count < 1 this predicate fails immediately.
  205limit(Count, Goal) :-
  206    Count == infinite,
  207    !,
  208    call(Goal).
  209limit(Count, Goal) :-
  210    Count > 0,
  211    State = count(0),
  212    call(Goal),
  213    arg(1, State, N0),
  214    N is N0+1,
  215    (   N =:= Count
  216    ->  !
  217    ;   nb_setarg(1, State, N)
  218    ).
 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.
  226offset(Count, Goal) :-
  227    Count > 0,
  228    !,
  229    State = count(0),
  230    call(Goal),
  231    arg(1, State, N0),
  232    (   N0 >= Count
  233    ->  true
  234    ;   N is N0+1,
  235        nb_setarg(1, State, N),
  236        fail
  237    ).
  238offset(Count, Goal) :-
  239    Count =:= 0,
  240    !,
  241    call(Goal).
  242offset(Count, _) :-
  243    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.
  251call_nth(Goal, Nth) :-
  252    integer(Nth),
  253    !,
  254    (   Nth > 0
  255    ->  (   call_nth(Goal, Sofar),
  256            Sofar =:= Nth
  257        ->  true
  258        )
  259    ;   domain_error(not_less_than_one, Nth)
  260    ).
  261call_nth(Goal, Nth) :-
  262    var(Nth),
  263    !,
  264    State = count(0),
  265    call(Goal),
  266    arg(1, State, N0),
  267    Nth is N0+1,
  268    nb_setarg(1, State, Nth).
  269call_nth(_Goal, Bad) :-
  270    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
  284order_by(Spec, Goal) :-
  285    must_be(list, Spec),
  286    non_empty_list(Spec),
  287    maplist(order_witness, Spec, Witnesses0),
  288    join_orders(Witnesses0, Witnesses),
  289    non_witness_template(Goal, Witnesses, Others),
  290    reverse(Witnesses, RevWitnesses),
  291    maplist(x_vars, RevWitnesses, WitnessVars),
  292    Template =.. [v,Others|WitnessVars],
  293    findall(Template, Goal, Results),
  294    order(RevWitnesses, 2, Results, OrderedResults),
  295    member(Template, OrderedResults).
  296
  297order([], _, Results, Results).
  298order([H|T], N, Results0, Results) :-
  299    order1(H, N, Results0, Results1),
  300    N2 is N + 1,
  301    order(T, N2, Results1, Results).
  302
  303order1(asc(_), N, Results0, Results) :-
  304    sort(N, @=<, Results0, Results).
  305order1(desc(_), N, Results0, Results) :-
  306    sort(N, @>=, Results0, Results).
  307
  308non_empty_list([]) :-
  309    !,
  310    domain_error(non_empty_list, []).
  311non_empty_list(_).
  312
  313order_witness(Var, _) :-
  314    var(Var),
  315    !,
  316    instantiation_error(Var).
  317order_witness(asc(Term), asc(Witness)) :-
  318    !,
  319    witness(Term, Witness).
  320order_witness(desc(Term), desc(Witness)) :-
  321    !,
  322    witness(Term, Witness).
  323order_witness(Term, _) :-
  324    domain_error(order_specifier, Term).
  325
  326x_vars(asc(Vars), Vars).
  327x_vars(desc(Vars), Vars).
  328
  329witness(Term, Witness) :-
  330    term_variables(Term, Vars),
  331    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))].
  338join_orders([], []).
  339join_orders([asc(O1)|T0], [asc(O)|T]) :-
  340    !,
  341    ascs(T0, OL, T1),
  342    join_witnesses(O1, OL, O),
  343    join_orders(T1, T).
  344join_orders([desc(O1)|T0], [desc(O)|T]) :-
  345    !,
  346    descs(T0, OL, T1),
  347    join_witnesses(O1, OL, O),
  348    join_orders(T1, T).
  349
  350ascs([asc(A)|T0], [A|AL], T) :-
  351    !,
  352    ascs(T0, AL, T).
  353ascs(L, [], L).
  354
  355descs([desc(A)|T0], [A|AL], T) :-
  356    !,
  357    descs(T0, AL, T).
  358descs(L, [], L).
  359
  360join_witnesses(O, [], O) :- !.
  361join_witnesses(O, OL, R) :-
  362    term_variables([O|OL], VL),
  363    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.
  370non_witness_template(Goal, Witness, Template) :-
  371    ordered_term_variables(Goal, AllVars),
  372    ordered_term_variables(Witness, WitnessVars),
  373    ord_subtract(AllVars, WitnessVars, TemplateVars),
  374    Template =.. [t|TemplateVars].
  375
  376ordered_term_variables(Term, Vars) :-
  377    term_variables(Term, Vars0),
  378    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.
  388group_by(By, Template, Goal, Bag) :-
  389    ordered_term_variables(Goal, GVars),
  390    ordered_term_variables(By+Template, UVars),
  391    ord_subtract(GVars, UVars, ExVars),
  392    bagof(Template, ExVars^Goal, Bag)