1/* Part of ClioPatria SeRQL and SPARQL server 2 3 Author: Jan Wielemaker 4 E-mail: J.Wielemaker@vu.nl 5 WWW: http://www.swi-prolog.org 6 Copyright (c) 2010-2018, University of Amsterdam, 7 VU University Amsterdam 8 All rights reserved. 9 10 Redistribution and use in source and binary forms, with or without 11 modification, are permitted provided that the following conditions 12 are met: 13 14 1. Redistributions of source code must retain the above copyright 15 notice, this list of conditions and the following disclaimer. 16 17 2. Redistributions in binary form must reproduce the above copyright 18 notice, this list of conditions and the following disclaimer in 19 the documentation and/or other materials provided with the 20 distribution. 21 22 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 23 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 24 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 25 FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 26 COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 27 INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 28 BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 29 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 30 CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 31 LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 32 ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 33 POSSIBILITY OF SUCH DAMAGE. 34*/ 35 36:- module(count, 37 [ proof_count/2, % :Goal, -Count 38 proof_count/3, % :Goal, +Max, -Count 39 answer_count/3, % ?Var, :Goal, -Count 40 answer_count/4, % ?Var, :Goal, +Max -Count 41 answer_set/3, % ?Var, :Goal, -Answers 42 answer_set/4, % ?Var, :Goal, +Max, -Answers 43 answer_pair_set/5, % ?Pair, :Goal, +MaxKeys, +MaxPerKey, -Answers 44 unique_solution/2 % :Goal, -Solution 45 ]). 46:- use_module(library(nb_set)). 47:- use_module(library(rbtrees)). 48:- use_module(library(nb_rbtrees)). 49 50 51/** <module> This module provides various ways to count solutions 52 53This module is based on a similar collection introduces in the first 54ClioPatria release. Most names have been changed to describe the 55semantics more accurately. 56 57The predicates in this library provide space-efficient solutions, 58avoiding findall/setof. Most predicates come with a variant that allows 59limiting the number of answers. 60 61@tbd The current implementation is often based on library(nb_set), which 62 implements _unbalanced_ binary trees. We should either provide a 63 balanced version or use Paul Tarau's interactors to solve these 64 problems without destructive datastructures. 65*/ 66 67:- meta_predicate 68 proof_count(, ), 69 proof_count(, , ), 70 answer_count(, , ), 71 answer_count(, , , ), 72 answer_set(, , ), 73 answer_set(, , , ), 74 answer_pair_set(, , , , ), 75 unique_solution(, ). 76 77%! proof_count(:Goal, -Count) is det. 78%! proof_count(:Goal, +Max, -Count) is det. 79% 80% True if Count is the number of times Goal succeeds. Note that 81% this is not the same as the number of answers. E.g, repeat/0 has 82% infinite proofs that all have the same -empty- answer 83% substitution. 84% 85% @see answer_count/3 86 87proof_count(Goal, Count) :- 88 proof_count(Goal, infinite, Count). 89 90proof_count(Goal, Max, Count) :- 91 State = count(0), 92 ( , 93 arg(1, State, N0), 94 N is N0 + 1, 95 nb_setarg(1, State, N), 96 N == Max 97 -> Count = Max 98 ; arg(1, State, Count) 99 ). 100 101%! answer_count(?Var, :Goal, -Count) is det. 102%! answer_count(?Var, :Goal, +Max, -Count) is det. 103% 104% Count number of unique answers of Var Goal produces. Enumeration 105% stops if Max solutions have been found, unifying Count to Max. 106 107answer_count(T, G, Count) :- 108 answer_count(T, G, infinite, Count). 109 110answer_count(T, G, Max, Count) :- 111 empty_nb_set(Set), 112 C = c(0), 113 ( , 114 add_nb_set(T, Set, true), 115 arg(1, C, C0), 116 C1 is C0+1, 117 nb_setarg(1, C, C1), 118 C1 == Max 119 -> Count = Max 120 ; arg(1, C, Count) 121 ). 122 123%! answer_set(?Var, :Goal, -SortedSet) is det. 124%! answer_set(?Var, :Goal, +MaxResults, -SortedSet) is det. 125% 126% SortedSet is the set of bindings for Var for which Goal is true. 127% The predicate answer_set/3 is the same as findall/3 followed by 128% sort/2. The predicate answer_set/4 limits the result to the 129% first MaxResults. Note that this is *not* the same as the first 130% MaxResults from the entire answer set, which would require 131% computing the entire set. 132 133answer_set(T, G, Ts) :- 134 findall(T, G, Raw), 135 sort(Raw, Ts). 136 137answer_set(T, G, Max, Ts) :- 138 empty_nb_set(Set), 139 State = count(0), 140 ( , 141 add_nb_set(T, Set, true), 142 arg(1, State, C0), 143 C is C0 + 1, 144 nb_setarg(1, State, C), 145 C == Max 146 -> true 147 ; true 148 ), 149 nb_set_to_list(Set, Ts). 150 151%! answer_pair_set(Var, :Goal, +MaxKeys, +MaxPerKey, -Group) 152% 153% Bounded find of Key-Value pairs. MaxKeys bounds the maximum 154% number of keys. MaxPerKey bounds the maximum number of answers 155% per key. 156 157answer_pair_set(P, G, MaxKeys, MaxPerKey, Groups) :- 158 P = K-V, 159 ( MaxPerKey = inf 160 -> true 161 ; TooMany is MaxPerKey+1, 162 dif(New, values(TooMany)) 163 ), 164 rb_empty(Tree), 165 State = keys(0), 166 ( , 167 add_pair(Tree, K, V, New), 168 New == new_key, 169 arg(1, State, C0), 170 C is C0+1, 171 nb_setarg(1, State, C), 172 C == MaxKeys 173 -> true 174 ; true 175 ), 176 groups(Tree, Groups). 177 178add_pair(T, K, V, New) :- 179 nb_rb_get_node(T, K, N), 180 !, 181 nb_rb_node_value(N, NV), 182 NV = k(Count, VT), 183 ( nb_rb_get_node(VT, V, _) 184 -> New = false 185 ; NewCount is Count + 1, 186 New = values(NewCount), 187 nb_rb_insert(VT, V, true), 188 nb_setarg(1, NV, NewCount) 189 ). 190add_pair(T, K, V, new_key) :- 191 rb_one(V, true, RB), 192 nb_rb_insert(T, K, k(1, RB)). 193 194rb_one(K, V, Tree) :- 195 rb_empty(T0), 196 rb_insert(T0, K, V, Tree). 197 198groups(Tree, Groups) :- 199 rb_visit(Tree, Pairs), 200 maplist(expand_values, Pairs, Groups). 201 202expand_values(K-k(_Count,T), K-Vs) :- 203 rb_keys(T, Vs). 204 205%! unique_solution(:Goal, -Solution) is semidet. 206% 207% True if Goal produces exactly one solution for Var. Multiple 208% solutions are compared using =@=/2. This is semantically the 209% same as the code below, but fails early if a second nonequal 210% solution for Var is found. 211% 212% == 213% findall(Var, Goal, Solutions), sort(Solutions, [Solution]). 214% == 215 216unique_solution(Goal, Solution) :- 217 State = state(false, _), 218 ( , 219 ( arg(1, State, false) 220 -> nb_setarg(1, State, true), 221 nb_setarg(2, State, Solution), 222 fail 223 ; arg(2, State, Answer), 224 Answer =@= Solution 225 -> fail 226 ; !, fail % multiple answers 227 ) 228 ; arg(1, State, true), 229 arg(2, State, Solution) 230 )