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This file is part of Logtalk https://logtalk.org/ SPDX-FileCopyrightText: 1998-2023 Paulo Moura <pmoura@logtalk.org> SPDX-License-Identifier: Apache-2.0

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

% start by loading the example:

| ?- logtalk_load(coinduction(loader)). ...

% an elementary coinductive predicate:

| ?- simple::p. true ; false.

% similar:

| ?- simple::p(hoho). true ; false.

| ?- simple::p(hoho, X). X = hoho ; false.

% the following goal is true for any cyclic list containing only ones:

| ?- L = [1| L], binary::p(L). L = [1|L] ; false.

% ... or zeros:

| ?- L = [0| L], binary::p(L). L = [0|L] ; false.

% or a repetition of a pattern of ones and zeros:

| ?- L = [1,0,1| L], binary::p(L). L = [1, 0, 1|L] ; false.

% but not all solutions can be returned:

| ?- binary::p(X). X = [0|X] ; X = [1|X] ; false.

% infinite streams example:

| ?- streams::nat_stream([0, s(0), s(s(0))| T]). T = [s(s(0))|T] ; T = [s(0), s(s(0))|T] ; T = [0, s(0), s(s(0))|T] ; false.

| ?- X = [0, 1, 1, 0| X], streams::bit_stream(X). X = [0, 1, 1, 0|X] ; false.

% filtering odd numbers from a list:

| ?- L = [0, s(0), s(s(0))| L], filter::filter(L, F). L = [0, s(0), s(s(0))|L], F = [0, s(s(0))|F] ; false.

% using the Sieve of Eratosthenes to find prime numbers:

| ?- sieve::primes(20, P). P = [2, 3|_S1], % where _S1 = [5, 7, 11, 13, 17, 19, 2, 3|_S1] ; false.

% list membership example:

| ?- X = [1, 2, 3| X], lists::comember(2, X). X = [1, 2, 3|X] ; false.

| ?- X = [1, 2, 3, 1, 2, 3], lists::comember(2, X). false.

| ?- X = [1, 2, 3| X], lists::comember(Y, X). X = [1, 2, 3|X], Y = 1 ; X = [1, 2, 3|X], Y = 2 ; X = [1, 2, 3|X], Y = 3 ; false.

| ?- X = [0, s(0), s(s(0))], lists::comember(s(0), X). false.

| ?- X = [0, s(0), s(s(0))| X], lists::comember(s(0), X). X = [0, s(0), s(s(0))|X] ; false.

% list append example:

| ?- Y = [4,5,6| Y], lists::append([1,2,3], Y, Z). Y = [4, 5, 6|Y], Z = [1, 2, 3, 4, 5, 6|Y].

| ?- X = [1,2,3| X], Y = [3,4| Y], lists::append(X, Y, Z). X = [1, 2, 3|X], Y = [3, 4|Y], Z = [1|_S1], % where _S1 = [2, 3, 1|_S1] ; false.

| ?- Z = [1,2| Z], lists::append(X, Y, Z). Z = Y, Y = [1, 2|Y], X = [] ; Z = [1, 2|Z], X = [1], Y = [2|Z] ; Z = X, X = [1, 2|X] ; false.

% list non-membership example:

| ?- X = [1,2,3], lists::absent(2, X). false.

| ?- X = [1,2,3], lists::absent(4, X). false.

| ?- X = [1,2,3| X], lists::absent(4, X). X = [1, 2, 3|X] ; false.

| ?- X = [1,2,3| X], lists::absent(2, X). false.

% sorting example:

?- X = [1-2,2-3,1-4|X], sorting::keysort(X, L). X = [1-2, 2-3, 1-4|X], L = [1-2|_S1], % where _S1 = [1-2|_S1] .

?- X = [1-2,2-3|Y], Y = [1-4|Y], sorting::keysort(X, L). X = [1-2, 2-3|_S1], % where _S1 = [1-4|_S1], Y = [1-4|_S1], L = [1-2|_S2], % where _S2 = [1-4|_S2] .

% omega-automaton example:

?- automaton::automaton(s0, X). X = [a, b, c, d|X] ; X = [a, b, e|X] ; false.

% module 4 counter example:

| ?- counter::verify. true.

% nested automata example:

?- nested::state(s0, X), lists::absent(s2, X). X = [s0|_S1], % where _S1 = [s1|_S1] ; X = [s0, s3|X] ; false.

% timed automata example:

| ?- train::driver(s0, s0, s0, X, R). X = [approach, lower|_S1], % where _S1 = [down, in, out, exit, raise, approach, up, lower|_S1], R = [ (approach, 0), (lower, 1.0)|_S2], % where _S2 = [ (down, _G4969), (in, _G4975), (out, _G4981), (exit, _G4987), (raise, _G4993), (approach, _G4999), (up, _G5005), (lower, 1.0)|_S2], {_G5024>0.0, _G5033= ... + ... + _G5049+_G5046+_G5043-_G5040+_G5024, _G5040> -1.0, _G5040<0.0, _G5078= ... + ... + _G5046+_G5043, _G5093>0.0, _G5005= ... - ..., ... = ..., ..., ...} ; X = [approach|_S1], % where _S1 = [lower, down, in, out, exit, raise, up, approach|_S1], R = [ (approach, 0)|_S2], % where _S2 = [ (lower, 1.0), (down, _G4919), (in, _G4925), (out, _G4931), (exit, _G4937), (raise, _G4943), (up, _G4949), (approach, 0)|_S2], {_G4965>0.0, _G4974=_G4925+_G4990+_G4987+_G4984+_G4981+_G4965, _G4995=_G4925+_G4990+_G4987+_G4984, _G4981>1.0, _G4981<2.0, _G4949= ... + ... + _G4981, _G5046= ... + ..., ... > ..., ..., ...} ; false.

% timed automata coroutining example:

| ?- cotrain::comain(A, B, C). A = [approach, in, out, exit|A], B = [approach, exit|B], C = [lower, raise|C] ; false.

| ?- cotrain::test_max(M, N, R). R = [ (approach, 0), (lower, 1.0), (down, _G3563), (in, _G3569), (out, _G3575), (exit, _G3581), (raise, _G3587), (up, _G3593)], {_G3600>0.0, M= ... + ... + _G3625+_G3622+_G3619+_G3616+_G3600, _G3635>0.0, N= ... + ... + _G3619+_G3616-_G3635, ... - ... - _G3616+_G3635< -0.0, _G3697>0.0, _G3706= ... + ..., ... > ..., ..., ...} ; false.

% finding the cyclic paths in graphs:

?- cp1::path(a, Path). Path = [a, b|_S1], % where _S1 = [b|_S1] ; Path = [a, b, c, d|_S1], % where _S1 = [d|_S1] ; Path = [a|_S1], % where _S1 = [b, c, a|_S1] ; false.

?- cp2::path(a, Path). Path = [a|_S1], % where _S1 = [b, c, a|_S1] ; Path = [a|_S1], % where _S1 = [b, c, d, a|_S1] ; false.

?- cp3::path(a, Path, 3). Path = [a|_S1], % where _S1 = [b, c, a|_S1] ; false.

% testing for bipartite graphs (vertex adjacency lists must be ordered):

?- A = v(a, [F]), B = v(b, [F, G]), C = v(c, [H, I]), D = v(d, [G]), E = v(e, [F, I]), F = v(f, [A, B]), G = v(g, [B, D]), H = v(h, [C]), I = v(i, [C, E]), graph::bipartite(A). A = v(a, [_S1]), % where _S1 = v(f, [v(a, [_S1]), v(b, [_S1, _S2])]), _S2 = v(g, [v(b, [_S1, _S2]), v(d, [_S2])]), F = v(f, [v(a, [_S1]), v(b, [_S1, _S2])]), B = v(b, [_S1, _S2]), G = v(g, [v(b, [_S1, _S2]), v(d, [_S2])]), C = _S3, % where _S3 = v(c, [v(h, [_S3]), _S4]), _S4 = v(i, [_S3, v(e, [_S1, _S4])]), H = v(h, [_S3]), I = v(i, [_S3, v(e, [_S1, _S4])]), D = v(d, [_S2]), E = v(e, [_S1, _S4]) ; false.