# Copyright 2023 DeepMind Technologies Limited # # 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. # ============================================================================== """Unit tests for ar.py.""" import unittest from absl.testing import absltest import ar import graph as gh import problem as pr class ARTest(unittest.TestCase): @classmethod def setUpClass(cls): super().setUpClass() cls.defs = pr.Definition.from_txt_file('defs.txt', to_dict=True) cls.rules = pr.Theorem.from_txt_file('rules.txt', to_dict=True) def test_update_groups(self): """Test for update_groups.""" groups1 = [{1, 2}, {3, 4, 5}, {6, 7}] groups2 = [{2, 3, 8}, {9, 10, 11}] _, links, history = ar.update_groups(groups1, groups2) self.assertEqual( history, [ [{1, 2, 3, 4, 5, 8}, {6, 7}], [{1, 2, 3, 4, 5, 8}, {6, 7}, {9, 10, 11}], ], ) self.assertEqual(links, [(2, 3), (3, 8), (9, 10), (10, 11)]) groups1 = [{1, 2}, {3, 4}, {5, 6}, {7, 8}] groups2 = [{2, 3, 8, 9, 10}, {3, 6, 11}] _, links, history = ar.update_groups(groups1, groups2) self.assertEqual( history, [ [{1, 2, 3, 4, 7, 8, 9, 10}, {5, 6}], [{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}], ], ) self.assertEqual(links, [(2, 3), (3, 8), (8, 9), (9, 10), (3, 6), (6, 11)]) groups1 = [] groups2 = [{1, 2}, {3, 4}, {5, 6}, {2, 3}] _, links, history = ar.update_groups(groups1, groups2) self.assertEqual( history, [ [{1, 2}], [{1, 2}, {3, 4}], [{1, 2}, {3, 4}, {5, 6}], [{1, 2, 3, 4}, {5, 6}], ], ) self.assertEqual(links, [(1, 2), (3, 4), (5, 6), (2, 3)]) def test_generic_table_simple(self): tb = ar.Table() # If a-b = b-c & d-a = c-d tb.add_eq4('a', 'b', 'b', 'c', 'fact1') tb.add_eq4('d', 'a', 'c', 'd', 'fact2') tb.add_eq4('x', 'y', 'z', 't', 'fact3') # distractor fact # Then b=d, because {fact1, fact2} but not fact3. result = list(tb.get_all_eqs_and_why()) self.assertIn(('b', 'd', ['fact1', 'fact2']), result) def test_angle_table_inbisector_exbisector(self): """Test that AR can figure out bisector & ex-bisector are perpendicular.""" # Load the scenario that we have cd is bisector of acb and # ce is the ex-bisector of acb. p = pr.Problem.from_txt( 'a b c = triangle a b c; d = incenter d a b c; e = excenter e a b c ?' ' perp d c c e' ) g, _ = gh.Graph.build_problem(p, ARTest.defs) # Create an external angle table: tb = ar.AngleTable('pi') # Add bisector & ex-bisector facts into the table: ca, cd, cb, ce = g.names2nodes(['d(ac)', 'd(cd)', 'd(bc)', 'd(ce)']) tb.add_eqangle(ca, cd, cd, cb, 'fact1') tb.add_eqangle(ce, ca, cb, ce, 'fact2') # Add a distractor fact to make sure traceback does not include this fact ab = g.names2nodes(['d(ab)'])[0] tb.add_eqangle(ab, cb, cb, ca, 'fact3') # Check for all new equalities result = list(tb.get_all_eqs_and_why()) # halfpi is represented as a tuple (1, 2) halfpi = (1, 2) # check that cd-ce == halfpi and this is because fact1 & fact2, not fact3 self.assertCountEqual( result, [ (cd, ce, halfpi, ['fact1', 'fact2']), (ce, cd, halfpi, ['fact1', 'fact2']), ], ) def test_angle_table_equilateral_triangle(self): """Test that AR can figure out triangles with 3 equal angles => each is pi/3.""" # Load an equaliteral scenario p = pr.Problem.from_txt('a b c = ieq_triangle ? cong a b a c') g, _ = gh.Graph.build_problem(p, ARTest.defs) # Add two eqangles facts because ieq_triangle only add congruent sides a, b, c = g.names2nodes('abc') g.add_eqangle([a, b, b, c, b, c, c, a], pr.EmptyDependency(0, None)) g.add_eqangle([b, c, c, a, c, a, a, b], pr.EmptyDependency(0, None)) # Create an external angle table: tb = ar.AngleTable('pi') # Add the fact that there are three equal angles ab, bc, ca = g.names2nodes(['d(ab)', 'd(bc)', 'd(ac)']) tb.add_eqangle(ab, bc, bc, ca, 'fact1') tb.add_eqangle(bc, ca, ca, ab, 'fact2') # Now check for all new equalities result = list(tb.get_all_eqs_and_why()) result = [(x.name, y.name, z, t) for x, y, z, t in result] # 1/3 pi is represented as a tuple angle_60 angle_60 = (1, 3) angle_120 = (2, 3) # check that angles constants are created and figured out: self.assertCountEqual( result, [ ('d(bc)', 'd(ac)', angle_120, ['fact1', 'fact2']), ('d(ab)', 'd(bc)', angle_120, ['fact1', 'fact2']), ('d(ac)', 'd(ab)', angle_120, ['fact1', 'fact2']), ('d(ac)', 'd(bc)', angle_60, ['fact1', 'fact2']), ('d(bc)', 'd(ab)', angle_60, ['fact1', 'fact2']), ('d(ab)', 'd(ac)', angle_60, ['fact1', 'fact2']), ], ) def test_incenter_excenter_touchpoints(self): """Test that AR can figure out incenter/excenter touchpoints are equidistant to midpoint.""" p = pr.Problem.from_txt( 'a b c = triangle a b c; d1 d2 d3 d = incenter2 a b c; e1 e2 e3 e =' ' excenter2 a b c ? perp d c c e', translate=False, ) g, _ = gh.Graph.build_problem(p, ARTest.defs) a, b, c, ab, bc, ca, d1, d2, d3, e1, e2, e3 = g.names2nodes( ['a', 'b', 'c', 'ab', 'bc', 'ac', 'd1', 'd2', 'd3', 'e1', 'e2', 'e3'] ) # Create an external distance table: tb = ar.DistanceTable() # DD can figure out the following facts, # we manually add them to AR. tb.add_cong(ab, ca, a, d3, a, d2, 'fact1') tb.add_cong(ab, ca, a, e3, a, e2, 'fact2') tb.add_cong(ca, bc, c, d2, c, d1, 'fact5') tb.add_cong(ca, bc, c, e2, c, e1, 'fact6') tb.add_cong(bc, ab, b, d1, b, d3, 'fact3') tb.add_cong(bc, ab, b, e1, b, e3, 'fact4') # Now we check whether tb has figured out that # distance(b, d1) == distance(e1, c) # linear comb exprssion of each variables: b = tb.v2e['bc:b'] c = tb.v2e['bc:c'] d1 = tb.v2e['bc:d1'] e1 = tb.v2e['bc:e1'] self.assertEqual(ar.minus(d1, b), ar.minus(c, e1)) if __name__ == '__main__': absltest.main()