def testSearchStep(self):
test_data = []
for rules, hyps, lines, concls in test_data:
hyps = [parser.parse_fact(fact) for fact in hyps]
lines = [parser.parse_line(line) for line in lines]
concls = [parser.parse_fact(concl) for concl in concls]
expr.search_step(rules, hyps, lines=lines)
self.assertEqual(set(hyps), set(concls))
def testApplyRule(self):
test_data = [
# ("D44", ["midp(P, E, F)", "midp(Q, E, G)"], ["line(E, F)", "line(G, E)"], [], ["para(P, Q, F, G)"]),
# ("D56", ["cong(D, A, D, B)", "cong(E, A, E, B)"], [], [], ["perp(A, B, D, E)"]),
# (ruleset["D5"], ["para(E, F, G, H)"], ["line(E, F)", "line(G, H)"], [],
# ["para(G, H, E, F)"]),
# (ruleset["D44"], ["midp(P, E, F)", "midp(Q, E, G)"], ["line(E, F)", "line(G, E)"], [],
# ["para(P, Q, F, G)"]),
# (ruleset["D45"], ["midp(N, B, D)", "para(E, N, C, D)", "coll(E, B, C)"],
# ["line(M, N, E)", "line(C, D)", "line(D, N, B)", "line(C, E, B)"], [],
# ["midp(E, B, C)"]),
# (ruleset["D56"], ["cong(D, A, D, B)", "cong(E, A, E, B)"],
# [], [], ["perp(A, B, D, E)"]),
# (ruleset["D13"], ["cong(E, P, P, F)", "cong(P, E, G, P)", "cong(P, E, H, P)"], [], [],
# ["cyclic(E, F, G, H)"]),
# (ruleset["D43"], ["eqangle(E, F, E, G, C, D, C, B)", "cyclic(E, D, G, B, F, C)"],
# ["line(E, F)", "line(E, G)", "line(D, C)", "line(D, B)", "line(F, G)", "line(C, B)"],
# ["circle(None, E, D, G, B, F, C)"], ["cong(F, G, D, B)"]),
# (ruleset["D42"], ["eqangle(A, F, B, C, A, C, B, E)"],
# ["line(E, A, C)", "line(F, B, C)", "line(H, A, F)", "line(H, B, E)", "line(G, A, B)", "line(G, C, H)"],
# [], ["cyclic(A, B, F, E)"]),
# (ruleset["D9"], ["perp(B, E, A, C)", "perp(A, C, B, E)"], [], [], []),
# ("D9", ["perp(G, F, D, E)", "perp(A, B, D, E)"], [], [], ["para(G, F, A, B)"]),
# ("D9", ["perp(A, B, D, E)", "perp(D, E, G, F)"], [], [], ["para(A, B, G, F)"]),
# (ruleset["D43"], ["eqangle(B, E, A, C, B, C, A, F)", "cyclic(B, A, E, F)"],
# ["line(E, A, C)", "line(F, B, C)", "line(H, A, F)", "line(H, B, E)", "line(G, A, B)", "line(G, C, H)"], [],
# []),
# (ruleset["D42"], ["eqangle(B, E, A, C, A, F, B, C)"],
# ["line(E, A, C)", "line(F, B, C)", "line(H, A, F)", "line(H, B, E)", "line(G, A, B)", "line(G, C, H)"],
# [], ["cyclic(H, C, E, F)"]),
# (ruleset["D76"], ["perp(B, E, A, C)", "perp(A, F, B, C)"],
# ["line(E, A, C)", "line(F, B, C)", "line(H, A, F)", "line(H, B, E)", "line(G, A, B)", "line(G, C, H)"], [],
# ["eqangle(B,E,A,C,A,F,B,C,B,C,A,F,A,C,B,E)"]),
# (ruleset["D42"], ["eqangle(B, E, A, C, A, F, B, C, A, C, B, E, B, C, A, F)"],
# ["line(E, A, C)", "line(F, B, C)", "line(H, A, F)", "line(H, B, E)", "line(G, A, B)", "line(G, C, H)"],
# [], ["cyclic(E, C, F, H)", "cyclic(E, A, F, B)"]),
# ("D61", ["simtri(B, A, D, C, A, D)", "cong(A, B, A, C)"], [], [], ["contri(B, A, D, C, A, D)"]),
# ("D89", ["eqangle(A, F, A, B, A, E, D, E)", "eqangle(B, F, A, E, A, D, D, E)"], [], [],
# ["simtri(A, B, F, E, A, D)"]),
# ("D58", ["eqangle(A, B, A, F, A, E, E, D)", "eqangle(B, F, F, A, A, D, D, E)"], [], [],
# ["simtri(A, B, F, E, A, D)"]),
# ("D89", ["eqangle(A, F, A, B, D, E, E, A)", "eqangle(B, F, F, A, A, D, D, E)"], [], [],
# ["simtri(A, B, F, E, A, D)"]),
# ("D40", ["para(A, B, D, E)"], ["line(E, A, F)"], [], ["eqangle(B, A, A, F, A, E, E, D)"])
]
for rule, facts, lines, circles, concls in test_data:
facts = [parser.parse_fact(fact) for fact in facts]
concls = [parser.parse_fact(concl) for concl in concls]
lines = [parser.parse_line(line) for line in lines]
circles = [parser.parse_circle(circle) for circle in circles]
hyps = copy.copy(facts)
prover = expr.Prover(ruleset,
hyps=facts,
lines=lines,
circles=circles)
prover.apply_rule(rule, facts)
self.assertEqual(set(prover.hyps) - set(hyps), set(concls))
def testCheckImply(self):
test_data = [
("eqangle(A, B, C, D, E, F, G, H)",
"eqangle(E, F, G, H, A, B, C, D)", True),
# ("eqangle(A, B, C, D, E, F, G, H)", "eqangle(C, D, A, B, G, H, E, F)", True),
]
for fact, goal, res in test_data:
fact = parser.parse_fact(fact)
goal = parser.parse_fact(goal)
self.assertEqual(expr.Prover(ruleset).check_imply(fact, goal), res)
def testSearchFixpoint(self):
test_data = []
for rules, hyps, lines, circles, concl in test_data:
hyps = [parser.parse_fact(fact) for fact in hyps]
concl = parser.parse_fact(concl)
lines = [parser.parse_line(line) for line in lines]
circles = [parser.parse_circle(circle) for circle in circles]
hyps = expr.search_fixpoint(ruleset, hyps, lines, circles, concl)
fact = expr.find_goal(hyps, concl, lines, circles)
self.assertIsNotNone(fact)
def testCombineFactsList(self):
test_data = []
for fact, target, lines, circles, concl in test_data:
fact = parser.parse_fact(fact)
target = parser.parse_fact(target)
lines = [parser.parse_line(line) for line in lines]
circles = [parser.parse_circle(circle) for circle in circles]
r = expr.combine_facts()
concl = [parser.parse_fact(fact) for fact in concl]
self.assertEqual(set(r), set(concl))
def testApplyRuleHyps(self):
test_data = [
# ("D5", ["para(P, Q, R, S)"], [], ["para(P, Q, R, S)"]),
# ("D45", ["midp(N, B, D)", "para(E, N, C, D)", "coll(E, B, C)"],
# ["line(M, N, E)", "line(C, D)", "line(D, N, B)", "line(C, E, B)"],
# ["midp(N, B, D)", "para(E, N, C, D)", "coll(E, B, C)", "midp(E, B, C)"]),
]
for rule, hyps, lines, concls in test_data:
hyps = [parser.parse_fact(fact) for fact in hyps]
concls = [parser.parse_fact(concl) for concl in concls]
lines = [parser.parse_line(line) for line in lines]
expr.apply_rule_hyps(rule, hyps, lines=lines, ruleset=ruleset)
self.assertEqual(set(hyps), set(concls))
def testPrintSearchFailed(self):
test_data = [
# Following test shows how we handle rules that contain "not" fact.
# The goal cannot be reached because "coll(E, F, G, H)" is in hypotheses.
# The goal can be reached if remove "coll(E, F, G, H)" from hypotheses.
(ruleset, ["eqangle(E, G, G, F, H, E, F, H)",
"coll(E, F, G, H)"], [], [], "cyclic(E, F, G, H)"),
]
for rules, hyps, lines, circles, concl in test_data:
hyps = [parser.parse_fact(fact) for fact in hyps]
concl = parser.parse_fact(concl)
lines = [parser.parse_line(line) for line in lines]
circles = [parser.parse_circle(circle) for circle in circles]
prover = expr.Prover(ruleset, hyps, concl, lines, circles)
# print("--- Proof for", concl, "---")
res = prover.search_fixpoint()
assert not res, "✘ Goal has been proved."
def testGetArgTypeByFact(self):
test_data = [
("coll(A, B, C)", expr.POINT),
("cong(A, B, C, D)", expr.SEG),
("para(A, B, C, D)", expr.PonL),
]
for fact, r in test_data:
self.assertEqual(parser.parse_fact(fact).get_arg_type(), r)
def testMatchFactCircles(self):
test_data = [
# ("cyclic(A, B, C, D)", "cyclic(P, Q, R, S)", {}, [], [{"A": "P", "B": "Q", "C": "R", "D": "S"}]),
# ("cyclic(A, B, C, D)", "cyclic(P, Q, R, S)", {"A": "T"}, [], []),
# ("cyclic(A, B, C, D)", "cyclic(P, Q, R, S)", {"A": "R"}, ["circle(None, P, Q, R, S)"],
# [{"A": "R", "B": "P", "C": "Q", "D": "S"}]),
# ("cyclic(A, B, C, D)", "cyclic(P, Q, R, S)", {"A": "R", "B": "Q"}, ["circle(None, P, Q, R, S)"],
# [{"A": "R", "B": "Q", "C": "P", "D": "S"}]),
# ("circle(A, B, C, D)", "circle(P, Q, R, S)", {}, [], [{"A": "P", "B": "Q", "C": "R", "D": "S"}]),
# ("circle(A, B, C, D)", "circle(P, Q, R, S)", {"A": "P"}, [], [{"A": "P", "B": "Q", "C": "R", "D": "S"}]),
]
for pat, f, inst, circles, res in test_data:
pat = parser.parse_fact(pat)
f = parser.parse_fact(f)
circles = [parser.parse_circle(circle) for circle in circles]
insts = expr.match_expr(pat, f, inst, circles=circles)
self.assertEqual(insts, res)
def testParseFact(self):
test_data = [
("coll(A0, C, B)", Fact("coll", ["A0", "C", "B"])),
("coll(A,C,B)", Fact("coll", ["A", "C", "B"])),
("¬coll(A, C, B)", Fact("coll", ["A", "C", "B"], negation=True)),
]
for s, f in test_data:
self.assertEqual(parser.parse_fact(s), f)
def testPick(self):
test_data = [
[
"para(A, B, C)", "perp(D, E, F)", "perp(P, Q, R)",
"perp(R, S, T)", "coll(X, Y, Z)", "para(E, F, G, H)"
],
]
for hyps in test_data:
hyps = [parser.parse_fact(fact) for fact in hyps]
prover = expr.Prover(ruleset, hyps)
self.assertEqual(len(prover.get_applicable_facts(ruleset["D10"])),
6)
def testMatchFactTail(self):
test_data = [
("coll(A,B,C)", "coll(P,Q,R)", {
"A": "Q",
"B": "P",
"C": "R"
}, [{
"A": "Q",
"B": "P",
"C": "R"
}]),
("coll(A,B,C)", "coll(P,Q,R)", {
"A": "Q",
"B": "P"
}, []),
]
for pat, f, inst, res in test_data:
pat = parser.parse_fact(pat)
pat.tail = True
f = parser.parse_fact(f)
insts = expr.Prover(ruleset).match_expr(pat, f, inst)
insts = [p[0] for p in insts]
self.assertEqual(insts, res)
def testMatchFact(self):
test_data = [
("coll(A,B,C)", "coll(P,Q,R)", {}, [{
"A": "P",
"B": "Q",
"C": "R"
}]),
("coll(A,B,C)", "coll(P,Q,R)", {
"A": "P"
}, [{
"A": "P",
"B": "Q",
"C": "R"
}]),
("coll(A,B,C)", "coll(P,Q,R)", {
"A": "Q"
}, []),
("coll(A,B,C)", "para(P,Q,R,S)", {}, []),
("coll(A,B,C,D,E,F)", "coll(P,Q,R,S,T,U)", {}, [{
"A": "P",
"B": "Q",
"C": "R",
"D": "S",
"E": "T",
"F": "U"
}]),
("cong(A, B, A, D)", "cong(P, Q, R, S)", {}, []),
("cong(A, B, C, D)", "cong(P, Q, P, S)", {}, [{
"A": "P",
"B": "Q",
"C": "P",
"D": "S"
}, {
"A": "P",
"B": "Q",
"C": "S",
"D": "P"
}, {
"A": "Q",
"B": "P",
"C": "P",
"D": "S"
}, {
"A": "Q",
"B": "P",
"C": "S",
"D": "P"
}]),
("coll(A, B, A, D)", "coll(P, Q, P, S)", {}, [{
"A": "P",
"B": "Q",
"D": "S"
}]),
("cong(A, B, A, D)", "cong(P, Q, P, S)", {}, [{
"A": "P",
"B": "Q",
"D": "S"
}]),
("coll(A, B, C)", "coll(P, Q, R, T)", {
"A": "Q",
"B": "R"
}, [{
"A": "Q",
"B": "R",
"C": "T"
}]),
("coll(A, B, C)", "coll(P, Q, R, T)", {
"A": "P",
"B": "Q"
}, [{
"A": "P",
"B": "Q",
"C": "R"
}, {
"A": "P",
"B": "Q",
"C": "T"
}]),
("contri(A, B, C, D, E, F)", "contri(P, Q, R, X, Y, Z)", {}, [{
"A":
"P",
"B":
"Q",
"C":
"R",
"D":
"X",
"E":
"Y",
"F":
"Z"
}, {
"A":
"P",
"B":
"R",
"C":
"Q",
"D":
"X",
"E":
"Z",
"F":
"Y"
}, {
"A":
"Q",
"B":
"R",
"C":
"P",
"D":
"Y",
"E":
"Z",
"F":
"X"
}]),
]
for pat, f, inst, res in test_data:
pat = parser.parse_fact(pat)
f = parser.parse_fact(f)
insts = expr.Prover(ruleset).match_expr(pat, f, inst)
insts = [p[0] for p in insts]
self.assertEqual(insts, res)
def testPrintSearch(self):
test_data = [
# (ruleset, ["cong(D, A, D, B)", "cong(E, A, E, B)", "perp(G, F, D, E)", "coll(A, C, B)", "coll(A, G, E)",
# "coll(B, F, E)", "coll(D, C, E)"], [], [], "para(A, C, G, F)"),
#
# (ruleset, ["cong(A, B, B, C, C, D, D, A)"], [], [], "eqangle(A, B, B, D, B, D, A, D)"),
#
# (ruleset, ["eqangle(E, F, E, G, D, C, B, C)", "cyclic(E, D, G, B, F, C)"], [],
# ["circle(None, E, D, G, B, F, C)"], "cong(D, B, F, G)"),
#
# (
# ruleset_reduced, ["coll(E, A, C)", "perp(B, E, A, C)", "coll(F, B, C)", "perp(A, F, B, C)", "coll(H, A, F)",
# "coll(H, B, E)", "coll(G, A, B)", "coll(G, C, H)"], [], [], "perp(C, G, A, B)"),
#
# # Following 2 tests: testing if contri works.
# (ruleset, ["para(B, E, C, F)", "cong(B, E, C, F)", "coll(B, M, C)", "coll(F, M, E)"],
# [], [], "cong(B, M, C, M)"),
#
# # Following 4 tests: testing if simtri works.
# (ruleset, ["para(D, E, B, F)", "para(E, F, A, B)", "coll(A, D, B)", "coll(B, F, C)", "coll(A, E, C)"], [],
# [],
# "simtri(A, D, E, E, F, C)"),
#
# (ruleset, ["para(F, D, A, B)", "para(F, E, A, C)", "coll(B, D, E, C)"], [], [], "simtri(A, B, C, F, D, E)"),
#
# # (ruleset, ["perp(B, F, A, E)", "coll(A, F, E)", "coll(D, E, C)", "perp(A, B, A, D)", "perp(A, D, D, C)",
# # "perp(A, B, B, C)", "perp(D, C, C, B)"],
# # [], [], "simtri(A, B, F, E, A, D)"),
#
# # This is the Example 6.4. We are not able to add auxiliary point so far. So I add additional facts
# # in the hypothesis :midp(F, A, D) and coll(F, A, D).
# # A0 -> F
# (ruleset, ["para(A, B, C, D)", "midp(M, A, C)", "midp(F, A, D)", "midp(N, B, D)", "coll(M, N, E)",
# "coll(A, M, C)", "coll(D, N, B)", "coll(C, E, B)", "coll(F, A, D)"
# ], [], [], "midp(E, B, C)"),
#
# # Following tests proves some theorems in "Machine Proofs in Geometry".
# #
# # 6.45 (Failed)
# # If L is the harmonic conjugate of the centroid G of a triangle ABC
# # with respect to the ends A, D of the median AD, show that LD = AD.
# # (ruleset, ["midp(D, B, C)", "midp(E, A, C)", "midp(F, A, B)", "coll(B, G, E)",
# # "coll(F, G, C)", "eqratio(L, D, D, G, A, L, A, G)", "coll(B, D, C)"], [], [], "midp(D, L, A)"),
#
# # 6.46 (Failed)
# # Show that the distances of a point on a median of triangle from
# # the sides including the median are inversely proportional to these sides.
# # (ruleset, ["coll(A, K, C)", "coll(C, J, B)", "coll(A, F, B)", "coll(C, N, F)",
# # "midp(F, A, B)", "perp(K, N, A, C)", "perp(N, J, C, B)"], [], [], "eqratio(N, K, N, J, B, C, A, C)"),
#
# # 6.51 (Failed)
# # K1 -> P, K2 -> Q
# # (ruleset, ["midp(N, A, B)", "midp(M, A, C)", "coll(C, G, N)", "coll(B, G, M)",
# # "eqratio(B, K, B, C, C, P, B, C)", "coll(N, Q, M)", "coll(A, Q, K)",
# # "coll(Z, B, C)", "coll(Z, Q, G)"], [], [], "eqratio(B, Z, Z, C, B, P, P, C)"),
#
# # 6.60 (Failed)
# # H1 -> P, H2 -> Q, A1 -> R
# # (ruleset, ["midp(R, B, C)", "coll(H, B, C)", "para(A, R, H, N)", "coll(D, N, H)", "coll(B, A, D)", "coll(Q, A, P)",
# # "midp(K, N, C)", "midp(L, B, D)", "midp(K, H, P)", "midp(L, H, Q)"], [], [], "midp(A, P, Q)"),
#
# # Example 6.62 (Failed)
# # The dual of the orthocenter theorem.
# # (ruleset, ["coll(D, B, C)", "perp(D, O, O, A)", "coll(A, B, F)", "perp(F, O, O, C)", "coll(C, A, E)",
# # "perp(E, O, O, B)", "coll(E, D, Z)", "coll(A, B, Z)", "coll(E, F, D)"], [], [], "midp(Z, A, B)"),
#
# # 6.63 (Failed)
# # In a given triangle the three products of the segments into which
# # the orthocenter divides the altitudes are equal.
# # (ruleset, ["perp(D, C, A, B)", "perp(E, B, A, C)", "coll(E, H, B)", "coll(C, H, D)", "coll(A, E, C)",
# # "coll(A, D, B)"], [], [], "eqratio(C, H, B, H, H, E, H, D)"),
#
# # 6.64
# (ruleset, ["perp(F, C, A, B)", "perp(E, B, A, C)", "coll(A, E, C)", "coll(C, H, F)", "coll(E, H, B)",
# "coll(A, F, B)"], [], [], "eqratio(A, F, C, F, H, F, F, B)"),
#
# # 6.69
# (ruleset, ["perp(F, C, A, B)", "perp(E, B, A, C)", "perp(D, A, B, C)", "coll(A, F, B)", "coll(A, E, C)",
# "coll(B, D, C)"], [], [], "eqangle(E, D, D, C, B, D, D, F)"),
#
# # 6.70 (Failed)
# # (ruleset, ["perp(A, H, B, C)", "perp(B, H, A, C)", "perp(C, H, A, B)", "circle(OA, B, H, C)",
# # "circle(OB, A, C, H)", "circle(OC, A, B, H)", "circle(O, A, B, C)"], [], [], "cong(OB, OC, B, C)"),
#
# # 6.72 (Failed)
# # (ruleset, ["perp(D, A, B, C)", "perp(E, B, A, C)", "perp(F, C, A, B)", "cong(D1, B, C, D)",
# # "cong(E1, A, C, E)", "cong(F1, A, B, F)", "coll(A, E1, E, C)", "coll(C, D1, D, B)",
# # "coll(A, F1, F, B)", "perp(I, E1, A, C)", "perp(I, D1, C, D)"], [], [], "perp(I, F1, A, B)"),
#
# # 6.73 (Failed)
# # (ruleset, ["perp(D, A, B, C)", "perp(E, B, A, C)", "perp(F, C, A, B)", "perp(P, D, B, A)", "coll(J, F, E)",
# # "coll(J, P, D)", "coll(B, P, F, A)", "coll(A, E, C)", "coll(B, D, C)"], [], [], "midp(P, D, J)"),
#
# # 6.74
# (ruleset, ["perp(F, C, A, B)", "perp(E, B, A, C)", "perp(D, A, B, C)", "coll(A, F, B)", "coll(A, E, C)",
# "coll(B, D, C)"], [], [], "eqratio(B, D, E, D, F, D, D, C)"),
#
# # 6.75 (Failed)
# # (ruleset, ["perp(F, C, A, B)", "perp(E, B, A, C)", "perp(D, A, B, C)", "coll(A, F, B)", "coll(A, E, C)",
# # "coll(B, D, C)", "perp(Q, C, D, E)", "perp(P, B, D, F)", "coll(F, P, D)", "coll(E, Q, D)"],
# # [], [], "cong(E, Q, F, P)"),
#
# # 6.76 (Failed)
# # (ruleset, ["perp(C, F, A, B)", "perp(A, H, C, B)", "perp(B, H, C, A)", "perp(F, C, A, B)",
# # "perp(P, F, A, C)", "perp(T, F, B, C)", "perp(Q, F, A, H)", "coll(A, P, C)",
# # "coll(C, H, F)", "coll(C, T, B)", "coll(A, F, B)"], [], [],
# # "coll(P, Q, T)"),
#
# # 6.77
# (ruleset, ["perp(D, A, B, C)", "perp(Q, D, A, B)", "perp(P, D, A, C)", "coll(A, Q, B)", "coll(A, P, C)",
# "coll(B, D, C)"], [], [], "cyclic(B, C, P, Q)"),
#
# # 6.86 (Failed)
# # (ruleset, ["circle(O, A, B, C)", "perp(D, A, B, C)", "coll(B, D, C)"], [], [],
# # "eqangle(B, A, A, D, O, A, A, C)"),
#
# # 6.88 (Failed)
# # (ruleset, ["cyclic(O, A, B, C)", "midp(A1, B, C)", "midp(B1, A, C)", "midp(C1, A, B)", "coll(A, B1, C)",
# # "coll(B, A1, C)", "coll(A, C1, B)"], [], [], "perp(O, A1, B1, C1)"),
#
# # 6.90 (Failed)
# # (ruleset, ["circle(O, A, B, C)", "perp(F, C, A, B)", "perp(E, B, A, C)", "coll(A, E, C)", "coll(A, F, B)",
# # ], [], [], "perp(E, F, A, O)"),
#
# # This cannot be proved without additional D91 (the length of two radius are equal).
# # (ruleset, ["circle(O, A, B, C, D, E)"], [], [], "cong(O, C, O, E)"),
#
#
# # Following tests proves some examples in "Geometry Expert".
# # Examples -> 6_GDD_FULL -> 01-20
# # ... -> 01
# (ruleset, ["perp(D, C, A, B)", "perp(E, B, A, C)", "midp(F, C, B)", "midp(G, D, E)", "coll(A, D, B)",
# "coll(A, E, C)", "coll(D, G, E)", "coll(B, F, C)"], [], [], "perp(F, G, D, E)"),
# # ... -> 02
# (ruleset, ["midp(A1, C, B)", "midp(B1, C, A)", "midp(C1, B, A)", "circle(O, A, B, C)", "coll(A, B1, C)",
# "coll(C, A1, B)", "coll(A, C1, B)"], [], [], "perp(O, A1, B1, C1)"),
# # ... -> 03
# (ruleset, ["perp(D, A, B, C)", "perp(E, B, E, C)", "perp(F, C, A, B)", "midp(a1, C, B)", "midp(P, E, B)",
# "midp(Q, F, C)", "coll(A, F, B)", "coll(A, E, C)", "coll(A, H, D)",
# "coll(B, P, H, E)", "coll(F, Q, H, C)", "coll(B, a1, D, C)"], [], [], "cyclic(P, Q, H, D)"),
# # ... -> 04
# (ruleset, ["circle(O, A, B, C, D)", "midp(Q, C, B)", "midp(J, S, Q)", "cong(J, O, J, M)",
# "coll(A, S, D, I)", "coll(B, Q, C, I)", "coll(O, J, M)", "coll(S, J, Q)"], [], [],
# "perp(S, M, B, C)"),
# # ... -> 06
# (ruleset, ["perp(E, C, A, B)", "perp(F, A, B, C)", "coll(A, E, B)", "coll(B, F, C)", "coll(E, H, C)",
# "coll(A, H, F)"], [], [], "perp(B, H, A, C)"),
# # ... -> 07
# # TODO: Make use of "circle" facts when matching "cyclic" facts.
# # Adding "cyclic" fact with the same arguments as a "circle" fact (but without center) works smoothly.
# (ruleset, ["circle(O, A, B, C, D)", "perp(E, D, B, C)", "perp(F, D, A, C)", "perp(G, D, A, B)",
# "coll(A, G, B)", "coll(A, F, C)", "coll(E, C, B)", "cyclic(A, B, C, D)"], [], [],
# "coll(E, F, G)"),
# # ... -> 10
# (ruleset, ["circle(O1, C, D, E, Q)", "cyclic(C, D, E, Q)", "circle(O, B, E, A, Q)", "cyclic(B, E, A, Q)",
# "coll(C, D, P)", "coll(C, E, B)", "coll(D, E, A)", "coll(P, B, A)"], [], [],
# "cyclic(P, D, Q, A)"),
# # ... -> 11
# (ruleset, ["perp(D, A, B, C)", "midp(L, A, B)", "midp(M, C, B)", "midp(N, A, C)", "coll(A, L, B)",
# "coll(A, N, C)", "coll(B, D, M, C)"], [], [], "cyclic(L, D, M, N)"),
# # ... -> 12
# (ruleset, ["perp(B, D, A, C)", "circle(O, A, B, C, D)", "cyclic(A, B, C, D)", "coll(E, A, C)",
# "coll(E, B, D)", "coll(A, F, B)", "midp(F, B, A)"], [], [], "perp(F, E, C, D)"),
# # ... -> 13
# (ruleset, ["perp(E, B, A, C)", "perp(F, A, B, D)", "perp(G, D, A, C)", "perp(H, C, B, D)",
# "coll(A, E, G, C)", "coll(B, F, H, D)", "para(A, D, B, C)", "para(A, B, C, D)"],
# [], [], "para(E, F, G, H)"),
# # ... -> 14 (Failed)
# # Can be resolved by adding a new rule.˙
# (ruleset, ["circle(A, D, C, G)", "circle(B, C, F, G, E)", "cyclic(C, F, G, E)",
# "coll(D, C, E)", "coll(F, B, E)", "perp(B, C, C, A)"], [], [], "coll(D, F, G)"),
# # ... -> 15
# (ruleset, ["perp(D, A, B, C)", "perp(E, B, A, C)", "perp(F, C, A, B)", "perp(G, F, B, C)",
# "perp(H, F, A, C)", "perp(K, E, A, B)", "perp(I, D, A, B)", "coll(A, H, E, C)",
# "coll(C, D, G, B)", "coll(A, K, F, I, B)"], [], [], "cyclic(H, K, I, G)"),
# # ... -> 16
# (ruleset, ["perp(P, M, A, O)", "perp(Q, M, B, O)", "perp(D, B, A, O)", "perp(C, A, B, O)",
# "perp(T, Q, A, O)", "perp(K, P, B, O)", "coll(S, Q, T)", "coll(S, P, K)",
# "coll(O, T, D, P, A)", "coll(O, K, C, Q, B)", "coll(A, M, B)"], [], [], "perp(O, S, P, Q)"),
# # ... -> 17
# (ruleset, ["circle(O, A, C, K, N)", "cyclic(A, C, K, N)", "circle(O1, M, B, K, N)", "cyclic(M, B, K, N)",
# "coll(A, K, B)", "coll(C, N, B)", "cyclic(C, A, M, B)", "circle(G, C, A, M, B)"],
# [], [], "cyclic(M, K, O, N)"),
# # ... -> 19
# (ruleset, ["circle(O, A, C, D, B)", "cyclic(A, C, D, B)", "circle(P, A, E, F, B)", "cyclic(A, E, F, B)",
# "coll(C, A, E)", "coll(D, B, F)"], [], [], "para(C, D, E, F)"),
# # ... -> 20
# (ruleset, ["coll(A, E, C)", "coll(C, D, B)", "coll(A, G, B)", "coll(E, H, B)", "coll(A, H, D)",
# "perp(B, E, A, C)", "perp(A, D, C, B)", "perp(H, G, A, B)"], [], [],
# "eqangle(E, G, G, H, H, G, G, D)"),
# # Examples -> 6_GDD_FULL -> 21-40
# ... -> 22
# (ruleset, ["circle(O, A, M, B, C, N)", "cyclic(A, B, M, C, N)", "perp(P, O, A, C)", "perp(Q, O, A, B)",
# "coll(A, E, P, R, C)", "coll(A, D, Q, B)", "coll(N, P, O)", "coll(N, E, D, M)", "coll(R, O, Q, M)"],
# [], [], "eqangle(A, D, D, E, D, E, E, A)"),
# # ... -> 23
# (ruleset, ["circle(O, E, B, C, A, D)", "cyclic(E, B, C, A, D)", "coll(A, F, M, G, B)", "coll(C, F, D)",
# "coll(C, M, O)", "coll(C, G, E)", "perp(O, M, A, B)"], [], [], "eqangle(A, G, G, C, C, D, D, E)"),
# # ... -> 24
# (ruleset, ["circle(O1, P, Q, R, S)", "cyclic(P, Q, R, S)", "circle(O, P, Q, X, Y)", "cyclic(P, Q, X, Y)",
# "coll(I, Y, X)", "coll(I, S, R)", "coll(Q, Y, S)"], [], [], "eqangle(R, I, I, X, R, P, P, X)"),
# ... -> 28
# (ruleset, ["perp(F, C, A, B)", "perp(A, H, B, C)", "perp(B, H, A, C)", "perp(T, F, B, C)", "perp(Q, F, A, H)",
# "perp(P, F, A, C)", "coll(A, P, C)", "coll(C, T, B)", "coll(A, Q, H)", "coll(A, F, B)"], [], [],
# "coll(P, Q, T)"),
# ... -> 29
(ruleset, [
"perp(D, A, B, C)", "perp(Q, D, A, B)", "perp(P, D, A, C)",
"coll(A, Q, B)", "coll(A, P, C)", "coll(B, D, C)"
], [], [], "cyclic(B, Q, P, C)"),
# ... -> 30 (Add an auxiliary point F manually)
(ruleset, [
"circle(O, A, B, C, F)", "cyclic(A, B, C, F)",
"perp(D, C, A, B)", "perp(E, B, A, C)", "coll(A, E, C)",
"coll(A, D, B)", "coll(A, O, F)"
], [], [], "perp(A, O, D, E)")
]
# pr = cProfile.Profile()
# pr.enable()
start = time.time()
for ruleset_type, hyps, lines, circles, concl in test_data:
# pr.enable()
hyps = [parser.parse_fact(fact) for fact in hyps]
concl = parser.parse_fact(concl)
lines = [parser.parse_line(line) for line in lines]
circles = [parser.parse_circle(circle) for circle in circles]
prover = expr.Prover(ruleset_type, hyps, concl, lines, circles)
# print("--- Proof for", concl, "---")
res = prover.search_fixpoint()
assert res, "✘ Fixpoint reached without proving goal."
# print("Procedure: ")
# prover.print_search(res)
# print('')
end = time.time()
def testCombineFacts(self):
test_data = [
# para
("para(A, B, C, D)", "para(E, F, G, H)", [], [], False),
# ("para(A, B, C, D)", "para(E, F, G, H)", ["line(A, B, E, F)"], [], "para(A, B, C, D, G, H)"),
("para(A, B, C, D)", "para(C, D, E, F)", [], [],
"para(A, B, C, D, E, F)"),
# ("para(A, B, C, D, E, F, G, H)", "para(C, D, P, Q, R, S)", ["line(E, F, R, S)"], [],
# "para(A, B, C, D, E, F, G, H, P, Q)"),
# coll
("coll(A, B, C, D)", "coll(E, F, G, H)", [], [], False),
("coll(A, B, C, D)", "coll(A, D, P, Q)", [], [],
"coll(D, P, B, C, A, Q)"),
# eqangle
("eqangle(A, B, C, D, E, F, G, H)",
"eqangle(P, Q, R, S, W, X, Y, Z)", [], [], False),
# ("eqangle(A, B, C, D, E, F, G, H)", "eqangle(P, Q, R, S, W, X, Y, Z)",
# ["line(A, B, P, Q)", "line(C, D, R, S)"], [], "eqangle(A, B, C, D, E, F, G, H, W, X, Y, Z)"),
("eqangle(A, B, C, D, E, F, G, H)",
"eqangle(P, Q, R, S, W, X, Y, Z)", ["line(A, B, P, Q)"
], [], False),
("eqangle(B, E, A, C, A, F, B, C)",
"eqangle(A, C, B, E, A, F, B, C)", [], [],
"eqangle(B, E, A, C, A, F, B, C, A, C, B, E)"),
("eqangle(A, C, B, E, A, F, B, C)",
"eqangle(B, C, A, F, B, E, A, C)", [
"line(F, B, C)", "line(H, A, F)", "line(H, B, E)",
"line(G, A, B)", "line(G, C, H)"
], [], False),
("eqangle(B, E, A, C, A, F, B, C)",
"eqangle(A, C, B, E, A, F, B, C)", [
"line(F, B, C)", "line(H, A, F)", "line(H, B, E)",
"line(G, A, B)", "line(G, C, H)"
], [], "eqangle(B, E, A, C, A, F, B, C, A, C, B, E)"),
("eqangle(B, A, B, E, F, A, F, E)",
"eqangle(E, A, E, B, F, A, F, B)", [], [], False),
# circle
("circle(O, A, B, C, D)", "circle(O, B, C, D, E)", [], [],
"circle(O, A, B, C, D, E)"),
# cyclic
("cyclic(A, B, C, D)", "cyclic(B, C, D, E)", [], [],
"cyclic(A, B, C, D, E)"),
# cong
("cong(A, B, C, D)", "cong(B, A, E, F)", [], [],
"cong(A, B, C, D, E, F)"),
("cong(A, B, C, D)", "cong(P, Q, R, S)", [], [], False),
("cong(A, B, C, D, E, F)", "cong(F, E, A, B, P, Q)", [], [],
"cong(A, B, C, D, E, F, P, Q)"),
# perp
("perp(B, E, A, C)", "perp(A, C, B, E)", [], [], False),
]
for fact, goal, lines, circles, concl in test_data:
fact = parser.parse_fact(fact)
goal = parser.parse_fact(goal)
lines = [parser.parse_line(line) for line in lines]
circles = [parser.parse_circle(circle) for circle in circles]
res = expr.Prover(ruleset, lines=lines,
circles=circles).combine_facts(fact, goal)
if concl:
concl = parser.parse_fact(concl)
self.assertEqual(res, concl)
else:
self.assertEqual(res, None)
def testMatchFactLines(self):
test_data = [
("perp(l, m)", "perp(P, Q, R, S)", {}, ["line(O, P, Q)"], [{
"l": ("P", "Q"),
"m": ("R", "S")
}, {
"l": ("R", "S"),
"m": ("P", "Q")
}]),
("perp(l, m)", "perp(P, Q, R, S)", {
"l": ("Q", "P")
}, ["line(O, P, Q)"], [{
"l": ("Q", "P"),
"m": ("R", "S")
}]),
("perp(l, m)", "perp(P, Q, R, S)", {
"l": ("Q", "P")
}, [], [{
"l": ("Q", "P"),
"m": ("R", "S")
}]),
("perp(l, m)", "perp(P, Q, R, S)", {
"l": ("A", "P")
}, ["line(O, P, Q)"], []),
("para(p, q)", "para(E, N, C, D)", {}, [], [{
"p": ("E", "N"),
"q": ("C", "D")
}, {
"p": ("C", "D"),
"q": ("E", "N")
}]),
("para(A, B, C, D)", "para(P, Q, R, S)", {
'A': 'M',
'B': 'N'
}, ["line(E, F, G, H)"], []),
("cong(A, B, C, D)", "cong(P, Q, R, S)", {}, [], [
{
"A": "P",
"B": "Q",
"C": "R",
"D": "S"
},
{
"A": "P",
"B": "Q",
"C": "S",
"D": "R"
},
{
"A": "Q",
"B": "P",
"C": "R",
"D": "S"
},
{
"A": "Q",
"B": "P",
"C": "S",
"D": "R"
},
]),
("perp(B, A, C, A)", "perp(P, Q, P, R)", {}, [], [{
"A": "P",
"B": "Q",
"C": "R"
}]),
#
("cong(E, A, E, B)", "cong(A, Q, B, Q)", {
"A": "A",
"B": "B",
"D": "P"
}, [], [{
"A": "A",
"B": "B",
"D": "P",
"E": "Q"
}]),
("perp(m, n)", "perp(A, C, B, E)", {
"m": ("A", "C"),
"l": ("B", "E")
}, [], [{
"l": ("B", "E"),
"m": ("A", "C"),
"n": ("B", "E")
}]),
("eqangle(C, A, C, B, R, P, R, Q)",
"eqangle(C, F, C, E, H, F, H, E)", {}, ["line(C, F, G)"], [{
"A":
"F",
"B":
"E",
"C":
"C",
"P":
"F",
"Q":
"E",
"R":
"H"
}])
]
for pat, f, inst, lines, res in test_data:
pat = parser.parse_fact(pat)
f = parser.parse_fact(f)
lines = [parser.parse_line(line) for line in lines]
insts = expr.Prover(ruleset, lines=lines).match_expr(pat, f, inst)
insts = [p[0] for p in insts]
self.assertEqual(insts, res)
