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from typing import Any, TypeVar
import act4e_interfaces as I
from act4e_interfaces import FiniteRelation
from .relations_representation import MyFiniteRelation
E1 = TypeVar("E1")
E2 = TypeVar("E2")
E3 = TypeVar("E3")
E = TypeVar("E")
A = TypeVar("A")
B = TypeVar("B")
class SolFiniteRelationProperties(I.FiniteRelationProperties):
def is_surjective(self, fr: I.FiniteRelation[Any, Any]) -> bool:
# for all y in B there is an x in A s.t. x R y
# converse: there is a y in B s.t. for all x in A there is no x R y
for y in fr.target().elements():
there_is_one = any([fr.holds(x, y) for x in fr.source().elements()])
if not there_is_one:
return False
return True
def is_defined_everywhere(self, fr: I.FiniteRelation[Any, Any]) -> bool:
# for all x in A there is a y in B s.t. x R y
# converse: there is an x in A s.t. for all y in B there is no x R y
for x in fr.source().elements():
there_is_one = any([fr.holds(x, y) for y in fr.target().elements()])
if not there_is_one:
return False
return True
def is_injective(self, fr: I.FiniteRelation[Any, Any]) -> bool:
# x R y and z R y implies z = x
# converse: there is a z neq y such that x R y and z R y
image = []
for y in fr.target().elements():
for x in fr.source().elements():
if fr.holds(x, y):
if y in image:
return False
image.append(y)
return True
def is_single_valued(self, fr: I.FiniteRelation[Any, Any]) -> bool:
# x R y and x R u imply y = u
# converse: there is an y neq u such that x R y and x R u
domain = []
for x in fr.source().elements():
for y in fr.target().elements():
if fr.holds(x, y):
if x in domain:
return False
domain.append(x)
return True
class SolFiniteRelationOperations(I.FiniteRelationOperations):
def transpose(self, fr: I.FiniteRelation[A, B]) -> I.FiniteRelation[B, A]:
# reverses the arrows in the relation
values = []
for a in fr.source().elements():
for b in fr.target().elements():
if fr.holds(a, b):
values.append([b, a])
return MyFiniteRelation(fr.target(), fr.source(), values)
def as_relation(self, f: I.FiniteMap[A, B]) -> I.FiniteRelation[A, B]:
values = []
for a in f.source().elements():
values.append([a, f(a)])
return MyFiniteRelation(f.source(), f.target(), values)
class SolFiniteEndorelationProperties(I.FiniteEndorelationProperties):
def is_reflexive(self, fr: I.FiniteRelation[Any, Any]) -> bool:
raise NotImplementedError()
def is_irreflexive(self, fr: I.FiniteRelation[Any, Any]) -> bool:
raise NotImplementedError()
def is_transitive(self, fr: I.FiniteRelation[Any, Any]) -> bool:
raise NotImplementedError()
def is_symmetric(self, fr: I.FiniteRelation[Any, Any]) -> bool:
raise NotImplementedError()
def is_antisymmetric(self, fr: I.FiniteRelation[Any, Any]) -> bool:
raise NotImplementedError()
def is_asymmetric(self, fr: I.FiniteRelation[Any, Any]) -> bool:
raise NotImplementedError()
class SolFiniteEndorelationOperations(I.FiniteEndorelationOperations):
def transitive_closure(self, fr: I.FiniteRelation[E, E]) -> I.FiniteRelation[E, E]:
raise NotImplementedError()
class SolFiniteRelationCompose(I.FiniteRelationCompose):
def compose(self, fr1: FiniteRelation[E1, E2], fr2: FiniteRelation[E2, E3]) -> I.FiniteRelation[E1, E3]:
values = []
# Yeah O(n^3), i really should do this better
for a in fr1.source().elements():
for b in fr1.target().elements():
for c in fr2.target().elements():
if fr1.holds(a, b) and fr2.holds(b, c):
values.append([a, c])
return MyFiniteRelation(fr1.source(), fr2.target(), values)
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