quoracle/quorums/quorums.py
2021-01-20 16:12:26 -08:00

127 lines
3.1 KiB
Python

from typing import Iterator, Generic, List, Set, TypeVar
import itertools
T = TypeVar('T')
class Expr(Generic[T]):
def quorums(self) -> Iterator[Set[T]]:
raise NotImplementedError
def is_quorum(self, xs: Set[T]) -> bool:
raise NotImplementedError
def dual(self) -> 'Expr[T]':
raise NotImplementedError
def __add__(self, rhs: 'Expr[T]') -> 'Expr[T]':
return _or(self, rhs)
def __mul__(self, rhs: 'Expr[T]') -> 'Expr[T]':
return _and(self, rhs)
def _and(lhs: Expr[T], rhs: Expr[T]) -> Expr[T]:
if isinstance(lhs, And) and isinstance(rhs, And):
return And(lhs.es + rhs.es)
elif isinstance(lhs, And):
return And(lhs.es + [rhs])
elif isinstance(rhs, And):
return And([lhs] + rhs.es)
else:
return And([lhs, rhs])
def _or(lhs: Expr[T], rhs: Expr[T]) -> Expr[T]:
if isinstance(lhs, Or) and isinstance(rhs, Or):
return Or(lhs.es + rhs.es)
elif isinstance(lhs, Or):
return Or(lhs.es + [rhs])
elif isinstance(rhs, Or):
return Or([lhs] + rhs.es)
else:
return Or([lhs, rhs])
class Node(Expr[T]):
def __init__(self, x: T) -> None:
self.x = x
def __str__(self) -> str:
return str(self.x)
def __repr__(self) -> str:
return f'Node({self.x})'
def quorums(self) -> Iterator[Set[T]]:
yield {self.x}
def is_quorum(self, xs: Set[T]) -> bool:
return self.x in xs
def dual(self) -> Expr:
return self
class Or(Expr[T]):
def __init__(self, es: List[Expr[T]]) -> None:
if len(es) == 0:
raise ValueError(f'Or cannot be constructed with an empty list')
self.es = es
def __str__(self) -> str:
return '(' + ' + '.join(str(e) for e in self.es) + ')'
def __repr__(self) -> str:
return f'Or({self.es})'
def quorums(self) -> Iterator[Set[T]]:
for e in self.es:
yield from e.quorums()
def is_quorum(self, xs: Set[T]) -> bool:
return any(e.is_quorum(xs) for e in self.es)
def dual(self) -> Expr:
return And([e.dual() for e in self.es])
class And(Expr[T]):
def __init__(self, es: List[Expr[T]]) -> None:
if len(es) == 0:
raise ValueError(f'And cannot be constructed with an empty list')
self.es = es
def __str__(self) -> str:
return '(' + ' * '.join(str(e) for e in self.es) + ')'
def __repr__(self) -> str:
return f'And({self.es})'
def quorums(self) -> Iterator[Set[T]]:
for subquorums in itertools.product(*[e.quorums() for e in self.es]):
yield set.union(*subquorums)
def is_quorum(self, xs: Set[T]) -> bool:
return all(e.is_quorum(xs) for e in self.es)
def dual(self) -> Expr:
return Or([e.dual() for e in self.es])
class QuorumSystem:
def __init__(self, reads, writes) -> None:
pass
a = Node('a')
b = Node('b')
c = Node('c')
disjunction = a + b + c
conjunction = disjunction * disjunction * disjunction
print(conjunction)
print(conjunction.dual())
print(conjunction.dual().dual())