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