Lattice

Bases: Lattice[BoundedLatticeType]

              flowchart TD
              kirin.lattice.abc.BoundedLattice[BoundedLattice]
              kirin.lattice.abc.Lattice[Lattice]

                              kirin.lattice.abc.Lattice --> kirin.lattice.abc.BoundedLattice
                


              click kirin.lattice.abc.BoundedLattice href "" "kirin.lattice.abc.BoundedLattice"
              click kirin.lattice.abc.Lattice href "" "kirin.lattice.abc.Lattice"
            

ABC for bounded lattices as Python class.

BoundedLattice is an abstract class that can be inherited from. It requires the implementation of the bottom and top methods.

Bases: ABC, Generic[LatticeType]

              flowchart TD
              kirin.lattice.abc.Lattice[Lattice]

              

              click kirin.lattice.abc.Lattice href "" "kirin.lattice.abc.Lattice"
            

ABC for lattices as Python class.

While Lattice is only an interface, LatticeABC is an abstract class that can be inherited from. This provides a few default implementations for the lattice operations.

is_structurally_equal(
    other: LatticeType, context: dict | None = None
) -> bool

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def is_structurally_equal(
    self, other: LatticeType, context: dict | None = None
) -> bool:
    """Check if two lattices are equal."""
    if self is other:
        return True
    else:
        return self.is_subseteq(other) and other.is_subseteq(self)

is_subseteq(other: LatticeType) -> bool

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@abstractmethod
def is_subseteq(self, other: LatticeType) -> bool:
    """Subseteq operation."""
    ...

join(other: LatticeType) -> LatticeType

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@abstractmethod
def join(self, other: LatticeType) -> LatticeType:
    """Join operation."""
    ...

meet(other: LatticeType) -> LatticeType

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@abstractmethod
def meet(self, other: LatticeType) -> LatticeType:
    """Meet operation."""
    ...

Bases: LatticeMeta

              flowchart TD
              kirin.lattice.abc.SingletonMeta[SingletonMeta]
              kirin.lattice.abc.LatticeMeta[LatticeMeta]

                              kirin.lattice.abc.LatticeMeta --> kirin.lattice.abc.SingletonMeta
                


              click kirin.lattice.abc.SingletonMeta href "" "kirin.lattice.abc.SingletonMeta"
              click kirin.lattice.abc.LatticeMeta href "" "kirin.lattice.abc.LatticeMeta"
            

Singleton metaclass for lattices. It ensures that only one instance of a lattice is created.

See https://stackoverflow.com/questions/674304/why-is-init-always-called-after-new/8665179#8665179

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def __init__(cls, name, bases, attrs):
    super().__init__(name, bases, attrs)
    cls._instance = None

Bases: LatticeMeta

              flowchart TD
              kirin.lattice.abc.UnionMeta[UnionMeta]
              kirin.lattice.abc.LatticeMeta[LatticeMeta]

                              kirin.lattice.abc.LatticeMeta --> kirin.lattice.abc.UnionMeta
                


              click kirin.lattice.abc.UnionMeta href "" "kirin.lattice.abc.UnionMeta"
              click kirin.lattice.abc.LatticeMeta href "" "kirin.lattice.abc.LatticeMeta"
            

Meta class for union types. It simplifies the union if possible.

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def __init__(self, name, bases, attrs):
    super().__init__(name, bases, attrs)
    if not issubclass(base := bases[0], BoundedLattice):
        raise TypeError(f"Union must inherit from Lattice, got {bases[0]}")
    self._bottom = base.bottom()