Trait zfc::Set

pub trait Set {
    type Elem: Eq + ?Sized;

    // Required methods
    fn bounded_cardinality(&self) -> BoundedCardinality;
    fn contains<Q>(&self, elem: &Q) -> bool
       where Q: Borrow<Self::Elem> + Eq + ?Sized;
    fn is_proper_subset(&self, val: &Self) -> bool;
    fn is_subset(&self, val: &Self) -> bool;

    // Provided methods
    fn cardinality(&self) -> Option<Cardinality> { ... }
    fn is_proper_superset(&self, val: &Self) -> bool { ... }
    fn is_superset(&self, val: &Self) -> bool { ... }
    fn is_proper_subset_iter<T>(&self, val: &T) -> bool
       where Self::Elem: Borrow<T::Elem> + PartialEq<T::Elem>,
             for<'a> &'a Self: IntoIterator<Item = &'a Self::Elem>,
             T: Set + ?Sized,
             T::Elem: PartialEq<Self::Elem> { ... }
    fn is_subset_iter<T>(&self, val: &T) -> bool
       where Self::Elem: Borrow<T::Elem> + PartialEq<T::Elem>,
             for<'a> &'a Self: IntoIterator<Item = &'a Self::Elem>,
             T: Set + ?Sized,
             T::Elem: PartialEq<Self::Elem> { ... }
    fn is_proper_superset_iter<T>(&self, val: &T) -> bool
       where Self::Elem: PartialEq<T::Elem>,
             T: Set + ?Sized,
             for<'a> &'a T: IntoIterator<Item = &'a T::Elem>,
             T::Elem: Borrow<Self::Elem> + PartialEq<Self::Elem> { ... }
    fn is_superset_iter<T>(&self, val: &T) -> bool
       where Self::Elem: PartialEq<T::Elem>,
             T: Set + ?Sized,
             for<'a> &'a T: IntoIterator<Item = &'a T::Elem>,
             T::Elem: Borrow<Self::Elem> + PartialEq<Self::Elem> { ... }
}

Represents a set according to Zermelo–Fraenkel set theory with the axiom of choice (ZFC). Note that elements in a Set must not be distinguishable by order or frequency, so care must be taken in its implementation if the implementing type exposes an API that distinguishes between the order or frequency of Elem (e.g., Vec<T> where Elem = T).

Required Associated Types

type Elem: Eq + ?Sized

The elements that make up the set. Per ZFC, this must not be the same type as Self nor a recursive type based on Self.

Required Methods

fn bounded_cardinality(&self) -> BoundedCardinality

Returns the bounded cardinality of self.

fn contains<Q>(&self, elem: &Q) -> bool

where Q: Borrow<Self::Elem> + Eq + ?Sized,

Returns true iff Self contains elem.

fn is_proper_subset(&self, val: &Self) -> bool

Must conform to the following properties:

• Irreflexivity.
• Antisymmetry.
• Transitivity.
• ∀a, b: Self, a.is_proper_subset(b)⇒ ∀e: Elem | a.contains(e), b.contains(e) ∧ ∃f: Elem, b.contains(f) && !a.contains(f).
• ∀a, b: Self, a.is_proper_subset(b) ⇒ a.is_subset(b).
• ∀a, b: Self, a.is_proper_subset(b) ⇔ b.is_proper_superset(a).

fn is_subset(&self, val: &Self) -> bool

Must conform to the following properties:

• Reflexivity.
• Antisymmetry.
• Transitivity.
• ∀a, b: Self, a.is_subset(b)⇒ ∀e: Elem | a.contains(e), b.contains(e).
• ∀a, b: Self, a.is_subset(b) ⇔ b.is_superset(a).

Provided Methods

fn cardinality(&self) -> Option<Cardinality>

Returns the cardinality of self if it is known exactly.

The following property must be true:

• self.cardinality().unwrap() == self.bounded_cardinality().lower() ⇔ self.bounded_cardinality().lower() == self.bounded_cardinality().upper().

fn is_proper_superset(&self, val: &Self) -> bool

Must conform to the following properties:

• Irreflexivity.
• Antisymmetry.
• Transitivity.
• ∀a, b: Self, a.is_proper_superset(b) ⇒ a.is_superset(b).

fn is_superset(&self, val: &Self) -> bool

Must conform to the following properties:

• Reflexivity.
• Antisymmetry.
• Transitivity.

fn is_proper_subset_iter<T>(&self, val: &T) -> bool

where Self::Elem: Borrow<T::Elem> + PartialEq<T::Elem>, for<'a> &'a Self: IntoIterator<Item = &'a Self::Elem>, T: Set + ?Sized, T::Elem: PartialEq<Self::Elem>,

Read Set::is_proper_subset.

fn is_subset_iter<T>(&self, val: &T) -> bool

where Self::Elem: Borrow<T::Elem> + PartialEq<T::Elem>, for<'a> &'a Self: IntoIterator<Item = &'a Self::Elem>, T: Set + ?Sized, T::Elem: PartialEq<Self::Elem>,

Read Set::is_subset.

fn is_proper_superset_iter<T>(&self, val: &T) -> bool

where Self::Elem: PartialEq<T::Elem>, T: Set + ?Sized, for<'a> &'a T: IntoIterator<Item = &'a T::Elem>, T::Elem: Borrow<Self::Elem> + PartialEq<Self::Elem>,

Read Set::is_proper_superset.

fn is_superset_iter<T>(&self, val: &T) -> bool

where Self::Elem: PartialEq<T::Elem>, T: Set + ?Sized, for<'a> &'a T: IntoIterator<Item = &'a T::Elem>, T::Elem: Borrow<Self::Elem> + PartialEq<Self::Elem>,

Read Set::is_superset.

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl<T> Set for BTreeSet<T>

where T: Ord,

type Elem = T

fn cardinality(&self) -> Option<Cardinality>

fn bounded_cardinality(&self) -> BoundedCardinality

fn contains<Q>(&self, elem: &Q) -> bool

where Q: Borrow<Self::Elem> + Eq + ?Sized,

fn is_proper_subset(&self, val: &Self) -> bool

fn is_subset(&self, val: &Self) -> bool

impl<T> Set for Range<T>

where T: Ord, for<'a, 'b> &'a T: Sub<&'b T>, for<'a, 'b> <&'a T as Sub<&'b T>>::Output: Into<BigUint>,

type Elem = T

fn cardinality(&self) -> Option<Cardinality>

fn bounded_cardinality(&self) -> BoundedCardinality

fn contains<Q>(&self, elem: &Q) -> bool

where Q: Borrow<Self::Elem> + Eq + ?Sized,

fn is_proper_subset(&self, val: &Self) -> bool

fn is_subset(&self, val: &Self) -> bool

impl<T> Set for RangeInclusive<T>

where T: Ord, for<'a, 'b> &'a T: Sub<&'b T>, for<'a, 'b> <&'a T as Sub<&'b T>>::Output: Into<BigUint>,

type Elem = T

fn cardinality(&self) -> Option<Cardinality>

fn bounded_cardinality(&self) -> BoundedCardinality

fn contains<Q>(&self, elem: &Q) -> bool

where Q: Borrow<Self::Elem> + Eq + ?Sized,

fn is_proper_subset(&self, val: &Self) -> bool

fn is_subset(&self, val: &Self) -> bool

impl<T, S> Set for HashSet<T, S>

where T: Eq + Hash, S: BuildHasher,

Available on crate feature std only.

type Elem = T

fn cardinality(&self) -> Option<Cardinality>

fn bounded_cardinality(&self) -> BoundedCardinality

fn contains<Q>(&self, elem: &Q) -> bool

where Q: Borrow<Self::Elem> + Eq + ?Sized,

fn is_proper_subset(&self, val: &Self) -> bool

fn is_subset(&self, val: &Self) -> bool

Implementors