Struct Ordinal 

pub struct Ordinal { /* private fields */ }

An ordinal below ε₀. See the module documentation.

Implementations

impl Ordinal

pub fn zero() -> Ordinal

pub fn one() -> Ordinal

pub fn from_u64(n: u64) -> Ordinal

pub fn from_natural(n: BigInt) -> Ordinal

The finite ordinal n. Panics on a negative n.

pub fn omega() -> Ordinal

pub fn omega_pow(e: Ordinal) -> Ordinal

ω^e.

pub fn is_zero(&self) -> bool

pub fn is_finite(&self) -> bool

pub fn to_natural(&self) -> Option<BigInt>

pub fn successor(&self) -> Ordinal

α + 1.

pub fn is_successor(&self) -> bool

Ends in a finite term: α = β + 1 for some β.

pub fn is_limit(&self) -> bool

Nonzero and not a successor: the supremum of everything below it.

pub fn predecessor(&self) -> Option<Ordinal>

β with β + 1 = self, for a successor.

pub fn add(&self, o: &Ordinal) -> Ordinal

pub fn mul(&self, o: &Ordinal) -> Ordinal

pub fn pow(&self, e: &Ordinal) -> Ordinal

self^e (with 0^0 = 1).

Trait Implementations

impl Clone for Ordinal

fn clone(&self) -> Ordinal

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Ordinal

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for Ordinal

fn fmt(&self, f: &mut Formatter<'_>) -> Result

ω^2·3 + ω + 5, ω^(ω + 1), ω^ω^ω: an exponent is parenthesised unless it is a natural or a single bare power of ω.

impl ExactCodec for Ordinal

fn write(&self, out: &mut Vec<u8>)

The Cantor normal form: the number of terms, then each exponent (recursively) and its coefficient.

fn read(buf: &[u8], pos: &mut usize) -> Option<Self>

fn to_bytes(&self) -> Vec<u8>

fn from_bytes(buf: &[u8]) -> Option<Self>

The value buf canonically encodes, with nothing left over.

impl Hash for Ordinal

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Ord for Ordinal

fn cmp(&self, o: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for Ordinal

fn eq(&self, other: &Ordinal) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for Ordinal

fn partial_cmp(&self, o: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Eq for Ordinal

impl StructuralPartialEq for Ordinal