Trait Act

pub trait Act<M: Monoid> {
    type Monoid: Monoid<Element = Self::Element>;
    type Element;

    // Required methods
    fn monoid(&self) -> &Self::Monoid;
    fn act(
        &self,
        m: &M,
        val: M::Element,
        a: Self::Element,
        n: usize,
    ) -> M::Element;

    // Provided methods
    fn act_one(&self, m: &M, val: M::Element, a: Self::Element) -> M::Element { ... }
    fn op(&self, a: Self::Element, b: Self::Element) -> Self::Element { ... }
    fn id(&self) -> Self::Element { ... }
}

モノイド作用

Required Associated Types

type Monoid: Monoid<Element = Self::Element>

作用させるモノイド

type Element

モノイドの元

Required Methods

fn monoid(&self) -> &Self::Monoid

作用させるモノイドへの参照を返す。

fn act(&self, m: &M, val: M::Element, a: Self::Element, n: usize) -> M::Element

$val$をn個の値からなる列をモノイド$(\circ, e)$で畳み込んだ値であるとしたとき、 列の各値に$a$を作用させて畳み込んだ値を求める。

畳み込んだ値が同一になるような、長さnのいかなる列に対しても、$a$を作用させて畳み込んだ値はすべて同一でなければならない。

Provided Methods

fn act_one(&self, m: &M, val: M::Element, a: Self::Element) -> M::Element

self.act(m, val, a, 1)

fn op(&self, a: Self::Element, b: Self::Element) -> Self::Element

二項演算

fn id(&self) -> Self::Element

単位元

Implementors

impl<M, A> Act<M> for AddSum<A>

where M: Monoid + Additive, A: Monoid + Additive, M::Element: TryFrom<A::Element, Error: Debug>,

type Monoid = A

type Element = <A as Set>::Element

impl<S> Act<S> for MulProd<S>

where S: Monoid + Multiplicative, S::Element: Clone,

type Monoid = S

type Element = <S as Set>::Element

impl<T> Act<Max<T>> for ChmaxMax<T>

where Max<T>: Monoid<Element = T>,

type Monoid = Max<T>

type Element = T

impl<T> Act<Min<T>> for ChminMin<T>

where Min<T>: Monoid<Element = T>,

type Monoid = Min<T>

type Element = T

impl<T, M> Act<M> for UpdateFold<T>

where M: Monoid<Element = T>, M::Element: Clone,

type Monoid = Last<T>

type Element = Option<T>

impl<T, M> Act<M> for UpdateSum<T>

where M: Monoid<Element = T> + Additive,

type Monoid = Last<T>

type Element = Option<T>

impl<T, M, S> Act<M> for MulSum<S>

where M: Monoid<Element = T> + Additive, S: Monoid<Element = T> + Multiplicative,

type Monoid = S

type Element = <S as Set>::Element

impl<T, S, M> Act<M> for AffineSum<S>

where M: Monoid<Element = T> + Additive, S: Semiring<Element = T>, Dual<Composition<S>>: Monoid<Element = Linear<T>>,

type Monoid = Dual<Composition<S>>

type Element = Linear<T>

impl<T, U, A> Act<MinCount<T, U>> for AddMinCount<A>

where A: Monoid<Element = T> + Additive, MinCount<T, U>: Monoid<Element = (Option<T>, U)>,

type Monoid = A

type Element = <A as Set>::Element