Struct prop::True

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pub struct True;

Expand description

Logical true.

Trait Implementations

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impl Clone for True

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fn clone(&self) -> True

Returns a copy of the value. Read more

1.0.0 · source

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

Performs copy-assignment from source. Read more

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impl Decidable for True

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fn decide() -> ExcM<True>

Get excluded middle rule.

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impl<N: Nat> DecidableHomotopyLevel<N> for True

type H0 = True

A type such that it proves homotopy level 0.

type H = True

A type such that it proves a lower homotopy level.

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fn h0<Y: LProp>(_ty_y: Ty<Y, Self>) -> Q<Self::H0, Y> where
(N, Z ): EqNat,

Homotopy level 0.

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fn hn<X: LProp, Y: LProp>(
 _ty_x: Ty<X, Self>,
 _ty_y: Ty<Y, Self>
) -> Q<Self::H, Q<X, Y>> where
 Z: Lt<N>,

Higher homotopy level.

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impl Copy for True

Auto Trait Implementations

impl RefUnwindSafe for True

impl Send for True

impl Sync for True

impl Unpin for True

impl UnwindSafe for True

Blanket Implementations

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impl<T> Any for T where
T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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impl<T> Avatar<Inv<T>> for T

type Out = Inv<T>

The output avatar.

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fn inv(self) -> Inv<T>

Involve the avatar.

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impl<T> Borrow<T> for T where
T: ?Sized,

const: unstable · source

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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impl<T> BorrowMut<T> for T where
T: ?Sized,

const: unstable · source

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more

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impl<T> Existential for T where
T: Decidable,

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fn e(
) -> Either<Rc<dyn Fn(Rc<dyn Fn(T) + 'static>) + 'static>, Rc<dyn Fn(T) + 'static>>

Get existential rule.

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impl<T> From<T> for T

const: unstable · source

fn from(t: T) -> T

Returns the argument unchanged.

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impl<N, T> HomotopyLevel<N> for T where
N: Nat,
T: DecidableHomotopyLevel<N>,

type H0 = <T as DecidableHomotopyLevel<N>>::H0

A type such that it proves homotopy level 0.

type H = <T as DecidableHomotopyLevel<N>>::H

A type such that it proves a lower homotopy level.

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fn h0<Y>(
 ty_y: (Rc<dyn Fn(Y) + 'static>, POrdProof<Y, T>)
) -> Q<<T as HomotopyLevel<N>>::H0, Y> where
 Y: LProp,
 (N, Z ): EqNat,

Homotopy level 0.

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fn hn<X, Y>(
 ty_x: (Rc<dyn Fn(X) + 'static>, POrdProof<X, T>),
 ty_y: (Rc<dyn Fn(Y) + 'static>, POrdProof<Y, T>)
) -> Q<<T as HomotopyLevel<N>>::H, Q<X, Y>> where
 X: LProp,
 Y: LProp,
 Z: Lt<N>,

Higher homotopy level.

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impl<T, U> Into for T where
U: From<T>,

const: unstable · source

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> Prop for T where
T: 'static + Clone,

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fn double_neg(self) -> Dneg<Self>

Get double negation rule from proof.

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fn map_any<T>(self) -> Imply<T, Self>

Maps anything into itself.

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impl<T> ToOwned for T where
T: Clone,

type Owned = T

The resulting type after obtaining ownership.

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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

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fn clone_into(&self, target: &mut T)

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

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impl<T, U> TryFrom for T where
U: Into<T>,

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

fn try_from(value: U) -> Result<T, <T as TryFrom>::Error>

Performs the conversion.

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impl<T, U> TryInto for T where
U: TryFrom<T>,

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

fn try_into(self) -> Result<U, >::Error>

Performs the conversion.

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Struct prop::True

Trait Implementations

impl Clone for True

fn clone(&self) -> True

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

impl Decidable for True

fn decide() -> ExcM<True>

impl<N: Nat> DecidableHomotopyLevel<N> for True

type H0 = True

type H = True

fn h0<Y: LProp>(_ty_y: Ty<Y, Self>) -> Q<Self::H0, Y> where (N, Z): EqNat,

fn hn<X: LProp, Y: LProp>( _ty_x: Ty<X, Self>, _ty_y: Ty<Y, Self>) -> Q<Self::H, Q<X, Y>> where Z: Lt<N>,

impl Copy for True

Auto Trait Implementations

impl RefUnwindSafe for True

impl Send for True

impl Sync for True

impl Unpin for True

impl UnwindSafe for True

Blanket Implementations

impl<T> Any for T where T: 'static + ?Sized,

fn type_id(&self) -> TypeId

impl<T> Avatar<Inv<T>> for T

type Out = Inv<T>

fn inv(self) -> Inv<T>

impl<T> Borrow<T> for T where T: ?Sized,

fn borrow(&self) -> &T

impl<T> BorrowMut<T> for T where T: ?Sized,

fn borrow_mut(&mut self) -> &mut T

impl<T> Existential for T where T: Decidable,

fn e() -> Either<Rc<dyn Fn(Rc<dyn Fn(T) + 'static>) + 'static>, Rc<dyn Fn(T) + 'static>>

impl<T> From<T> for T

fn from(t: T) -> T

impl<N, T> HomotopyLevel<N> for T where N: Nat, T: DecidableHomotopyLevel<N>,

type H0 = <T as DecidableHomotopyLevel<N>>::H0

type H = <T as DecidableHomotopyLevel<N>>::H

fn h0<Y>( ty_y: (Rc<dyn Fn(Y) + 'static>, POrdProof<Y, T>)) -> Q<<T as HomotopyLevel<N>>::H0, Y> where Y: LProp, (N, Z): EqNat,

fn hn<X, Y>( ty_x: (Rc<dyn Fn(X) + 'static>, POrdProof<X, T>), ty_y: (Rc<dyn Fn(Y) + 'static>, POrdProof<Y, T>)) -> Q<<T as HomotopyLevel<N>>::H, Q<X, Y>> where X: LProp, Y: LProp, Z: Lt<N>,

impl<T, U> Into<U> for T where U: From<T>,

fn into(self) -> U

impl<T> Prop for T where T: 'static + Clone,

fn double_neg(self) -> Dneg<Self>

fn map_any<T>(self) -> Imply<T, Self>

impl<T> ToOwned for T where T: Clone,

type Owned = T

fn to_owned(&self) -> T

fn clone_into(&self, target: &mut T)

impl<T, U> TryFrom<U> for T where U: Into<T>,

type Error = Infallible

fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

impl<T, U> TryInto<U> for T where U: TryFrom<T>,

type Error = <U as TryFrom<T>>::Error

fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

impl<T> DProp for T where T: Decidable,

impl<T> EProp for T where T: Existential,

impl<N, T> HProp<N> for T where N: Nat, T: HomotopyLevel<N>,

impl<T, U> Lt<S<U>> for T where T: Lt<U>,

impl<U, T> NonUniform<U> for T where T: Avatar<U, Out = U>,

fn h0<Y: LProp>(_ty_y: Ty<Y, Self>) -> Q<Self::H0, Y> where
(N, Z ): EqNat,

fn hn<X: LProp, Y: LProp>(
_ty_x: Ty<X, Self>,
_ty_y: Ty<Y, Self>
) -> Q<Self::H, Q<X, Y>> where
Z: Lt<N>,

impl<T> Any for T where
T: 'static + ?Sized,

impl<T> Borrow<T> for T where
T: ?Sized,

impl<T> BorrowMut<T> for T where
T: ?Sized,

impl<T> Existential for T where
T: Decidable,

fn e(
) -> Either<Rc<dyn Fn(Rc<dyn Fn(T) + 'static>) + 'static>, Rc<dyn Fn(T) + 'static>>

impl<N, T> HomotopyLevel<N> for T where
N: Nat,
T: DecidableHomotopyLevel<N>,

fn h0<Y>(
ty_y: (Rc<dyn Fn(Y) + 'static>, POrdProof<Y, T>)
) -> Q<<T as HomotopyLevel<N>>::H0, Y> where
Y: LProp,
(N, Z ): EqNat,

fn hn<X, Y>(
ty_x: (Rc<dyn Fn(X) + 'static>, POrdProof<X, T>),
ty_y: (Rc<dyn Fn(Y) + 'static>, POrdProof<Y, T>)
) -> Q<<T as HomotopyLevel<N>>::H, Q<X, Y>> where
X: LProp,
Y: LProp,
Z: Lt<N>,

impl<T, U> Into<U> for T where
U: From<T>,

impl<T> Prop for T where
T: 'static + Clone,

impl<T> ToOwned for T where
T: Clone,

impl<T, U> TryFrom<U> for T where
U: Into<T>,

impl<T, U> TryInto<U> for T where
U: TryFrom<T>,

impl<T> DProp for T where
T: Decidable,

impl<T> EProp for T where
T: Existential,

impl<N, T> HProp<N> for T where
N: Nat,
T: HomotopyLevel<N>,

impl<T, U> Lt<S<U>> for T where
T: Lt<U>,

impl<U, T> NonUniform<U> for T where
T: Avatar<U, Out = U>,