/// A type-level boolean suitable to select conditional trait implementations.
/// Implementors are [True] and [False]
pub trait TLBool {}
/// [TLBool] value of `true`. The opposite is [False]
pub struct TLTrue;
impl TLBool for TLTrue {}
/// [TLBool] value of `false`. The opposite is [True]
pub struct TLFalse;
impl TLBool for TLFalse {}

/// A type that implements [Hierarchy]. Used to select implementations of traits
/// on the hierarchy
pub trait InHierarchy: Clone {
	/// Indicates that this hierarchy element is a leaf. Leaves can never have
	/// children
	type IsLeaf: TLBool;
	/// Indicates that this hierarchy element is a root. Roots can never have
	/// parents
	type IsRoot: TLBool;
}
/// A type that derives from a parent type.
pub trait Extends: InHierarchy<IsRoot = TLFalse> + Into<Self::Parent> {
	/// Specify the immediate parent of this type. This guides the
	type Parent: InHierarchy<IsLeaf = TLFalse>
		+ TryInto<Self>
		+ UnderRootImpl<<Self::Parent as InHierarchy>::IsRoot>;
}

pub trait UnderRootImpl<IsRoot: TLBool>: Sized {
	type __Root: UnderRoot<IsRoot = TLTrue, Root = Self::__Root>;
	fn __into_root(self) -> Self::__Root;
	fn __try_from_root(root: Self::__Root) -> Result<Self, Self::__Root>;
}

pub trait UnderRoot: InHierarchy {
	type Root: UnderRoot<IsRoot = TLTrue, Root = Self::Root>;
	fn into_root(self) -> Self::Root;
	fn try_from_root(root: Self::Root) -> Result<Self, Self::Root>;
}

impl<T: InHierarchy + UnderRootImpl<T::IsRoot>> UnderRoot for T {
	type Root = <Self as UnderRootImpl<<Self as InHierarchy>::IsRoot>>::__Root;
	fn into_root(self) -> Self::Root { self.__into_root() }
	fn try_from_root(root: Self::Root) -> Result<Self, Self::Root> { Self::__try_from_root(root) }
}

impl<T: InHierarchy<IsRoot = TLTrue>> UnderRootImpl<TLTrue> for T {
	type __Root = Self;
	fn __into_root(self) -> Self::__Root { self }
	fn __try_from_root(root: Self::__Root) -> Result<Self, Self::__Root> { Ok(root) }
}

impl<T: InHierarchy<IsRoot = TLFalse> + Extends> UnderRootImpl<TLFalse> for T {
	type __Root = <<Self as Extends>::Parent as UnderRootImpl<
		<<Self as Extends>::Parent as InHierarchy>::IsRoot,
	>>::__Root;
	fn __into_root(self) -> Self::__Root {
		<Self as Into<<Self as Extends>::Parent>>::into(self).into_root()
	}
	fn __try_from_root(root: Self::__Root) -> Result<Self, Self::__Root> {
		let parent = <Self as Extends>::Parent::try_from_root(root)?;
		parent.clone().try_into().map_err(|_| parent.into_root())
	}
}