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//! # Natural Numbers //! //! `natural_numbers` provides natural numbers and operations on them, based on the successor operation. /// Trait for types implementing natural numbers. pub trait Nat where Self: Sized + Clone, { /// Converts a value of type Nat into the corresponding value of type u32. /// # Examples /// ``` /// use natural_numbers::{Nat,U32Nat}; /// /// let zero = U32Nat::zero(); /// assert_eq!(zero.value(), 0); /// ``` fn value(&self) -> u32; /// Converts a value of type u32 into the corresponding value of type Nat. /// # Examples /// ``` /// use natural_numbers::{Nat,U32Nat}; /// /// assert_eq!(U32Nat::wrap(0), U32Nat::zero()); /// ``` fn wrap(n: u32) -> Self; fn zero() -> Self; fn is_zero(&self) -> bool; /// The successor of a value. /// # Examples /// ``` /// use natural_numbers::{Nat,U32Nat}; /// /// assert_eq!(U32Nat::wrap(1), U32Nat::zero().succ()); /// ``` fn succ(&self) -> Self; /// The value of which this is a successor, or None if the value is zero. /// # Examples /// ``` /// use natural_numbers::{Nat,U32Nat}; /// /// let one = U32Nat::zero().succ(); /// assert_eq!(one.pred().unwrap(), U32Nat::zero()); /// ``` fn pred(&self) -> Option<Self> { match self.value() { 0 => None, n => Some(Self::wrap(n - 1)), } } /// The sum of two values. /// # Examples /// ``` /// use natural_numbers::{Nat,U32Nat}; /// /// let two = U32Nat::wrap(2); /// let three = U32Nat::wrap(3); /// let five = U32Nat::wrap(5); /// assert_eq!(two.add(&three), five); fn add(&self, n: &Self) -> Self { match n.pred() { None => self.clone(), Some(m) => self.add(&m).succ(), } } } #[derive(Debug, PartialEq, Eq, Clone)] pub struct U32Nat(u32); // impl Ord for U32Nat { // fn cmp(&self, other: &Self) -> Ordering { // match other.pred() { // None => match self.pred() { // None => Ordering::Equal, // Some(_) => Ordering::Greater, // }, // Some(n) => match self.pred() { // None => Ordering::Less, // Some(m) => m.cmp(&n), // }, // } // } // } impl Nat for U32Nat { fn value(&self) -> u32 { self.0 } fn wrap(n: u32) -> Self { U32Nat(n) } fn zero() -> Self { U32Nat(0) } fn is_zero(&self) -> bool { self.0 == 0 } fn succ(&self) -> Self { U32Nat(self.0 + 1) } }