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Rollup merge of #85637 - RalfJung:partial-ord, r=m-ou-se

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document PartialEq, PartialOrd, Ord requirements more explicitly

This is the result of discussion in https://github.com/rust-lang/rust/issues/50230, in particular [this summary comment](https://github.com/rust-lang/rust/issues/50230#issuecomment-392819364).

Fixes https://github.com/rust-lang/rust/issues/50230.
This commit is contained in:
Yuki Okushi 2021-06-21 09:42:13 +09:00 committed by GitHub
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library/core/src/cmp.rs
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@ -27,12 +27,25 @@ use self::Ordering::*;
/// Trait for equality comparisons which are [partial equivalence
/// relations](https://en.wikipedia.org/wiki/Partial_equivalence_relation).
///
/// `x.eq(y)` can also be written `x == y`, and `x.ne(y)` can be written `x != y`.
/// We use the easier-to-read infix notation in the remainder of this documentation.
///
/// This trait allows for partial equality, for types that do not have a full
/// equivalence relation. For example, in floating point numbers `NaN != NaN`,
/// so floating point types implement `PartialEq` but not [`trait@Eq`].
///
/// Formally, the equality must be (for all `a`, `b`, `c` of type `A`, `B`,
/// `C`):
/// Implementations must ensure that `eq` and `ne` are consistent with each other:
///
/// - `a != b` if and only if `!(a == b)`
/// (ensured by the default implementation).
///
/// If [`PartialOrd`] or [`Ord`] are also implemented for `Self` and `Rhs`, their methods must also
/// be consistent with `PartialEq` (see the documentation of those traits for the exact
/// requirememts). It's easy to accidentally make them disagree by deriving some of the traits and
/// manually implementing others.
///
/// The equality relation `==` must satisfy the following conditions
/// (for all `a`, `b`, `c` of type `A`, `B`, `C`):
///
/// - **Symmetric**: if `A: PartialEq<B>` and `B: PartialEq<A>`, then **`a == b`
/// implies `b == a`**; and
@ -53,15 +66,6 @@ use self::Ordering::*;
///
/// ## How can I implement `PartialEq`?
///
/// `PartialEq` only requires the [`eq`] method to be implemented; [`ne`] is defined
/// in terms of it by default. Any manual implementation of [`ne`] *must* respect
/// the rule that [`eq`] is a strict inverse of [`ne`]; that is, `!(a == b)` if and
/// only if `a != b`.
///
/// Implementations of `PartialEq`, [`PartialOrd`], and [`Ord`] *must* agree with
/// each other. It's easy to accidentally make them disagree by deriving some
/// of the traits and manually implementing others.
///
/// An example implementation for a domain in which two books are considered
/// the same book if their ISBN matches, even if the formats differ:
///
@ -631,10 +635,25 @@ impl<T: Clone> Clone for Reverse<T> {
/// Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order).
///
/// An order is a total order if it is (for all `a`, `b` and `c`):
/// Implementations must be consistent with the [`PartialOrd`] implementation, and ensure
/// `max`, `min`, and `clamp` are consistent with `cmp`:
///
/// - total and asymmetric: exactly one of `a < b`, `a == b` or `a > b` is true; and
/// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
/// - `partial_cmp(a, b) == Some(cmp(a, b))`.
/// - `max(a, b) == max_by(a, b, cmp)` (ensured by the default implementation).
/// - `min(a, b) == min_by(a, b, cmp)` (ensured by the default implementation).
/// - For `a.clamp(min, max)`, see the [method docs](#method.clamp)
/// (ensured by the default implementation).
///
/// It's easy to accidentally make `cmp` and `partial_cmp` disagree by
/// deriving some of the traits and manually implementing others.
///
/// ## Corollaries
///
/// From the above and the requirements of `PartialOrd`, it follows that `<` defines a strict total order.
/// This means that for all `a`, `b` and `c`:
///
/// - exactly one of `a < b`, `a == b` or `a > b` is true; and
/// - `<` is transitive: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
///
/// ## Derivable
///
@ -659,12 +678,6 @@ impl<T: Clone> Clone for Reverse<T> {
/// Then you must define an implementation for [`cmp`]. You may find it useful to use
/// [`cmp`] on your type's fields.
///
/// Implementations of [`PartialEq`], [`PartialOrd`], and `Ord` *must*
/// agree with each other. That is, `a.cmp(b) == Ordering::Equal` if
/// and only if `a == b` and `Some(a.cmp(b)) == a.partial_cmp(b)` for
/// all `a` and `b`. It's easy to accidentally make them disagree by
/// deriving some of the traits and manually implementing others.
///
/// Here's an example where you want to sort people by height only, disregarding `id`
/// and `name`:
///
@ -824,15 +837,45 @@ impl PartialOrd for Ordering {
/// Trait for values that can be compared for a sort-order.
///
/// The `lt`, `le`, `gt`, and `ge` methods of this trait can be called using
/// the `<`, `<=`, `>`, and `>=` operators, respectively.
///
/// The methods of this trait must be consistent with each other and with those of `PartialEq` in
/// the following sense:
///
/// - `a == b` if and only if `partial_cmp(a, b) == Some(Equal)`.
/// - `a < b` if and only if `partial_cmp(a, b) == Some(Less)`
/// (ensured by the default implementation).
/// - `a > b` if and only if `partial_cmp(a, b) == Some(Greater)`
/// (ensured by the default implementation).
/// - `a <= b` if and only if `a < b || a == b`
/// (ensured by the default implementation).
/// - `a >= b` if and only if `a > b || a == b`
/// (ensured by the default implementation).
/// - `a != b` if and only if `!(a == b)` (already part of `PartialEq`).
///
/// If [`Ord`] is also implemented for `Self` and `Rhs`, it must also be consistent with
/// `partial_cmp` (see the documentation of that trait for the exact requirements). It's
/// easy to accidentally make them disagree by deriving some of the traits and manually
/// implementing others.
///
/// The comparison must satisfy, for all `a`, `b` and `c`:
///
/// - asymmetry: if `a < b` then `!(a > b)`, as well as `a > b` implying `!(a < b)`; and
/// - transitivity: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`.
/// - duality: `a < b` if and only if `b > a`.
///
/// Note that these requirements mean that the trait itself must be implemented symmetrically and
/// transitively: if `T: PartialOrd<U>` and `U: PartialOrd<V>` then `U: PartialOrd<T>` and `T:
/// PartialOrd<V>`.
///
/// ## Corollaries
///
/// The following corollaries follow from the above requirements:
///
/// - irreflexivity of `<` and `>`: `!(a < a)`, `!(a > a)`
/// - transitivity of `>`: if `a > b` and `b > c` then `a > c`
/// - duality of `partial_cmp`: `partial_cmp(a, b) == partial_cmp(b, a).map(Ordering::reverse)`
///
/// ## Derivable
///
/// This trait can be used with `#[derive]`. When `derive`d on structs, it will produce a
@ -850,10 +893,6 @@ impl PartialOrd for Ordering {
///
/// `PartialOrd` requires your type to be [`PartialEq`].
///
/// Implementations of [`PartialEq`], `PartialOrd`, and [`Ord`] *must* agree with each other. It's
/// easy to accidentally make them disagree by deriving some of the traits and manually
/// implementing others.
///
/// If your type is [`Ord`], you can implement [`partial_cmp`] by using [`cmp`]:
///
/// ```