From 86b031b7349594f23084c0599177975c47eb9925 Mon Sep 17 00:00:00 2001 From: Jan Behrens Date: Wed, 26 Jul 2023 19:36:26 +0200 Subject: [PATCH] docs: Correct terminology in std::cmp MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Some clarifications regarding used (mathematical) terminology: * Avoid using the terms "total equality" and "partial equality" in favor of "equivalence relation" and "partial equivalence relation", which are well-defined and unambiguous. * Clarify that `Ordering` is an ordering between two values (and not an order in the mathematical sense). * Avoid saying that `PartialEq` and `Eq` are "equality comparisons" because the terminology "equality comparison" could be misleading: it's possible to implement `PartialEq` and `Eq` for other (partial) equivalence relations, in particular for relations where `a == b` for some `a` and `b` even when `a` and `b` are not the same value. * Added a section "Strict and non-strict partial orders" to document that the `<=` and `>=` operators do not correspond to non-strict partial orders. * Corrected section "Corollaries" in documenation of Ord in regard to `<` only describing a strict total order in cases where `==` conforms to mathematical equality. Made documentation easier to understand: * Explicitly state at the beginning of `PartialEq`'s documentation comment that implementing the trait will provide the `==` and `!=` operators. * Added an easier to understand rule when to implement `Eq` in addition to `PartialEq`: "if it’s guaranteed that `PartialEq::eq(a, a)` always returns `true`." * Explicitly mention in documentation of `Eq` that the properties "symmetric" and "transitive" are already required by `PartialEq`. --- library/core/src/cmp.rs | 67 ++++++++++++++++++++++++++++++----------- 1 file changed, 50 insertions(+), 17 deletions(-) diff --git a/library/core/src/cmp.rs b/library/core/src/cmp.rs index 360806167671d..f59a965be5a37 100644 --- a/library/core/src/cmp.rs +++ b/library/core/src/cmp.rs @@ -3,14 +3,17 @@ //! This module contains various tools for comparing and ordering values. In //! summary: //! -//! * [`Eq`] and [`PartialEq`] are traits that allow you to define total and -//! partial equality between values, respectively. Implementing them overloads -//! the `==` and `!=` operators. +//! * [`PartialEq`] overloads the `==` and `!=` operators. In cases where +//! `Rhs` (the right hand side's type) is `Self`, this trait corresponds to a +//! partial equivalence relation. +//! * [`Eq`] indicates that the overloaded `==` operator corresponds to an +//! equivalence relation. //! * [`Ord`] and [`PartialOrd`] are traits that allow you to define total and //! partial orderings between values, respectively. Implementing them overloads //! the `<`, `<=`, `>`, and `>=` operators. //! * [`Ordering`] is an enum returned by the main functions of [`Ord`] and -//! [`PartialOrd`], and describes an ordering. +//! [`PartialOrd`], and describes an ordering of two values (less, equal, or +//! greater). //! * [`Reverse`] is a struct that allows you to easily reverse an ordering. //! * [`max`] and [`min`] are functions that build off of [`Ord`] and allow you //! to find the maximum or minimum of two values. @@ -27,16 +30,21 @@ pub(crate) use bytewise::BytewiseEq; use self::Ordering::*; -/// Trait for equality comparisons. +/// Trait for comparisons using the equality operator. +/// +/// Implementing this trait for types provides the `==` and `!=` operators for +/// those types. /// /// `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 speaking, when `Rhs == Self`, this trait corresponds to a [partial equivalence -/// relation](https://en.wikipedia.org/wiki/Partial_equivalence_relation). +/// This trait allows for comparisons using the equality operator, 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 speaking, when `Rhs == Self`, this trait corresponds +/// to a [partial equivalence relation]. +/// +/// [partial equivalence relation]: https://en.wikipedia.org/wiki/Partial_equivalence_relation /// /// Implementations must ensure that `eq` and `ne` are consistent with each other: /// @@ -242,15 +250,15 @@ pub macro PartialEq($item:item) { /* compiler built-in */ } -/// Trait for equality comparisons which are [equivalence relations]( +/// Trait for comparisons corresponding to [equivalence relations]( /// https://en.wikipedia.org/wiki/Equivalence_relation). /// -/// This means, that in addition to `a == b` and `a != b` being strict inverses, the equality must -/// be (for all `a`, `b` and `c`): +/// This means, that in addition to `a == b` and `a != b` being strict inverses, +/// the relation must be (for all `a`, `b` and `c`): /// /// - reflexive: `a == a`; -/// - symmetric: `a == b` implies `b == a`; and -/// - transitive: `a == b` and `b == c` implies `a == c`. +/// - symmetric: `a == b` implies `b == a` (required by `PartialEq` as well); and +/// - transitive: `a == b` and `b == c` implies `a == c` (required by `PartialEq` as well). /// /// This property cannot be checked by the compiler, and therefore `Eq` implies /// [`PartialEq`], and has no extra methods. @@ -260,6 +268,10 @@ pub macro PartialEq($item:item) { /// undefined behavior. This means that `unsafe` code **must not** rely on the correctness of these /// methods. /// +/// Implement `Eq` in addition to `PartialEq` if it's guaranteed that +/// `PartialEq::eq(a, a)` always returns `true` (reflexivity), in addition to +/// the symmetric and transitive properties already required by `PartialEq`. +/// /// ## Derivable /// /// This trait can be used with `#[derive]`. When `derive`d, because `Eq` has @@ -676,12 +688,19 @@ impl Clone for Reverse { /// /// ## 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`: +/// From the above and the requirements of `PartialOrd`, it follows 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 `>`. /// +/// Mathematically speaking, the `<` operator defines a strict [weak order]. In +/// cases where `==` conforms to mathematical equality, it also defines a +/// strict [total order]. +/// +/// [weak order]: https://en.wikipedia.org/wiki/Weak_ordering +/// [total order]: https://en.wikipedia.org/wiki/Total_order +/// /// ## Derivable /// /// This trait can be used with `#[derive]`. @@ -920,6 +939,20 @@ pub macro Ord($item:item) { /// - 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)` /// +/// ## Strict and non-strict partial orders +/// +/// The `<` and `>` operators behave according to a *strict* partial order. +/// However, `<=` and `>=` do **not** behave according to a *non-strict* +/// partial order. +/// That is because mathematically, a non-strict partial order would require +/// reflexivity, i.e. `a <= a` would need to be true for every `a`. This isn't +/// always the case for types that implement `PartialOrd`, for example: +/// +/// ``` +/// let a = f64::sqrt(-1.0); +/// assert_eq!(a <= a, false); +/// ``` +/// /// ## Derivable /// /// This trait can be used with `#[derive]`.