Document variance

Author: matthewjasper

src/special-types-and-traits.md

@@ -150,4 +150,4 @@ compiler, not by [implementation items].
 [trait object]: types.html#trait-objects
 [Tuples]: types.html#tuple-types
 [Type parameters]: types.html#type-parameters
-[variance]: ../nomicon/subtyping.html
+[variance]: subtyping.html#variance

src/subtyping.md

@@ -1,4 +1,4 @@
-# Subtyping
+# Subtyping and Variance
 
 Subtyping is implicit and can occur at any stage in type checking or
 inference. Subtyping in Rust is very restricted and occurs only due to
@@ -15,5 +15,71 @@ fn bar<'a>() {
     let t: &'a str = s;
 }
 ```
-Since `'static` "lives longer" than `'a`, `&'static str` is a subtype of
-`&'a str`.
+
+Since `'static` outlives `'a`, `&'static str` is a subtype of `&'a str`.
+
+Subtyping also exists for [higher-ranked types]. Replacing a higher ranked
+lifetime with a concrete lifetime produces a subtype.
+
+```rust
+fn bar() {
+    // Explicitly f: for<'a> fn(&'a i32) -> &'a i32.
+    let f: fn(&i32) -> &i32 = |x| x;
+    let g: fn(&'static i32) -> &'static i32 = f;
+}
+```
+
+The subtype must be a valid type:
+
+```rust,compile_fail
+fn bar<'a>() {
+    let h: for<'b, 'c> fn(&'c &'b i32) -> &'b i32 = |x| &**x;
+    let j: fn(&'static &'a i32) -> &'a i32 = h;
+    // Error: in type `&'static &'a i32`, reference has a longer lifetime than
+    // the data it references
+}
+```
+
+## Variance
+
+Variance is a property that generic types have with respect to their arguments.
+A generic type's *variance* in a parameter is how the subtyping of the
+parameter affects the subtyping of the type.
+
+* `F<T>` is *covariant* over `T` if `T` being a subtype of `U` implies that
+  `F<T>` is a subtype of `F<U>` (subtyping "passes through")
+* `F<T>` is *contravariant* over `T` if `T` being a subtype of `U` implies
+  that `F<U>` is a subtype of `F<T>`
+* `F<T>` is *invariant* over `T` otherwise (no subtyping relation can be derived)
+
+Variance of types is automatically determined as follows
+
+* `&'a T` is covariant in `'a` and `T`.
+* `&'a mut T` is covariant in `'a`, invariant in `T`.
+* `[T]` and `[T; n]` are covariant in `T`.
+* `*const T` is covariant in `T`.
+* `*mut T` is invariant in `T`.
+* `fn(T) -> U` is covariant in `U` and contravariant in `T`.
+* `std::cell::UnsafeCell<T>` is invariant in `T`.
+* `std::marker::PhantomData<T>` is covariant in `T`.
+* Trait objects are invariant in their type parameters and associated types and
+  covariant in their [lifetime bound].
+
+The variance of `struct`, `enum`, `union` and tuple types is decided by looking
+at the variance of the types of their fields. If a type parameter is used more
+than once then the more restrictive variance is used. For example the following
+struct is covariant in `'a` and `T` and invariant in `'b` and `U`.
+
+```rust
+use std::cell::UnsafeCell;
+struct Variance<'a, 'b, T, U: 'a> {
+    x: &'a U,
+    y: *const T,
+    z: UnsafeCell<&'b f64>,
+    w: *mut U,
+}
+```
+
+[coercions]: type-coercions.html
+[higher-ranked types]: ../nomicon/hrtb.html
+[lifetime bound]: types.html#trait-object-lifetime-bounds