Const generics

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+- Feature Name: const_generics
+- Start Date: 2017-05-01
+- RFC PR: https://github.com/rust-lang/rfcs/pull/2000
+- Rust Issue: https://github.com/rust-lang/rust/issues/44580
+
+# Summary
+[summary]: #summary
+
+Allow types to be generic over constant values; among other things this will
+allow users to write impls which are abstract over all array types.
+
+# Motivation
+[motivation]: #motivation
+
+Rust currently has one type which is parametric over constants: the built-inf
+array type `[T; LEN]`. However, because const generics are not a first class
+feature, users cannot define their own types which are generic over constant
+values, and cannot implement traits for all arrays.
+
+As a result of this limitation, the standard library only contains trait
+implementations for arrays up to a length of 32; as a result, arrays are often
+treated as a second-class language feature. Even if the length of an array
+might be statically known, it is more common to heap allocate it using a
+vector than to use an array type (which has certain performance trade offs).
+
+Const parameters can also be used to allow users to more naturally specify
+variants of a generic type which are more accurately reflected as values,
+rather than types. For example, if a type takes a name as a parameter for
+configuration or other reasons, it may make more sense to take a `&'static str`
+than take a unit type which provides the name (through an associated const or
+function). This can simplify APIs.
+
+Lastly, consts can be used as parameters to make certain values determined at
+typecheck time. By limiting which values a trait is implemented over, the
+orphan rules can enable a crate to ensure that only some safe values are used,
+with the check performed at compile time (this is especially relevant to
+cryptographic libraries for example).
+
+# Detailed design
+[design]: #detailed-design
+
+Today, types in Rust can be parameterized by two kinds: types and lifetimes. We
+will additionally allow types to be parameterized by values, so long as those
+values can be computed at compile time. A single constant parameter must be of
+a single, particular type, and can be validly substituted with any value of
+that type which can be computed at compile time and the type meets the equality
+requirements laid out later in this RFC.
+
+(Exactly which expressions are evaluable at compile time is orthogonal to this
+RFC. For our purposes we assume that integers and their basic arithmetic
+operations can be computed at compile time, and we will use them in all
+examples.)
+
+## Glossary
+
+* __Const (constant, const value):__ A Rust value which is guaranteed to be
+fully evaluated at compile time. Unlike statics, consts will be inlined at
+their use sites rather than existing in the data section of the compiled
+binary.
+
+* __Const parameter (generic const):__ A const which a type or function is
+abstract over; this const is input to the concrete type of the item, such as
+the length parameter of a static array.
+
+* __Associated const:__ A const associated with a trait, similar to an
+associated type. Unlike a const parameter, an associated const is *determined*
+by a type.
+
+* __Const variable:__ Either a const parameter or an associated const,
+contrast with concrete const; a const which is undetermined in this context
+(prior to monomorphization).
+
+* __Concrete const:__ In contrast to a const variable, a const which has a
+known and singular value in this context.
+
+* __Const expression:__ An expression which evaluates to a const. This may be
+an identity expression or a more complex expression, so long as it can be
+evaluated by Rust's const system.
+
+* __Abstract const expression:__ A const expression which involves a const
+variable (and therefore the value that it evaluates to cannot be determined
+until after monomorphization).
+
+* __Const projection:__ The value of an abstract const expression (which cannot
+be determined in a generic context because it is dependent on a const
+variable).
+
+* __Identity expression:__ An expression which cannot be evaluated further
+except by substituting it with names in scope. This includes all literals as
+well all idents - e.g. `3`, `"Hello, world"`, `foo_bar`.
+
+## Declaring a const parameter
+
+In any sequence of type parameter declarations (such as in the definition of a
+type or on the `impl` header of an impl block) const parameters can also be
+declared. Const parameters declarations take the form `const $ident: $ty`:
+
+```rust
+struct RectangularArray<T, const WIDTH: usize, const HEIGHT: usize> {
+    array: [[T; WIDTH]; HEIGHT],
+}
+```
+
+The idents declared are the names used for these const parameters
+(interchangeably called "const variables" in this RFC text), and all values
+must be of the type ascribed to it. Which types can be ascribed to const
+parameters is restricted later in this RFC.
+
+The const parameter is in scope for the entire body of the item (type, impl,
+function, method, etc) in which it is declared.
+
+## Applying a const as a parameter
+
+Any const expression of the type ascribed to a const parameter can be applied
+as that parameter. When applying an expression as const parameter (except for
+arrays), which is not an identity expression, the expression must be contained
+within a block. This syntactic restriction is necessary to avoid requiring
+infinite lookahead when parsing an expression inside of a type.
+
+```rust
+const X: usize = 7;
+
+let x: RectangularArray<i32, 2, 4>;
+let y: RectangularArray<i32, X, {2 * 2}>;
+```
+
+### Arrays
+Arrays have a special construction syntax: `[T; CONST]`. In array syntax,
+braces are not needed around any const expressions; `[i32; N * 2]` is a
+syntactically valid type.
+
+## When a const variable can be used
+
+A const variable can be used as a const in any of these contexts:
+
+1. As an applied const to any type which forms a part of the signature of
+the item in question: `fn foo<const N: usize>(arr: [i32; N])`.
+2. As part of a const expression used to define an associated const, or as a
+parameter to an associated type.
+3. As a value in any runtime expression in the body of any functions in the
+item.
+4. As a parameter to any type used in the body of any functions in the item,
+as in `let x: [i32; N]` or `<[i32; N] as Foo>::bar()`.
+5. As a part of the type of any fields in the item (as in
+`struct Foo<const N: usize>([i32; N]);`).
+
+In general, a const variable can be used where a const can. There is one
+significant exception: const variables cannot be used in the construction of
+consts, statics, functions, or types inside a function body. That is, these
+are invalid:
+
+```rust
+fn foo<const X: usize>() {
+    const Y: usize = X * 2;
+    static Z: (usize, usize)= (X, X);
+
+    struct Foo([i32; X]);
+}
+```
+
+This restriction can be analogized to the restriction on using type variables
+in types constructed in the body of functions - all of these declarations,
+though private to this item, must be independent of it, and do not have any
+of its parameters in scope.
+
+## Theory of equality for type equality of two consts
+
+During unification and the overlap check, it is essential to determine when two
+types are equivalent or not. Because types can now be dependent on consts, we
+must define how we will compare the equality of two constant expressions.
+
+For most cases, the equality of two consts follows the same reasoning you would
+expect - two constant values are equal if they are equal to one another. But
+there are some particular caveats.
+
+### Structural equality
+
+Const equality is determined according to the definition of structural equality
+defined in [RFC 1445][1445]. Only types which have the "structural match"
+property can be used as const parameters. This would exclude floats, for
+example.
+
+The structural match property is intended as a stopgap until a final solution
+for matching against consts has been arrived at. It is important for the
+purposes of type equality that whatever solution const parameters use will
+guarantee that the equality is *reflexive*, so that a type is always the same
+type as itself. (The standard definition of equality for floating point numbers
+is not reflexive.)
+
+This may diverge someday from the definition used by match; it is not necessary
+that matching and const parameters use the same definition of equality, but the
+definition of equality used by match today is good enough for our purposes.
+
+Because consts must have the structural match property, and this property
+cannot be enforced for a type variable, it is not possible to introduce a const
+parameter which is ascribed to a type variable (`Foo<T, const N: T>` is not
+valid).
+
+### Equality of two abstract const expressions
+
+When comparing the equality of two abstract const expressions (that is, those
+that depend on a variable) we cannot compare the equality of their values
+because their values are determined by a const variable, the value of which is
+unknown prior to monomorphization.
+
+For this reason we will (initially, at least) treat the return value of const
+expressions as *projections* - values determined by the input, but which are
+not themselves known. This is similar to how we treat associated types today.
+When comparing the evaluation of an abstract const expression - which we'll
+call a *const projection* - to another const of the same type, its equality is
+always unknown.
+
+Each const expression generates a new projection, which is inherently
+anonymous. It is not possible to unify two anonymous projections (imagine two
+associated types on a generic - `T::Assoc` and `T::Item`: you can't prove or
+disprove that they are the same type). For this reason, const expressions do
+not unify with one another unless they are *literally references to the same
+AST node*. That means that one instance of `N + 1` does not unify with another
+instance of `N + 1` in a type.
+
+To be clearer, this does not typecheck, because `N + 1` appears in two
+different types:
+
+```rust
+fn foo<const N: usize>() -> [i32; N + 1] {
+    let x: [i32; N + 1] = [0; N + 1];
+    x
+}
+```
+
+But this does, because it appears only once:
+
+```rust
+type Foo<const N: usize> = [i32; N + 1];
+
+fn foo<const N: usize>() -> Foo<N> {
+    let x: Foo<N> = Default::default();
+    x
+}
+```
+
+#### Future extensions
+
+Someday we could introduce knowledge of the basic properties of some operations
+- such as the commutativity of addition and multiplication - to begin making
+smarter judgments on the equality of const projections. However, this RFC does
+not proposing building any knowledge of that sort into the language and doing
+so would require a future RFC.
+
+## Specialization on const parameters
+
+It is also necessary for specialization that const parameters have a defined
+ordering of specificity. For this purpose, literals are defined as more
+specific than other expressions, otherwise expressions have an indeterminate
+ordering.
+
+Just as we could some day support more advanced notions of equality between
+const projections, we could some day support more advanced definitions of
+specificity. For example, given the type `(i32, i32)`, we could determine that
+`(0, PARAM2)` is more specific than `(PARAM1, PARAM2)` - roughly the analog
+of understanding that `(i32, U)` is more specific than the type `(T, U)`. We
+could also someday support intersectional and other more advanced definitions
+of specialization on constants.
+
+# How We Teach This
+[how-we-teach-this]: #how-we-teach-this
+
+Const generics is a large feature, and will require significant educational
+materials - it will need to be documented in both the book and the reference,
+and will probably need its own section in the book. Documenting const generics
+will be a big project in itself.
+
+However, const generics should be treated as an advanced feature, and it should
+not be something we expose to new users early in their use of Rust.
+
+# Drawbacks
+[drawbacks]: #drawbacks
+
+This feature adds a significant amount of complexity to the type system,
+allowing types to be determined by constants. It requires determining the rules
+around abstract const equality, which result in surprising edge cases. It adds
+a lot of syntax to the language. The language would definitely be simpler if we
+don't adopt this feature.
+
+However, we have already introduced a type which is determined by a constant -
+the array type. Generalizing this feature seems natural and even inevitable
+given that early decision.
+
+# Alternatives
+[alternatives]: #alternatives
+
+There are not really alternatives other than not doing this, or staging it
+differently.
+
+We could limit const generics to the type `usize`, but this would not make the
+implementation simpler.
+
+We could move more quickly to more complex notions of equality between consts,
+but this would make the implementation more complex up front.
+
+We could choose a slightly different syntax, such as separating consts from
+types with a semicolon.
+
+# Unresolved questions
+[unresolved]: #unresolved-questions
+
+- **Unification of abstract const expressions:** This RFC performs the most
+  minimal unification of abstract const expressions possible - it essentially
+  doesn't unify them. Possibly this will be an unacceptable UX for
+  stabilization and we will want to perform some more advanced unification
+  before we stabilize this feature.
+- **Well formedness of const expressions:** Types should be considered well
+  formed only if during monomorphization they will not panic. This is tricky
+  for overflow and out of bound array access. However, we can only actually
+  provide well formedness constraints of expressions in the signature of
+  functions; what to do about abstract const expressions appearing in function
+  bodies in regards to well formedness is currently unclear & is delayed to
+  implementation.
+- **Ordering and default parameters:** Do all const parameters come last, or
+  can they be mixed with types? Do all parameters with defaults have to come
+  after parameters without defaults? We delay this decision to implementation
+  of the grammar.
+
+[1445]: https://github.com/rust-lang/rfcs/blob/master/text/1445-restrict-constants-in-patterns.md