RangeLimits naming: inconsistent meaning of "half open"

[dtolnay]

In dtolnay/syn#1373 I noticed an inconsistency between how ranges are described in the reference vs how the compiler uses the same terminology.

Rustc has the following enum which distinguishes .. vs ..= in range patterns and expressions:
https://github.com/rust-lang/rust/blob/1.67.0/compiler/rustc_ast/src/ast.rs#L1323-L1328

pub enum RangeLimits {
    /// Inclusive at the beginning, exclusive at the end (..)
    HalfOpen,
    /// Inclusive at the beginning and end (..=)
    Closed,
}

Ranges in rustc are effectively (Option<Expr>, RangeLimits, Option<Expr>).

Meanwhile a different approach is currently taken by the Rust Reference: https://doc.rust-lang.org/1.67.0/reference/patterns.html#range-patterns

RangePattern :
    InclusiveRangePattern | HalfOpenRangePattern

InclusiveRangePattern :
    RangePatternBound `..=` RangePatternBound

HalfOpenRangePattern :
    RangePatternBound `..` | `..=` RangePatternBound

Notice how it has a ..= pattern which it refers to as half open, even though ..= is never considered half open in rustc.

range	rustc terminology	reference terminology
lo..	half open	half open
..=hi	closed (opposite of half open)	half open (!)
lo..=hi	closed	inclusive

Do we know whether one of these uses of the "half open" terminology is more preferred? Might we reach agreement about which of rustc or the reference should be changed?

[dtolnay]

Mentioning @workingjubilee since the Reference's use of "half open" comes from #900.

[ehuss]

It seem curious to me that the compiler calls that "closed". In math terms, isn't ..=hi equivalent to $(-∞,hi]$?

One option is to give the three styles separate names that are more similar to the standard library names (RangeToInclusivePattern, etc.).

[workingjubilee]

Oh, hello. Sorry, somehow missed this amidst my notifications. I am fine with the chosen resolution. I believe I flubbed what might have been intended to be a usage of "half-closed" there.