Operators

Every operator in Verum, by category, with precedence, associativity, and the protocol you overload to change its behaviour.

Precedence table

From tightest (evaluated first) to loosest.

Prec	Operators	Associativity	Overload protocol
1	.field, .method(), ?., [idx], (), ?, .await	left	—
2	-x, !x, ~x, &x, &mut x, &checked x, &unsafe x, *x	prefix	Neg, Not, BitNot / Deref
3	as (cast)	left	From, Into
4	** (exponent)	right	Pow
5	*, /, %	left	Mul, Div, Rem
6	+, -	left	Add, Sub
7	<<, >>	left	Shl, Shr
8	& (bitand)	left	BitAnd
9	^ (bitxor)	left	BitXor
10	| (bitor)	left	BitOr
11	==, !=, <, <=, >, >=, in, is	left	Eq, Ord / PartialOrd
12	&& (logical and)	left	short-circuit
13	|| (logical or)	left	short-circuit
14	??, .., ..=, -> / implies, =>, <-> / iff	right	—
15	=, +=, -=, *=, /=, %=, &=, |=, ^=, <<=, >>=	right	AddAssign, SubAssign, …
16	|> (pipe)	left	—

Lower number = tighter binding. a + b * c parses as a + (b * c) because * (5) binds tighter than + (6).

The three bitwise operators are three levels, not one — & tighter than ^ tighter than |, as in C. So a | b & c is a | (b & c), and diff | a ^ b accumulates a ^ b into diff rather than xor-ing diff | a.

Comparison is a single left-associative level, so a == b < c groups as (a == b) < c. Chained comparisons parse and are then rejected by the type checker (a Bool compared with a number); write a < b && b < c instead. is and in sit on this level too.

Assignment takes the whole right-hand side: x = a ?? b is x = (a ?? b). Only the pipeline |> is looser, so x = a |> f groups as (x = a) |> f — parenthesise if you meant to pipe the value: x = (a |> f).

A prefix operator binds tighter than as: -a as Int is (-a) as Int, and -2 ** 2 is (-2) ** 2.

Overloadable operators

Implement the listed protocol to make an operator work on your type.

Operator	Protocol	Method signature
a + b	Add<Rhs = Self>	fn add(self, rhs: Rhs) -> Self.Output
a - b	Sub	fn sub(self, rhs: Rhs) -> Self.Output
a * b	Mul	fn mul(self, rhs: Rhs) -> Self.Output
a / b	Div	fn div(self, rhs: Rhs) -> Self.Output
a % b	Rem	fn rem(self, rhs: Rhs) -> Self.Output
a ** b	Pow	fn pow(self, rhs: Rhs) -> Self.Output
-a	Neg	fn neg(self) -> Self.Output
!a	Not	fn not(self) -> Self.Output
~a	BitNot	fn not(self) -> Self.Output
a & b	BitAnd	fn bitand(self, rhs: Rhs) -> Self.Output
a | b	BitOr	fn bitor(self, rhs: Rhs) -> Self.Output
a ^ b	BitXor	fn bitxor(self, rhs: Rhs) -> Self.Output
a << b	Shl	fn shl(self, rhs: Rhs) -> Self.Output
a >> b	Shr	fn shr(self, rhs: Rhs) -> Self.Output
a += b	AddAssign	fn add_assign(&mut self, rhs: Rhs)
a -= b	SubAssign	fn sub_assign(&mut self, rhs: Rhs)
(similarly for *=, /=, %=, &=, |=, ^=, <<=, >>=)
a == b	Eq, PartialEq	fn eq(&self, other: &Self) -> Bool
a < b	Ord, PartialOrd	via cmp(&Self) -> Ordering
a[i]	Index<Idx>	fn index(&self, i: Idx) -> &Self.Output
a[i] = v	IndexMut<Idx>	fn index_mut(&mut self, i: Idx) -> &mut Self.Output
*a	Deref<Target = T>	fn deref(&self) -> &Self.Target
a()	FnOnce / FnMut / Fn	(closure protocols — see below)

Closure protocols

Function types come in three flavours:

• FnOnce — consumes captured values; callable once.
• FnMut — may mutate captures; callable many times.
• Fn — immutable captures only; callable many times and re-entrantly.

FnMut: FnOnce and Fn: FnMut: FnOnce — a more capable closure type subsumes a less capable one.

Non-overloadable operators

These operators have fixed semantics:

Operator	Meaning
&&	Logical AND, short-circuit (right side skipped if left is false).
||	Logical OR, short-circuit.
=	Assignment.
..	Exclusive range.
..=	Inclusive range.
?	Propagate Result.Err / Maybe.None.
.await	Future suspension.
is	Pattern test (value is Pattern, x is Type).
as	Type cast (x as Int, &x as *unsafe mut T).
|>	Pipe — a |> f(args) desugars to f(a, args).
??	Null-coalesce — a ?? b = a.unwrap_or(b).
.	Field / method access.
?.	Optional chaining — a?.b = a.and_then(|x| x.b).
..	Rest / record-update (in patterns and record exprs).
@	Pattern alias binding; x @ Pattern binds x and tests.
->	Function type / return type arrow.
=>	Match-arm arrow / closure / lambda.

Range operators

0..10         // exclusive:  0, 1, ..., 9       Range<Int>
0..=10        // inclusive:  0, 1, ..., 10      RangeInclusive<Int>
..10          // prefix:     anything up to 10  RangeTo<Int>
0..           // suffix:     0 and above        RangeFrom<Int>
..            // unbounded                      RangeFull

Ranges are values. They implement Iterator when the element type is ordered and incrementable (integers, characters). Float ranges don't iterate — use stride(0.0, 1.0, 0.1) or a manual for.

Unary reference operators

&x              // tier-0 managed (CBGR ~0.93 ns measured)
&checked x      // tier-1 compiler-proven (0 ns)
&unsafe x       // tier-2 programmer-proven (0 ns), needs `unsafe` block
&mut x          // mutable reference
&checked mut x
&unsafe mut x
*x              // dereference — safe for &T/&checked T; unsafe for &unsafe T and raw pointers

See language/references.

Compound assignment

a += b is sugar for a = a + b, but the compiler calls the AddAssign protocol when implemented, avoiding a temporary copy:

let mut xs = [1, 2, 3];
xs += 4;                        // desugars to xs.add_assign(4)

Every binary arithmetic/bitwise operator has a *Assign counterpart.

The is operator

if value is Maybe.Some(x)    { ... }                 // pattern test
while result is Pending()    { poll(); }             // loop condition
if x is not None             { use(x); }             // negation
let flag = value is Int;                             // type-test pattern

is has the same precedence as ==/</> (level 11). It's a pattern test; bindings introduced by the pattern scope outside the test expression where accessible.

See language/patterns and language/active-patterns.

The as operator

as performs a value conversion — not a raw reinterpret:

let n: Int = 3.7 as Int;        // truncates to 3 (via Float.to_int)
let s: Int = "42" as Int;       // parses — error at compile time if impossible
let p: *unsafe mut Byte = slice.as_ptr();
let b: Byte = (n as u8);

as dispatches to the From/Into protocol when implemented, or to a compiler-built-in conversion for primitives.

Pipe |> and method pipe |> .method()

let sum =
    list
    |> .filter(|x| x > 0)
    |> .map(|x| x * 2)
    |> .sum();

// equivalent to:
let sum = list.filter(|x| x > 0).map(|x| x * 2).sum();

For ordinary functions:

value |> transform(extra_arg)
// desugars to:
transform(value, extra_arg)

The method-pipe form (|> .method(args)) is grammar-level sugar for chainable pipelines; see language/syntax.

Optional chaining ?.

user?.address?.city?.name       // returns `Maybe.None` if any step is None

// Equivalent to:
user.and_then(|u| u.address)
    .and_then(|a| a.city)
    .and_then(|c| c.name)

Each ?.method() short-circuits on Maybe.None; the result type is Maybe<Final>.

Null coalesce ??

let name = preferred ?? default ?? "anonymous";
// preferred and default are Maybe<Text>; "anonymous" is the final fallback

a ?? b returns a.unwrap() if a.is_some(), else b. Chains left-associatively.

Error propagation ?

fn load() -> Result<Config, Error> {
    let text = read_file(path)?;                     // propagate IoError → Error
    let cfg  = parse(&text)?;                        // propagate ParseError → Error
    Result.Ok(cfg)
}

? is postfix. On Result.Ok(v) it evaluates to v; on Result.Err(e) it returns early with Result.Err(From.from(e)), which converts the inner error type via From.

Also works on Maybe:

fn first(xs: &List<Int>) -> Maybe<Int> {
    let head = xs.first()?;                          // None propagates
    Maybe.Some(*head * 2)
}

Precedence examples

a + b * c == b * c + a          // parses as:  ((a + (b * c)) == ((b * c) + a))
let v = x ?? y |> .foo();       // parses as:  let v = (x ?? y) |> .foo();
a && b || c                     // parses as:  ((a && b) || c)
match x is Some(v) && v > 0 { ... }   // parses as: match (x is Some(v) && v > 0)
-x.y                             // parses as:  -(x.y)

For ambiguous-looking code, parenthesise.

See also

• Syntax — how operators fit into the grammar.
• Protocols — Add, Ord, Display, …
• Patterns — the is pattern test.
• Error Handling — ? in context.
• References — &T / &checked T / &unsafe T.