Domains and operator resolution

Domains are not terms; they elaborate operator syntax to named functions.

Surface	Desugaring
a + b	(+)_D ⟦a⟧ ⟦b⟧ where D is the resolved domain for the carrier of a
date + 1m	addMonth date 1m (or domain-specific applyDelta)
col + 3l	applyLightness col 3l

This is a static rewrite: (operator, carrier-type) ↦ implementation.

9.1 Delta Literal Resolution

Delta literals are domain-scoped. Resolution follows a two-step process:

Step	Action	Example
1. Lexical lookup	Find delta binding in used domains	1m → defined in Calendar, Physics
2. Carrier disambiguation	Select domain matching operand type	date + 1m → Calendar (date : Date)

Resolution Chain

date + 1m
  ↓ (step 1: find delta)
  1m is defined in: Calendar.Delta.Month, Physics.Delta.Meter
  ↓ (step 2: carrier type)
  date : Date → Calendar domain
  ↓ (step 3: expand delta)
  date + (Month 1)
  ↓ (step 4: resolve operator)
  Calendar.(+) date (Month 1)
  ↓ (step 5: desugar to implementation)
  addMonth date (Month 1)

9.2 Ambiguity Errors

When carrier type cannot disambiguate:

x + 1m  // Error: x : Int, neither Calendar nor Physics apply

When multiple domains match:

// If both Calendar and Physics define (+) over the same carrier
ambiguous + 1m  // Error: Ambiguous domain for (+)

Resolution: Use qualified literals or operators.

date + Calendar.1m
position + Physics.1m

9.3 Operator Precedence

Domain operators follow standard precedence. Domains do not redefine precedence — only semantics:

1 + 2 * 3      // Parsed as: 1 + (2 * 3)
date + 1m      // Parsed as: (date + 1m)

9.4 Desugaring Order

1. Type inference — Determine carrier types
2. Delta expansion — Replace literals with constructors
3. Domain resolution — Match (operator, carrier) to domain
4. Function substitution — Replace operator with implementation