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ValueDomain — Semantic Specification

1. Definition

A ValueDomain defines the set of admissible values for a Variable.

It establishes semantic validity constraints over values without imposing representation, storage, sampling, or reasoning behavior.

A ValueDomain answers exactly one question:

Is this value admissible within this domain?

2. Declaration

A ValueDomain exists as an abstract semantic construct that:

  • Defines admissibility conditions for values
  • Can validate candidate values against those conditions
  • May expose domain metadata for introspection

Minimal declaration requirements:

  • A validation predicate over values
  • Deterministic behavior for identical inputs

No assumptions are made about value type, cardinality, or structure.

3. Semantic Invariants

Properties that MUST hold for all valid ValueDomain instances.

D1: Deterministic Validation

Validation of a given value MUST always yield the same result.

D2: Purity

Validation MUST NOT modify the value, the domain, or any external state.

D3: Total Decision

For any input value, validation MUST return either:

  • admissible, or
  • inadmissible

Undefined or partial results are not permitted.

D4: Non-Transformative

A ValueDomain MUST NOT transform, coerce, normalize, or generate values.

D5: Context Independence

Validation MUST NOT depend on time, external systems, or mutable global state.

4. Negative Definition

What ValueDomain is NOT.

  • Not a type system
  • Not a sampler or generator
  • Not a probability distribution
  • Not a storage schema
  • Not a reasoning engine
  • Not responsible for uncertainty quantification

5. Impossibilities

States or operations that cannot occur.

  • A ValueDomain cannot generate values
  • A ValueDomain cannot infer missing values
  • A ValueDomain cannot rank admissible values
  • A ValueDomain cannot resolve conflicts between values
  • A ValueDomain cannot change after validation begins

Any such behavior constitutes a semantic violation.

6. Boundary Conditions

Defined behavior at semantic limits.

Empty domain

A domain that admits no values is valid but degenerate.

Universal domain

A domain that admits all values is valid.

Invalid input

All inputs, including None, malformed, or unexpected types, MUST be handled deterministically.

Resource exhaustion

Behavior is undefined if validation cannot complete due to external constraints.

If undefined behavior exists, it MUST be explicitly stated.

7. Composition Rules

Semantic combination constraints.

Allowed

  • Variable ∘ ValueDomain → constrained Variable
  • CompositeDomain(ValueDomain₁, …, ValueDomainₙ)

Forbidden

  • ValueDomain ∘ Variable (domains do not depend on variables)
  • ValueDomain ∘ ReasoningResult
  • ValueDomain ∘ History

Domains constrain values; they do not observe outcomes.

8. Example (Non-Normative)

Examples do not define semantics.

domain admits values between 0 and 100 inclusive
validate(42)  → admissible
validate(-1)  → inadmissible

No assumptions are made about numeric representation.

9. Validation Rules

How violations are detected.

  • Static: Domains with non-deterministic validation are invalid.

  • Runtime: Supplying values that cannot be decisively validated is a semantic violation.

  • Structural: Any component that mutates values during validation violates domain semantics.

Validation enforces semantics; it does not define them.

10. Semantic Notes (Non-Binding)

Rationale and intent.

  • Separates value admissibility from reasoning
  • Enables clear validation boundaries for Variables
  • Prevents implicit coercion and hidden transformations
  • Allows multiple concrete domain specializations without semantic drift
  • Serves as a foundation for numeric, categorical, temporal, and composite domains