Luna-Generic

English documentation for the intended v0.3.3 release of Luna-Flow/luna-generic.

Overview

luna-generic provides general algebraic traits and default numeric instances for Luna projects.

The current release candidate centers on three changes:

• BigInt is now part of the default exported numeric surface.
• Integral-to-target conversions are expressed through explicit homomorphism traits.
• Integral::normalize now provides a canonical BigInt form for all integral source types.

Exported Traits

• AddMonoid, MulMonoid
• AddGroup, MulGroup
• Semiring, Ring, Field
• Integral, Nat
• NatHomomorphism, IntegralHomomorphism
• Num

Exported Operations and Default Types

• Operations: One, Zero, Inverse, Conjugate
• Default numeric types: Int, Int16, Int64, UInt, UInt16, UInt64, BigInt, Float, Double

Integer Model

• Nat covers UInt, UInt16, and UInt64
• Integral covers signed integers, unsigned integers, and BigInt
• Unsigned integer instances stop at Semiring
• Integral::normalize canonicalizes any integral value into BigInt
• Nat reuses Integral::normalize for its exact embedding into BigInt

Embeddings

• NatHomomorphism::from_nat provides polymorphic target-side embeddings from any Nat source type
• IntegralHomomorphism::from_integral provides polymorphic target-side embeddings from any Integral source type
• The default implementation strategy is Integral::normalize followed by target-specific BigInt conversion
• BigInt embeddings are exact
• Float and Double embeddings are approximate and may round large values

Validation

Recommended release checks:

moon check
moon test