Algebraic traits and default numeric instances that define the generic foundation for LunaFlow math packages.

math

algebra

interface

moon add Luna-Flow/luna-generic@0.3.3

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Author

Luna-Flow

Version

0.3.3

License

Apache-2.0

Repository

github.com/Luna-Flow/luna-generic

Last updated

2 months ago

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README

#Luna-Generic

General algebraic traits and default numeric instances for Luna projects.

#v0.3.3 - Normalize-Driven Homomorphism Cleanup

This documentation tracks the intended v0.3.3 release content.

#Package Positioning

luna-generic provides lightweight algebraic traits for additive, multiplicative, ring-like, field-like, and numeric behavior.
The package ships default instances for signed integers, unsigned integers, BigInt, Float, and Double.
Integral-to-target embeddings are now modeled explicitly through homomorphism traits instead of being mixed into Integral.

#What Defines v0.3.3

BigInt is now part of the default exported numeric surface.
Integral now provides normalize, which canonicalizes any integral value into BigInt.
NatHomomorphism and IntegralHomomorphism provide polymorphic target-side embeddings for natural and integral source types.
Integral::normalize is the canonical source-side entry point for both Integral and Nat.
Floating-point embeddings remain approximate and follow target floating-point precision limits.

#Public Surface

Traits: AddMonoid, MulMonoid, AddGroup, MulGroup, Semiring, Ring, Field, Integral, Nat, NatHomomorphism, IntegralHomomorphism, Num
Operations: One, Zero, Inverse, Conjugate
Default numeric types: Int, Int16, Int64, UInt, UInt16, UInt64, BigInt, Float, Double

#Integer Families

Nat covers pure unsigned integer types: UInt, UInt16, UInt64
Integral covers signed and unsigned integers plus BigInt: Int, Int16, Int64, UInt, UInt16, UInt64, BigInt
Byte is intentionally excluded from both traits
Unsigned integer instances stop at Semiring and do not implement AddGroup, Ring, or Num

#Embedding Guidance

Integral::normalize provides a canonical BigInt representation for any integral value
Nat sources reuse the same normalize(Self) -> BigInt path through trait inheritance
NatHomomorphism::from_nat embeds any Nat source via normalize
IntegralHomomorphism::from_integral embeds any Integral source via normalize
BigInt embeddings are exact
Float and Double embeddings are approximate and may round large values

#Documentation

Comprehensive API documentation is available at mooncakes.io.

We provide README-level documentation in multiple languages:

English: doc/en_US/README.md
Simplified Chinese: doc/zh_CN/README.md
Japanese: doc/ja_JP/README.md

#Version History

Version	Date	Status	Notes
0.3.3	2026-06-12	release candidate	Refactors homomorphism traits around polymorphic methods and unifies natural/integral embeddings through normalize
0.3.2	2026-06-06	published on mooncakes	Adds Integral::normalize as the canonical BigInt normalization entry point and aligns docs with the new integral embedding model
0.3.1	2026-06-06	published on mooncakes	Adds BigInt coverage, explicit integral embedding traits, and trilingual documentation refresh
0.3.0	2026-06-06	previous release baseline	Earlier generic algebraic trait surface before the current integral embedding redesign

#Development

Useful local commands:

moon check
moon test

#Release Checklist

Before triggering the publish workflow:

Confirm moon.mod contains the intended version.
Confirm the README files match the exported package surface.
Run moon check and moon test.
Trigger publish-package after the release commit is pushed.

#
AddGroup

source

pub(open) trait AddGroup : AddMonoid + Neg + Sub {
}

impl AddGroup for Int

impl AddGroup for Int16

impl AddGroup for Int64

impl AddGroup for Float

impl AddGroup for Double

impl AddGroup for BigInt

#
AddMonoid

source

pub(open) trait AddMonoid : Add + Zero {
}

impl AddMonoid for Int

impl AddMonoid for Int16

impl AddMonoid for Int64

impl AddMonoid for UInt

impl AddMonoid for UInt16

impl AddMonoid for UInt64

impl AddMonoid for Float

impl AddMonoid for Double

impl AddMonoid for BigInt

#
Conjugate

source

pub(open) trait Conjugate {
  fn conjugate(Self) -> Self
}

#
Field

source

pub(open) trait Field : Ring + Inverse + Div {
}

impl Field for Float

impl Field for Double

#
Integral

source

pub(open) trait Integral : Semiring {
  fn normalize(Self) -> @moonbitlang/core/bigint.BigInt
BigInt
}

impl Integral for Int

impl Integral for Int16

impl Integral for Int64

impl Integral for UInt

impl Integral for UInt16

impl Integral for UInt64

impl Integral for BigInt

#
IntegralHomomorphism

source

pub(open) trait IntegralHomomorphism : NatHomomorphism {
  fn[S : Integral + Semiring + AddMonoid + Add + Zero + MulMonoid + Mul + One] from_integral(value : S) -> Self
}

impl IntegralHomomorphism for Float

impl IntegralHomomorphism for Double

impl IntegralHomomorphism for BigInt

#
Inverse

source

pub(open) trait Inverse {
  fn inv(Self) -> Self
}

impl Inverse for Float

impl Inverse for Double

#
MulGroup

source

pub(open) trait MulGroup : MulMonoid + Inverse + Div {
}

impl MulGroup for Float

impl MulGroup for Double

#
MulMonoid

source

pub(open) trait MulMonoid : Mul + One {
}

impl MulMonoid for Int

impl MulMonoid for Int16

impl MulMonoid for Int64

impl MulMonoid for UInt

impl MulMonoid for UInt16

impl MulMonoid for UInt64

impl MulMonoid for Float

impl MulMonoid for Double

impl MulMonoid for BigInt

#
Nat

source

pub(open) trait Nat : Integral {
}

impl Nat for UInt

impl Nat for UInt16

impl Nat for UInt64

#
NatHomomorphism

source

pub(open) trait NatHomomorphism {
  fn[S : Nat + Integral + Semiring + AddMonoid + Add + Zero + MulMonoid + Mul + One] from_nat(value : S) -> Self
}

impl NatHomomorphism for Float

impl NatHomomorphism for Double

impl NatHomomorphism for BigInt

#
Num

source

pub(open) trait Num : Ring {
  fn abs(Self) -> Self
  fn signum(Self) -> Self
}

impl Num for Int

impl Num for Int16

impl Num for Int64

impl Num for Float

impl Num for Double

impl Num for BigInt

#
One

source

pub(open) trait One {
  fn one() -> Self
}

impl One for Int

impl One for Int16

impl One for Int64

impl One for UInt

impl One for UInt16

impl One for UInt64

impl One for Float

impl One for Double

impl One for BigInt

#
Ring

source

pub(open) trait Ring : Semiring + Neg + Sub {
}

impl Ring for Int

impl Ring for Int16

impl Ring for Int64

impl Ring for Float

impl Ring for Double

impl Ring for BigInt

#
Semiring

source

pub(open) trait Semiring : AddMonoid + MulMonoid {
}

impl Semiring for Int

impl Semiring for Int16

impl Semiring for Int64

impl Semiring for UInt

impl Semiring for UInt16

impl Semiring for UInt64

impl Semiring for Float

impl Semiring for Double

impl Semiring for BigInt

#
Zero

source

pub(open) trait Zero {
  fn zero() -> Self
}

impl Zero for Int

impl Zero for Int16

impl Zero for Int64

impl Zero for UInt

impl Zero for UInt16

impl Zero for UInt64

impl Zero for Float

impl Zero for Double

impl Zero for BigInt

Source Files

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luna-generic

#Luna-Generic

#v0.3.3 - Normalize-Driven Homomorphism Cleanup

#Package Positioning

#What Defines v0.3.3

#Public Surface

#Integer Families

#Embedding Guidance

#Documentation

#Version History

#Development

#Release Checklist

#AddGroup

#AddMonoid

#Conjugate

#Field

#Integral

#IntegralHomomorphism

#Inverse

#MulGroup

#MulMonoid

#Nat

#NatHomomorphism

#Num

#One

#Ring

#Semiring

#Zero

Source Files

#
AddGroup

#
AddMonoid

#
Conjugate

#
Field

#
Integral

#
IntegralHomomorphism

#
Inverse

#
MulGroup

#
MulMonoid

#
Nat

#
NatHomomorphism

#
Num

#
One

#
Ring

#
Semiring

#
Zero