moonlight-algebra

Part of Moonlight, the sheaf-theoretic computation layer beneath Melusine and Pale Meridian.

The law-governed algebraic tower the rest of the cathedral stands on.

moonlight-algebra is Moonlight's algebraic tier, building on moonlight-core. The front door is the umbrella module Moonlight.Algebra, whose header carries the tower's shape and its relationship to core; the public finite-lattice sublibrary has its own front door, Moonlight.FiniteLattice, whose header carries the compiled-lattice cookbook.

Public modules

Module	Surface
Moonlight.Algebra	Umbrella re-export of the whole tower, plus the operation-bearing numeric classes from moonlight-core.
Moonlight.Algebra.Pure.Group	Standard Semigroup/Monoid, Group/AbelianGroup, and Additive/Multiplicative wrappers.
Moonlight.Algebra.Pure.FreeMonoid, .FreeAbelianGroup	Free monoids and free abelian groups.
Moonlight.Algebra.Pure.Action	Monoid actions (Action) and their group-acting refinement (InvertibleAction).
Moonlight.Algebra.Pure.Orientation	The two-element sign/orientation group ℤ/2 with a direct standard monoid/group instance.
Moonlight.Algebra.Pure.Lattice	Join/meet semilattices up to Heyting and Boolean algebras.
Moonlight.FiniteLattice.*	Public finite-lattice sublibrary: checked finite-order compilation, dense query plans, resident keys, Heyting implication, fixpoints, covers, presentation builders, and support kernels.
Moonlight.Algebra.Pure.Ring	Re-exported semiring/commutative-ring law classes plus integral/GCD/Euclidean/canonical-domain refinements.
Moonlight.Algebra.Pure.Zn, .Quotient	Modular arithmetic and quotient rings R/(n).
Moonlight.Algebra.Pure.NumberTheory, .GCD	Number theory and gcd.
Moonlight.Algebra.Pure.Polynomial	Univariate polynomials over a coefficient ring; a free module on monomial degrees.
Moonlight.Algebra.Pure.Module	Modules, free modules, vector spaces, and bilinear spaces over a field.
Moonlight.Algebra.Pure.Magnitude	Real-valued magnitudes for obstructions.
Moonlight.Algebra.Pure.PowerSet, .Product	Power-set lattices and finite n-fold product algebras (coordinatewise structure).
Moonlight.Algebra.Pure.SparseVec	Sparse vectors with finite support.

All Moonlight.Algebra.Pure.* leaves are exposed by the public abstract sublibrary and gathered by the Moonlight.Algebra surface. The unsafe GCD witness (Moonlight.Algebra.Unsafe.GCDWitness) lives in the private moonlight-algebra-internal sublibrary, the compiled finite lattice realization lives in the public finite-lattice sublibrary, and the law suite (Moonlight.Algebra.Effect.Laws, Moonlight.Algebra.Test.Generators) lives in the private moonlight-algebra-laws sublibrary.

Performance

Compilation and the resident-key and <= query paths are fast; join/meet throughput and the compiled ContextLattice query surface are under active performance work.

License

MIT; see LICENSE.

cabal install moonlight-algebra