The Monoiad: an epic poem on monoids
summary
Scala and Haskell code and a companion repo (Cheshire, plus a sister library doll) demonstrate encoding monoids at the type and categorical level, using SBT and kind-projector for higher-kinded work. The claim is concrete: type-level monoid proofs as implementations replace property tests by providing isomorphism functions; examples include Cartesian (tuples/unit) and co-Cartesian (either/nothing) monoidal categories, monads as monoids of endofunctors, rigs/distributivity and lattice interactions, and notes on applicability to linear types.
AI-written summary · about
chapters (5)
- 0:00Start
- 4:46Associativity
- 7:11Concatenation
- 24:15Type Constructors
- 28:57The Relationship between Parallel and Sequential Applicatives
related talks
55mMonoids, Monoids, Monoids
57mApplied category theory and abstract algebra
29mMonoids and Software Engineering
52mCategory Theory Through Functional Programming (part 1/3)
42mA pragmatic introduction to Category Theory
42mMonoidal Parsing
42mMonads you already use without knowing it
56mCategory Theory Through Functional Programming (part 2/3)