haskeller.net
where pure functions find their form in honeycomb geometry
The Honeycomb
Functor
Monad
Maybe a
IO ()
Either e
Applicative
a -> b
MonadIO
>>=
fmap
forall a
Traversable
State s
Reader r
:: *
Foldable
Semigroup
Monoid
The Lambda
Purity is not a restriction. It is the liberation from implicit state, hidden mutation, and temporal coupling. When every function is a mathematical function, every program becomes a proof.
Composition is the fundamental operation of thought. In Haskell, f . g is not syntactic sugar -- it is the expression of a universal truth about how complex systems emerge from simple parts.
Types are not annotations added after the fact. They are the architecture that precedes implementation. The type signature is the blueprint; the function body is the building.
The Proof
haskeller.net
The types align. The functions compose. The proof compiles.