A Journey Through Types
The foundation of all things functional. A pure function is a covenant: given the same inputs, it will always return the same output, with no side effects to corrupt the world outside. In Haskell, purity is not a guideline -- it is the law of the land.
add :: Int -> Int -> Int
Type classes are Haskell's mechanism for ad-hoc polymorphism -- a way of saying "any type that can do X belongs to this class." They are the building blocks of abstraction, stacking neatly like cubes to form towering structures of shared behavior.
class Eq a where (==) :: a -> a -> Bool
Functions that accept or return other functions -- the fundamental lever of composition. Map, filter, fold: these are the tools that transform lists, trees, and any traversable structure with elegant precision.
map :: (a -> b) -> [a] -> [b]
Sum types and product types -- the algebra of data itself. With ADTs, you describe every possible shape your data can take, and the compiler ensures you handle them all. No nulls, no surprises, no forgotten edge cases.
data Maybe a = Nothing | Just a
The summit that every Haskell learner must eventually face. A monad is a type with context -- a container that sequences computations while managing effects. IO, Maybe, Either, State: each a different flavor of controlled impurity within the pure world.
class Monad m where (>>=) :: m a -> (a -> m b) -> m b
Where imperative languages loop, Haskell recurses. A recursive function calls itself with transformed arguments, ascending the spiral staircase of computation until reaching a base case. With lazy evaluation, even infinite structures become tractable.
fib :: Int -> Int
fib 0 = 0; fib 1 = 1
fib n = fib (n-1) + fib (n-2)
The bridge between pure computation and the messy real world. Haskell's IO monad provides a way to perform side effects -- reading files, printing to the console, making network requests -- while maintaining referential transparency through type-level discipline.
main :: IO ()
main = putStrLn "Hello, World!"
The quest does not end here. Every type signature is a theorem, every program a proof. The path descends into dependent types, category theory, and formalisms yet unimagined. Walk on.