The Lambda
Calculus
Where every function tells a story.
ITypes as Propositions
The Curry-Howard correspondence reveals a profound connection between the world of types and the world of logic. Every type is a proposition; every program is a proof. When you write a function of type a -> b, you are constructing evidence that proposition A implies proposition B.
This isn't mere analogy — it is an isomorphism, a structural identity that runs deep enough to unify two great traditions of formal thought. The logician and the programmer, it turns out, have been doing the same work all along.
In Haskell, the type system becomes your proof assistant. Each successful compilation is a small theorem, verified mechanically. The compiler doesn't merely check syntax — it validates reasoning.
Composition
Maybe
A computation that might fail. Maybe wraps a value in the possibility of absence — Nothing is not an error, it is an honest answer. The bind operator threads potential failure through a chain of operations, short-circuiting gracefully when meaning runs out.
List
A computation with multiple results. The List monad models nondeterminism — each step branches into many possibilities, and bind explores them all. A search through a space of answers, expressed as naturally as a single value.
IO
A computation that touches the world. IO is Haskell's answer to the ancient tension between purity and effect — it separates the description of an action from its execution, letting you reason about side effects with the same rigor as pure functions.
Every expression has a type.
Every type tells a truth.
Begin your quest.