A global revolution in theoretical foundations using type theory, category theory, and formal verification.
-- Type safety prevents physical nonsense
velocity :: Quantity Velocity
velocity = distance |/| time ✓
-- This is a COMPILE-TIME error:
error = meter |+| second ✗
-- Cannot add Length to Time!Type-safe physics leverages advanced mathematics to construct physical theories where meaningless expressions cannot be written.
Adding meters to seconds? That's a compile-time type error, not a runtime surprise.
Complex theories built from verified components. Category theory ensures everything composes correctly.
The no-cloning theorem follows from type structure alone—no physics input required!
Under Curry-Howard, well-typed programs ARE proofs. The type checker is your proof assistant.
Master type-safe physics step by step, from foundational concepts to cutting-edge applications.
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Advanced / Research-level
The Haskell implementation demonstrates type safety in practice.
-- SI base units as types
type Length = '(1, 0, 0, 0, 0, 0, 0)
type Time = '(0, 1, 0, 0, 0, 0, 0)
type Velocity = '(1, -1, 0, 0, 0, 0, 0)
-- Operations check dimensions at compile time
velocity :: Quantity Velocity
velocity = (100 *| meter) |/| (5 *| second)
-- Kinetic energy: type enforces E = ½mv²
kineticEnergy :: Quantity Mass -> Quantity Velocity -> Quantity Energy
kineticEnergy m v = 0.5 *| (m |*| v |*| v)-- Physical theories ARE categories
class Category cat where
identity :: cat a a
compose :: cat b c -> cat a b -> cat a c
-- Physical laws are natural transformations
newtype NaturalTransformation f g = NatTrans
{ runNatTrans :: forall a. f a -> g a }
-- Naturality: α_B ∘ F(f) = G(f) ∘ α_A
-- This is VERIFIED by the type system!-- States as morphisms I → H
ket0, ket1 :: State Qubit
ket0 = State $ V.fromList [1 :+ 0, 0 :+ 0]
ket1 = State $ V.fromList [0 :+ 0, 1 :+ 0]
-- Superposition
ketPlus = State $ V.fromList [r :+ 0, r :+ 0]
where r = 1 / sqrt 2
-- Measurement probabilities: always non-negative!
measure :: State Qubit -> [(String, Double)]git clone https://github.com/MagnetonIO/type-safe-physics
cd type-safe-physics/haskell
stack build && stack exec type-safe-physics-exeA comprehensive survey of the emerging paradigm of type-safe physics—a revolutionary movement transforming theoretical physics across institutions worldwide. This paradigm leverages advanced mathematical structures from type theory, category theory, and formal verification to construct physical theories with unprecedented rigor and conceptual clarity.
Download PDF"Physical theories should be formulated within formal systems that make it impossible to write down meaningless expressions."
"The no-cloning theorem is a theorem of type theory, not a peculiarity of Hilbert spaces."
"Physical consistency is a type property. A well-typed theory cannot contain certain classes of errors."
"Spacetime may not be fundamental but emergent from more fundamental categorical structures."