Furthermore, higher-order functions allow for the abstraction of coordinate transformations. A single Lagrangian function can be passed into a generic Euler-Lagrange solver, allowing students to switch between Cartesian and Polar coordinates without rewriting the core physics logic. 5. Conclusion
Traditional physics education often relies on imperative programming or manual calculus, which can obscure the underlying symmetries and laws of nature. This paper proposes a functional programming (FP) approach—specifically using Haskell—to model physical systems. By leveraging strong typing, immutability, and higher-order functions, students can map mathematical equations directly to executable code, fostering a deeper conceptual understanding of mechanics and field theory. 1. Introduction Learn Physics with Functional Programming: A Ha...
One of the most powerful features of FP in physics is . By using dimensional analysis within the type system, we can prevent "unit errors" at compile time. For example, a compiler can be configured to throw an error if a student attempts to add a Mass type to a Length type. Double) type State = (Vector
) is not a command to change a variable, but a function that transforms a state into an acceleration. Vector) -- (Position
Learn Physics with Functional Programming: A Haskell-Based Approach
type Vector = (Double, Double) type State = (Vector, Vector) -- (Position, Velocity) applyGravity :: Double -> State -> State applyGravity dt ((x, y), (vx, vy)) = let g = -9.81 newVy = vy + g * dt newX = x + vx * dt newY = y + vy * dt in ((newX, newY), (vx, newVy)) Use code with caution.