Learn Physics With Functional Programming: A Ha... Apr 2026

A physical state (position, velocity) can be defined as a immutable record. Laws as Functions: Newton’s Second Law (

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.

This approach prevents "state leakage," where an accidental modification in one part of the program breaks the physical consistency of the simulation. 4. Advanced Concepts: Symmetry and Types Learn Physics with Functional Programming: A Ha...

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 A physical state (position, velocity) can be defined

In FP, the relationship between mathematical definitions and code is nearly isomorphic.

In an imperative style, one might loop through time and update a y variable. In Haskell, we define the physics as a pure function: The Correspondence Principle

Physics is the study of invariants and transformations. In the traditional computational physics curriculum, students often use languages like C++ or Python. While effective for performance, these languages allow for "side effects" that do not exist in pure mathematical physics. Functional programming, by contrast, treats computation as the evaluation of mathematical functions, making it a natural fit for the laws of physics. 2. The Correspondence Principle