open Leibniz

let () =
  print_endline "physics: kinetic energy\n";

  let ke = Parser.parse "0.5 * m * v^2" in
  print_endline ("KE = " ^ Expr.to_string ke);

  let dke_dv = Diff.diff "v" ke in
  print_endline ("dKE/dv = " ^ Expr.to_string dke_dv);

  print_endline "\nphysics: circular motion\n";

  let circumference = Parser.parse "2 * pi * r" in
  print_endline ("C = " ^ Expr.to_string circumference);

  let dc_dr = Diff.diff "r" circumference in
  print_endline ("dC/dr = " ^ Expr.to_string dc_dr);

  let r_val = 5.0 in
  let c_val = Eval.eval [("r", r_val)] circumference in
  Printf.printf "C(%.1f) = %.4f\n" r_val c_val