open Leibniz

let () =
  print_endline "symbolic constants\n";

  let area = Parser.parse "pi * r^2" in
  print_endline ("circle area: A = " ^ Expr.to_string area);

  let dA_dr = Diff.diff "r" area in
  print_endline ("dA/dr = " ^ Expr.to_string dA_dr);

  let r_val = 3.0 in
  let a_val = Eval.eval [("r", r_val)] area in
  Printf.printf "A(%.1f) = %.6f\n" r_val a_val;

  print_endline "\nexponential growth\n";

  let growth = Parser.parse "e^(k * t)" in
  print_endline ("N(t) = " ^ Expr.to_string growth);

  let dN_dt = Diff.diff "t" growth in
  print_endline ("dN/dt = " ^ Expr.to_string dN_dt)