import <Utilities/Conversion.sl>;
import <Utilities/Sequence.sl>;

T0 := 100.0;
TR := 20.0;
k := 0.07;

main(args(2)) :=
	let
		results[i] := euler(newtonCooling, T0, 100, stringToInt(args[i]), 0, "delta_t = " ++ args[i]);
	in
		delimit(results, '\n');

newtonCooling(t) := -k * (t - TR);

euler: (float -> float) * float * int * int * int * char(1) -> char(1);
euler(f, y, n, h, x, output(1)) :=
	let
		newOutput := output ++ "\n\t" ++ intToString(x) ++ "\t" ++ floatToString(y, 3);
		newY := y + h * f(y);
		newX := x + h;
	in
			output when x > n
		else
			euler(f, newY, n, h, newX, newOutput);