/* Test function composition implementation */

f : x -> x * 2;
g : x -> x + 1;
h : x -> x * x;

/* Test 1: Basic composition */
result1 : f via g 5;  /* Should be compose(f, g)(5) = f(g(5)) = f(6) = 12 */

/* Test 2: Multiple composition */
result2 : f via g via h 3;  /* Should be compose(f, compose(g, h))(3) = f(g(h(3))) = f(g(9)) = f(10) = 20 */

/* Test 3: Function references */
result3 : @f;  /* Should return the function f */

/* Test 4: Function reference in composition */
result4 : @f via @g 5;  /* Should be compose(f, g)(5) = 12 */

/* Test 5: Pipe function */
result5 : pipe(f, g) 5;  /* Should be g(f(5)) = g(10) = 11 */

/* Test 6: Backward compatibility */
result6 : f 5;  /* Should still work: apply(f, 5) = 10 */
result7 : f g 5;  /* Should still work: apply(apply(f, g), 5) - may fail as expected */

/* Test 7: Natural language examples */
data : {1, 2, 3, 4, 5};
result8 : data via filter via map via reduce;  /* Pipeline example */

/* Test 8: Enhanced compose with multiple functions */
result9 : compose(f, g, h) 2;  /* Should be f(g(h(2))) = f(g(4)) = f(5) = 10 */

/* Test 9: Enhanced pipe with multiple functions */
result10 : pipe(h, g, f) 2;  /* Should be f(g(h(2))) = f(g(4)) = f(5) = 10 */