Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/4=110
M:4/4
K:C
['c2 c2']  
X:1
L:1/8
Q:1/4=110
M:4/4
K:C
 c2 z z/ c/"^Intro" c4 | c3 c/ c4 | c2 c2 c2 c2 | d4 d4 | e8 | e3 e/ e4 | e3 d/ c4 | 
 c3 c/ c2 (ed) | c4 B4 | (c4 c2) z2 |[K:F][M:6/8]"^Carol" F2 G A2 B | c2 d (BA) G | F2 D F2 D | 
 (FG) A (A2 G) | F2 G A2 B | c2 d (BA) G | A2 E (FG) A | G2 F F2 z | c2 d (cB) A | f2 c (AG) F | 
 A3 G3 | F4 z2 |]  