Who was the Carpenter's friend in 'Through the Looking Glass'?

The Walrus was the Carpenter's friend.

The Walrus and the Carpenter
Were walking close at hand;
They wept like anything to see
Such quantities of sand:
"If this were only cleared away,"
They said, "it would be grand!"

-Excerpt from:

The Walrus and The Carpenter

Lewis Carroll

(from Through the Looking-Glass and What Alice Found There, 1872)