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This game represents the untyped lambda calculus. A hungry alligator is a lambda abstraction, an old alligator is parentheses, and eggs are variables. The eating rule corresponds to beta-reduction. The color rule corresponds to (over-cautious) alpha-conversion. The old age rule says that if a pair of parentheses contains a single term, the parentheses can be removed.
Next year, Ninja Theory's Devil May Cry reboot (entitled DMC) will be released, featuring a more youthful demon hunting protagonist. While he shares the same name as the Dante from the original Devil May Cry games, he's actually not technically a "younger" version of Dante. According to Dengeki PlayStation, this Dante exists in a parallel world.