### The game of carnivorous math

You know how sometimes something cool comes along and wows you with its novelty, and then you look at the date and realize it's eight months old? And everyone already knows about it but you? This is one of those times.

But just in case it's not, and you don't know about it yet: Alligator Eggs is a children's game about - well, read it and see.

OK. Read it? Now for the criticism.

1. Old alligators are a wart. They're a wart in the form of parentheses too, but they're even worse here. In either case, the problem is that they arise purely from syntax - there's no corresponding feature in the math; all they do is patch up an ambiguity in the surface representation.

There has to be a better way. Perhaps predator-prey pairs could be disambiguated by just putting a piece of paper underneath, to serve as a visual box and a way to move them. This could also help delimit very large families, which are easy to lose track of when playing with bits of paper. It's hard when your alligators don't magically change size to cover their nests.

2. After only a few η-adoptions and β-devourings, I missed combinators and global variables. I'm not sure they would make a better game (adding random features doesn't usually improve a game), so maybe this is just my programmerhood talking, but I think they would at least increase the range of concepts you can teach with the game. It shouldn't be hard to get players to give names to a few of the simpler alligator families. Indeed, I suspect they'd eagerly adopt them, because they save so much paper-shuffling. They could be represented as non-alligator animals - the `i`bis, who is replaced by whatever she eats; the `k`angaroo, who hops away and leaves his dinner in the care of an alligator; the `ω`ombat, who feeds anything to itself; the `ki`tten, who turns anything into an ibis; and so on. (How do kittens turn whole families of alligators into ibises? Well, have you ever seen what a kitten does to a board game? That's how.)

3. You could add non-carnivorous data like integers, and operators on them. But I have a better idea: despite my functional preference, I think side-effecting operators could be fun. A puzzle that does something is more interesting than one that only puzzles. State makes reduction order matter, but that's not a bad thing - the order exists anyway, so it might as well mean something. A suitable choice of initial configuration and state objectives offers the bizarre prospect of controlling a game by choosing evaluation order.

Another application of state is in multiplayer play. Suppose players take turns, each independently performing one operation on their own menagerie. This game becomes much more interesting if the players can interact - and stateful operators provide a natural way to do that. Operations could have side effects on the opponent's alligators - feeding them things, for example. But their power is restrained by the difficulty of handling them.

And you could draw animals from a deck of cards... Okay, this is getting too complicated. But the complexity does have one advantage: it makes it easier to not think too hard about the biology.