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I like this idea. However, I would make the mutators functions instead and use function notation, for example M(G) instead of G[M]. Limit is not a mutator it is a function that returns a mutator, so Limit(50) is a mutator. You could make a game also a function, which takes a move as its parameter and returns a game starting from the new position. You could also make something which is both a game and a mutator (so moves in that game would also be games). My idea is a strange idea. also, you could say other things as well: A mutator M is redundant with game G if G=M(G).