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> The expression given in the OP is, according to Wikipedia, sometimes cited as the y combinator itself (and is beta equivalent). That's actually true, and ver
by qsort 6y ago
> The expression given in the OP is, according to Wikipedia, sometimes cited as the y combinator itself (and is beta equivalent).
That's actually true, and very obviously so. I'm sorry.
> The arbitrariness...
I agree that clear notation is important; the pictorial style made me think of Feynman diagrams. My comment was a bit tongue-in-cheek, maybe unnecessarily so, but the point is that I fail to see how those pictures are clearer than plain text: you are not replacing complex stuff with a simple representation, you are just rewriting a simple formula in a different style.
> Also there are issues with the lambda calculus notation...
Are there? That's the same problem you face whenever you have dummy variables, e.g. the 'dx' in integrals.
- dan-robertson 6y agoYeah I don’t see much from this notation (I also find it hard to tell the difference between the result of an abstraction and an application which feels like a somewhat important difference). I mostly wanted to suggest that diagrams or notation changes in general can be very useful. It’s true that variable renaming comes up in other parts of mathematics but scope matters a lot less in most other mathematics, so much so that it is basically implicit and left to be inferred based on the mathematical context. You wouldn’t normally rename a variable to avoid a conflict so much as you would avoid giving it a conflicting name in the first place. The recursive nature of the lambda calculus means you can’t avoid the problem this way.