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Comment by wyager | Hacker News Reader

No offense, but this is exactly the sort of nonsense I associate with urbit.

>ideally, all values in its range are fixpoints, f(x) == f(f(x)).

This doesn't make any sense whatsoever. The only function for which this is true is identity, and I assure you it takes more than just the identity function to make a useful program. This isn't even possible unless the function has the type "a -> a".

The only other thing I can see you trying to express here is some butchery of set notation, where by f(x) you actually mean {f(x) | forall x of the correct type}. Even then, what you're saying is still completely nonsensical.

I honestly cannot tell if urbit is some sort of coordinated trolling effort.

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Identity is not the only function for which that holds. As an immediate example, constant functions have this property as well. More interesting examples exist as well.

Also what was stated was not an equation for any old fixed point but instead idempotence—a specific kind of fixed point. In particular, this describes precisely the shape of a "validation" function so long as it either succeeds on all inputs or has a notion of failure in either its computational context or it's range ("span" I guess).

'a "validation" function'

Or "normalization"

Yeah, that's exactly right. I usually say "normalization."

> The only function for which this is true is identity, [...]

Any projection suffices.

> The only function for which this is true is identity

If you want to clamp a value to some arbitrary range (a hint to the name), then any function that does so has this property.

    unsigned char f(unsigned long x) { return x & 255; }
    long f(long x) { return x < 0 ? x : -x; }

The return type isn't the same as the input type there. It only looks that way because of C's limitations.

Put it this way: f(f(x)) never makes sense for those definitions of f; it would always indicate a programming error. And so the type system ought to prevent it.

To be slightly clearer, the values here are Urbit "nouns."

A noun is an atom or a cell. An atom is an unsigned integer of any size. A cell is an ordered pair of nouns.

I am fairly confident that many useful sets can be specified as the fixpoint set of a function in this space.

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