• Subject: Re: Tables for mathematicians
• From: Philipp Janda <siffiejoe@...>
• Date: Sat, 20 Aug 2016 09:23:36 +0200

```Am 20.08.2016 um 09:03 schröbte Daurnimator:
```
```On 20 August 2016 at 16:59, Dirk Laurie <dirk.laurie@gmail.com> wrote:
```
```Just in case you thought tables were easy :-)

Let V be the set of all Lua values.

A key in V is a subset k of V, other than {nil}, such that any two members
of k are raw equal. Let K be the set of all keys.

Remarks:
1. Many keys consist of only one value.
2. The subset consisting of only NaN is not a valid key, since NaN is not
raw equal to itself.

An association is any mapping f from K to V.

An implementation of an association f is a Lua table t such that, if j
is any member of a key k, rawget(t,k) returns f(k).

An assocation is said to be implementable if an implementation of it exists.

If t is the implementation of an association f, the operation t[j]=v,
where j belongs to the key k, modifies t to be the implementation of a
a different association f' in such that f'[a] == f[a] when a ~= k.

Postulate: The keys of an implementable association which are mapped
to a non-nil value form a well-ordered set.

The `next` function is a generator for one of the possible orderings
of that well-ordered set.

I could go on ... but note we have not even got close to the issues
people have been dicussing recently!
```
```

Don't forget the conversion of integer floats to integers:

t = {}; f=1.0; t[1.0] = true; k = next(t); print(math.type(f), math.type(k))
```
```
He didn't. I believe that's handled via

```
```A key in V is a subset k of V, other than {nil}, such that any two members
of k are raw equal. Let K be the set of all keys.
```
```
i.e. the set {1, 1.0} is the "key" in this case.

Philipp

```