Seems to be very slow though...
And Idris is unable to find the depth-inv instance for `r10Proof`.
Could be that auto-search is not as strong as Agda's? Or more likely,
I've set things up slightly wrong...
This also caught an implementation error in the Global formula
definitions:
AG f = A[ f U (f AND' Completed) ]
and **not**
AG f = A[ (f U f) AND' Completed ]
(both of which are valid parsings of the original
AG f = A[ f u f AND' Completed]
)
This makes more sense in terms of `EU` being efficient and only
evaluating as much as it needs to. However, I'm not sure `model.follow`
is implemented correctly (Agda delays the call to `model.followAll`,
which I'm unsure if we can do (and if so, how to do it) in Idris)...
This reveals an unfortunate problem/misunderstanding: For `ExistsUntil`
to make sense, in terms of evaluation speedups, the list needs to be
lazy. Which is _not_ what `Lazy (List a)` does /!\
I need to switch to LazyList...
And here's a good case against allowing custom unicode syntax:
〈$〉 is `<$>`, i.e. the infix notation for `map`. That's fine; If you
happen to know it!
ESPECIALLY, if your paper defines 〈_〉 as custom notation for a guarded
expression! Then there is **no way** to tell that the expression 〈$〉
is not a guarded expression over `$`, but is instead the alias for
`map`!! You just have to magically know this beforehand!
We also need an explicit `Lazy` annotation for Idris to be happy with
the implicit `ms` in the `IsCompleted` constructor.
The proofs of depth-invariance for Always Until and Exists Until require
mapping the proofs over the Formulae's internal `All` and `Any`
respectively. Idris provides some functions for this, but they erase the
list and so don't quite work. Instead we need to implement our own,
which don't erase the list.
Don't you love when papers introduce syntax and functions which you've
never seen before and don't seem to match the types of the existing
stuff?
P.S. YEET! (aka. that's probably enough for today ^^)
The original Agda code declares the module with L and Sigma (Lbls and
Sts) with type Set. This is apparently close to a parameter block, which
solves the unification error I was having with `now`! Huge thanks to
gallais for showing me that!
I should have put this under version-control WAAAAAY sooner than this!
Oh well, better late than never...
There are some fun problems to solve in terms of type-mismatch and
erasure, but that's for another day.
