This PR performs minor maintenance on the String API
- Rename `String.Pos.toCopy` to `String.Pos.copy` to adhere to the
naming convention
- Rename `String.Pos.extract` to `String.extract` to get sane dot
notation again
- Add `String.Slice.Pos.extract`
This PR renames `String.ValidPos` to `String.Pos`, `String.endValidPos`
to `String.endPos` and `String.startValidPos` to `String.startPos`.
Accordingly, the deprecations of `String.Pos` to `String.Pos.Raw` and
`String.endPos` to `String.rawEndPos` are removed early, after an
abbreviated deprecation cycle of two releases.
This PR adds the basic infrastructure to perform termination proofs
about `String.ValidPos` and `String.Slice.Pos`.
We choose approach where the intended way to do termination arguments is
to argue about the position itself rather than some projection of it
like `remainingBytes`.
The types `String.ValidPos` and `String.Slice.Pos` are equipped with a
`WellFoundedRelation` instance given by the greater-than relation. This
means that if a function takes a position `p` and performs a recursive
call on `q`, then the decreasing obligation will be `p < q`. This works
well in the common case where `q` is `p.next h`, in which case the goal
`p < p.next h` is solved by the simplifier.
For stepping through a string backwards, we introduce a type synonym
with a `WellFoundedRelation` instance given by the less-than relation.
This means that if a function takes a position `p` and performs a
recursive call on `q` and specifies `termination_by p.down`, then the
decreasing obligation will be `q < p`. This works well in the case where
`q` is `p.prev h`, in which case the goal `p.prev h < p` is solved by
the simplifier.
For termination arguments invoving multiple strings, the lower-level
primitive `p.remainingBytes` (landing in `Nat`) is also available.
In a future PR, we will additionally provide the necessary typeclasses
instances to register `String.ValidPos` and `String.Slice.Pos` with
`grind` to make complex termination arguments more convenient in user
code.
