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This will enable to define numeral notation on non inductive by using
an inductive type as proxy and those translations to translate to/from
the actual type to the inductive type.
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Add headers to a few files which were missing them.
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We move `binder_kind` to the pretyping AST, removing the last data
type in the now orphaned file `Decl_kinds`.
This seems a better fit, as this data is not relevant to the lower
layers but only used in `Impargs`.
We also move state keeping to `Impargs`, so now implicit declaration
must include the type. We also remove a duplicated function.
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Not pretty, but it had to be done some day, as `Globnames` seems to be
on the way out.
I have taken the opportunity to reduce the number of `open` in the
codebase.
The qualified style would indeed allow us to use a bit nicer names
`GlobRef.Inductive` instead of `IndRef`, etc... once we have the
tooling to do large-scale refactoring that could be tried.
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Since their introduction, these notations were incorrectly using the
proof-local environment.
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This should make https://github.com/coq/coq/pull/9129 easier.
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As per https://github.com/coq/coq/pull/8965#issuecomment-441440779
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Users can now register string notations for custom inductives.
Much of the code and documentation was copied from numeral notations.
I chose to use a 256-constructor inductive for primitive string syntax
because (a) it is easy to convert between character codes and
constructors, and (b) it is more efficient than the existing `ascii`
type.
Some choices about proofs of the new `byte` type were made based on
efficiency. For example, https://github.com/coq/coq/issues/8517 means
that we cannot simply use `Scheme Equality` for this type, and I have
taken some care to ensure that the proofs of decidable equality and
conversion are fast. (Unfortunately, the `Init/Byte.v` file is the
slowest one in the prelude (it takes a couple of seconds to build), and
I'm not sure where the slowness is.)
In String.v, some uses of `0` as a `nat` were replaced by `O`, because
the file initially refused to check interactively otherwise (it
complained that `0` could not be interpreted in `string_scope` before
loading `Coq.Strings.String`).
There is unfortunately a decent amount of code duplication between
numeral notations and string notations.
I have not put too much thought into chosing names; most names have been
chosen to be similar to numeral notations, though I chose the name
`byte` from
https://github.com/coq/coq/issues/8483#issuecomment-421671785.
Unfortunately, this feature does not support declaring string syntax for
`list ascii`, unless that type is wrapped in a record or other inductive
type. This is not a fundamental limitation; it should be relatively
easy for someone who knows the API of the reduction machinery in Coq to
extend both this and numeral notations to support any type whose hnf
starts with an inductive type. (The reason for needing an inductive
type to bottom out at is that this is how the plugin determines what
constructors are the entry points for printing the given notation.
However, see also https://github.com/coq/coq/issues/8964 for
complications that are more likely to arise if inductive type families
are supported.)
N.B. I generated the long lists of constructors for the `byte` type with
short python scripts.
Closes #8853
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