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Fixes #14003: Ltac2 redefinition check is broken.
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This allows to embed Ltac2 functions manipulating Ltac1 values as simple
Ltac1 values.
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This allows proper treatment in notations, ie fixes #13303
The "glob" representation of universes (what pretyping sees) contains
only fully interpreted (kernel) universes and unbound universe
ids (for non Strict Universe Declaration).
This means universes need to be understood at intern time, so intern
now has a new "universe binders" argument. We cannot avoid this due to
the following example:
~~~coq
Module Import M. Universe i. End M.
Definition foo@{i} := Type@{i}.
~~~
When interning `Type@{i}` we need to know that `i` is locally bound to
avoid interning it as `M.i`.
Extern has a symmetrical problem:
~~~coq
Module Import M. Universe i. End M.
Polymorphic Definition foo@{i} := Type@{M.i} -> Type@{i}.
Print foo. (* must not print Type@{i} -> Type@{i} *)
~~~
(Polymorphic as otherwise the local `i` will be called `foo.i`)
Therefore extern also takes a universe binders argument.
Note that the current implementation actually replaces local universes
with names at detype type. (Asymmetrical to pretyping which only gets
names in glob terms for dynamically declared univs, although it's
capable of understanding bound univs too)
As such extern only really needs the domain of the universe
binders (ie the set of bound universe ids), we just arbitrarily pass
the whole universe binders to avoid putting `Id.Map.domain` at every
entry point.
Note that if we want to change so that detyping does not name locally
bound univs we would need to pass the reverse universe binders (map
from levels to ids, contained in the ustate ie in the evar map) to
extern.
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Add headers to a few files which were missing them.
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We implement a new type of "preterms" that represent untyped ASTs, corresponding
to glob_expr in the ML implementations. Ltac2 quotations inside notations are
provided with such preterms, and have to pretype them in order to do anything
of relevance with them.
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Most of these files were introduced after #6543 but used older headers
copied from somewhere else.
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Since Ltac2 cannot be put under the stdlib logical root (some file names
would clash), we move it to the `user-contrib` directory, to avoid adding
another hardcoded path in `coqinit.ml`, following a suggestion by @ejgallego.
Thanks to @Zimmi48 for the thorough documentation review and the
numerous suggestions.
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