This PR introduces an explicit `defeq` attribute to mark theorems that
can be used by `dsimp`. The benefit of an explicit attribute over the
prior logic of looking at the proof body is that we can reliably omit
theorem bodies across module boundaries. It also helps with intra-file
parallelism.
If a theorem is syntactically defined by `:= rfl`, then the attribute is
assumed and need not given explicitly. This is a purely syntactic check
and can be fooled, e.g. if in the current namespace, `rfl` is not
actually “the” `rfl` of `Eq`. In that case, some other syntax has be
used, such as `:= (rfl)`. This is also the way to go if a theorem can be
proved by `defeq`, but one does not actually want `dsimp` to use this
fact.
The `defeq` attribute will look at the *type* of the declaration, not
the body, to check if it really holds definitionally. Because of
different reduction settings, this can sometimes go wrong. Then one
should also write `:= (rfl)`, if one does not want this to be a defeq
theorem. (If one does then this is currently not possible, but it’s
probably a bad idea anyways).
The `set_option debug.tactic.simp.checkDefEqAttr true`, `dsimp` will
warn if could not apply a lemma due to a missing `defeq` attribute.
With `set_option backward.dsimp.useDefEqAttr.get false` one can revert
to the old behavior of inferring rfl-ness based on the theorem body.
Both options will go away eventually (too bad we can’t mark them as
deprecated right away, see #7969)
Meta programs that generate theorems (e.g. equational theorems) can use
`inferDefEqAttr` to set the attribute based on the theorem body of the
just created declaration.
This builds on #8501 to update Init to `@[expose]` a fair amount of
definitions that, if not exposed, would prevent some existing `:= rfl`
theorems from being `defeq` theorems. In the interest of starting
backwards compatible, I exposed these function. Hopefully many can be
un-exposed later again.
A mathlib adaption branch exists that includes both the meta programming
fixes and changes to the theorems (e.g. changing `:= by rfl` to `:=
rfl`).
With the module system there is now no special handling for `defeq`
theorem bodies, because we don’t look at the body anymore. The previous
hack is removed. The `defeq`-ness of the theorem needs to be checked in
the context of the theorem’s *type*; the error message contains a hint
if the defeq check fails because of the exported context.
This PR makes the equational theorems of non-exposed defs private. If
the author of a module chose not to expose the body of their function,
then they likely don't want that implementation to leak through
equational theorems. Helps with #8419.
There is some amount of incidential complexity due to how `private`
works in lean, by mangling the name: lots of code paths that need now do
the right thing™ about private and non-private names, including the
whole reserved name machinery.
So this includes a number of refactorings:
* The logic for calculating an equational theorem name (or similar) is
now done by a single function, `mkEqLikeNameFor`, rather than all over
the place.
* Since the name of the equational theorem now depends on the current
context (in particular whether it’s a proper module, or a non-module
file), the forward map from declaration to equational theorem doesn’t
quite work anymore. This map is deleted; the list of equational theorems
are now always found by looking for declaration of the expected names
(`alreadyGenerated). If users define such theorems themselves (and make
it past the “do not allow reserved names to be declared”) they get to
keep both pieces.
* Because this map was deleted, mathlib’s `eqns` command can no longer
easily warn if equational lemmas have already been generated too early
(adaption branch exists). But in general I think lean could provide a
more principled way of supporting custom unfold lemmas, and ideally the
whole equational theorem machinery is just using that.
* The ReservedNamePredicate is used by `resolveExact`, so we need to
make sure that it returns the right name, including privateness. It is
not ok to just reserve both the private and non-private name but then
later in the ReservedNameAction produce just one of the two.
* We create `foo.def_eq` eagerly for well-founded recursion. This is
needed because we need feed in the proof of the rewriting done by
`wf_preprocess`. But if `foo.def_eq` is private in a module, then a
non-module importing it will still expect a non-private `foo.def_eq` to
exist. To patch that, we install a `copyPrivateUnfoldTheorem :
GetUnfoldEqnFn` that declares a theorem aliasing the private one. Seems
to work.
This PR adjusts the experimental module system to not export the bodies
of `def`s unless opted out by the new attribute `@[expose]` on the `def`
or on a surrounding `section`.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This PR adds support for the following import variants to the
experimental module system:
* `private import`: Makes the imported constants available only in
non-exported contexts such as proofs. In particular, the import will not
be loaded, or required to exist at all, when the current module is
imported into other modules.
* `import all`: Makes non-exported information such as proofs of the
imported module available in non-exported contexts in the current
module. Main purpose is to allow for reasoning about imported
definitions when they would otherwise be opaque. TODO: adjust name
resolution so that imported `private` decls are accessible through
syntax.
They can be combined into `private import all`, which will likely be the
most common usage of `import all`.
This PR ensures that for modules opted into the experimental module
system, we do not import module docstrings or declaration ranges.
Excluding declaration docstrings as well would require some more work to
make `[inherit_doc]` leave a mere reference to the other declaration
instead of copying its docstring eagerly.
