This PR introduces stricter inference for the `@[defeq]` attribute and a
companion `@[backward_defeq]` attribute that preserves the pre-PR
behavior
as an opt-in.
### What changed
* `@[defeq]` is now inferred only when the equation holds at
`.instances` transparency (the transparency `dsimp` operates at).
* `@[backward_defeq]` is the old set: every theorem whose `rfl` proof
the legacy inference would have accepted is tagged `@[backward_defeq]`,
so `defeq ⊆ backward_defeq` holds by construction.
* The option `backward.defeqAttrib.useBackward` (default `false`) makes
`dsimp` also use `@[backward_defeq]` theorems, restoring the pre-PR
behavior for a specific proof or file.
* The option is eqn-affecting: its value at the point of a function's
definition is recorded so that the equation lemmas later generated for
that function use the same value, regardless of the ambient option at
the use site.
### Mathlib adaption
A companion adaption branch (`lean-pr-testing-backward-defeq-attrib` on
mathlib4) builds cleanly against this PR and passes `lake test` without
warnings. Most adaption changes are scoped
`set_option backward.defeqAttrib.useBackward true in` additions on the
failing declarations; a small number of files needed proof-level edits
where the stored form of a `dsimp%`/`@[reassoc]`/`@[elementwise]`
/`@[simps]`/`@[to_app]`-generated lemma had drifted under the stricter
regime.
---------
Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This PR fixes two aspects of pretty printing of private names.
1. Name unresolution. Now private names are not special cased: the
private prefix is stripped off and the `_root_` prefix is added, then it
tries resolving all suffixes of the result. This is sufficient to handle
imported private names in the new module system. (Additionally,
unresolution takes macro scopes into account now.)
2. Delaboration. Inaccessible private names use a deterministic
algorithm to convert private prefixes into macro scopes. The effect is
that the same private name appearing in multiple times in the same
delaborated expression will now have the same `✝` suffix each time. It
used to use fresh macro scopes per occurrence.
Note: There is currently a small hack to support pretty printing in the
compiler's trace messages, which print constants that do not exist (e.g.
`obj`, `tobj`, and auxiliary definitions being compiled). Even though
these names are inaccessible (for the stronger reason that they don't
exist), we make sure that the pretty printer won't add macro scopes. It
also does some analysis of private names to see if the private names are
for the current module.
Closes#10771, closes#10772, and closes#10773
This PR sets the `irreducible` attribute before generating the equations
for recursive definitions. This prevents these equations to be marked as
`defeq`, which could lead to `simp` generation proofs that do not type
check at default transparency.
This issue is surfacing more easily since well-founded recursion on
`Nat` is implemented with a dedicated fix point operator (#7965). Before
that, `WellFounded.fix` was used, which is inherently not reducing, so
we did get the desired result even without the explicit reducibility
setting.
Fixes#12398.
This PR fixes an issue where `grind` fails when trying to unfold a
definition by pattern matching imported by `import all` (or from a
non-`module`).
Fixes#11715
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR lets recursive functions defined by well-founded recursion use a
different `fix` function when the termination measure is of type `Nat`.
This fix-point operator use structural recursion on “fuel”, initialized
by the given measure, and is thus reasonable to reduce, e.g. in `by
decide` proofs.
Extra provisions are in place that the fixpoint operator only starts
reducing when the fuel is fully known, to prevent “accidential” defeqs
when the remaining fuel for the recursive calls match the initial fuel
for that recursive argument.
To opt-out, the idiom `termination_by (n,0)` can be used.
We still use `@[irreducible]` as the default for such recursive
definitions, to avoid unexpected `defeq` lemmas. Making these functions
`@[semireducible]` by default showed performance regressions in lean.
When the measure is of type `Nat`, the system will accept an explicit
`@[semireducible]` without the usual warning.
Fixes#5234. Fixes: #11181.
This PR ensures private declarations are accessible from the private
scope iff they are local or imported through an `import all` chain,
including for anonymous notation and structure instance notation.
This PR addresses an outstanding feature in the module system to
automatically mark `let rec` and `where` helper declarations as private
unless they are defined in a public context such as under `@[expose]`.
This PR updates the formatting of, and adds explanations for, "unknown
identifier" errors as well as "failed to infer type" errors for binders
and definitions.
It attempts to ameliorate some of the confusion encountered in #1592 by
modifying the wording of the "header is elaborated before body is
processed" note and adding further discussion and examples of this
behavior in the corresponding error explanation.
This PR improves the “expected type mismatch” error message by omitting
the type's types when they are defeq, and putting them into separate
lines when not.
I found it rather tediuos to parse the error message when the expected
type is long, because I had to find the `:` in the middle of a large
expression somewhere. Also, when both are of sort `Prop` or `Type` it
doesn't add much value to print the sort (and it’s only one hover away
anyways).
This PR adjusts the experimental module system to make `private` the
default visibility modifier in `module`s, introducing `public` as a new
modifier instead. `public section` can be used to revert the default for
an entire section, though this is more intended to ease gradual adoption
of the new semantics such as in `Init` (and soon `Std`) where they
should be replaced by a future decl-by-decl re-review of visibilities.
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`.
