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 ensures `grind` can use constructors and axioms for heuristic
instantiation based on E-matching. It also allows patterns without
pattern variables for theorems such as `theorem evenz : Even 0`.
This PR splits the environment used by the kernel from that used by the
elaborator, providing the foundation for tracking of asynchronously
elaborated declarations, which will exist as a concept only in the
latter.
Minor changes:
* kernel diagnostics are moved from an environment extension to a direct
environment as they are the only extension used directly by the kernel
* `initQuot` is moved from an environment header field to a direct
environment as it is the only header field used by the kernel; this also
makes the remaining header immutable after import
This PR ensures the new code generator produces code for `opaque`
definitions that are not tagged as `@[extern]`.
Remark: This is the behavior of the old code generator.
It's difficult to distinguish theorems from regular definitions in the
completion menu, which is annoying when using completion for searching
one or the other. This PR makes theorem completions use the "Eureka!"
icon ()
to distinguish them more clearly from other completions.
NB: We are very limited in terms of which icons we can pick here since
[the completion kinds provided by LSP / VS
Code](https://code.visualstudio.com/docs/editor/intellisense#_types-of-completions)
are optimized for object-oriented programming languages, but I think
this choice strikes a nice balance between being easy to identify,
having some visual connection to theorem proving and not being used a
lot in other languages and thus not clashing with pre-existing
associations.
Previously `RecursorVal.getInduct` would return the prefix of the
recursor’s name, which is unlikely the right value for the “derived”
recursors in nested recursion. The code using `RecursorVal.getInduct`
seems to expect the name of the inductive type of major argument here.
If we return that name, this fixes#5661.
This bug becomes more visible now that we have structural mutual
recursion.
Also, to avoid confusion, renames the function to ``getMajorInduct`.
right now, in order to find out how many auxilary datatype are in a
mutual group of inductive with nested data type, one has to jump
through hoops like this:
```
private def numNestedInducts (indName : Name) : MetaM Nat := do
let .inductInfo indVal ← getConstInfo indName | panic! "{indName} is an inductive"
let .recInfo recVal ← getConstInfo (mkRecName indName) | panic! "{indName} has a recursor"
return recVal.numMotives - indVal.all.lengt
```
The `InductiveVal` data structure already has `.isNested : Bool`, so it
seems to be a natural extension to beef that up to `.numNested: Nat`.
This touched kernel code.
this is a first step towards porting the code `constructions.cpp` to
Lean: It leaves the construction of the `Declaration` untouched, but
moves adding the declarations to the environment, and setting various
attributes, to the Lean world.
This allows the remaining logic (the construction of the `Declaration`)
to be implemented in Lean separately and easily compared to the C++
implementation, before we replace that too.
To that end, `Declaraion` gains an `BEq` instance.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
Co-authored-by: Arthur Adjedj <arthur.adjedj@ens-paris-saclay.fr>
* doc: Add explanations to MetavarContext
The explanations were taken from Leo's talk at the ICERM
Mathlib porting hackathon.
* doc: Add documentation for Declaration
This is explanations taken from Leo's talk given
at the post ICERM Mathlib porting hackathon.
* Update src/Lean/Declaration.lean
Co-authored-by: Scott Morrison <scott@tqft.net>
* Update src/Lean/Declaration.lean
Co-authored-by: Scott Morrison <scott@tqft.net>
* Update src/Lean/MetavarContext.lean
Co-authored-by: Scott Morrison <scott@tqft.net>
* fix depth comment
Co-authored-by: Scott Morrison <scott@tqft.net>
@Kha I was tired of writing `arbitrary _` :)
There 0 places in the stdlib where the type needs to be provided.
If in the future we need to specify the type we can use
`arbitrary (α := <type>)`
