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 completes the `ToInt` family of typeclasses which `grind` will
use to embed types into the integers for `cutsat`. It contains instances
for the usual concrete data types (`Fin`, `UIntX`, `IntX`, `BitVec`),
and is extensible (e.g. for Mathlib's `PNat`).
This PR removes the `NatCast (Fin n)` global instance (both the direct
instance, and the indirect one via `Lean.Grind.Semiring`), as that
instance causes causes `x < n` (for `x : Fin k`, `n : Nat`) to be
elaborated as `x < ↑n` rather than `↑x < n`, which is undesirable. Note
however that in Mathlib this happens anyway!
This PR adds the `@[expose]` attribute to many functions (and changes
some theorems to be by `:= (rfl)`) in preparation for the `@[defeq]`
attribute change in #8419.
This PR reworks the `simp` set around the `Id` monad, to not elide or
unfold `pure` and `Id.run`
In particular, it stops encoding the "defeq abuse" of `Id X = X` in the
statements of theorems, instead using `Id.run` and `pure` to pass back
and forth between these two spellings. Often when writing these with
`pure`, they generalize to other lawful monads; though such changes were
split off to other PRs.
This fixes the problem with the current simp set where `Id.run (pure x)`
is simplified to `Id.run x`, instead of the desirable `x`.
This is particularly bad because the` x` is sometimes inferred with type
`Id X` instead of `X`, which prevents other `simp` lemmas about `X` from
firing.
Making `Id` reducible instead is not an option, as then the `Monad`
instances would have nothing to key on.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR adds the `List/Array/Vector.ofFnM`, the monadic analogues of
`ofFn`, along with basic theory.
At the same time we pave some potholes in nearby API.
---------
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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 the instances `Grind.CommRing (Fin n)` and `Grind.IsCharP
(Fin n) n`. New tests:
```lean
example (x y z : Fin 13) :
(x + y + z) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 * (x * y + y * z + z * x) := by
grind +ring
example (x y : Fin 17) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * x * y * (x + y) := by
grind +ring
example (x y : Fin 19) : (x - y) * (x ^ 2 + x * y + y ^ 2) = x ^ 3 - y ^ 3 := by
grind +ring
```
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This PR makes functions defined by well-founded recursion use an
`opaque` well-founded proof by default. This reliably prevents kernel
reduction of such definitions and proofs, which tends to be
prohibitively slow (fixes#2171), and which regularly causes
hard-to-debug kernel type-checking failures. This changes renders
`unseal` ineffective for such definitions. To avoid the opaque proof,
annotate the function definition with `@[semireducible]`.
This PR introduces `Fin.toNat` as an alias for `Fin.val`. We add this
function for discoverability and consistency reasons. The normal form
for proofs remains `Fin.val`, and there is a `simp` lemma rewriting
`Fin.toNat` to `Fin.val`.
This PR aligns current coverage of `find`-type theorems across
`List`/`Array`/`Vector`. There are still quite a few holes in this API,
which will be filled later.
This PR adds `protected` to `Fin.cast` and `BitVec.cast`, to avoid
confusion with `_root_.cast`. These should mostly be used via
dot-notation in any case.
This PR deprecates `Fin.ofNat` in favour of `Fin.ofNat'` (which takes an
`[NeZero]` instance, rather than returning an element of `Fin (n+1)`).
After leaving the deprecation warning in place for some time, we will
then rename `ofNat'` back to `ofNat`.
This PR fixes a bug where the monad lift coercion elaborator would
partially unify expressions even if they were not monads. This could be
taken advantage of to propagate information that could help elaboration
make progress, for example the first `change` worked because the monad
lift coercion elaborator was unifying `@Eq _ _` with `@Eq (Nat × Nat)
p`:
```lean
example (p : Nat × Nat) : p = p := by
change _ = ⟨_, _⟩ -- used to work (yielding `p = (p.fst, p.snd)`), now it doesn't
change ⟨_, _⟩ = _ -- never worked
```
As such, this is a breaking change; you may need to adjust expressions
to include additional implicit arguments.
In LNSym we often use the pattern `ofBool (a.getLsbD i)` to pick out a
specific bit (`i`) from a bitvector (`a`).
By adding a rewrite to `extractLsb` to `bv_decide`s normalization set,
we can still automatically close goals that have this pattern. In the
process, I also added a simp-lemma about the value of a `Fin 1`.
This PR refactors the 'ext' attribute and implements the following
features:
- The 'local' and 'scoped' attribute kinds are now usable.
- The attribute realizes the `ext`/`ext_iff` lemmas when they do not
already exist, rather than always generating them. This is useful in
conjunction with `@[local ext]`.
- Adding `@[ext]` to a user ext lemma now realizes an `ext_iff` lemma as
well; formerly this was only for structures. The name of the generated
`ext_iff` theorem for a user `ext` theorem named `A.B.myext` is
`A.B.myext_iff`. If this process leads to an error, the user can write
`@[ext (iff := false)]` to disable this feature.
Breaking changes:
- Now the "x" and "y" term arguments to the realized `ext` and `ext_iff`
lemmas are implicit.
- Now the realized `ext` and `ext_iff` lemmas are protected.
Bootstrapping notes:
- There are a few `ext_iff` lemmas to address after the next stage0
update.
Closes https://github.com/leanprover/lean4/issues/3643
Suggested by Floris [on
Zulip](https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/.22Missing.20Tactics.22.20list/near/446267660).
