This PR changes how WF.Eqns unfolds the fixpoint. Instead of delta'ing
until we have `fix`, and then blindly applying `fix_eq`, we delta one
step less and preserve the function on the right hand side. This leads
to smaller terms in the next step, so easier to debug, possibly faster,
possibly more robust.
This PR adds BitVec lemmas required to cancel multiplicative negatives,
and plumb support through to bv_normalize to make use of this result in
the normalized twos-complement form.
I include some bmod lemmas I found useful to prove this result, the two
helper lemmas I add use the same naming/proofs as their emod
equivalents.
This PR makes `take`/`drop`/`extract` available for each of
`List`/`Array`/`Vector`. The simp normal forms differ, however: in
`List`, we simplify `extract` to `take+drop`, while in `Array` and
`Vector` we simplify `take` and `drop` to `extract`. We also provide
`Array/Vector.shrink`, which simplifies to `take`, but is implemented by
repeatedly popping. Verification lemmas for `Array/Vector.extract` to
follow in a subsequent PR.
This PR adds a convenience for inductive predicates in `grind`. Now,
give an inductive predicate `C`, `grind [C]` marks `C` terms as
case-split candidates **and** `C` constructors as E-matching theorems.
Here is an example:
```lean
example {B S T s t} (hcond : B s) : (ifThenElse B S T, s) ==> t → (S, s) ==> t := by
grind [BigStep]
```
Users can still use `grind [cases BigStep]` to only mark `C` as a case
split candidate.
This PR makes `bv_normalize` rewrite shifts by `BitVec` constants to
shifts by `Nat` constants. This is part of the greater effort in
providing good support for constant shift simplification in
`bv_normalize`.
This PR fixes#6789 by ensuring metadata generated for inaccessible
variables in pattern-matches is consumed in `casesOnStuckLHS`
accordingly.
Closes#6789
This PR adds missing monadic higher order functions on
`List`/`Array`/`Vector`. Only the most basic verification lemmas
(relating the operations on the three container types) are provided for
now.
This PR adds add/sub injectivity lemmas for BitVec, and then adds
specialized forms with additional symmetries for the `bv_normalize`
normal form.
Since I need `neg_inj`, I add `not_inj`/`neg_inj` at once, and use it in
`BitVec.not_beq_not` instead of re-proving it.
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 adds "performance" counters (e.g., number of instances per
theorem) to `grind`. The counters are always reported on failures, and
on successes when `set_option diagnostics true`.
This PR adds injectivity theorems for inductives that did not get them
automatically (because they are defined too early) but also not yet
manuall later.
It also adds a test case to notice when new ones fall through.o
It does not add them for clearly meta-programming related types that are
not yet defined in `Init/Core.lean`, and uses `#guard_msgs` as an
allowlist.
---------
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
This PR adds a BitVec lemma that `(x >> x) = 0` and plumbs it through to
bv_normalize. I also move some theorems I found useful to the top of the
ushiftRight section.
This PR adds a few builtin case-splits for `grind`. They are similar to
builtin `simp` theorems. They reduce the noise in the tactics produced
by `grind?`.
This PR adds a number of simple comparison lemmas to the top/bottom
element for BitVec. Then they are applied to teach bv_normalize that
`(a<1) = (a==0)` and to remove an intermediate proof that is no longer
necessary along the way.
This PR fixes a significant auto-completion performance regression that
was introduced in #5666, i.e. v4.14.0.
#5666 introduced tactic docstrings, which were attempted to be collected
for every single completion item. This is slow for hundreds of thousands
of completion items. To fix this, this PR moves the docstring
computation into the completion item resolution, which is only called
when users select a specific completion item in the UI.
A downside of this approach is that we currently can't test completion
item resolution, so we lose a few tests that cover docstrings in
completions in this PR.
This PR adds infrastructure for the `grind?` tactic. It also adds the
new modifier `usr` which allows users to write `grind only [usr
thmName]` to instruct `grind` to only use theorem `thmName`, but using
the patterns specified with the command `grind_pattern`.
This PR adds support for closing goals using `match`-expression
conditions that are known to be true in the `grind` tactic state.
`grind` can now solve goals such as:
```lean
def f : List Nat → List Nat → Nat
| _, 1 :: _ :: _ => 1
| _, _ :: _ => 2
| _, _ => 0
example : z = a :: as → y = z → f x y > 0
```
Without `grind`, we would use the `split` tactic. The first two goals,
corresponding to the first two alternatives, are closed using `simp`,
and the the third using the `match`-expression condition produced by
`split`. The proof would proceed as follows.
```lean
example : z = a :: as → y = z → f x y > 0 := by
intros
unfold f
split
next => simp
next => simp
next h =>
/-
...
_ : z = a :: as
_ : y = z
...
h : ∀ (head : Nat) (tail : List Nat), y = head :: tail → False
|- 0 > 0
-/
subst_vars
/-
...
h : ∀ (head : Nat) (tail : List Nat), a :: as = head :: tail → False
|- 0 > 0
-/
have : False := h a as rfl
contradiction
```
Here is the same proof using `grind`.
```lean
example : z = a :: as → y = z → f x y > 0 := by
grind [f.eq_def]
```
This PR implements the `zetaUnused` simp and reduction option (added in
#6754).
True by default, and implied by `zeta`, this can be turned off to make
simp even more careful about preserving the expression structure,
including unused let and have expressions.
Breaking change: The `split` tactic no longer removes unused let and
have expressions as a side-effect, in rare cases this may break proofs.
`dsimp only` can be used to remove unused have and let expressions.
This PR fixes the support for case splitting on data in the `grind`
tactic. The following example works now:
```lean
inductive C where
| a | b | c
def f : C → Nat
| .a => 2
| .b => 3
| .c => 4
example : f x > 1 := by
grind [
f, -- instructs `grind` to use `f`-equation theorems,
C -- instructs `grind` to case-split on free variables of type `C`
]
```
This PR fixes a bug in the internalization of offset terms in the
`grind` tactic. For example, `grind` was failing to solve the following
example because of this bug.
```lean
example (f : Nat → Nat) : f (a + 1) = 1 → a = 0 → f 1 = 1 := by
grind
```
This PR fixes a `partial_fixpoint` error message to suggest the option
`trace.Elab.Tactic.monotonicity` rather than the nonexistent
`trace.Elab.Tactic.partial_monotonicity`.
This PR fixes a few bugs in the `grind` tactic: missing issues, bad
error messages, incorrect threshold in the canonicalizer, and bug in the
ground pattern internalizer.
This PR ensures that conditional equation theorems for function
definitions are handled correctly in `grind`. We use the same
infrastructure built for `match`-expression equations. Recall that in
both cases, these theorems are conditional when there are overlapping
patterns.
Avoids build time overhead until the option is proven to speed up
average projects. Adds Init.Prelude (many tiny declarations, "worst
case") and Init.List.Sublist (many nontrivial theorems, "best case")
under -DElab.async=true as new benchmarks for tracking.
