This PR adds `instance [Pure f] : Inhabited (OptionT f α)`, so that
`Inhabited (OptionT Id Empty)` synthesizes.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR shuffles some results about integers around to make sure that
all material that currently exists about `Int.bmod` is located in
`DivMod/Lemmas.lean` and not downstream of that.
This PR adds a mixin typeclass for `Lean.Grind.CommRing` recording the
characteristic of the ring, and constructs instances for `Int`, `IntX`,
`UIntX`, and `BitVec`.
This PR adds `BitVec.pow` and `Pow (BitVec w) Nat`. The implementation
is the naive one, and should later be replaced by an `@[extern]`. This
is tracked at https://github.com/leanprover/lean4/issues/7887.
This PR adds `Int.toNat_sub''` a variant of `Int.toNat_sub` taking
inequality hypotheses, rather than expecting the arguments to be casts
of natural numbers. This is parallel to the existing `toNat_add` and
`toNat_mul`.
This PR adds `UIntX.pow` and `Pow UIntX Nat` instances, and similarly
for signed fixed-width integers. These are currently only the naive
implementation, and will need to be subsequently replaced via
`@[extern]` with fast implementations (tracked at #7887).
This PR generalizes the typeclass assumptions on monadic `Option`
functions.
`Option.mapA` is now an alias for `Option.mapM`, which now works for
applicative functors. The changed definition is exactly equivalent for
monads which use the default implementation of `map`, and those who
change it will hopefully choose a definition for `map` that is more
efficient and not less efficient. `Option.mapA` is not deprecated in
order to keep the API aligned with `List` (`List.mapA` and `List.mapM`
cannot be unified because the monadic version is much more efficient
than the applicative version).
This PR fixes a regression introduced in #7445 where the new
`Array.emptyWithCapacity` was accidentally not tagged with the correct
function to actually allocate the capacity.
This PR partially reverts #7818, because the function called
`Option.zipWith` in that PR does not actually correspond to
`List.zipWith`. We choose `Option.merge` as the name instead.
This PR changes definitions and theorems not to use the membership
instance on `Option` unless the theorem is specifically about the
membership instance.
The reasoning for this change is that the lemma `a ∈ o ↔ o = some a` is
a `simp` lemma, and we generally want theorem statements to use `simp`
normal forms.
One notable exception is the `ForIn'` instance, which must use
`Membership` because unlike `GetElem`, `ForIn'` requires the validity
predicate to be expressed via `Membership`.
This PR improves the normalization of `Bool` terms in `grind`. Recall
that `grind` currently does not case split on Boolean terms to reduce
the size of the search space.
This PR adds `BitVec.[toInt_append|toFin_append]`.
`toInt_append` states:
```lean
(x ++ y).toInt = if n == 0 then y.toInt else (2 ^ m) * x.toInt + y.toNat
```
We also add the following `Nat` theorem (derived from a corresponding
theorem `two_pow_add_eq_or_of_lt`) as it faciliates the `append` proofs:
```lean
theorem shiftLeft_add_eq_or_of_lt {b : Nat} (b_lt : b < 2^i) (a : Nat) :
a <<< i + b = a <<< i ||| b
```
This PR proves `List.head_of_mem_head?` and the analogous
`List.getLast_of_mem_getLast?`.
These are similar to the existing `List.head_eq_iff_head?_eq_some` and
`List.getLast_eq_iff_getLast?_eq_some`, with the added convenience that
the proof term needs not be given.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This PR updates `rw?`, `show_term`, and other tactic-suggesting tactics
to suggest `expose_names` when necessary and validate tactics prior to
suggesting them, as `exact?` already did, and it also ensures all such
tactics produce hover info in the messages showing tactic suggestions.
This introduces a breaking change in the `TryThis` API: the `type?`
parameter of `addRewriteSuggestion` is now an `LOption`, not an
`Option`, to obviate the need for a hack we previously used to indicate
that a rewrite closed the goal.
Closes#7350
This PR fixes an issue in the cutsat counterexamples. It removes the
optimization (`Cutsat.State.terms`) that was used to avoid the new
theorem `eq_def`. In the two new tests, prior to this PR, `cutsat`
produced a bogus counterexample with `b := 2`.
This PR improves support for `Nat` in the `cutsat` procedure used in
`grind`:
- `cutsat` no longer *pollutes* the local context with facts of the form
`-1 * NatCast.natCast x <= 0` for each `x : Nat`. These facts are now
stored internally in the `cutsat` state.
- A single context is now used for all `Nat` terms.
The PR also introduces a mapping mechanism for all "foreign" types that
can be converted to `Int`. Currently, only `Nat` is supported, but
additional types will be added in the future.
This PR adds SMT-LIB operators to detect overflow
`BitVec.(umul_overflow, smul_overflow)`, according to the definitions
[here](https://github.com/SMT-LIB/SMT-LIB-2/blob/2.7/Theories/FixedSizeBitVectors.smt2),
and the theorems proving equivalence of such definitions with the
`BitVec` library functions (`umulOverflow_eq`, `smulOverflow_eq`).
Support theorems for these proofs are `BitVec.toInt_one_of_lt,
BitVec.toInt_mul_toInt_lt, BitVec.le_toInt_mul_toInt,
BitVec.toNat_mul_toNat_lt, BitVec.two_pow_le_toInt_mul_toInt_iff,
BitVec.toInt_mul_toInt_lt_neg_two_pow_iff` and `Int.neg_mul_le_mul,
Int.bmod_eq_self_of_le_mul_two, Int.mul_le_mul_of_natAbs_le,
Int.mul_le_mul_of_le_of_le_of_nonneg_of_nonpos, Int.pow_lt_pow`. The PR
also includes a set of tests.
Co-authored by @tobiasgrosser.
---------
Co-authored-by: Tobias Grosser <tobias@grosser.es>
Co-authored-by: Tobias Grosser <github@grosser.es>
Co-authored-by: Siddharth <siddu.druid@gmail.com>
This PR adds `Option.pfilter`, a variant of `Option.filter` and several
lemmas for it and other `Option` functions. These lemmas are split off
from #7400.
This PR adds a new propagation rule for `Bool` disequalities to `grind`.
It now propagates `x = true` (`x = false`) from the disequality `x =
false` (`x = true`). It ensures we don't have to perform case analysis
on `x` to learn this fact. See tests.
This PR adds missing propagation rules for `LawfulBEq A` to `grind`.
They are needed in a context where the instance `DecidableEq A` is not
available. See new test.
This PR adds the Bitwuzla rewrite `NORM_BV_ADD_CONCAT` for symbolic
simplification of add-of-append.
---------
Co-authored-by: Tobias Grosser <github@grosser.es>
