This PR upstreams lemmas about List/Array operations already defined in
Lean from std/batteries.
Happy to take suggestions about increasing or decreasing scope.
---------
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Because of the last-added-tried-first rule for macros, all the special
purpose `decreasing_trivial` rules are tried for most recursive
definitions out there, and because they use `apply` and `assumption`
with default transparency may cause some definitoins to be unfolded over
and over again.
A quick test with one of the functions in the leansat project shows that
elaboration time goes down from 600ms to 375ms when using
```
decreasing_by all_goals decreasing_with with_reducible decreasing_trivial
```
instead of
```
decreasing_by all_goals decreasing_with decreasing_trivial
```
This change uses `with_reducible` in most of these macros.
This means that these tactics will no longer work when the
relations/definitions they look for is hidden behind a definition.
This affected in particular `Array.sizeOf_get`, which now has a
companion `sizeOf_getElem`.
In addition, there were three tactics using `apply` to apply Nat-related
lemmas
that we now expect `omega` to solve. We still need them when building
`Init` modules
that don’t have access to `omega`, but they now live in
`decreasing_trivial_pre_omega`,
meant to be only used internally.
Previously the `ac_rfl` tactic was only really usable when depending on
mathlib. With these instances, `ac_rfl` can deal with the various
operations defined in Lean.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
This removes simp attributes from `Nat.succ.injEq` and
`Nat.succ_sub_succ_eq_sub` to replace them with simprocs. This is
because any reductions involving `Nat.succ` has a high risk of leading
proof performance problems when dealing with even moderately large
numbers.
Here are a couple examples that will both report a maximum recursion
depth error currently. These examples are fixed by this PR.
```
example : (123456: Nat) = 12345667 := by
simp
example (x : Nat) (p : x = 0) : 1000 - (x + 1000) = 0 := by
simp
```
This makes changes to the `GetElem` class so that it does not lead to
unnecessary overhead in container like `RBMap`.
The changes are to:
1. Make `getElem?` and `getElem!` part of the `GetElem` class so they
can be overridden in instances.
2. Introduce a `LawfulGetElem` class that contains correctness theorems
for `getElem?` and `getElem!` using the original definitions.
3. Reorganize definitions (e.g, by moving `GetElem` out of
`Init.Prelude`) so that the `GetElem` changes are feasible.
4. Provide `LawfulGetElem` instances to complement all existing
`GetElem` instances in Lean core.
To reduce the size of the PR, this doesn't do the work of providing new
`GetElem` instances for `RBMap`, `HashMap` etc. That will be done in a
separate PR (#3688) that depends on this.
---------
Co-authored-by: Mac Malone <tydeu@hatpress.net>
This adds a number of lemmas for simplification of `Bool` and `Prop`
terms. It pulls lemmas from Mathlib and adds additional lemmas where
confluence or consistency suggested they are needed.
It has been tested against Mathlib using some automated test
infrastructure.
That testing module is not yet included in this PR, but will be included
as part of this.
Note. There are currently some comments saying the origin of the simp
rule. These will be removed prior to merging, but are added to clarify
where the rule came from during review.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
This will collect definitions from Std.Logic
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
The example was looping with the new `simp` reduction strategy. Here
is the looping trace.
```
List.reverseAux (List.reverseAux as []) bs
==> rewrite using reverseAux_reverseAux
List.reverseAux [] (List.reverseAux (List.reverseAux as []) bs)
==> unfold reverseAux
List.reverseAux (List.reverseAux as []) bs
==> rewrite using reverseAux_reverseAux
List.reverseAux [] (List.reverseAux (List.reverseAux as []) bs)
==> ...
```
Changes the implementation of `List.all` and `List.any` so they
short-circuit. The implementations are tail-recursive.
This replaces https://github.com/leanprover/std4/pull/392, which was
going to do this with `@[csimp]`.
