The linters in Batteries can be used to spot mistakes in Lean. See the
message on
[Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Go-to-def.20on.20typeclass.20fields.20and.20type-dependent.20notation/near/442613564).
These are the different linters with errors:
- unusedArguments:
There are many unused instance arguments, especially a redundant `[Monad
m]` is very common
- checkUnivs:
There was a problem with universes in a definition in
`Init.Control.StateCps`. I fixed it by adding a `variable` statement for
the implicit arguments in the file.
- defLemma:
many proofs are written as `def` instead of `theorem`, most notably
`rfl`. Because `rfl` is used as a match pattern, it must be a def. Is
this desirable?
The keyword `abbrev` is sometimes used for an alias of a theorem, which
also results in a def. I would want to replace it with the `alias`
keyword to fix this, but it isn't available.
- dupNamespace:
I fixed some of these, but left `Tactic.Tactic` and `Parser.Parser` as
they are as these seem intended.
- unusedHaveSuffices:
I cleaned up a few proofs with unused `have` or `suffices`
- explicitVarsOfIff:
I didn't fix any of these, because that would be a breaking change.
- simpNF:
I didn't fix any of these, because I think that requires knowing the
intended simplification order.
The `simp` tactic uses a discrimination tree to select candidate
theorems that will be used to rewrite an expression. This indexing data
structure minimizes the number of theorems that need to be tried and
improves performance. However, indexing modulo reducibility is
challenging, and a theorem that could be applied, when taking reduction
into account, may be missed. For example, suppose we have a `simp`
theorem `foo : forall x y, f x (x, y).2 = y`, and we are trying to
simplify the expression `f a b <= b`. `foo` will not be tried by `simp`
because the second argument of `f a b` is not a projection of a pair.
However, `f a b` is definitionally equal to `f a (a, b).2` since we can
reduce `(a, b).2`.
In Lean 3, we had a much simpler indexing data structure where only the
head symbol was taken into account. For the theorem `foo`, the head
symbol is `f`. Thus, the theorem would be considered by `simp`.
This commit adds the option `Simp.Config.index`. When `simp (config := {
index := false })`, only the head symbol is considered when retrieving
theorems, as in Lean 3. Moreover, if `set_option diagnostics true`,
`simp` will check whether every applied theorem would also have been
applied if `index := true`, and report them. This feature can help users
diagnose tricky issues in code that has been ported from libraries
developed using Lean 3 and then ported to Lean 4. In the following
example, it will report that `foo` is a problematic theorem.
```lean
opaque f : Nat → Nat → Nat
@[simp] theorem foo : f x (x, y).2 = y := by sorry
example : f a b ≤ b := by
set_option diagnostics true in
simp (config := { index := false })
```
In the example above, the following diagnostic message is produced.
```lean
[simp] theorems with bad keys
foo, key: [f, *, Prod.1, Prod.mk, Nat, Nat, *, *]
```
With the information above, users can annotate theorems such as `foo`
using `no_index` for problematic subterms.
Example:
```lean
opaque f : Nat → Nat → Nat
@[simp] theorem foo : f x (no_index (x, y).2) = y := by sorry
example : f a b ≤ b := by
simp -- `foo` is still applied
```
cc @semorrison
cc @PatrickMassot
A small fix to the `DiscrTree` documentation to reflect the fact that
implicit type arguments *are* indexed and do not become `star` or
`other`. The following is a reproduction:
```lean
import Lean
open Lean Meta Elab Tactic
elab "test_tac" t:term : tactic => do
Tactic.withMainContext do
let e ← Term.elabTerm t none
let a : DiscrTree Nat ← DiscrTree.empty.insert e 1 {}
logInfo m!"{a}"
example (α : Type) (ringAdd : Add α) : True := by
/- (Add.add => (node (Nat => (node (* => (node (0 => (node (1 => (node #[1])))))))))) -/
test_tac @Add.add Nat instAddNat 0 1
/- (Add.add => (node (_uniq.1154 => (node (* => (node (◾ => (node (◾ => (node #[1])))))))))) -/
test_tac @Add.add α ringAdd ?_ ?_
```
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
This commit also removes parameter `simpleReduce` from discrimination
trees, and take WHNF configuration options.
Reason: it is more dynamic now. For example, the simplifier
will be able to use different configurations for discrimination tree insertion
and retrieval. We need this feature to address issues #2669 and #2281
This commit also removes the dead Meta.Config field `zetaNonDep`.
