This PR adds support for higher-order Miller patterns in `grind`'s
e-matching engine.
Previously, lambda arguments in e-matching patterns were always treated
as `dontCare`, meaning
they could not contribute to matching or bind pattern variables. This
was a significant limitation
for theorems where lambda arguments carry essential structure, such as
`List.foldl`, `List.foldrM`,
or any combinator that takes a function argument.
With this change, when a pattern argument is a lambda whose body
satisfies the **Miller pattern
condition** — i.e., pattern variables are applied only to distinct
lambda-bound variables — the
lambda is preserved as an `ho[...]` pattern. At instantiation time,
these higher-order patterns
are matched via `isDefEq` after all first-order pattern variables have
been assigned by the E-graph.
### Example
```lean
@[grind =] theorem applyFlip_spec (f : Nat → Nat → Nat) (a b : Nat)
: applyFlip (fun x y => f y x) a b = f b a := sorry
```
The pattern `applyFlip ho[fun x => fun y => #2 y x] #1 #0` captures the
lambda argument
structurally: `#2` (the pattern variable for `f`) is applied to distinct
lambda-bound
variables `y` and `x`. When `grind` encounters `applyFlip (fun x y =>
Nat.add y x) 3 4`,
it binds `f := Nat.add` via `isDefEq` and fires the rewrite.
### Key design decisions
- **Miller condition check**: Only lambdas where at least one pattern
variable appears
in applied Miller position (applied to distinct lambda-bound vars) are
promoted to
`ho[...]`. Other lambdas remain `dontCare`.
- **Redundancy elimination**: A post-processing pass demotes `ho[...]`
patterns to `dontCare`
if all their pattern variables already appear in non-HO positions of the
same pattern. This
avoids unnecessary `isDefEq` calls when the lambda doesn't contribute
new variable bindings.
- **E-graph bypass**: HO patterns are not internalized into the E-graph.
They are accumulated
during matching and checked via `isDefEq` after the first-order
assignment is complete.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
022bf2f822