This PR reorganizes the monad hierarchy for symbolic computation in
Lean.
## Motivation
We want a clean layering where:
1. A foundational monad (`SymM`) provides maximally shared terms and
structural/syntactic `isDefEq`
2. `GrindM` builds on this foundation, adding E-graphs, congruence
closure, and decision procedures
3. Symbolic execution / VCGen uses `GrindM` directly without introducing
a third monad
## Changes
The core symbolic computation layer still lives in `Lean.Meta.Sym`. This
monad (`SymM`) provides:
- Maximally shared terms with pointer-based equality
- Structural/syntactic `isDefEq` and matching (no reduction, predictable
cost)
- Monotonic local contexts (no `revert` or `clear`), enabling O(1)
metavariable validation
- Efficient `intro`, `apply`, and `simp` implementations
The name "Sym" reflects that this is infrastructure for symbolic
computation: symbolic simulation, verification condition generation, and
decision procedures.
### Updated hierarchy
```
Lean.Meta.Sym -- SymM: shared terms, syntactic isDefEq, intro, apply, simp
Lean.Meta.Grind -- GrindM: E-graphs, congruence closure (extends SymM)
```
Symbolic execution is a usage pattern of `GrindM` operating on
`Grind.Goal`, not a separate monad. This keeps the API surface minimal:
users learn two monads, and VCGen is "how you use `GrindM`" (for users
that want to use `grind`) rather than a third abstraction to understand.
This PR implements `PersistentHashMap.findKeyD` and
`PersistentHashSet.findD`. The motivation is avoid two memory
allocations (`Prod.mk` and `Option.some`) when the collections contains
the key.
This PR fixes an issue where `grind` failed to prove `f ≠ 0` from `f * r
≠ 0` when using `Lean.Grind.CommSemiring`, but succeeded with
`Lean.Grind.Semiring`.
The `propagateMul` propagator handles `0 * a = 0` and `a * 0 = 0` rules
for semirings that don't have full ring support in grind. Previously,
`CommSemiring` was excluded because it uses a ring envelope for
normalization, but that approach doesn't propagate these equalities back
to the original terms. Now `CommSemiring` also uses `propagateMul`.
Reported as
https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Grind.20failure.20for.20CommSemiring.2C.20not.20Semiring🤖 Prepared with Claude Code
---------
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
This PR adds a `done` flag to the result returned by `Simproc`s in
`Sym.simp`.
The `done` flag controls whether simplification should continue after
the result:
- `done = false` (default): Continue with subsequent simplification
steps
- `done = true`: Stop processing, return this result as final
## Use cases for `done = true`
### In `pre` simprocs
Skip simplification of certain subterms entirely:
```
def skipLambdas : Simproc := fun e =>
if e.isLambda then return .rfl (done := true)
else return .rfl
```
### In `post` simprocs
Perform single-pass normalization without recursive simplification:
```
def singlePassNormalize : Simproc := fun e =>
if let some (e', h) ← tryNormalize e then
return .step e' h (done := true)
else return .rfl
```
With `done = true`, the result `e'` won't be recursively simplified.
This PR adds support for simplifying lambda expressions in `Sym.simp`.
It is much more efficient than standard simp for very large lambda
expressions with many binders. The key idea is to generate a custom
function extensionality theorem for the type of the lambda being
simplified.
This technique is compatible with the standard `simp` tactic, and will
be ported in a separate PR.
<img width="581" height="455" alt="image"
src="https://github.com/user-attachments/assets/5911dc6c-03f0-48ed-843b-b8cb4f67ee61"
/>
### `lambda` benchmark summary
| Lambda size | MetaM (ms) | SymM (ms) | Speedup |
|-------------|------------|-----------|---------|
| 50 | 22.7 | 0.74 | ~31× |
| 100 | 120.5 | 1.75 | ~69× |
| 150 | 359.6 | 2.90 | ~124× |
| 200 | 809.5 | 4.51 | ~180× |
This PR adds a guard to `TagDeclarationExtension.tag` to check if the
declaration name is anonymous and return early if so. This prevents a
panic that could occur when modifiers like `meta` or `noncomputable` are
used in combination with syntax errors.
Reproducer:
```lean
public meta section
def private
```
Previously this would panic with:
```
PANIC at Lean.EnvExtension.modifyState: called on `async` extension,
must set `asyncDecl` in that case
```
This follows the same pattern as the fix in #10131 for `addDocString`
and the existing guard in `markNotMeta`.
See
https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/panic.20on.20doc-string/near/566110399🤖 Prepared with Claude Code
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
This PR ensures that `Sym.simp` checks thresholds for maximum recursion
depth and maximum number of steps. It also invokes `checkSystem`.
Additionally, this PR simplifies the main loop. Assigned metavariables
and `zetaDelta` reduction are now handled by installing `pre`/`post`
methods.
This PR adds `getMatch` and `getMatchWithExtra` for retrieving patterns
from
discrimination trees in the symbolic simulation framework.
The PR also adds uses `DiscrTree` to implement indexing in `Sym.simp`.
This PR adds discrimination tree support for the symbolic simulation
framework.
The new `DiscrTree.lean` module converts `Pattern` values into
discrimination
tree keys, treating proof/instance arguments and pattern variables as
wildcards
(`Key.star`). Motivation: efficient pattern retrieval during rewriting.
This PR adds a `with_unfolding_none` tactic that sets the transparency
mode to `.none`, in which no definitions are unfolded. This complements
the existing `with_unfolding_all` tactic and provides tactic-level
access to the `TransparencyMode.none` added in
https://github.com/leanprover/lean4/pull/11810.
🤖 Prepared with Claude Code
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
This PR adds the directory `Meta/DiscrTree` and reorganizes the code
into different files. Motivation: we are going to have new functions for
retrieving simplification theorems for the new structural simplifier.
This PR makes `mvcgen with tac` fail if `tac` fails on one of the VCs,
just as `induction ... with tac` fails if `tac` fails on one of the
goals. The old behavior can be recovered by writing `mvcgen with try
tac` instead.
This PR adds configuration flag `Meta.Context.cacheInferType`. You can
use it to disable the `inferType` cache at `MetaM`. We use this flag to
implement `SymM` because it has its own cache based on pointer equality.
This PR adds `CongrInfo` analysis for function applications in the
symbolic simulator framework. `CongrInfo` determines how to build
congruence proofs for rewriting subterms efficiently, categorizing
functions into:
- `none`: no arguments can be rewritten (e.g., proofs)
- `fixedPrefix`: common case where implicit/instance arguments form a
fixed prefix and explicit arguments can be rewritten (e.g., `HAdd.hAdd`,
`Eq`)
- `interlaced`: rewritable and non-rewritable arguments alternate (e.g.,
`HEq`)
- `congrTheorem`: uses auto-generated congruence theorems for functions
with dependent proof arguments (e.g., `Array.eraseIdx`)
This PR changes `bv_decide`'s heuristic for what kinds of structures to
split on to also allow
splitting on structures where the fields have dependently typed widths.
For example:
```lean
structure Byte (w : Nat) where
/-- A two's complement integer value of width `w`. -/
val : BitVec w
/-- A per-bit poison mask of width `w`. -/
poison : BitVec w
```
This is to allow handling situations such as `(x : Byte 8)` where the
width becomes concrete after
splitting is done.
This PR adds an incremental variant of `shareCommon` for expressions
constructed from already-shared subterms. We use this when an expression
`e` was produced by a Lean API (e.g., `inferType`, `mkApp4`) that does
not preserve maximal sharing, but the inputs to that API were already
maximally shared. Unlike `shareCommon`, this function does not use a
local `Std.HashMap ExprPtr Expr` to track visited nodes. This is more
efficient when the number of new (unshared) nodes is small, which is the
common case when wrapping API calls that build a few constructor nodes
around shared inputs.
This PR fixes a bug in the new pattern matching procedure for the Sym
framework. It was not correctly handling assigned metavariables during
pattern matching.
It also improves the support for free variables.
This PR adds `BackwardRule` for efficient goal transformation via
backward chaining in `SymM`.
`BackwardRule` stores a theorem expression, precomputed pattern for
fast unification, and argument indices that become new subgoals. The
subgoal ordering lists non-dependent goals first to match the behavior
of `MetaM.apply`.
`BackwardRule.apply` unifies the goal type with the rule's pattern,
assigns the goal metavariable to the theorem application, and returns
new subgoals for unassigned arguments.
This PR adds `num?` parameter to `mkPatternFromTheorem` to control how
many leading quantifiers are stripped when creating a pattern. This
enables matching theorems where only some quantifiers should be
converted to pattern variables.
For example, to match `mk_forall_and : (∀ x, P x) → (∀ x, Q x) → (∀ x, P
x ∧ Q x)` against a goal `∀ x, q x 0 ∧ q (f (f x)) y`, we use
`mkPatternFromTheorem ``mk_forall_and (some 5)` to create the pattern `∀
x, ?P x ∧ ?Q x`, keeping the outermost `∀` in the pattern rather than
converting it to a pattern variable.
This PR completes the new pattern matching and unification procedures
for the symbolic simulation framework using a two-phase approach.
**Phase 1 (Syntactic Matching):**
- Patterns use de Bruijn indices for expression variables and renamed
level params for universe variables
- Purely structural matching after reducible definitions are unfolded
- Universe levels treat `max`/`imax` as uninterpreted functions
- Proof arguments skipped via proof irrelevance
- Instance and binder constraints deferred to Phase 2
**Phase 2 (Pending Constraints):**
- Level constraints: structural equality with mvar assignment
- Instance constraints: `isDefEqI` (full `isDefEq` for TC synthesis)
- Expression constraints: `isDefEqS` with Miller pattern support
- Unassigned instance pattern variables synthesized via
`trySynthInstance`
**`isDefEqS` (Structural DefEq):**
- Miller pattern detection and assignment (`?m x y z := rhs` → `?m :=
fun x y z => rhs`)
- Scope checking via `maxFVar` to prevent out-of-scope assignments
- Optional zeta-delta reduction for let-declarations
- Proof irrelevance and instance delegation to `isDefEqI`
**Key optimizations:**
- `abstractFVars` skips metavariables and uses `maxFVar` for early
cutoff
- Per-pattern `ProofInstInfo` cache for fast argument classification
- Maximal sharing.
This PR implements `isDefEqS`, a lightweight structural definitional
equality for the symbolic simulation framework. Unlike the full
`isDefEq`, it avoids expensive operations while still supporting Miller
pattern unification.
**Key features:**
- Structural matching with optional zeta-delta reduction for
let-declarations
- Miller pattern detection and assignment (`?m x y z := rhs` → `?m :=
fun x y z => rhs`)
- Scope checking via `maxFVar` to prevent out-of-scope assignments
- Proof arguments skipped via proof irrelevance
- Instance arguments delegated to full `isDefEq` (need TC machinery)
- Universe levels treated structurally (`max`/`imax` as uninterpreted)
This PR adds optimized `abstractFVars` and `abstractFVarsRange` for
converting free variables to de Bruijn indices during pattern
matching/unification.
**Optimizations:**
- Metavariables are skipped (their contexts must not include abstracted
fvars)
- Subterms whose `maxFVar` is below the minimal abstracted fvar are
skipped via early cutoff
- Results are maximally shared via `AlphaShareBuilderM`
These optimizations are sound for Miller pattern matching where
metavariables are created before entering binders.
This PR implements `instantiateRevBetaS`, which is similar to
`instantiateRevS` but beta-reduces nested applications whose function
becomes a lambda after substitution.
For example, if `e` contains a subterm `#0 a` and we apply the
substitution `#0 := fun x => x + 1`, then `instantiateRevBetaS` produces
`a + 1` instead of `(fun x => x + 1) a`.
This is useful when applying theorems. For example, when applying
`Exists.intro`:
```lean
Exists.intro.{u} {α : Sort u} {p : α → Prop} (w : α) (h : p w) : Exists p
```
to a goal of the form `∃ x : Nat, p x ∧ q x`, we create metavariables
`?w` and `?h`. With `instantiateRevBetaS`, the type of `?h` becomes `p
?w ∧ q ?w` instead of `(fun x => p x ∧ q x) ?w`.
This PR introduces a fast pattern matching and unification module for
the symbolic simulation framework (`Sym`). The design prioritizes
performance by using a two-phase approach:
**Phase 1 (Syntactic Matching)**
- Patterns use de Bruijn indices for expression variables and renamed
level params (`_uvar.0`, `_uvar.1`, ...) for universe variables
- Matching is purely structural after reducible definitions are unfolded
during preprocessing
- Universe levels treat `max` and `imax` as uninterpreted functions (no
AC reasoning)
- Binders and term metavariables are deferred to Phase 2
**Phase 2 (Pending Constraints)** [WIP]
- Handles binders (Miller patterns) and metavariable unification
- Converts remaining de Bruijn variables to metavariables
- Falls back to `isDefEq` when necessary
**Key design decisions:**
- Preprocessing unfolds reducible definitions and performs beta/zeta
reduction
- Kernel projections are expected to be folded as projection
applications before matching
- Assignment conflicts are deferred to pending rather than invoking
`isDefEq` inline
- `instantiateRevS` ensures maximal sharing of result expressions
**TODO:**
- Skip instance arguments during matching, synthesize later
- Skip proof arguments (proof irrelevance)
- Implement `processPending` for Phase 2 constraints
This PR refactors the `Goal` type used in `grind`. The new
representation allows multiple goals with different metavariables to
share the same `GoalState`. This is useful for automation such as
symbolic simulator, where applying theorems create multiple goals that
inherit the same E-graph, congruence closure and solvers state, and
other accumulated facts.
This PR implements `intro` (and its variants) for `SymM`. These versions
do not use reduction or infer types, and ensure expressions are
maximally shared.
This PR adds the function `Sym.instantiateS` and its variants, which are
similar to `Expr.instantiate` but assumes the input is maximally shared
and ensures the output is also maximally shared.
This PR adds the function `Sym.replaceS`, which is similar to
`replace_fn` available in the kernel but assumes the input is maximally
shared and ensures the output is also maximally shared. The PR also
generalizes the `AlphaShareBuilder` API.
This PR simplifies `AlphaShareCommon.State` by separating the persistent
and transient parts of the state.
The `map` field caches visited sub-expressions during a single
`shareCommonAlpha` call to handle DAGs efficiently, the input expression
may contain shared sub-expressions that are not yet maximally shared.
However, this cache does not need to persist between different
`shareCommonAlpha` calls.
**Changes:**
- Moved `map` from the persistent `AlphaShareCommon.State` to a private
`State` used only within individual `shareCommonAlpha` calls.
- Replaced `PHashMap ExprPtr Expr` with (the more efficient)
`Std.HashMap ExprPtr Expr` for `map`, since it is now local to each call
and does not need persistence.
- The public `AlphaShareCommon.State` now only contains the `set` of
alpha-equivalent expressions that should persist
