# Lean Quality Analysis Tools

This directory contains quality analysis tools specifically for Lean (.lean and .yaml) files.

## Scripts

### 1. `check_lean_definitions.py`
**Purpose**: Analyzes Lean files to detect definitions, theorems, and lemmas that use `sorry` instead of proper implementations.

**What it detects**:
- 🚀 **Proper implementation**: Definitions with meaningful implementation content
- ⚠️ **Uses sorry**: Definitions that use `sorry` as placeholder (incomplete proofs)
- 🔄 **Placeholder**: Definitions that are empty or use other placeholder patterns

**Usage**:
```bash
# Full analysis with statistics (default directory)
python3 check_lean_definitions.py

# Check single Lean file
python3 check_lean_definitions.py /path/to/file.lean

# Check specific directory
python3 check_lean_definitions.py /path/to/directory

# Only list files with sorry definitions
python3 check_lean_definitions.py --list-sorry

# List sorry for single file
python3 check_lean_definitions.py file.lean --list-sorry

# Quiet mode for scripting
python3 check_lean_definitions.py --list-sorry --quiet
```

## Expected Patterns

### Proper Implementations
```lean
-- Definition with actual implementation
def factorial (n : ℕ) : ℕ :=
  match n with
  | 0 => 1
  | n + 1 => (n + 1) * factorial n

-- Theorem with complete proof
theorem add_comm (a b : ℕ) : a + b = b + a := by
  induction a with
  | zero => simp
  | succ a ih => simp [Nat.succ_add, ih]
```

### Problematic Patterns
```lean
-- Definition using sorry (incomplete)
def some_function (x : ℕ) : ℕ := sorry

-- Theorem with sorry proof (incomplete)
theorem some_theorem (a b : ℕ) : a + b = b + a := by sorry

-- Lemma with sorry
lemma helper_lemma (x : List ℕ) : x.length ≥ 0 := sorry
```

## File Types Supported

- **`.lean` files**: Direct Lean source files
- **`.yaml` files**: YAML files with embedded Lean code in `vc-preamble` sections

## YAML Structure Analysis

The tool specifically looks for Lean code in YAML files within the `vc-preamble` section:

```yaml
vc-preamble: |-
  def some_function (x : ℕ) : ℕ := sorry  -- ← Detected as problematic
  
  theorem good_theorem (a b : ℕ) : a + b = b + a := by
    ring  -- ← Detected as proper implementation
```

## Common Issues Found

### ❌ Incomplete Definitions
```lean
-- Function stub
def parse_input (s : String) : List ℕ := sorry

-- Unproven theorem
theorem main_correctness : ∀ x, P(x) := sorry

-- Empty lemma
lemma helper : True := by sorry
```

### ✅ Proper Implementations
```lean
-- Complete function
def parse_input (s : String) : List ℕ :=
  s.splitOn " " |>.map String.toNat!

-- Proven theorem
theorem main_correctness : ∀ x, P(x) := by
  intro x
  cases x with
  | zero => trivial
  | succ n => induction_step n

-- Complete proof
lemma helper : True := by trivial
```

## Detection Patterns

The tool looks for these `sorry` patterns:
- `sorry` (standalone)
- `by sorry` (tactic proof)
- `:= sorry` (definition)
- `exact sorry` (exact tactic)

And these placeholder patterns:
- `???` (placeholder holes)
- `undefined`
- `todo`
- `admit`
- `_` (underscore placeholders)
- Empty definitions

## Output Files

- `lean_definitions_with_sorry.txt`: Files containing definitions with sorry
- `lean_definitions_with_placeholders.txt`: Files with other placeholder patterns
- `lean_proper_implementations.txt`: Files with meaningful implementations

## Integration Notes

This tool is particularly useful for:
- **Translation quality**: Checking if Lean translations from other languages are complete
- **Proof completion**: Identifying which theorems/lemmas need proofs
- **Code quality**: Ensuring definitions have proper implementations
- **Progress tracking**: Monitoring completion of formal verification projects

## Example Workflow

```bash
# Check all Lean files for sorry usage
python3 check_lean_definitions.py

# Focus on files that need attention
python3 check_lean_definitions.py --list-sorry

# Check a specific benchmark directory
python3 check_lean_definitions.py --dir ../../../benchmarks/lean/apps_from_dafny_apps
```
