# Phase 2 FlatZinc Integration - Reification Comparison Constraints

## Summary

This document describes the implementation of reified comparison constraints for FlatZinc Phase 2 integration.

## Implementation Date

October 1, 2025

## What Was Implemented

### New Reification Constraints

Added four new reified comparison constraints to complement the existing `int_eq_reif` and `int_ne_reif`:

1. **`int_lt_reif(x, y, b)`** - Reified less-than: `b ⇔ (x < y)`
2. **`int_le_reif(x, y, b)`** - Reified less-or-equal: `b ⇔ (x ≤ y)`
3. **`int_gt_reif(x, y, b)`** - Reified greater-than: `b ⇔ (x > y)`
4. **`int_ge_reif(x, y, b)`** - Reified greater-or-equal: `b ⇔ (x ≥ y)`

### How Reification Works

A reified constraint `b ⇔ C` creates a bidirectional implication:
- If `b = 1` (true), then constraint `C` must hold
- If `b = 0` (false), then constraint `C` must NOT hold
- If `C` holds, then `b` must be 1
- If `C` does not hold, then `b` must be 0

### Propagation Strategy

All reification propagators use **bidirectional propagation** without early returns:

**Direction 1: From variable domains → infer boolean**
- If the constraint is definitely true (domains force it), set `b = 1`
- If the constraint is definitely false (domains prevent it), set `b = 0`

**Direction 2: From boolean → enforce constraint**
- If `b = 1`, enforce the constraint on the variables
- If `b = 0`, enforce the negation of the constraint

This design ensures:
- No dependency on constraint posting order
- Deterministic behavior regardless of propagation scheduling
- Proper interaction with other constraints (bool_clause, linear, etc.)

## Files Modified

### Core Implementation
- `src/constraints/props/reification.rs` - Added 4 new propagator structs
- `src/constraints/props/mod.rs` - Added registration methods and fixed optimization bug
- `src/model/constraints.rs` - Added 4 public API methods
- `src/optimization/constraint_metadata.rs` - Added 4 new constraint types

### Testing
- `tests/test_phase2_integration.rs` - Created 12 comprehensive integration tests
  - All tests passing ✅

### Documentation
- `examples/reification_comparison.rs` - Comprehensive examples demonstrating:
  - Conditional constraints (if-then-else logic)
  - Maximum computation using reification
  - Counting constraints
  - Partial ordering constraints
  - Range membership checking

## Critical Bug Fix

### Problem
The `optimize_universal_constraint_order()` function was removing reification constraints during optimization because they weren't in the `constraint_types_to_optimize` list. This caused reification propagators to be deleted before search started.

### Symptoms
- Reification propagators were created successfully
- They were registered in the dependency graph
- But they disappeared during `prepare_for_search()`
- Tests failed with incorrect solutions
- No errors or warnings were generated

### Root Cause
The optimization function clears `self.state` and rebuilds it with only the constraints in the optimization list:

```rust
// Reorder propagators based on priority
self.state.clear();  // ← CLEARS ALL PROPAGATORS
for &(prop_idx, _, _) in &constraint_priorities {
    self.state.push(original_state[prop_idx].clone());  // ← Only adds optimized ones!
}
```

### Solution
Added all 6 reification constraint types to the `constraint_types_to_optimize` array:

```rust
let constraint_types_to_optimize = [
    // ... existing types ...
    ConstraintType::EqualityReified,
    ConstraintType::InequalityReified,
    ConstraintType::LessThanReified,
    ConstraintType::LessEqualReified,
    ConstraintType::GreaterThanReified,
    ConstraintType::GreaterEqualReified,
];
```

## Test Results

All 12 integration tests pass consistently:

```
running 12 tests
test test_cnf_with_linear_le ... ok
test test_cnf_with_linear_eq ... ok
test test_multiple_linear_with_clause ... ok
test test_reified_linear_eq ... ok
test test_linear_eq_with_bool_clause ... ok
test test_3sat_with_linear ... ok
test test_reified_ne_with_clause ... ok
test test_negative_coeff_with_clause ... ok
test test_linear_le_with_bool_clause ... ok
test test_chained_reifications ... ok
test test_reified_linear_eq_false ... ok
test test_large_integration ... ok

test result: ok. 12 passed; 0 failed
```

## Usage Examples

### Basic Reification

```rust
use selen::prelude::*;

let mut m = Model::default();
let x = m.int(0, 10);
let y = m.int(0, 10);
let b = m.bool();

// b will be 1 iff x < y
m.int_lt_reif(x, y, b);
```

### Conditional Constraints

```rust
// If x > 5, then y = 10, else y = 0
let x = m.int(0, 10);
let y = m.int(0, 10);
let b = m.bool();
let five = m.int(5, 5);

m.int_gt_reif(x, five, b);

let y_eq_10 = m.bool();
let y_eq_0 = m.bool();
let ten = m.int(10, 10);
let zero = m.int(0, 0);

m.int_eq_reif(y, ten, y_eq_10);
m.int_eq_reif(y, zero, y_eq_0);

// b → y_eq_10 and ¬b → y_eq_0
m.bool_clause(&[y_eq_10], &[b]);
m.bool_clause(&[b, y_eq_0], &[]);
```

### Counting

```rust
// Count how many of x, y, z are greater than 5
let x = m.int(0, 10);
let y = m.int(0, 10);
let z = m.int(0, 10);
let five = m.int(5, 5);

let x_gt_5 = m.bool();
let y_gt_5 = m.bool();
let z_gt_5 = m.bool();

m.int_gt_reif(x, five, x_gt_5);
m.int_gt_reif(y, five, y_gt_5);
m.int_gt_reif(z, five, z_gt_5);

// Require exactly 2 to be > 5
m.int_lin_eq(&[1, 1, 1], &[x_gt_5, y_gt_5, z_gt_5], 2);
```

## Design Decisions

### Why Bidirectional Propagation Without Early Returns?

The original implementation used early returns after checking one direction:

```rust
// OLD - BAD
if x_max < y_min {
    self.b.try_set_min(Val::ValI(1), ctx)?;
    return Some(());  // ← Early return
}
```

This caused non-deterministic failures when constraints were posted in certain orders. The fix removes early returns and always checks all directions:

```rust
// NEW - GOOD
if x_max < y_min {
    self.b.try_set_min(Val::ValI(1), ctx)?;
}
// Continue to check other directions...
```

This ensures the propagator makes progress regardless of when it runs or what other constraints have propagated.

### Why Include Reification in Optimization?

Reification constraints can be expensive to propagate, so including them in constraint optimization allows the solver to:
- Schedule them appropriately relative to other constraints
- Prioritize them based on variable connectivity
- Maintain consistency with the optimization framework

Without inclusion in optimization, they would be silently removed, causing subtle and hard-to-debug failures.

## API Completeness

All six comparison reification constraints are now available:

| Constraint | Meaning | API Method |
|-----------|---------|-----------|
| `b ⇔ (x = y)` | Equality | `int_eq_reif(x, y, b)` ✅ |
| `b ⇔ (x ≠ y)` | Inequality | `int_ne_reif(x, y, b)` ✅ |
| `b ⇔ (x < y)` | Less than | `int_lt_reif(x, y, b)` ✅ |
| `b ⇔ (x ≤ y)` | Less or equal | `int_le_reif(x, y, b)` ✅ |
| `b ⇔ (x > y)` | Greater than | `int_gt_reif(x, y, b)` ✅ |
| `b ⇔ (x ≥ y)` | Greater or equal | `int_ge_reif(x, y, b)` ✅ |

## Next Steps

### Immediate
- ✅ Run full test suite to ensure no regressions
- ✅ Document the implementation
- Commit changes with clear message

### Future Phase 2 Work
- Implement more FlatZinc global constraints
- Add set constraints
- Implement float constraints
- Create FlatZinc parser integration tests

## References

- FlatZinc specification: https://www.minizinc.org/doc-2.5.5/en/fzn-spec.html
- Reification documentation: `docs/development/ZINC_REIFICATION_FIX.md`
- Integration tests: `tests/test_phase2_integration.rs`
- Examples: `examples/reification_comparison.rs`
