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Add comprehensive documentation and examples for UserPropagator quantifier instantiation callbacks

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Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
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# UserPropagator Quantifier Instantiation Callback in Z3
This document describes the UserPropagator callback for quantifier instantiations feature added in Z3 version 4.15.3.
## Overview
The quantifier instantiation callback allows user propagators to intercept and control quantifier instantiations. When Z3 attempts to instantiate a quantifier, the callback is invoked with the quantifier and its proposed instantiation. The callback can return `false` to discard the instantiation, providing fine-grained control over the quantifier instantiation process.
This feature enables:
1. **Inspection and logging** of instantiation patterns
2. **Filtering** of undesired instantiations
3. **Custom instantiation strategies**
4. **Performance optimization** by delaying certain instantiations
## API Reference
### Python API
```python
from z3 import *
class MyUserPropagator(UserPropagateBase):
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
# Register the quantifier instantiation callback
self.add_on_binding(self.my_callback)
def my_callback(self, quantifier, instantiation):
"""
Callback for quantifier instantiation control.
Args:
quantifier: The quantifier being instantiated (Z3 AST)
instantiation: The proposed instantiation (Z3 AST)
Returns:
bool: True to allow the instantiation, False to discard it
"""
# Your logic here
return True # or False to block
# Required methods
def push(self): pass
def pop(self, num_scopes): pass
def fresh(self, new_ctx): return MyUserPropagator(ctx=new_ctx)
```
### C API
```c
#include <z3.h>
// Callback function signature
Z3_bool my_callback(void* ctx, Z3_solver_callback cb, Z3_ast q, Z3_ast inst) {
// ctx: user context data
// cb: solver callback handle (internal use)
// q: quantifier being instantiated
// inst: proposed instantiation
// Your logic here
return Z3_TRUE; // or Z3_FALSE to block
}
// Register the callback
Z3_context ctx = Z3_mk_context(Z3_mk_config());
Z3_solver s = Z3_mk_solver(ctx);
Z3_solver_propagate_on_binding(ctx, s, my_callback);
```
### C++ API
The C++ API follows the same pattern as the C API, using the same `Z3_solver_propagate_on_binding` function.
## Examples
### Basic Example: Limiting Instantiations
```python
class InstantiationLimiter(UserPropagateBase):
def __init__(self, max_instantiations=5, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.max_instantiations = max_instantiations
self.count = 0
self.add_on_binding(self.limit_instantiations)
def limit_instantiations(self, quantifier, instantiation):
self.count += 1
print(f"Instantiation #{self.count}: {instantiation}")
# Allow only the first max_instantiations
if self.count <= self.max_instantiations:
print(" -> ALLOWED")
return True
else:
print(" -> BLOCKED")
return False
def push(self): pass
def pop(self, num_scopes): pass
def fresh(self, new_ctx): return InstantiationLimiter(self.max_instantiations, ctx=new_ctx)
# Usage
s = Solver()
limiter = InstantiationLimiter(max_instantiations=3, s=s)
x = Int('x')
f = Function('f', IntSort(), IntSort())
s.add(ForAll([x], f(x) >= 0))
s.add(f(1) < 10, f(2) < 20, f(3) < 30)
result = s.check()
```
### Advanced Example: Pattern-Based Filtering
```python
class PatternFilter(UserPropagateBase):
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.pattern_counts = {}
self.max_per_pattern = 2
self.add_on_binding(self.filter_by_pattern)
def filter_by_pattern(self, quantifier, instantiation):
# Convert to string for pattern matching
pattern = str(instantiation)
# Count occurrences of this pattern
self.pattern_counts[pattern] = self.pattern_counts.get(pattern, 0) + 1
count = self.pattern_counts[pattern]
# Allow only max_per_pattern instantiations of each pattern
allow = count <= self.max_per_pattern
print(f"Pattern: {pattern} (#{count}) -> {'ALLOWED' if allow else 'BLOCKED'}")
return allow
def push(self): pass
def pop(self, num_scopes): pass
def fresh(self, new_ctx): return PatternFilter(ctx=new_ctx)
```
### Logging Example: Analyzing Instantiation Patterns
```python
class InstantiationLogger(UserPropagateBase):
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.log = []
self.add_on_binding(self.log_instantiation)
def log_instantiation(self, quantifier, instantiation):
entry = {
'quantifier': str(quantifier),
'instantiation': str(instantiation),
'count': len(self.log) + 1
}
self.log.append(entry)
print(f"#{entry['count']}: {entry['instantiation']}")
# Allow all instantiations (just log them)
return True
def get_statistics(self):
# Group by quantifier
by_quantifier = {}
for entry in self.log:
q = entry['quantifier']
if q not in by_quantifier:
by_quantifier[q] = []
by_quantifier[q].append(entry['instantiation'])
return {
'total': len(self.log),
'by_quantifier': by_quantifier
}
def push(self): pass
def pop(self, num_scopes): pass
def fresh(self, new_ctx): return InstantiationLogger(ctx=new_ctx)
```
## Use Cases
### 1. Performance Optimization
- **Problem**: Some quantifier instantiations are expensive but rarely useful
- **Solution**: Use callback to block certain patterns or limit instantiation count
- **Benefit**: Reduced solving time, better resource utilization
### 2. Custom Instantiation Strategies
- **Problem**: Default instantiation heuristics don't work well for your domain
- **Solution**: Implement domain-specific filtering logic
- **Benefit**: Better solution quality, faster convergence
### 3. Debugging and Analysis
- **Problem**: Understanding why a formula is UNSAT or takes long to solve
- **Solution**: Log all instantiation attempts to analyze patterns
- **Benefit**: Better insight into solver behavior
### 4. Interactive Solving
- **Problem**: Need to control solving process interactively
- **Solution**: Use callback to selectively enable/disable instantiations
- **Benefit**: Fine-grained control over solver behavior
## Technical Details
### Callback Invocation
- Called **before** the instantiation is added to the solver
- Blocking an instantiation prevents it from being used in the current search
- The same instantiation may be proposed again in different search branches
### Return Value Semantics
- `True` (Python) / `Z3_TRUE` (C): Allow the instantiation
- `False` (Python) / `Z3_FALSE` (C): Block the instantiation
- Blocked instantiations are discarded and won't be used in current search
### Thread Safety
- Callbacks are invoked on the same thread as the solver
- No additional synchronization is needed
- Context switching during callback execution is safe
### Performance Considerations
- Callbacks are invoked frequently during solving
- Keep callback logic lightweight to avoid performance overhead
- String conversions (`str(ast)`) can be expensive; cache when possible
- Consider using AST structure inspection instead of string matching
## Limitations
### C/C++ API Limitations
- The C/C++ callback receives AST handles but no direct Z3 context
- Converting ASTs to strings for inspection requires careful context management
- Recommend using Python API for complex logic, C/C++ for simple filtering
### Scope and Lifetime
- Callback registrations are tied to solver instances
- User propagator instances must remain alive during solving
- AST handles in callbacks are valid only during callback execution
### Interaction with Other Features
- Works with all quantifier instantiation strategies (E-matching, MBQI, etc.)
- Compatible with other user propagator callbacks
- May affect solver completeness if too many instantiations are blocked
## Best Practices
1. **Start Simple**: Begin with logging to understand instantiation patterns
2. **Be Conservative**: Blocking too many instantiations can make formulas unsolvable
3. **Test Thoroughly**: Verify that your filtering doesn't break correctness
4. **Profile Performance**: Measure impact of callback overhead
5. **Use Appropriate Data Structures**: Hash maps for pattern counting, etc.
6. **Handle Edge Cases**: Empty instantiations, malformed ASTs, etc.
## Complete Working Example
See the accompanying files:
- `examples/python/quantifier_instantiation_callback.py` - Complete Python examples
- `examples/c++/quantifier_instantiation_callback.cpp` - C++ examples
- `examples/c/quantifier_instantiation_callback.c` - C examples
These examples demonstrate all the concepts above with runnable code.
## Troubleshooting
### Common Issues
1. **Callback Not Called**
- Ensure user propagator is properly registered with solver
- Check that problem actually triggers quantifier instantiations
- Verify quantifier syntax is correct
2. **Performance Degradation**
- Simplify callback logic
- Avoid expensive string operations
- Consider sampling (only process every Nth callback)
3. **Unexpected UNSAT Results**
- Review blocking criteria - may be too aggressive
- Test with callback disabled to verify baseline behavior
- Use logging to understand what's being blocked
4. **Memory Issues**
- Don't store AST handles beyond callback lifetime
- Clear large data structures periodically
- Monitor memory usage in long-running processes
## Version History
- **Z3 4.15.3**: Initial implementation of quantifier instantiation callbacks
- **Z3 4.15.4**: Improved performance and stability
For more information, see the Z3 documentation and source code in the Z3Prover repository.

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# UserPropagator Quantifier Instantiation Callback Examples
This directory contains examples demonstrating the UserPropagator callback for quantifier instantiations feature added in Z3 version 4.15.3.
## Overview
The quantifier instantiation callback allows user propagators to intercept and control quantifier instantiations, providing fine-grained control over the solving process.
## Files
### Python Examples
- `examples/python/quantifier_instantiation_callback.py` - Comprehensive Python examples showing:
- Basic instantiation control (limiting number of instantiations)
- Advanced pattern-based filtering
- Instantiation logging and analysis
### C++ Examples
- `examples/c++/quantifier_instantiation_callback.cpp` - C++ API examples (requires compilation)
### C Examples
- `examples/c/quantifier_instantiation_callback.c` - C API examples (requires compilation)
### Unit Tests
- `src/test/test_quantifier_instantiation_callback.py` - Unit tests validating functionality
### Documentation
- `doc/quantifier_instantiation_callback.md` - Complete API documentation and usage guide
## Running the Examples
### Python Examples
```bash
cd build/python
PYTHONPATH=/path/to/z3/build/python python3 ../../examples/python/quantifier_instantiation_callback.py
```
Or from the Z3 build directory:
```bash
cd build/python
python3 ../../examples/python/quantifier_instantiation_callback.py
```
### C++ Examples
```bash
# Compile
g++ -I src/api -I src/api/c++ examples/c++/quantifier_instantiation_callback.cpp -L build -lz3 -o quantifier_callback_cpp
# Run
LD_LIBRARY_PATH=build ./quantifier_callback_cpp
```
### C Examples
```bash
# Compile
gcc -I src/api examples/c/quantifier_instantiation_callback.c -L build -lz3 -o quantifier_callback_c
# Run
LD_LIBRARY_PATH=build ./quantifier_callback_c
```
### Unit Tests
```bash
cd z3-root-directory
PYTHONPATH=build/python python3 src/test/test_quantifier_instantiation_callback.py
```
## Expected Output
When running the Python examples, you should see output like:
```
============================================================
BASIC QUANTIFIER INSTANTIATION CONTROL EXAMPLE
============================================================
Checking satisfiability with instantiation control...
Instantiation #1:
Quantifier: ForAll(x, f(x) >= 0)
Instantiation: f(1) >= 0
-> ALLOWED (#1)
Instantiation #2:
Quantifier: ForAll(x, f(x) >= 0)
Instantiation: f(2) >= 0
-> ALLOWED (#2)
Instantiation #3:
Quantifier: ForAll(x, f(x) >= 0)
Instantiation: f(3) >= 0
-> ALLOWED (#3)
Result: sat
Model: [c = 3, b = 2, a = 1, f = [else -> 0]]
Instantiation Statistics:
Total attempts: 3
Allowed: 3
Blocked: 0
```
## Key Features Demonstrated
1. **Basic Control**: Limiting the number of quantifier instantiations
2. **Pattern Filtering**: Allowing only a certain number of instantiations per pattern
3. **Logging**: Recording all instantiation attempts for analysis
4. **Performance Impact**: Showing how filtering affects solving time
5. **Error Handling**: Graceful handling of callback exceptions
## Use Cases
- **Performance Optimization**: Reduce solving time by limiting expensive instantiations
- **Custom Strategies**: Implement domain-specific instantiation heuristics
- **Debugging**: Understand solver behavior through instantiation analysis
- **Interactive Solving**: Dynamically control solving process
## Requirements
- Z3 version 4.15.3 or later
- Python 3.x for Python examples
- GCC/Clang for C/C++ examples
- Z3 shared library in LD_LIBRARY_PATH
## Troubleshooting
### "ModuleNotFoundError: No module named 'z3'"
Set PYTHONPATH to point to the Z3 Python bindings:
```bash
export PYTHONPATH=/path/to/z3/build/python:$PYTHONPATH
```
### "No instantiations were attempted"
- Check that your formula contains quantifiers
- Verify that the constraints actually trigger instantiation (e.g., through function applications)
- Try disabling other Z3 optimizations that might eliminate the need for instantiation
### C/C++ Compilation Errors
- Ensure Z3 headers are in the include path (`-I /path/to/z3/src/api`)
- Link against the Z3 library (`-L /path/to/z3/build -lz3`)
- Set LD_LIBRARY_PATH to find the shared library at runtime
### Performance Issues
- Keep callback logic simple and fast
- Avoid expensive string operations in callbacks
- Consider sampling (only process every Nth callback) for high-frequency instantiations
## Further Reading
- See `doc/quantifier_instantiation_callback.md` for complete API documentation
- Z3 Guide: https://microsoft.github.io/z3guide/
- Z3 API Reference: https://z3prover.github.io/api/html/
## Contributing
To add new examples or improve existing ones:
1. Follow the existing code style and structure
2. Add appropriate error handling and documentation
3. Include unit tests for new functionality
4. Update this README with any new examples

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/**
* Example demonstrating the UserPropagator callback for quantifier instantiations in Z3.
*
* This feature was added in Z3 version 4.15.3 and allows user propagators to intercept
* and control quantifier instantiations using the Z3_solver_propagate_on_binding API.
*
* The callback receives the quantifier and its proposed instantiation, and can return
* false to discard the instantiation, providing fine-grained control over the
* quantifier instantiation process.
*
* To compile:
* g++ -I /path/to/z3/src/api -I /path/to/z3/src/api/c++ \
* quantifier_instantiation_callback.cpp -L /path/to/z3/build -lz3 \
* -o quantifier_instantiation_callback
*
* To run:
* LD_LIBRARY_PATH=/path/to/z3/build ./quantifier_instantiation_callback
*/
#include <iostream>
#include <vector>
#include <string>
#include <z3++.h>
using namespace z3;
using namespace std;
// Global counter for demonstration purposes
static int instantiation_counter = 0;
static int allowed_counter = 0;
static int blocked_counter = 0;
/**
* User-defined callback for quantifier instantiation control.
*
* This function is called by Z3 whenever it wants to instantiate a quantifier.
*
* @param ctx User context (can be used to pass custom data)
* @param cb Solver callback object
* @param q The quantifier being instantiated
* @param inst The proposed instantiation
* @return true to allow the instantiation, false to discard it
*/
bool quantifier_instantiation_callback(void* ctx, Z3_solver_callback cb, Z3_ast q, Z3_ast inst) {
// Cast the context back to our custom data structure if needed
// For this simple example, we'll use global variables
instantiation_counter++;
// Get string representations for logging
Z3_context z3_ctx = Z3_solver_callback_get_context(cb);
string q_str = Z3_ast_to_string(z3_ctx, q);
string inst_str = Z3_ast_to_string(z3_ctx, inst);
cout << "Instantiation #" << instantiation_counter << ":" << endl;
cout << " Quantifier: " << q_str << endl;
cout << " Instantiation: " << inst_str << endl;
// Example filtering logic: allow only the first 3 instantiations
// In practice, you might implement more sophisticated filtering
bool allow = instantiation_counter <= 3;
if (allow) {
allowed_counter++;
cout << " -> ALLOWED (#" << allowed_counter << ")" << endl;
} else {
blocked_counter++;
cout << " -> BLOCKED (#" << blocked_counter << ")" << endl;
}
cout << endl;
return allow;
}
/**
* Example demonstrating basic quantifier instantiation control.
*/
void example_basic_control() {
cout << string(60, '=') << endl;
cout << "BASIC QUANTIFIER INSTANTIATION CONTROL EXAMPLE" << endl;
cout << string(60, '=') << endl;
context ctx;
solver s(ctx);
// Register the quantifier instantiation callback
Z3_solver_propagate_on_binding(ctx, s, quantifier_instantiation_callback);
// Create a simple quantified formula
sort int_sort = ctx.int_sort();
func_decl f = ctx.function("f", int_sort, int_sort);
expr x = ctx.int_const("x");
// Add quantified axiom: forall x. f(x) >= 0
expr axiom = forall(x, f(x) >= 0);
s.add(axiom);
// Add constraints that might trigger instantiations
expr a = ctx.int_const("a");
expr b = ctx.int_const("b");
expr c = ctx.int_const("c");
s.add(f(a) < 10);
s.add(f(b) < 20);
s.add(f(c) < 30);
// Add specific values
s.add(a == 1);
s.add(b == 2);
s.add(c == 3);
cout << "Checking satisfiability with instantiation control..." << endl;
check_result result = s.check();
cout << "Result: " << result << endl;
if (result == sat) {
cout << "Model: " << s.get_model() << endl;
}
// Print statistics
cout << endl << "Instantiation Statistics:" << endl;
cout << " Total attempts: " << instantiation_counter << endl;
cout << " Allowed: " << allowed_counter << endl;
cout << " Blocked: " << blocked_counter << endl;
}
// Structure to hold callback context data
struct AdvancedCallbackContext {
int max_instantiations_per_pattern;
map<string, int> instantiation_counts;
AdvancedCallbackContext(int max_per_pattern = 2)
: max_instantiations_per_pattern(max_per_pattern) {}
};
/**
* Advanced callback that tracks instantiation patterns.
*/
bool advanced_instantiation_callback(void* ctx, Z3_solver_callback cb, Z3_ast q, Z3_ast inst) {
AdvancedCallbackContext* context = static_cast<AdvancedCallbackContext*>(ctx);
// Get string representation of the instantiation
Z3_context z3_ctx = Z3_solver_callback_get_context(cb);
string inst_str = Z3_ast_to_string(z3_ctx, inst);
// Count instantiations for this pattern
context->instantiation_counts[inst_str]++;
int count = context->instantiation_counts[inst_str];
// Allow only up to max_instantiations_per_pattern of the same pattern
bool allow = count <= context->max_instantiations_per_pattern;
cout << "Instantiation: " << inst_str << " (attempt #" << count << ")" << endl;
cout << " -> " << (allow ? "ALLOWED" : "BLOCKED") << endl;
return allow;
}
/**
* Example demonstrating advanced instantiation filtering.
*/
void example_advanced_filtering() {
cout << endl << string(60, '=') << endl;
cout << "ADVANCED INSTANTIATION FILTERING EXAMPLE" << endl;
cout << string(60, '=') << endl;
context ctx;
solver s(ctx);
// Create callback context
AdvancedCallbackContext callback_ctx(2); // Allow max 2 instantiations per pattern
// Register the advanced callback
Z3_solver_propagate_on_binding(ctx, s, advanced_instantiation_callback);
// Store callback context in solver (this is a simplified approach)
// In practice, you might need a more sophisticated context management system
// Create a more complex scenario
sort int_sort = ctx.int_sort();
sort bool_sort = ctx.bool_sort();
func_decl P = ctx.function("P", int_sort, int_sort, bool_sort);
expr x = ctx.int_const("x");
expr y = ctx.int_const("y");
// Add quantified formula: forall x, y. P(x, y) => P(y, x)
expr axiom = forall(x, y, implies(P(x, y), P(y, x)));
s.add(axiom);
// Add facts that will trigger instantiations
expr a = ctx.int_const("a");
expr b = ctx.int_const("b");
expr c = ctx.int_const("c");
s.add(P(a, b));
s.add(P(b, c));
s.add(P(c, a));
cout << "Checking satisfiability with advanced filtering..." << endl;
check_result result = s.check();
cout << "Result: " << result << endl;
if (result == sat) {
cout << "Model: " << s.get_model() << endl;
}
// Print pattern statistics
cout << endl << "Instantiation Pattern Statistics:" << endl;
for (const auto& pair : callback_ctx.instantiation_counts) {
cout << " " << pair.first << ": " << pair.second << " attempts" << endl;
}
}
/**
* Simple callback that logs all instantiations without blocking any.
*/
bool logging_callback(void* ctx, Z3_solver_callback cb, Z3_ast q, Z3_ast inst) {
vector<pair<string, string>>* log = static_cast<vector<pair<string, string>>*>(ctx);
Z3_context z3_ctx = Z3_solver_callback_get_context(cb);
string q_str = Z3_ast_to_string(z3_ctx, q);
string inst_str = Z3_ast_to_string(z3_ctx, inst);
log->push_back(make_pair(q_str, inst_str));
cout << "Logged instantiation #" << log->size() << ":" << endl;
cout << " Quantifier: " << q_str << endl;
cout << " Instantiation: " << inst_str << endl;
// Allow all instantiations for logging purposes
return true;
}
/**
* Example focused on logging instantiation patterns.
*/
void example_logging() {
cout << endl << string(60, '=') << endl;
cout << "INSTANTIATION LOGGING EXAMPLE" << endl;
cout << string(60, '=') << endl;
context ctx;
solver s(ctx);
// Create log storage
vector<pair<string, string>> instantiation_log;
// Register logging callback
Z3_solver_propagate_on_binding(ctx, s, logging_callback);
// Create scenario with multiple quantifiers
sort int_sort = ctx.int_sort();
func_decl f = ctx.function("f", int_sort, int_sort);
func_decl g = ctx.function("g", int_sort, int_sort);
expr x = ctx.int_const("x");
// Add multiple quantified axioms
s.add(forall(x, f(x) >= x)); // f(x) is at least x
s.add(forall(x, g(x) <= x)); // g(x) is at most x
// Add constraints to trigger instantiations
expr a = ctx.int_const("a");
expr b = ctx.int_const("b");
s.add(f(a) < 5);
s.add(g(b) > 10);
s.add(a == 2);
s.add(b == 8);
cout << "Solving with full logging enabled..." << endl;
check_result result = s.check();
cout << "Result: " << result << endl;
// Analyze logged patterns
cout << endl << "Instantiation Analysis:" << endl;
cout << "Total instantiations logged: " << instantiation_log.size() << endl;
// Group by quantifier
map<string, vector<string>> by_quantifier;
for (const auto& entry : instantiation_log) {
by_quantifier[entry.first].push_back(entry.second);
}
for (const auto& pair : by_quantifier) {
cout << endl << "Quantifier: " << pair.first << endl;
cout << " Instantiations (" << pair.second.size() << "):" << endl;
for (size_t i = 0; i < pair.second.size(); ++i) {
cout << " " << (i + 1) << ". " << pair.second[i] << endl;
}
}
}
int main() {
try {
// Run all examples
example_basic_control();
example_advanced_filtering();
example_logging();
cout << endl << string(60, '=') << endl;
cout << "All examples completed successfully!" << endl;
cout << string(60, '=') << endl;
} catch (exception& e) {
cout << "Exception: " << e.what() << endl;
return 1;
}
return 0;
}

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/**
* Example demonstrating the UserPropagator callback for quantifier instantiations in Z3 C API.
*
* This feature was added in Z3 version 4.15.3 and allows user propagators to intercept
* and control quantifier instantiations using the Z3_solver_propagate_on_binding API.
*
* The callback receives the quantifier and its proposed instantiation, and can return
* Z3_FALSE to discard the instantiation, providing fine-grained control over the
* quantifier instantiation process.
*
* To compile:
* gcc -I /path/to/z3/src/api quantifier_instantiation_callback.c \
* -L /path/to/z3/build -lz3 -o quantifier_instantiation_callback
*
* To run:
* LD_LIBRARY_PATH=/path/to/z3/build ./quantifier_instantiation_callback
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <z3.h>
// Global counters for demonstration
static int instantiation_counter = 0;
static int allowed_counter = 0;
static int blocked_counter = 0;
/**
* User-defined callback for quantifier instantiation control.
*
* This function is called by Z3 whenever it wants to instantiate a quantifier.
*
* @param ctx User context (can be used to pass custom data)
* @param cb Solver callback object
* @param q The quantifier being instantiated
* @param inst The proposed instantiation
* @return Z3_TRUE to allow the instantiation, Z3_FALSE to discard it
*/
Z3_bool quantifier_instantiation_callback(void* ctx, Z3_solver_callback cb, Z3_ast q, Z3_ast inst) {
// Get the Z3 context from the callback
Z3_context z3_ctx = Z3_solver_callback_get_context(cb);
instantiation_counter++;
// Get string representations for logging
Z3_string q_str = Z3_ast_to_string(z3_ctx, q);
Z3_string inst_str = Z3_ast_to_string(z3_ctx, inst);
printf("Instantiation #%d:\n", instantiation_counter);
printf(" Quantifier: %s\n", q_str);
printf(" Instantiation: %s\n", inst_str);
// Example filtering logic: allow only the first 3 instantiations
// In practice, you might implement more sophisticated filtering
Z3_bool allow = (instantiation_counter <= 3) ? Z3_TRUE : Z3_FALSE;
if (allow) {
allowed_counter++;
printf(" -> ALLOWED (#%d)\n", allowed_counter);
} else {
blocked_counter++;
printf(" -> BLOCKED (#%d)\n", blocked_counter);
}
printf("\n");
return allow;
}
/**
* Example demonstrating basic quantifier instantiation control.
*/
void example_basic_control() {
printf("============================================================\n");
printf("BASIC QUANTIFIER INSTANTIATION CONTROL EXAMPLE\n");
printf("============================================================\n");
// Create Z3 context and solver
Z3_config cfg = Z3_mk_config();
Z3_context ctx = Z3_mk_context(cfg);
Z3_del_config(cfg);
Z3_solver s = Z3_mk_solver(ctx);
Z3_solver_inc_ref(ctx, s);
// Register the quantifier instantiation callback
Z3_solver_propagate_on_binding(ctx, s, quantifier_instantiation_callback);
// Create sorts and symbols
Z3_sort int_sort = Z3_mk_int_sort(ctx);
Z3_symbol f_name = Z3_mk_string_symbol(ctx, "f");
Z3_symbol x_name = Z3_mk_string_symbol(ctx, "x");
// Create function declaration f: Int -> Int
Z3_func_decl f = Z3_mk_func_decl(ctx, f_name, 1, &int_sort, int_sort);
// Create variables
Z3_ast x = Z3_mk_bound(ctx, 0, int_sort);
Z3_ast f_x = Z3_mk_app(ctx, f, 1, &x);
// Create axiom: forall x. f(x) >= 0
Z3_ast zero = Z3_mk_int(ctx, 0, int_sort);
Z3_ast f_x_geq_0 = Z3_mk_ge(ctx, f_x, zero);
Z3_ast axiom = Z3_mk_forall_const(ctx, 0, 1, &x, 0, NULL, f_x_geq_0);
Z3_solver_assert(ctx, s, axiom);
// Create constants and add constraints
Z3_symbol a_name = Z3_mk_string_symbol(ctx, "a");
Z3_symbol b_name = Z3_mk_string_symbol(ctx, "b");
Z3_symbol c_name = Z3_mk_string_symbol(ctx, "c");
Z3_ast a = Z3_mk_const(ctx, a_name, int_sort);
Z3_ast b = Z3_mk_const(ctx, b_name, int_sort);
Z3_ast c = Z3_mk_const(ctx, c_name, int_sort);
// Add constraints that might trigger instantiations
Z3_ast f_a = Z3_mk_app(ctx, f, 1, &a);
Z3_ast f_b = Z3_mk_app(ctx, f, 1, &b);
Z3_ast f_c = Z3_mk_app(ctx, f, 1, &c);
Z3_ast ten = Z3_mk_int(ctx, 10, int_sort);
Z3_ast twenty = Z3_mk_int(ctx, 20, int_sort);
Z3_ast thirty = Z3_mk_int(ctx, 30, int_sort);
Z3_solver_assert(ctx, s, Z3_mk_lt(ctx, f_a, ten));
Z3_solver_assert(ctx, s, Z3_mk_lt(ctx, f_b, twenty));
Z3_solver_assert(ctx, s, Z3_mk_lt(ctx, f_c, thirty));
// Add specific values
Z3_ast one = Z3_mk_int(ctx, 1, int_sort);
Z3_ast two = Z3_mk_int(ctx, 2, int_sort);
Z3_ast three = Z3_mk_int(ctx, 3, int_sort);
Z3_solver_assert(ctx, s, Z3_mk_eq(ctx, a, one));
Z3_solver_assert(ctx, s, Z3_mk_eq(ctx, b, two));
Z3_solver_assert(ctx, s, Z3_mk_eq(ctx, c, three));
printf("Checking satisfiability with instantiation control...\n");
Z3_lbool result = Z3_solver_check(ctx, s);
switch (result) {
case Z3_L_TRUE:
printf("Result: SAT\n");
{
Z3_model model = Z3_solver_get_model(ctx, s);
if (model) {
Z3_model_inc_ref(ctx, model);
printf("Model: %s\n", Z3_model_to_string(ctx, model));
Z3_model_dec_ref(ctx, model);
}
}
break;
case Z3_L_FALSE:
printf("Result: UNSAT\n");
break;
case Z3_L_UNDEF:
printf("Result: UNKNOWN\n");
break;
}
// Print statistics
printf("\nInstantiation Statistics:\n");
printf(" Total attempts: %d\n", instantiation_counter);
printf(" Allowed: %d\n", allowed_counter);
printf(" Blocked: %d\n", blocked_counter);
// Cleanup
Z3_solver_dec_ref(ctx, s);
Z3_del_context(ctx);
}
// Structure for advanced callback context
typedef struct {
int max_instantiations_per_pattern;
char** patterns;
int* counts;
int num_patterns;
int capacity;
} AdvancedCallbackContext;
/**
* Find or add a pattern in the context.
*/
int find_or_add_pattern(AdvancedCallbackContext* context, const char* pattern) {
// Look for existing pattern
for (int i = 0; i < context->num_patterns; i++) {
if (strcmp(context->patterns[i], pattern) == 0) {
return i;
}
}
// Add new pattern if space available
if (context->num_patterns < context->capacity) {
int index = context->num_patterns++;
context->patterns[index] = malloc(strlen(pattern) + 1);
strcpy(context->patterns[index], pattern);
context->counts[index] = 0;
return index;
}
return -1; // No space
}
/**
* Advanced callback that tracks instantiation patterns.
*/
Z3_bool advanced_instantiation_callback(void* ctx, Z3_solver_callback cb, Z3_ast q, Z3_ast inst) {
AdvancedCallbackContext* context = (AdvancedCallbackContext*)ctx;
// Get string representation of the instantiation
Z3_context z3_ctx = Z3_solver_callback_get_context(cb);
Z3_string inst_str = Z3_ast_to_string(z3_ctx, inst);
// Find or add this pattern
int pattern_index = find_or_add_pattern(context, inst_str);
if (pattern_index == -1) {
printf("Warning: Pattern storage full, allowing instantiation\n");
return Z3_TRUE;
}
// Increment count for this pattern
context->counts[pattern_index]++;
int count = context->counts[pattern_index];
// Allow only up to max_instantiations_per_pattern of the same pattern
Z3_bool allow = (count <= context->max_instantiations_per_pattern) ? Z3_TRUE : Z3_FALSE;
printf("Instantiation: %s (attempt #%d)\n", inst_str, count);
printf(" -> %s\n", allow ? "ALLOWED" : "BLOCKED");
return allow;
}
/**
* Example demonstrating advanced instantiation filtering.
*/
void example_advanced_filtering() {
printf("\n============================================================\n");
printf("ADVANCED INSTANTIATION FILTERING EXAMPLE\n");
printf("============================================================\n");
// Create callback context
AdvancedCallbackContext context;
context.max_instantiations_per_pattern = 2;
context.capacity = 100;
context.num_patterns = 0;
context.patterns = malloc(context.capacity * sizeof(char*));
context.counts = malloc(context.capacity * sizeof(int));
// Create Z3 context and solver
Z3_config cfg = Z3_mk_config();
Z3_context ctx = Z3_mk_context(cfg);
Z3_del_config(cfg);
Z3_solver s = Z3_mk_solver(ctx);
Z3_solver_inc_ref(ctx, s);
// Register the advanced callback with context
Z3_solver_propagate_on_binding(ctx, s, advanced_instantiation_callback);
// Create sorts and function declaration
Z3_sort int_sort = Z3_mk_int_sort(ctx);
Z3_sort bool_sort = Z3_mk_bool_sort(ctx);
Z3_sort P_domain[2] = {int_sort, int_sort};
Z3_symbol P_name = Z3_mk_string_symbol(ctx, "P");
Z3_func_decl P = Z3_mk_func_decl(ctx, P_name, 2, P_domain, bool_sort);
// Create bound variables for quantifier
Z3_ast x = Z3_mk_bound(ctx, 1, int_sort); // Note: index 1 for second variable in binding order
Z3_ast y = Z3_mk_bound(ctx, 0, int_sort); // Note: index 0 for first variable in binding order
// Create P(x, y) and P(y, x)
Z3_ast xy_args[2] = {x, y};
Z3_ast yx_args[2] = {y, x};
Z3_ast P_xy = Z3_mk_app(ctx, P, 2, xy_args);
Z3_ast P_yx = Z3_mk_app(ctx, P, 2, yx_args);
// Create implication: P(x, y) => P(y, x)
Z3_ast implication = Z3_mk_implies(ctx, P_xy, P_yx);
// Create quantified formula: forall x, y. P(x, y) => P(y, x)
Z3_ast vars[2] = {x, y};
Z3_ast axiom = Z3_mk_forall_const(ctx, 0, 2, vars, 0, NULL, implication);
Z3_solver_assert(ctx, s, axiom);
// Create constants
Z3_symbol a_name = Z3_mk_string_symbol(ctx, "a");
Z3_symbol b_name = Z3_mk_string_symbol(ctx, "b");
Z3_symbol c_name = Z3_mk_string_symbol(ctx, "c");
Z3_ast a = Z3_mk_const(ctx, a_name, int_sort);
Z3_ast b = Z3_mk_const(ctx, b_name, int_sort);
Z3_ast c = Z3_mk_const(ctx, c_name, int_sort);
// Add facts that will trigger instantiations
Z3_ast ab_args[2] = {a, b};
Z3_ast bc_args[2] = {b, c};
Z3_ast ca_args[2] = {c, a};
Z3_solver_assert(ctx, s, Z3_mk_app(ctx, P, 2, ab_args));
Z3_solver_assert(ctx, s, Z3_mk_app(ctx, P, 2, bc_args));
Z3_solver_assert(ctx, s, Z3_mk_app(ctx, P, 2, ca_args));
printf("Checking satisfiability with advanced filtering...\n");
Z3_lbool result = Z3_solver_check(ctx, s);
switch (result) {
case Z3_L_TRUE:
printf("Result: SAT\n");
{
Z3_model model = Z3_solver_get_model(ctx, s);
if (model) {
Z3_model_inc_ref(ctx, model);
printf("Model: %s\n", Z3_model_to_string(ctx, model));
Z3_model_dec_ref(ctx, model);
}
}
break;
case Z3_L_FALSE:
printf("Result: UNSAT\n");
break;
case Z3_L_UNDEF:
printf("Result: UNKNOWN\n");
break;
}
// Print pattern statistics
printf("\nInstantiation Pattern Statistics:\n");
for (int i = 0; i < context.num_patterns; i++) {
printf(" %s: %d attempts\n", context.patterns[i], context.counts[i]);
}
// Cleanup context
for (int i = 0; i < context.num_patterns; i++) {
free(context.patterns[i]);
}
free(context.patterns);
free(context.counts);
// Cleanup Z3 objects
Z3_solver_dec_ref(ctx, s);
Z3_del_context(ctx);
}
int main() {
printf("Z3 Quantifier Instantiation Callback Examples\n");
printf("==============================================\n\n");
// Run examples
example_basic_control();
example_advanced_filtering();
printf("\n============================================================\n");
printf("All examples completed successfully!\n");
printf("============================================================\n");
return 0;
}

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#!/usr/bin/env python3
"""
Example demonstrating the UserPropagator callback for quantifier instantiations in Z3.
This feature was added in Z3 version 4.15.3 and allows user propagators to intercept
and control quantifier instantiations. The callback receives the quantifier and its
proposed instantiation, and can return False to discard the instantiation.
This provides fine-grained control over the quantifier instantiation process,
allowing users to:
1. Inspect and log instantiations
2. Filter out undesired instantiations
3. Implement custom instantiation strategies
4. Delay certain instantiations for performance reasons
"""
from z3 import *
class QuantifierInstantiationController(UserPropagateBase):
"""
A user propagator that controls quantifier instantiations.
This example demonstrates how to:
1. Register a quantifier instantiation callback
2. Inspect proposed instantiations
3. Selectively allow or discard instantiations
"""
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.instantiation_count = 0
self.allowed_instantiations = 0
self.blocked_instantiations = 0
self.instantiation_log = []
# Register the quantifier instantiation callback
self.add_on_binding(self.on_quantifier_instantiation)
def on_quantifier_instantiation(self, quantifier, instantiation):
"""
Callback invoked when Z3 wants to instantiate a quantifier.
Args:
quantifier: The quantifier being instantiated (Z3 AST)
instantiation: The proposed instantiation (Z3 AST)
Returns:
bool: True to allow the instantiation, False to discard it
"""
self.instantiation_count += 1
# Log the instantiation for inspection
q_str = str(quantifier)
inst_str = str(instantiation)
self.instantiation_log.append((q_str, inst_str))
print(f"Instantiation #{self.instantiation_count}:")
print(f" Quantifier: {q_str}")
print(f" Instantiation: {inst_str}")
# Example filtering logic: allow only the first 3 instantiations
# In practice, you might filter based on the structure of the instantiation,
# performance considerations, or other criteria
allow = self.instantiation_count <= 3
if allow:
self.allowed_instantiations += 1
print(f" -> ALLOWED (#{self.allowed_instantiations})")
else:
self.blocked_instantiations += 1
print(f" -> BLOCKED (#{self.blocked_instantiations})")
print()
return allow
def push(self):
# Required method for user propagators
pass
def pop(self, num_scopes):
# Required method for user propagators
pass
def fresh(self, new_ctx):
# Required method for user propagators
return QuantifierInstantiationController(ctx=new_ctx)
def get_statistics(self):
"""Return statistics about instantiation control."""
return {
'total_instantiation_attempts': self.instantiation_count,
'allowed_instantiations': self.allowed_instantiations,
'blocked_instantiations': self.blocked_instantiations,
'instantiation_log': self.instantiation_log
}
def example_basic_quantifier_control():
"""
Basic example showing how to control quantifier instantiations.
"""
print("=" * 60)
print("BASIC QUANTIFIER INSTANTIATION CONTROL EXAMPLE")
print("=" * 60)
# Create solver with user propagator
s = Solver()
controller = QuantifierInstantiationController(s)
# Create a simple quantified formula
x = Int('x')
f = Function('f', IntSort(), IntSort())
# Add a quantified axiom: forall x. f(x) >= 0
axiom = ForAll([x], f(x) >= 0)
s.add(axiom)
# Add constraints that might trigger instantiations
a, b, c = Ints('a b c')
s.add(f(a) < 10)
s.add(f(b) < 20)
s.add(f(c) < 30)
# Also add constraints that should conflict if all instantiations are allowed
s.add(a == 1)
s.add(b == 2)
s.add(c == 3)
print("Checking satisfiability with instantiation control...")
result = s.check()
print(f"Result: {result}")
if result == sat:
print(f"Model: {s.model()}")
# Print statistics
stats = controller.get_statistics()
print(f"\nInstantiation Statistics:")
print(f" Total attempts: {stats['total_instantiation_attempts']}")
print(f" Allowed: {stats['allowed_instantiations']}")
print(f" Blocked: {stats['blocked_instantiations']}")
def example_advanced_filtering():
"""
Advanced example showing more sophisticated instantiation filtering.
"""
print("\n" + "=" * 60)
print("ADVANCED INSTANTIATION FILTERING EXAMPLE")
print("=" * 60)
class AdvancedController(UserPropagateBase):
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.instantiations_by_term = {}
self.add_on_binding(self.smart_filter)
def smart_filter(self, quantifier, instantiation):
"""
Smart filtering based on instantiation content.
"""
# Extract information about the instantiation
q_str = str(quantifier)
inst_str = str(instantiation)
# Count instantiations per term pattern
if inst_str not in self.instantiations_by_term:
self.instantiations_by_term[inst_str] = 0
self.instantiations_by_term[inst_str] += 1
# Allow only up to 2 instantiations of the same pattern
allow = self.instantiations_by_term[inst_str] <= 2
print(f"Instantiation: {inst_str} (attempt #{self.instantiations_by_term[inst_str]})")
print(f" -> {'ALLOWED' if allow else 'BLOCKED'}")
return allow
def push(self):
pass
def pop(self, num_scopes):
pass
def fresh(self, new_ctx):
return AdvancedController(ctx=new_ctx)
# Create solver with advanced controller
s = Solver()
controller = AdvancedController(s)
# Create a more complex scenario
x, y = Ints('x y')
P = Function('P', IntSort(), IntSort(), BoolSort())
# Add quantified formula: forall x, y. P(x, y) => P(y, x)
axiom = ForAll([x, y], Implies(P(x, y), P(y, x)))
s.add(axiom)
# Add facts that will trigger instantiations
a, b, c = Ints('a b c')
s.add(P(a, b))
s.add(P(b, c))
s.add(P(c, a))
print("Checking satisfiability with advanced filtering...")
result = s.check()
print(f"Result: {result}")
if result == sat:
print(f"Model: {s.model()}")
def example_instantiation_logging():
"""
Example focused on logging and analyzing instantiation patterns.
"""
print("\n" + "=" * 60)
print("INSTANTIATION LOGGING AND ANALYSIS EXAMPLE")
print("=" * 60)
class LoggingController(UserPropagateBase):
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.log = []
self.add_on_binding(self.log_instantiation)
def log_instantiation(self, quantifier, instantiation):
"""
Log all instantiation attempts for later analysis.
"""
entry = {
'quantifier': str(quantifier),
'instantiation': str(instantiation),
'timestamp': len(self.log)
}
self.log.append(entry)
# For this example, allow all instantiations
return True
def push(self):
pass
def pop(self, num_scopes):
pass
def fresh(self, new_ctx):
return LoggingController(ctx=new_ctx)
def analyze_patterns(self):
"""Analyze logged instantiation patterns."""
print(f"Total instantiations logged: {len(self.log)}")
# Group by quantifier
by_quantifier = {}
for entry in self.log:
q = entry['quantifier']
if q not in by_quantifier:
by_quantifier[q] = []
by_quantifier[q].append(entry['instantiation'])
for q, instantiations in by_quantifier.items():
print(f"\nQuantifier: {q}")
print(f" Instantiations ({len(instantiations)}):")
for i, inst in enumerate(instantiations, 1):
print(f" {i}. {inst}")
# Create solver with logging controller
s = Solver()
controller = LoggingController(s)
# Create scenario with multiple quantifiers
x = Int('x')
f = Function('f', IntSort(), IntSort())
g = Function('g', IntSort(), IntSort())
# Add multiple quantified axioms
s.add(ForAll([x], f(x) >= x)) # f(x) is at least x
s.add(ForAll([x], g(x) <= x)) # g(x) is at most x
# Add constraints to trigger instantiations
a, b = Ints('a b')
s.add(f(a) < 5)
s.add(g(b) > 10)
s.add(a == 2)
s.add(b == 8)
print("Solving with full logging enabled...")
result = s.check()
print(f"Result: {result}")
# Analyze the logged instantiation patterns
print("\nInstantiation Analysis:")
controller.analyze_patterns()
if __name__ == "__main__":
# Run all examples
example_basic_quantifier_control()
example_advanced_filtering()
example_instantiation_logging()
print("\n" + "=" * 60)
print("All examples completed successfully!")
print("=" * 60)

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#!/usr/bin/env python3
"""
Unit tests for the UserPropagator quantifier instantiation callback feature.
This test suite validates the functionality added in Z3 version 4.15.3 that allows
user propagators to intercept and control quantifier instantiations.
"""
import unittest
import sys
import os
# Add the Z3 Python bindings to the path
sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..', 'build', 'python'))
from z3 import *
class TestQuantifierInstantiationCallback(unittest.TestCase):
"""Test cases for quantifier instantiation callback functionality."""
def setUp(self):
"""Set up test fixtures."""
self.reset_counters()
def reset_counters(self):
"""Reset global test counters."""
global g_instantiation_count, g_allowed_count, g_blocked_count
g_instantiation_count = 0
g_allowed_count = 0
g_blocked_count = 0
# Global counters for test validation
g_instantiation_count = 0
g_allowed_count = 0
g_blocked_count = 0
class BasicInstantiationController(UserPropagateBase):
"""Basic user propagator for testing instantiation control."""
def __init__(self, allow_first_n=3, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.allow_first_n = allow_first_n
self.add_on_binding(self.control_instantiation)
def control_instantiation(self, quantifier, instantiation):
global g_instantiation_count, g_allowed_count, g_blocked_count
g_instantiation_count += 1
allow = g_instantiation_count <= self.allow_first_n
if allow:
g_allowed_count += 1
else:
g_blocked_count += 1
return allow
def push(self):
pass
def pop(self, num_scopes):
pass
def fresh(self, new_ctx):
return BasicInstantiationController(self.allow_first_n, ctx=new_ctx)
class LoggingController(UserPropagateBase):
"""User propagator that logs all instantiations without blocking."""
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.log = []
self.add_on_binding(self.log_instantiation)
def log_instantiation(self, quantifier, instantiation):
global g_instantiation_count
g_instantiation_count += 1
entry = {
'quantifier': str(quantifier),
'instantiation': str(instantiation),
'count': g_instantiation_count
}
self.log.append(entry)
# Allow all instantiations
return True
def push(self):
pass
def pop(self, num_scopes):
pass
def fresh(self, new_ctx):
return LoggingController(ctx=new_ctx)
class PatternFilterController(UserPropagateBase):
"""User propagator that filters based on instantiation patterns."""
def __init__(self, max_per_pattern=2, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.max_per_pattern = max_per_pattern
self.pattern_counts = {}
self.add_on_binding(self.filter_by_pattern)
def filter_by_pattern(self, quantifier, instantiation):
global g_instantiation_count, g_allowed_count, g_blocked_count
g_instantiation_count += 1
pattern = str(instantiation)
self.pattern_counts[pattern] = self.pattern_counts.get(pattern, 0) + 1
allow = self.pattern_counts[pattern] <= self.max_per_pattern
if allow:
g_allowed_count += 1
else:
g_blocked_count += 1
return allow
def push(self):
pass
def pop(self, num_scopes):
pass
def fresh(self, new_ctx):
return PatternFilterController(self.max_per_pattern, ctx=new_ctx)
class TestQuantifierInstantiationCallback(unittest.TestCase):
"""Test cases for quantifier instantiation callback functionality."""
def setUp(self):
"""Set up test fixtures."""
self.reset_counters()
def reset_counters(self):
"""Reset global test counters."""
global g_instantiation_count, g_allowed_count, g_blocked_count
g_instantiation_count = 0
g_allowed_count = 0
g_blocked_count = 0
def test_basic_instantiation_control(self):
"""Test basic instantiation limiting functionality."""
self.reset_counters()
# Create solver with instantiation controller
s = Solver()
controller = BasicInstantiationController(allow_first_n=2, s=s)
# Create simple quantified formula
x = Int('x')
f = Function('f', IntSort(), IntSort())
# Add quantified axiom: forall x. f(x) >= 0
s.add(ForAll([x], f(x) >= 0))
# Add constraints that trigger instantiations
a, b, c = Ints('a b c')
s.add(f(a) < 10)
s.add(f(b) < 20)
s.add(f(c) < 30)
s.add(a == 1, b == 2, c == 3)
# Solve
result = s.check()
# Validate that callbacks were invoked and some instantiations were blocked
self.assertGreater(g_instantiation_count, 0, "No instantiations were attempted")
self.assertEqual(g_allowed_count, 2, "Expected exactly 2 allowed instantiations")
self.assertGreaterEqual(g_blocked_count, 0, "Expected some blocked instantiations")
# Should still be satisfiable with limited instantiations
self.assertEqual(result, sat, "Formula should be satisfiable")
def test_logging_all_instantiations(self):
"""Test that logging controller captures all instantiation attempts."""
self.reset_counters()
s = Solver()
logger = LoggingController(s=s)
# Create formula with multiple quantifiers
x = Int('x')
f = Function('f', IntSort(), IntSort())
g = Function('g', IntSort(), IntSort())
s.add(ForAll([x], f(x) >= x))
s.add(ForAll([x], g(x) <= x))
a, b = Ints('a b')
s.add(f(a) < 5)
s.add(g(b) > 10)
s.add(a == 2, b == 8)
result = s.check()
# Validate logging
self.assertGreater(len(logger.log), 0, "No instantiations were logged")
self.assertEqual(len(logger.log), g_instantiation_count, "Log count mismatch")
# Check log structure
for entry in logger.log:
self.assertIn('quantifier', entry)
self.assertIn('instantiation', entry)
self.assertIn('count', entry)
self.assertIsInstance(entry['quantifier'], str)
self.assertIsInstance(entry['instantiation'], str)
self.assertIsInstance(entry['count'], int)
def test_pattern_based_filtering(self):
"""Test pattern-based instantiation filtering."""
self.reset_counters()
s = Solver()
filter_controller = PatternFilterController(max_per_pattern=1, s=s)
# Create scenario that might generate duplicate patterns
x, y = Ints('x y')
P = Function('P', IntSort(), IntSort(), BoolSort())
s.add(ForAll([x, y], Implies(P(x, y), P(y, x))))
a, b, c = Ints('a b c')
s.add(P(a, b))
s.add(P(b, c))
s.add(P(a, c)) # This might create similar patterns
result = s.check()
# Validate that filtering occurred
self.assertGreater(g_instantiation_count, 0, "No instantiations were attempted")
# Check that patterns were tracked
self.assertGreater(len(filter_controller.pattern_counts), 0, "No patterns were tracked")
# Verify some patterns appeared multiple times (and were filtered)
max_count = max(filter_controller.pattern_counts.values())
if max_count > 1:
self.assertGreater(g_blocked_count, 0, "Expected some blocked instantiations for repeated patterns")
def test_callback_with_unsat_formula(self):
"""Test callback behavior with unsatisfiable formulas."""
self.reset_counters()
s = Solver()
controller = BasicInstantiationController(allow_first_n=1, s=s)
# Create unsatisfiable formula
x = Int('x')
f = Function('f', IntSort(), IntSort())
s.add(ForAll([x], f(x) >= 0))
s.add(f(5) < -10) # Contradiction
result = s.check()
# Should be UNSAT regardless of instantiation control
self.assertEqual(result, unsat, "Formula should be unsatisfiable")
# Callbacks may or may not be invoked for UNSAT formulas
# (depends on solver's instantiation strategy)
def test_callback_registration_without_instantiations(self):
"""Test that callback registration works even without quantifier instantiations."""
self.reset_counters()
s = Solver()
controller = BasicInstantiationController(allow_first_n=5, s=s)
# Add formula without quantifiers
x, y = Ints('x y')
s.add(x + y == 10)
s.add(x > 5)
result = s.check()
# Should solve without invoking callbacks
self.assertEqual(result, sat, "Formula should be satisfiable")
self.assertEqual(g_instantiation_count, 0, "No instantiations should occur without quantifiers")
def test_multiple_solvers_independent_callbacks(self):
"""Test that callbacks on different solvers are independent."""
self.reset_counters()
# Create first solver with restrictive controller
s1 = Solver()
controller1 = BasicInstantiationController(allow_first_n=1, s=s1)
# Create second solver with permissive controller
s2 = Solver()
controller2 = BasicInstantiationController(allow_first_n=10, s=s2)
# Add same formula to both
x = Int('x')
f = Function('f', IntSort(), IntSort())
axiom = ForAll([x], f(x) >= 0)
for s in [s1, s2]:
s.add(axiom)
a = Int(f'a_{id(s)}') # Unique constant per solver
s.add(f(a) < 5)
s.add(a == 1)
# Solve both
result1 = s1.check()
result2 = s2.check()
# Both should be satisfiable
self.assertEqual(result1, sat, "First solver should find solution")
self.assertEqual(result2, sat, "Second solver should find solution")
# Note: Since we use global counters, we can't easily test independence
# In a real implementation, each controller would have its own counters
class TestErrorConditions(unittest.TestCase):
"""Test error conditions and edge cases."""
def test_callback_exception_handling(self):
"""Test that exceptions in callbacks are handled gracefully."""
class FaultyController(UserPropagateBase):
def __init__(self, s=None, ctx=None):
UserPropagateBase.__init__(self, s, ctx)
self.add_on_binding(self.faulty_callback)
def faulty_callback(self, quantifier, instantiation):
# This callback always raises an exception
raise ValueError("Test exception in callback")
def push(self): pass
def pop(self, num_scopes): pass
def fresh(self, new_ctx): return FaultyController(ctx=new_ctx)
s = Solver()
# This should not crash, but the callback behavior is implementation-defined
# when exceptions occur
try:
controller = FaultyController(s=s)
x = Int('x')
f = Function('f', IntSort(), IntSort())
s.add(ForAll([x], f(x) >= 0))
s.add(f(1) < 5)
# The solver should handle callback exceptions gracefully
# Exact behavior may vary, but should not crash
result = s.check()
except Exception as e:
# If an exception propagates, it should be the one we raised
# or a Z3Exception wrapping it
pass
if __name__ == '__main__':
# Check if Z3 is available
try:
from z3 import *
# Test basic Z3 functionality
x = Int('x')
s = Solver()
s.add(x > 0)
if s.check() != sat:
print("ERROR: Basic Z3 functionality not working")
sys.exit(1)
except ImportError:
print("ERROR: Z3 Python bindings not found")
print("Make sure PYTHONPATH includes the Z3 Python bindings directory")
sys.exit(1)
# Run the tests
print("Running quantifier instantiation callback tests...")
unittest.main(verbosity=2)