Updated driver file R.py to showcase SMT techinques

Fixed minor bugs concerning lack of falsification rules and interfaces between VSP and SMT

smt.py

@@ -1,18 +1,26 @@
 from itertools import product
-from typing import Dict, Generator, Optional, Tuple
+from typing import Dict, Generator, Optional, Set, Tuple, TYPE_CHECKING
 
 from logic import Logic, Operation, Rule, PropositionalVariable, Term, OpTerm, get_prop_vars_from_rule
 from model import Model, ModelValue, ModelFunction
 
-from z3 import (
-    And, BoolSort, Context, EnumSort, Function, Implies, Or, sat, Solver, z3
-)
+SMT_LOADED = True
+try:
+    from z3 import (
+        And, BoolSort, Context, EnumSort, Function, Implies, Or, sat, Solver, z3
+    )
+except ImportError:
+    SMT_LOADED = False
+
+def smt_is_loaded() -> bool:
+    global SMT_LOADED
+    return SMT_LOADED
 
 def term_to_smt(
     t: Term,
-    op_mapping: Dict[Operation, z3.FuncDeclRef],
-    var_mapping: Dict[PropositionalVariable, z3.DatatypeRef]
-) -> z3.DatatypeRef:
+    op_mapping: Dict[Operation, "z3.FuncDeclRef"],
+    var_mapping: Dict[PropositionalVariable, "z3.DatatypeRef"]
+) -> "z3.DatatypeRef":
     """Convert a logic term to its SMT representation."""
     if isinstance(t, PropositionalVariable):
         return var_mapping[t]
@@ -26,10 +34,10 @@ def term_to_smt(
 
 def logic_rule_to_smt_constraints(
     rule: Rule,
-    IsDesignated: z3.FuncDeclRef,
+    IsDesignated: "z3.FuncDeclRef",
     smt_carrier_set,
-    op_mapping: Dict[Operation, z3.FuncDeclRef]
-) -> Generator[z3.BoolRef, None, None]:
+    op_mapping: Dict[Operation, "z3.FuncDeclRef"]
+) -> Generator["z3.BoolRef", None, None]:
     """
     Encode a logic rule as SMT constraints.
 
@@ -63,10 +71,10 @@ def logic_rule_to_smt_constraints(
 
 def logic_falsification_rule_to_smt_constraints(
     rule: Rule,
-    IsDesignated: z3.FuncDeclRef,
+    IsDesignated: "z3.FuncDeclRef",
     smt_carrier_set,
-    op_mapping: Dict[Operation, z3.FuncDeclRef]
-) -> z3.BoolRef:
+    op_mapping: Dict[Operation, "z3.FuncDeclRef"]
+) -> "z3.BoolRef":
     """
     Encode a falsification rule as an SMT constraint.
 
@@ -132,7 +140,7 @@ class SMTLogicEncoder:
         self.carrier_sort, self.smt_carrier_set = EnumSort("C", element_names, ctx=self.ctx)
 
         # Create operation functions
-        self.operation_function_map: Dict[Operation, z3.FuncDeclRef] = {}
+        self.operation_function_map: Dict[Operation, "z3.FuncDeclRef"] = {}
         for operation in logic.operations:
             self.operation_function_map[operation] = self.create_function(operation.symbol, operation.arity)
 
@@ -143,10 +151,10 @@ class SMTLogicEncoder:
         self._add_logic_constraints()
         self._add_designation_symmetry_constraints()
 
-    def create_predicate(self, name: str, arity: int) -> z3.FuncDeclRef:
+    def create_predicate(self, name: str, arity: int) -> "z3.FuncDeclRef":
         return Function(name, *(self.carrier_sort for _ in range(arity)), BoolSort(ctx=self.ctx))
 
-    def create_function(self, name: str, arity: int) -> z3.FuncDeclRef:
+    def create_function(self, name: str, arity: int) -> "z3.FuncDeclRef":
         return Function(name, *(self.carrier_sort for _ in range(arity + 1)))
 
     def _add_logic_constraints(self):
@@ -171,9 +179,9 @@ class SMTLogicEncoder:
             )
             self.solver.add(constraint)
 
-    def extract_model(self, smt_model) -> Model:
+    def extract_model(self, smt_model) -> Tuple[Model, Dict[Operation, ModelFunction]]:
         """
-        Extract a Model object from an SMT model.
+        Extract a Model object and interpretation from an SMT model.
         """
         carrier_set = {ModelValue(f"{i}") for i in range(self.size)}
 
@@ -185,7 +193,8 @@ class SMTLogicEncoder:
         designated_values = {ModelValue(str(x)) for x in smt_designated}
 
         # Extract operation functions
-        model_functions = set()
+        model_functions: Set[ModelFunction] = set()
+        interpretation: Dict[Operation, ModelFunction] = dict()
         for (operation, smt_function) in self.operation_function_map.items():
             mapping: Dict[Tuple[ModelValue], ModelValue] = {}
             for smt_inputs in product(self.smt_carrier_set, repeat=operation.arity):
@@ -193,9 +202,12 @@ class SMTLogicEncoder:
                 smt_output = smt_model.evaluate(smt_function(*smt_inputs))
                 model_output = ModelValue(str(smt_output))
                 mapping[model_inputs] = model_output
-            model_functions.add(ModelFunction(operation.arity, mapping, operation.symbol))
+            model_function = ModelFunction(operation.arity, mapping, operation.symbol)
+            model_functions.add(model_function)
+            interpretation[operation] = model_function
 
-        return Model(carrier_set, model_functions, designated_values)
+
+        return Model(carrier_set, model_functions, designated_values), interpretation
 
 
     def _add_designation_symmetry_constraints(self):
@@ -218,7 +230,7 @@ class SMTLogicEncoder:
                 )
             )
 
-    def create_exclusion_constraint(self, model: Model) -> z3.BoolRef:
+    def create_exclusion_constraint(self, model: Model) -> "z3.BoolRef":
         """
         Create a constraint that excludes the given model from future solutions.
         """
@@ -254,7 +266,7 @@ class SMTLogicEncoder:
 
         return Or(constraints)
 
-    def find_model(self) -> Optional[Model]:
+    def find_model(self) -> Optional[Tuple[Model, Dict[Operation, ModelFunction]]]:
         """
         Find a single model satisfying the logic constraints.
 
@@ -274,12 +286,12 @@ class SMTLogicEncoder:
             pass
 
 
-def find_model(logic: Logic, size: int) -> Optional[Model]:
+def find_model(logic: Logic, size: int) -> Optional[Tuple[Model, Dict[Operation, ModelFunction]]]:
     """Find a single model for the given logic and size."""
     encoder = SMTLogicEncoder(logic, size)
     return encoder.find_model()
 
-def find_all_models(logic: Logic, size: int) -> Generator[Model, None, None]:
+def find_all_models(logic: Logic, size: int) -> Generator[Tuple[Model, Dict[Operation, ModelFunction]], None, None]:
     """
     Find all models for the given logic and size.
 
@@ -294,13 +306,14 @@ def find_all_models(logic: Logic, size: int) -> Generator[Model, None, None]:
 
     while True:
         # Try to find a model
-        model = encoder.find_model()
-        if model is None:
+        solution = encoder.find_model()
+        if solution is None:
             break
 
-        yield model
+        yield solution
 
         # Add constraint to exclude this model from future solutions
+        model, _ = solution
         exclusion_constraint = encoder.create_exclusion_constraint(model)
         encoder.solver.add(exclusion_constraint)
 
@@ -346,13 +359,13 @@ class SMTModelEncoder:
             is_designated = model_value in model.designated_values
             self.solver.add(self.is_designated(self.model_value_to_smt[model_value]) == is_designated)
 
-    def create_predicate(self, name: str, arity: int) -> z3.FuncDeclRef:
+    def create_predicate(self, name: str, arity: int) -> "z3.FuncDeclRef":
         return Function(name, *(self.carrier_sort for _ in range(arity)), BoolSort(ctx=self.ctx))
 
-    def create_function(self, name: str, arity: int) -> z3.FuncDeclRef:
+    def create_function(self, name: str, arity: int) -> "z3.FuncDeclRef":
         return Function(name, *(self.carrier_sort for _ in range(arity + 1)))
 
-    def add_function_constraints_from_table(self, smt_fn: z3.FuncDeclRef, model_fn: ModelFunction):
+    def add_function_constraints_from_table(self, smt_fn: "z3.FuncDeclRef", model_fn: ModelFunction):
         for inputs, output in model_fn.mapping.items():
             smt_inputs = tuple(self.model_value_to_smt[inp] for inp in inputs)
             smt_output = self.model_value_to_smt[output]