"""
Symbolic Processor Module for NSAF
---------------------------------
Author: Bolorerdene Bundgaa
Contact: bolor@ariunbolor.org
Website: https://bolor.me
Implements symbolic reasoning capabilities that integrate with quantum operations.
"""
from typing import Dict, List, Optional, Union, Any
from dataclasses import dataclass
from enum import Enum
import numpy as np
from .circuit import QuantumCircuit, GateType
class SymbolicType(Enum):
"""Types of symbolic expressions"""
VARIABLE = "Variable"
CONSTANT = "Constant"
OPERATOR = "Operator"
FUNCTION = "Function"
PREDICATE = "Predicate"
QUANTIFIER = "Quantifier"
class LogicalOperator(Enum):
"""Logical operators for symbolic expressions"""
AND = "AND"
OR = "OR"
NOT = "NOT"
IMPLIES = "IMPLIES"
EQUIVALENT = "EQUIVALENT"
XOR = "XOR"
@dataclass
class SymbolicExpression:
"""Represents a symbolic expression"""
expr_type: SymbolicType
value: Any
children: Optional[List['SymbolicExpression']] = None
metadata: Optional[Dict[str, Any]] = None
def __str__(self) -> str:
"""String representation of the symbolic expression"""
if self.expr_type == SymbolicType.VARIABLE:
return str(self.value)
elif self.expr_type == SymbolicType.CONSTANT:
return str(self.value)
elif self.expr_type == SymbolicType.OPERATOR:
if not self.children:
return str(self.value)
op_str = f" {self.value} "
return f"({op_str.join(str(child) for child in self.children)})"
elif self.expr_type == SymbolicType.FUNCTION:
args = ", ".join(str(child) for child in (self.children or []))
return f"{self.value}({args})"
return str(self.value)
class SymbolicProcessor:
"""Main symbolic processing class"""
def __init__(self):
"""Initialize symbolic processor"""
self.variables: Dict[str, SymbolicExpression] = {}
self.axioms: List[SymbolicExpression] = []
self.theorems: List[SymbolicExpression] = []
def create_variable(self, name: str) -> SymbolicExpression:
"""Create a new symbolic variable"""
var = SymbolicExpression(SymbolicType.VARIABLE, name)
self.variables[name] = var
return var
def create_constant(self, value: Union[int, float, str]) -> SymbolicExpression:
"""Create a symbolic constant"""
return SymbolicExpression(SymbolicType.CONSTANT, value)
def create_operator(self, op: LogicalOperator,
operands: List[SymbolicExpression]) -> SymbolicExpression:
"""Create a symbolic operator expression"""
return SymbolicExpression(SymbolicType.OPERATOR, op, children=operands)
def add_axiom(self, axiom: SymbolicExpression) -> None:
"""Add an axiom to the symbolic system"""
self.axioms.append(axiom)
def add_theorem(self, theorem: SymbolicExpression) -> None:
"""Add a proven theorem to the symbolic system"""
self.theorems.append(theorem)
def to_quantum_circuit(self, expr: SymbolicExpression) -> QuantumCircuit:
"""Convert symbolic expression to quantum circuit"""
# Determine number of qubits needed
num_qubits = self._count_variables(expr)
circuit = QuantumCircuit(num_qubits)
# Convert expression to quantum operations
self._build_quantum_circuit(expr, circuit)
return circuit
def _count_variables(self, expr: SymbolicExpression) -> int:
"""Count number of unique variables in expression"""
if expr.expr_type == SymbolicType.VARIABLE:
return 1
elif expr.children:
return sum(self._count_variables(child) for child in expr.children)
return 0
def _build_quantum_circuit(self, expr: SymbolicExpression,
circuit: QuantumCircuit,
qubit_map: Optional[Dict[str, int]] = None) -> None:
"""Recursively build quantum circuit from symbolic expression"""
if qubit_map is None:
qubit_map = {}
if expr.expr_type == SymbolicType.OPERATOR:
if expr.value == LogicalOperator.AND:
self._build_and_gate(expr, circuit, qubit_map)
elif expr.value == LogicalOperator.OR:
self._build_or_gate(expr, circuit, qubit_map)
elif expr.value == LogicalOperator.NOT:
self._build_not_gate(expr, circuit, qubit_map)
# Add more operators as needed
def _build_and_gate(self, expr: SymbolicExpression,
circuit: QuantumCircuit,
qubit_map: Dict[str, int]) -> None:
"""Build quantum AND gate"""
if not expr.children or len(expr.children) < 2:
return
# Implement AND gate using CNOT and Toffoli gates
control = self._get_qubit_index(expr.children[0], qubit_map)
target = self._get_qubit_index(expr.children[1], qubit_map)
circuit.cnot(control, target)
def _build_or_gate(self, expr: SymbolicExpression,
circuit: QuantumCircuit,
qubit_map: Dict[str, int]) -> None:
"""Build quantum OR gate"""
if not expr.children or len(expr.children) < 2:
return
# Implement OR gate using X gates and CNOT
control = self._get_qubit_index(expr.children[0], qubit_map)
target = self._get_qubit_index(expr.children[1], qubit_map)
# X gates before and after CNOT implement OR
circuit.add_gate(GateType.X, [control])
circuit.add_gate(GateType.X, [target])
circuit.cnot(control, target)
circuit.add_gate(GateType.X, [target])
def _build_not_gate(self, expr: SymbolicExpression,
circuit: QuantumCircuit,
qubit_map: Dict[str, int]) -> None:
"""Build quantum NOT gate"""
if not expr.children:
return
target = self._get_qubit_index(expr.children[0], qubit_map)
circuit.add_gate(GateType.X, [target])
def _get_qubit_index(self, expr: SymbolicExpression,
qubit_map: Dict[str, int]) -> int:
"""Get or assign qubit index for variable"""
if expr.expr_type != SymbolicType.VARIABLE:
raise ValueError("Expression must be a variable")
var_name = str(expr.value)
if var_name not in qubit_map:
qubit_map[var_name] = len(qubit_map)
return qubit_map[var_name]
def evaluate(self, expr: SymbolicExpression,
assignments: Dict[str, bool]) -> bool:
"""Evaluate symbolic expression with given variable assignments"""
if expr.expr_type == SymbolicType.VARIABLE:
return assignments.get(str(expr.value), False)
elif expr.expr_type == SymbolicType.CONSTANT:
return bool(expr.value)
elif expr.expr_type == SymbolicType.OPERATOR:
if expr.value == LogicalOperator.AND:
return all(self.evaluate(child, assignments)
for child in (expr.children or []))
elif expr.value == LogicalOperator.OR:
return any(self.evaluate(child, assignments)
for child in (expr.children or []))
elif expr.value == LogicalOperator.NOT:
return not self.evaluate(expr.children[0], assignments)
return False
