terse_fields.py

from typing import Protocol, Callable, Union, Any, TypeVar
from enum import Enum
from dataclasses import dataclass
import hashlib
import cmath

#------------------------------------------------------------------------------
# Type Definitions
#------------------------------------------------------------------------------
"""
Type Definitions for Morphological Source Code (MSC).
MSC is built upon T (Types), V (Values), and C (Computations) acting in
mutually transforming, Noetherian symmetry-preserving roles.
"""

T = TypeVar('T')
V = TypeVar('V', bound=Union[int, float, str, bool, list, dict, tuple, set, object, Callable, type])
C = TypeVar('C', bound=Callable[..., Any])

#------------------------------------------------------------------------------
# Enums and Data Classes for Symmetries and Manifolds
#------------------------------------------------------------------------------
class Symmetry(Enum):
    TRANSLATION = "Translation"
    ROTATION = "Rotation"
    PHASE = "Phase"

class Conservation(Enum):
    INFORMATION = "Information"
    COHERENCE = "Coherence"
    BEHAVIORAL = "Behavioral"

@dataclass
class State:
    type_space: T
    value_space: V
    computation_space: C
    symmetry: Symmetry
    conservation: Conservation

#------------------------------------------------------------------------------
# Protocols - Structures for Feedback and Dynamics
#------------------------------------------------------------------------------
class Field(Protocol):
    """
    Defines a dynamic field space, leveraging symmetries and manifold mappings.
    """
    def interact(self, state: State) -> State:
        ...

class Gauge:
    """
    Manages the field's influence on type, value, and computation manifolds.
    """
    def __init__(self, local: State, global_: State, emergent: State):
        self.fields = [local, global_, emergent]

    def apply_transformation(self, state: State) -> State:
        transformed_state = state
        for field in self.fields:
            transformed_state = self._combine_states(transformed_state, field)
        return transformed_state

    def _combine_states(self, state_a: State, state_b: State) -> State:
        # Apply computation from state_b to the value space of state_a
        new_value = [state_b.computation_space(val) for val in state_a.value_space]

        return State(
            type_space=state_a.type_space,
            value_space=new_value,
            computation_space=state_a.computation_space,
            symmetry=state_a.symmetry,
            conservation=state_b.conservation,
        )

#------------------------------------------------------------------------------
# Core System - Deamon-Core
#------------------------------------------------------------------------------

class MorphologicalKernel:
    """
    Central to running feedback-driven transformations.
    Interprets configuration space in accordance with Noetherian symmetries.
    """
    def __init__(self):
        self.state_history = []

    def run(self, initial_state: State, gauge: Gauge, steps: int) -> State:
        current_state = initial_state
        for _ in range(steps):
            current_state = gauge.apply_transformation(current_state)
            self.state_history.append(current_state)
        return current_state

    def __repr__(self):
        return f"Kernel with {len(self.state_history)} state transitions."

#------------------------------------------------------------------------------
# Example Usage
#------------------------------------------------------------------------------

def visualize_state_history(state_history):
    """
    Visualizes the evolution of the state transformations over time.
    
    This function takes the state history from the MorphologicalKernel's execution
    and generates a simple line plot representing the "value space" at each
    transformation step. This is a simplistic visualization to help illustrate
    how the value space evolves, a key concept in understanding transformations
    in this framework.

    Parameters:
    - state_history: A list of State objects created during the kernel's run.
      Each State object represents the system's configuration at a specific point
      in time.

    Returns:
    - Matplotlib Figure showcasing the value space over time.
    
    Raises:
    - ValueError: If the state_history is not provided or is empty.
    """
    if not state_history:
        raise ValueError("state_history cannot be empty!")

    values = [state.value_space for state in state_history]
    #plt.plot(values)
    #plt.title('Evolution of Value Space')
    #plt.xlabel('Step')
    #plt.ylabel('Value Space')
    #plt.grid(True)
    #plt.show()

def main():
    """
    Main Execution and Example of Morphological Kernel.

    This function outlines the setup and execution process for the Morphological Kernel.
    It showcases how initial states and Gauge configurations are used to propagate system
    transformations through the invocation of the kernel's `run` method. Additionally,
    it provides a demonstration of visualizing the resulting state evolution.

    Steps included:
    1. Definition of the initial state as a combination of type, value, and computation
       spaces, decorated with symmetry and conservation laws.
    2. Setup of Gauge states: local, global, and emergent, each providing specific
       transformation rules for manipulating system configurations.
    3. Initialization and execution of the Morphological Kernel, running a series of
       transformations over the specified steps.
    4. Display of the final state and visualization of the state history to illustrate
       the cumulative impact of transformation steps.

    Outputs:
    - Terminal output of the final state configuration after running the kernel.
    - A visual plot showing Value Space evolution for ease of conceptual understanding.
    """
    initial_state = State(
        type_space=lambda x: x,
        value_space=[0],
        computation_space=lambda x: x,
        symmetry=Symmetry.TRANSLATION,
        conservation=Conservation.INFORMATION
    )

    local_gauge = State(
        type_space=lambda x: x,
        value_space=[1],
        computation_space=lambda x: x + 1,
        symmetry=Symmetry.ROTATION,
        conservation=Conservation.COHERENCE
    )

    global_gauge = State(
        type_space=lambda x: x,
        value_space=[4],
        computation_space=lambda x: 2 * x,
        symmetry=Symmetry.PHASE,
        conservation=Conservation.BEHAVIORAL
    )

    emergent_gauge = State(
        type_space=lambda x: x,
        value_space=[0],
        computation_space=lambda x: x,
        symmetry=Symmetry.TRANSLATION,
        conservation=Conservation.INFORMATION
    )

    gauge = Gauge(local=local_gauge, global_=global_gauge, emergent=emergent_gauge)
    
    kernel = MorphologicalKernel()
    final_state = kernel.run(initial_state, gauge, steps=10)
    
    print(f"Final state: {final_state}")
    
    visualize_state_history(kernel.state_history)

if __name__ == '__main__':
    main()