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Add executable grammar examples demonstrating U1-U4 constraints
Co-authored-by: fermga <203334638+fermga@users.noreply.github.com>
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‎docs/grammar/examples/01-basic-bootstrap.py‎

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#!/usr/bin/env python
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"""
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Grammar Example 01: Basic Bootstrap Pattern
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Demonstrates U1a (Initiation) and U1b (Closure) constraints.
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This is the simplest valid TNFR sequence - a basic bootstrap pattern that:
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1. Starts with a generator (U1a)
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2. Stabilizes the structure
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3. Ends with a closure (U1b)
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Pattern: [Generator → Stabilizer → Closure]
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Health: Excellent (minimal, focused, complete)
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"""
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from tnfr.operators.definitions import (
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Emission, # Generator (U1a)
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Coherence, # Stabilizer
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Silence, # Closure (U1b)
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)
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from tnfr.operators.grammar import validate_grammar
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import networkx as nx
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print("="*70)
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print(" " * 15 + "Grammar Example 01: Basic Bootstrap")
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print("="*70)
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print()
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# ============================================================================
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# Example 1: Valid Bootstrap from EPI=0
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# ============================================================================
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print("Example 1: Valid Bootstrap (Starting from EPI=0)")
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print("-" * 70)
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sequence_1 = [
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Emission(), # U1a: Generator (creates EPI from vacuum)
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Coherence(), # Stabilizes the new structure
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Silence() # U1b: Closure (freezes evolution)
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]
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print("Sequence: Emission → Coherence → Silence")
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print()
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print("Why this works:")
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print(" ✓ U1a: Emission is a generator (can create from EPI=0)")
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print(" ✓ U1b: Silence is a closure (provides terminal endpoint)")
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print(" ✓ Coherence stabilizes without needing U2 (no destabilizers)")
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print()
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try:
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is_valid = validate_grammar(sequence_1, epi_initial=0.0)
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print(f"Validation: {'✓ PASS' if is_valid else '✗ FAIL'}")
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print()
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except ValueError as e:
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print(f"Validation: ✗ FAIL - {e}")
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print()
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# ============================================================================
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# Example 2: Invalid - No Generator
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# ============================================================================
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print("Example 2: Invalid Bootstrap (No generator when EPI=0)")
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print("-" * 70)
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sequence_2 = [
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Coherence(), # NOT a generator!
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Silence()
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]
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print("Sequence: Coherence → Silence")
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print()
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print("Why this fails:")
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print(" ✗ U1a violation: Coherence is NOT a generator")
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print(" ✗ Cannot evolve from EPI=0 without generator")
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print(" ✗ ∂EPI/∂t undefined at EPI=0")
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print()
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try:
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is_valid = validate_grammar(sequence_2, epi_initial=0.0)
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print(f"Validation: {'✓ PASS' if is_valid else '✗ FAIL'}")
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except ValueError as e:
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print(f"Validation: ✗ FAIL - {e}")
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print()
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# ============================================================================
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# Example 3: Valid - Starting from EPI>0
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# ============================================================================
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print("Example 3: Valid Bootstrap (Starting from existing EPI)")
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print("-" * 70)
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sequence_3 = [
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Coherence(), # No generator needed when EPI>0
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Silence() # Closure
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]
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print("Sequence: Coherence → Silence")
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print()
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print("Why this works:")
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print(" ✓ U1a: No generator needed when epi_initial > 0")
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print(" ✓ U1b: Silence is a closure")
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print(" ✓ Can operate on existing structure without creation")
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print()
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try:
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is_valid = validate_grammar(sequence_3, epi_initial=1.0) # EPI > 0!
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print(f"Validation: {'✓ PASS' if is_valid else '✗ FAIL'}")
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except ValueError as e:
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print(f"Validation: ✗ FAIL - {e}")
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print()
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# ============================================================================
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# Summary
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# ============================================================================
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print("="*70)
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print(" " * 25 + "Summary")
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print("="*70)
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print()
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print("Key Lessons:")
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print()
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print("1. U1a (Initiation):")
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print(" • When EPI=0, MUST start with generator {Emission, Transition, Recursivity}")
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print(" • Generators create structure from null/dormant states")
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print(" • When EPI>0, no generator needed")
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print()
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print("2. U1b (Closure):")
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print(" • All sequences MUST end with closure {Silence, Transition, Recursivity, Dissonance}")
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print(" • Closures provide coherent endpoints")
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print(" • Like action potentials need repolarization")
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print()
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print("3. Bootstrap Pattern:")
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print(" • Simplest valid pattern: Generator → Stabilizer → Closure")
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print(" • Creates structure, stabilizes it, provides endpoint")
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print(" • Foundation for more complex sequences")
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print()
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print("Next: See 02-intermediate-exploration.py for U2 (Convergence)")
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print()
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print("="*70)

‎docs/grammar/examples/02-intermediate-exploration.py‎

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#!/usr/bin/env python
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"""
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Grammar Example 02: Intermediate Exploration
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Demonstrates U2 (Convergence & Boundedness) constraint.
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This example shows controlled destabilization with stabilization:
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1. Destabilizers increase |ΔNFR|
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2. Must include stabilizers to prevent divergence
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3. ∫νf·ΔNFR dt must converge
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Pattern: [Generator → Destabilizer → Stabilizer → Closure]
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Health: Good (balanced feedback)
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"""
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from tnfr.operators.definitions import (
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Emission, # Generator (U1a)
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Dissonance, # Destabilizer (U2)
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Coherence, # Stabilizer (U2)
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Silence, # Closure (U1b)
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Expansion, # Destabilizer (U2)
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)
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from tnfr.operators.grammar import validate_grammar
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print("="*70)
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print(" " * 10 + "Grammar Example 02: Intermediate Exploration")
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print("="*70)
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print()
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# ============================================================================
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# Example 1: Valid Exploration with Destabilizer + Stabilizer
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# ============================================================================
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print("Example 1: Valid Exploration (Dissonance + Coherence)")
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print("-" * 70)
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sequence_1 = [
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Emission(), # Generator (U1a)
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Dissonance(), # Destabilizer - increases |ΔNFR|
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Coherence(), # Stabilizer - prevents divergence (U2)
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Silence() # Closure (U1b)
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]
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print("Sequence: Emission → Dissonance → Coherence → Silence")
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print()
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print("Why this works:")
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print(" ✓ U1a: Emission is generator")
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print(" ✓ U2: Dissonance (destabilizer) + Coherence (stabilizer)")
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print(" ✓ U1b: Silence is closure")
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print()
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print("Physics:")
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print(" • Dissonance increases |ΔNFR| (positive feedback)")
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print(" • Without Coherence: ∫νf·ΔNFR dt → ∞ (divergence)")
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print(" • With Coherence: integral converges (bounded evolution)")
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print()
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try:
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is_valid = validate_grammar(sequence_1, epi_initial=0.0)
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print(f"Validation: {'✓ PASS' if is_valid else '✗ FAIL'}")
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except ValueError as e:
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print(f"Validation: ✗ FAIL - {e}")
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print()
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# ============================================================================
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# Example 2: Invalid - Destabilizer without Stabilizer
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# ============================================================================
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print("Example 2: Invalid Exploration (Destabilizer without stabilizer)")
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print("-" * 70)
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sequence_2 = [
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Emission(),
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Dissonance(), # Destabilizer
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Silence() # No stabilizer!
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]
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print("Sequence: Emission → Dissonance → Silence")
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print()
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print("Why this fails:")
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print(" ✗ U2 violation: Destabilizer without stabilizer")
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print(" ✗ |ΔNFR| grows unbounded (exponential)")
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print(" ✗ ∫νf·ΔNFR dt diverges → fragmentation")
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print()
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print("Physics failure:")
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print(" dΔNFR/dt > 0 always (only positive feedback)")
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print(" → ΔNFR(t) ~ e^(λt)")
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print(" → System loses coherence")
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print()
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try:
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is_valid = validate_grammar(sequence_2, epi_initial=0.0)
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print(f"Validation: {'✓ PASS' if is_valid else '✗ FAIL'}")
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except ValueError as e:
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print(f"Validation: ✗ FAIL - {e}")
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print()
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# ============================================================================
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# Example 3: Multiple Destabilizers
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# ============================================================================
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print("Example 3: Multiple Destabilizers (still need ONE stabilizer)")
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print("-" * 70)
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sequence_3 = [
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Emission(),
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Dissonance(), # Destabilizer 1
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Expansion(), # Destabilizer 2
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Coherence(), # Stabilizer (covers both)
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Silence()
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]
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print("Sequence: Emission → Dissonance → Expansion → Coherence → Silence")
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print()
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print("Why this works:")
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print(" ✓ Multiple destabilizers allowed")
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print(" ✓ One stabilizer can handle multiple destabilizers")
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print(" ✓ Coherence provides sufficient negative feedback")
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print()
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print("Physics:")
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print(" • Both Dissonance and Expansion increase |ΔNFR|")
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print(" • Cumulative positive feedback")
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print(" • Coherence stabilizes entire accumulated gradient")
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print()
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try:
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is_valid = validate_grammar(sequence_3, epi_initial=0.0)
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print(f"Validation: {'✓ PASS' if is_valid else '✗ FAIL'}")
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except ValueError as e:
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print(f"Validation: ✗ FAIL - {e}")
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print()
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# ============================================================================
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# Summary
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# ============================================================================
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print("="*70)
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print(" " * 25 + "Summary")
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print("="*70)
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print()
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print("Key Lessons:")
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print()
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print("1. U2 (Convergence & Boundedness):")
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print(" • Destabilizers {Dissonance, Mutation, Expansion} increase |ΔNFR|")
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print(" • Must include stabilizers {Coherence, SelfOrganization}")
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print(" • Without stabilizers: ∫νf·ΔNFR dt → ∞ (divergence)")
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print()
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print("2. Destabilizers:")
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print(" • Dissonance (OZ): Strong positive feedback")
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print(" • Mutation (ZHIR): Phase transformation")
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print(" • Expansion (VAL): Increases dimensionality")
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print()
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print("3. Stabilizers:")
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print(" • Coherence (IL): Direct negative feedback")
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print(" • SelfOrganization (THOL): Emergent self-limiting")
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print()
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print("4. Exploration Pattern:")
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print(" • Generator → Destabilizer(s) → Stabilizer → Closure")
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print(" • Controlled instability with recovery")
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print(" • Enables adaptation while maintaining coherence")
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print()
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print("Next: See 03-advanced-bifurcation.py for U4 (Bifurcation)")
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print()
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print("="*70)

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