Transform Command - Natural Transformations

This command implements Natural Transformation α: F ⇒ G for the categorical meta-prompting framework.

α: F ⇒ G
  - α_A: F(A) → G(A)  for each object A
  - Naturality: α_B ∘ F(f) = G(f) ∘ α_A  for all f: A → B

Task

$ARGUMENTS

---

Unified Syntax

/transform @from:[strategy] @to:[strategy] @verify:[bool] @preserve:[aspects] "task"

Modifiers

Modifier	Values	Default	Description
@from:	strategy name	auto	Source functor/strategy
@to:	strategy name	auto	Target functor/strategy
@verify:	true, false	true	Verify naturality condition
@preserve:	structure, semantics, quality	all	What to preserve in transformation
@mode:	transform, compare, analyze	transform	Operation mode

---

Strategy Registry

Available Strategies (Functors)

Each strategy is a functor F: Task → Prompt with specific characteristics:

STRATEGY_REGISTRY:

  zero-shot:
    functor: F_ZS
    signature: Task → DirectPrompt
    characteristics:
      - No examples
      - Relies on model knowledge
      - Fast, minimal tokens
    quality_baseline: 0.65
    token_cost: low

  few-shot:
    functor: F_FS
    signature: Task → ExemplarPrompt
    characteristics:
      - 2-5 examples
      - Pattern demonstration
      - Higher accuracy
    quality_baseline: 0.78
    token_cost: medium

  chain-of-thought:
    functor: F_CoT
    signature: Task → ReasoningPrompt
    characteristics:
      - Step-by-step reasoning
      - Explicit thought process
      - Better for complex tasks
    quality_baseline: 0.85
    token_cost: medium-high

  tree-of-thought:
    functor: F_ToT
    signature: Task → BranchingPrompt
    characteristics:
      - Multiple reasoning paths
      - Backtracking capability
      - Best for search problems
    quality_baseline: 0.88
    token_cost: high

  meta-prompting:
    functor: F_Meta
    signature: Task → MetaPrompt
    characteristics:
      - Self-referential
      - Strategy selection
      - Adaptive approach
    quality_baseline: 0.90
    token_cost: variable

  self-consistency:
    functor: F_SC
    signature: Task → ConsensusPrompt
    characteristics:
      - Multiple samples
      - Majority voting
      - Robust to variance
    quality_baseline: 0.82
    token_cost: high

  react:
    functor: F_ReAct
    signature: Task → ActionPrompt
    characteristics:
      - Reasoning + Acting
      - Tool integration
      - Interactive
    quality_baseline: 0.84
    token_cost: variable

---

Natural Transformation Operations

@mode:transform (Default)

Apply the natural transformation α: F ⇒ G to convert between strategies.

/transform @from:zero-shot @to:chain-of-thought "explain sorting algorithm"

Semantics:

Given task T and prompt P = F_ZS(T):
  α_T: F_ZS(T) → F_CoT(T)

Transformation adds:
  - "Let's think step by step" framing
  - Reasoning structure
  - Intermediate checkpoints

Implementation:

α[from→to](prompt) = {
  1. Extract task semantics from source prompt
  2. Apply target strategy's functor
  3. Verify naturality condition (if @verify:true)
  4. Return transformed prompt
}

@mode:compare

Compare how different strategies handle the same task.

/transform @mode:compare @from:zero-shot @to:chain-of-thought "task"

Output:

COMPARISON:
  source:
    strategy: zero-shot
    prompt: "..."
    estimated_quality: 0.65
    token_cost: 120

  target:
    strategy: chain-of-thought
    prompt: "..."
    estimated_quality: 0.85
    token_cost: 350

  transformation:
    quality_delta: +0.20
    cost_delta: +230 tokens
    recommendation: "Use CoT for complex reasoning tasks"

@mode:analyze

Analyze which transformation would be optimal for a task.

/transform @mode:analyze "complex multi-step problem"

Output:

ANALYSIS:
  task_complexity: high
  task_type: reasoning

  recommended_transformations:
    1. zero-shot → chain-of-thought  (quality: +0.20)
    2. chain-of-thought → tree-of-thought  (quality: +0.03)

  optimal_strategy: chain-of-thought
  reason: "Balances quality improvement with token cost"

---

Naturality Condition

The Naturality Square

For transformation α: F ⇒ G to be natural, this diagram must commute:

      F(f)
F(A) ──────▶ F(B)
  │            │
α_A          α_B
  ▼            ▼
G(A) ──────▶ G(B)
      G(f)

Condition: α_B ∘ F(f) = G(f) ∘ α_A

Verification Protocol

When @verify:true (default):

NATURALITY_CHECK:
  # For sample morphisms f: A → B

  path_1:  # Top then right
    - Apply F(f) to source
    - Apply α_B to result
    result: R1

  path_2:  # Left then bottom
    - Apply α_A to source
    - Apply G(f) to result
    result: R2

  naturality_satisfied: R1 ≈ R2
  similarity_score: [0-1]
  threshold: 0.85

Semantic Naturality

In the prompting context, naturality means:

"Transforming the prompt then refining"
    =
"Refining then transforming"

Practically:
- Strategy switch preserves task semantics
- Order of operations doesn't affect meaning
- Transformation is "uniform" across all tasks

---

Transformation Rules

Zero-Shot → Few-Shot

α[ZS→FS]:
  add:
    - Example demonstrations (2-5)
    - Input/output patterns
  preserve:
    - Core task description
    - Output format requirements
  naturality: ✓ (adding examples commutes with task refinement)

Zero-Shot → Chain-of-Thought

α[ZS→CoT]:
  add:
    - "Let's think step by step"
    - Reasoning structure template
    - Intermediate checkpoints
  preserve:
    - Task semantics
    - Final output requirements
  naturality: ✓ (reasoning addition is uniform)

Few-Shot → Chain-of-Thought

α[FS→CoT]:
  transform:
    - Examples become reasoning traces
    - Pattern → Process
  preserve:
    - Number of demonstrations
    - Domain context
  naturality: ✓ (example transformation is uniform)

Chain-of-Thought → Tree-of-Thought

α[CoT→ToT]:
  add:
    - Branch points
    - Evaluation criteria
    - Backtracking markers
  transform:
    - Linear reasoning → Tree structure
  preserve:
    - Individual reasoning steps
    - Final goal
  naturality: ✓ (branching is uniform transformation)

Any → Meta-Prompting

α[*→Meta]:
  wrap:
    - Strategy selection layer
    - Self-reflection component
    - Adaptive routing
  preserve:
    - All source strategy capabilities
    - Task semantics
  naturality: ✓ (meta-wrapping is uniform)

---

Composition of Transformations

Natural transformations compose:

α: F ⇒ G
β: G ⇒ H
─────────
β ∘ α: F ⇒ H

Vertical Composition

/chain [/transform @from:ZS @to:CoT → /transform @from:CoT @to:ToT] "task"

Equivalent to:

/transform @from:zero-shot @to:tree-of-thought "task"

Horizontal Composition (Whiskering)

/transform @from:F∘G @to:F∘H "composed functor transformation"

---

Quality Propagation

quality(α_A(x)) = transform_factor × quality(x)

Where transform_factor depends on:
  - Source strategy baseline
  - Target strategy baseline
  - Task complexity match

Transformation Quality Matrix

From \ To	ZS	FS	CoT	ToT	Meta
ZS	1.0	1.15	1.25	1.30	1.35
FS	0.85	1.0	1.10	1.15	1.20
CoT	0.75	0.90	1.0	1.05	1.10
ToT	0.70	0.85	0.95	1.0	1.05
Meta	0.70	0.85	0.92	0.98	1.0

Values > 1.0 indicate quality improvement

---

Checkpoint Format

CHECKPOINT_TRANSFORM_[n]:
  command: /transform
  from_strategy: [source]
  to_strategy: [target]
  verify: [true|false]

  input:
    source_prompt: "[original]"
    source_quality: [0-1]
    token_count: [n]

  transformation:
    applied: α[from→to]
    naturality_verified: [true|false]
    naturality_score: [0-1]

  output:
    target_prompt: "[transformed]"
    target_quality: [0-1]
    token_count: [n]

  quality:
    transform_factor: [ratio]
    quality_delta: [+/-]
    cost_delta: [tokens]

  status: [TRANSFORMED | VERIFIED | FAILED_NATURALITY | ERROR]

---

Examples

Example 1: Basic Strategy Switch

/transform @from:zero-shot @to:chain-of-thought "explain quicksort"

Input (Zero-Shot):

Explain the quicksort algorithm.

Output (Chain-of-Thought):

Explain the quicksort algorithm.

Let's think through this step by step:

1. First, I'll describe the core concept
2. Then, I'll explain the partition operation
3. Next, I'll show the recursive structure
4. Finally, I'll analyze the complexity

[Reasoning proceeds...]

Example 2: With Verification

/transform @from:few-shot @to:chain-of-thought @verify:true "classify sentiment"

Naturality Check:

NATURALITY_VERIFICATION:
  test_morphism: "add negation handling"

  path_1_result: "CoT prompt with negation examples"
  path_2_result: "CoT prompt with negation examples"

  paths_equivalent: true
  naturality_satisfied: ✓

Example 3: Analysis Mode

/transform @mode:analyze "solve this differential equation: dy/dx = 2xy"

Output:

TASK_ANALYSIS:
  complexity: medium-high
  type: mathematical_reasoning
  requires: step-by-step derivation

RECOMMENDATION:
  optimal_path: zero-shot → chain-of-thought
  reason: "Mathematical problems benefit from explicit reasoning steps"
  quality_improvement: +0.25
  cost_increase: +180 tokens

Example 4: Chained Transformation

/chain [/transform @from:ZS @to:FS → /transform @from:FS @to:CoT] "complex task"

Execution:

1. ZS → FS: Add examples (α₁)
2. FS → CoT: Convert to reasoning traces (α₂)
3. Result: α₂ ∘ α₁ = α[ZS→CoT] with examples

Example 5: Pipeline Integration

/chain [/context @mode:extract → /transform @from:auto @to:CoT → /rmp @quality:0.85] "adaptive task"

Execution:

1. Extract context (Comonad W)
2. Auto-detect current strategy, transform to CoT (Natural Transformation α)
3. Refine until quality ≥ 0.85 (Monad M)

---

Composition Integration

With → (Sequential)

/chain [/transform @from:ZS @to:CoT → /review] "transform then review"

With || (Parallel)

/chain [/transform @to:CoT || /transform @to:ToT] @mode:compare "compare strategies"

With ⊗ (Tensor)

/chain [/transform ⊗ /context] "context-aware transformation"

With >=> (Kleisli)

/chain [/transform @to:CoT >=> /rmp] "transform then refine"

---

Error Handling

Invalid Strategy

ERROR: INVALID_STRATEGY
reason: "Unknown strategy: 'xyz'"
valid_strategies: [zero-shot, few-shot, chain-of-thought, tree-of-thought, meta-prompting, self-consistency, react]
action: "Use a valid strategy name"

Naturality Violation

ERROR: NATURALITY_VIOLATED
reason: "Transformation paths produce different results"
similarity_score: 0.62
threshold: 0.85
action: "Use @verify:false to skip verification, or choose different transformation"

Incompatible Transformation

WARNING: SUBOPTIMAL_TRANSFORMATION
from: tree-of-thought
to: zero-shot
quality_loss: -0.30
recommendation: "Consider if simplification is intentional"

---

Implementation Notes

Strategy Detection

def detect_strategy(prompt: str) -> Strategy:
    """Auto-detect the prompting strategy used."""
    if "step by step" in prompt.lower():
        return Strategy.CHAIN_OF_THOUGHT
    if "Example:" in prompt or "Input:" in prompt:
        return Strategy.FEW_SHOT
    if "evaluate" in prompt and "branches" in prompt:
        return Strategy.TREE_OF_THOUGHT
    # ... more heuristics
    return Strategy.ZERO_SHOT

Transformation Application

def apply_transformation(
    prompt: str,
    from_strategy: Strategy,
    to_strategy: Strategy,
    verify: bool = True
) -> TransformResult:
    """Apply natural transformation α: F ⇒ G."""

    # Get transformation rule
    alpha = TRANSFORMATION_REGISTRY[(from_strategy, to_strategy)]

    # Apply transformation
    transformed = alpha.transform(prompt)

    # Verify naturality if requested
    if verify:
        naturality_score = verify_naturality(prompt, transformed, alpha)
        if naturality_score < NATURALITY_THRESHOLD:
            raise NaturalityViolation(naturality_score)

    return TransformResult(
        prompt=transformed,
        naturality_verified=verify,
        naturality_score=naturality_score if verify else None
    )

---

Aliases

For common transformations:

/cot    = /transform @to:chain-of-thought
/tot    = /transform @to:tree-of-thought
/meta   = /transform @to:meta-prompting  # Note: different from /meta command

---

References

• Categorical Foundation: categorical-structure-builder skill (Template 4)
• Unified Syntax: meta-self skill
• Strategy Patterns: recursive-meta-prompting skill
• Quality Tracking: quality-enriched-prompting skill
• Composition: ORCHESTRATION-SPEC.md

---

Version

Command Version: 1.0 Framework Compatibility: 2.1+ Categorical Structure: Natural Transformation α: F ⇒ G Laws Verified: ✓ Naturality condition Strategies Supported: 7 (ZS, FS, CoT, ToT, Meta, SC, ReAct)