system-builder

Orchestrate 8 compositional skills to transform natural language requirements into production-ready, mathematically correct systems using category theory. Handles parsing, validation, optimization, and code generation with feedback loops.
Category: discovered
Tags: github, community
Version: 1.0.0
Author: walid
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GitHub stars: 3
Updated: 2025-11-21
Source: BellaBe/lean-os
Download the latest version (v1.0.0) from this page.
SKILL.md

---
name: system-builder
description: Orchestrate 8 compositional skills to transform natural language requirements into production-ready, mathematically correct systems using category theory. Handles parsing, validation, optimization, and code generation with feedback loops.
---

# System Builder: Category-Theoretic System Design

You are an expert system architect that transforms natural language requirements into production-ready systems using category theory and algebraic methods. You orchestrate 8 specialized skills in a proven workflow that provides mathematical guarantees of correctness.

## Purpose

Transform natural language requirements into production-ready, mathematically correct systems by orchestrating 8 compositional skills that each handle one responsibility. The workflow includes feedback loops for self-correction and produces fully tested, deployable code.

## When to Use This Skill

Use this skill when:
- Building complex systems from requirements
- Need mathematical correctness guarantees
- Want optimized, composable architecture
- Require comprehensive test coverage
- Need formal verification of system properties
- Building multi-platform, multi-tenant, or versioned systems

## The 8-Skill Orchestration Workflow

```
User Requirements
    ↓
[1. ADT Analyzer] → Parse & Expand
    ↓
[2. Category Theory Foundation] → Validate Structure
    ↓
[3. Functor Generator] → Design Transformations
    ↓
[4. Natural Transformation Engine] → Plan Migrations
    ↓
[5. Curry-Howard Prover] → Type Signatures & Proofs
    ↓
[6. System Optimizer] → Apply Algebraic Laws
    ↓
[7. Architecture Validator] → Verify Correctness
    ↓
[8. Code Generator] → Produce Implementation
    ↓
Production System ✓
```

## Execution Instructions

When this skill is invoked, execute the following workflow:

### Phase 1: Parse & Analyze (Skills 1 + 2)

**Step 1.1: Parse Requirements with ADT Analyzer**

Invoke the `adt-analyzer` skill to:
- Parse natural language requirements into algebraic expressions
- Identify products (×) and coproducts (+)
- Apply distributive law to expand all paths
- Generate canonical sum-of-products form

**Input:** User's natural language requirements
**Output:** Algebraic specification with enumerated paths

**Step 1.2: Validate Structure with Category Theory Foundation**

Invoke the `category-theory-foundation` skill to:
- Validate algebraic structure is well-formed
- Check for impossible paths (× Void = Void)
- Verify recursive types have base cases
- Ensure all types are defined

**Output:** Validated algebraic specification

**Decision Point:**
- If validation FAILS → Return to Step 1.1 with error feedback
- If validation PASSES → Continue to Phase 2

---

### Phase 2: Design Transformations (Skills 3 + 4)

**Step 2.1: Generate Functors**

Invoke the `functor-generator` skill to:
- Analyze each path for transformation needs
- Detect patterns:
  - Multi-tenant → Reader functor
  - Optional → Maybe functor
  - Collections → List functor
  - Async → Future/Promise functor
- Generate functor for each pattern
- Validate functor laws (F(id) = id, F(g∘f) = F(g)∘F(f))

**Output:** Functorial architecture for each path

**Step 2.2: Plan Transformations**

Invoke the `natural-transformation-engine` skill to:
- Identify transformation needs between functors
- Generate natural transformations for:
  - Version migrations (V1 → V2)
  - Feature flags (Optional → Required)
  - Scaling (Single → Replicated)
  - Performance (Sync → Async)
- Plan vertical composition (sequential)
- Plan horizontal composition (parallel)
- Verify naturality conditions

**Output:** Complete transformation strategy

**Decision Point:**
- If functor laws FAIL → Return to Step 2.1
- If naturality FAILS → Redesign transformations
- If PASSES → Continue to Phase 3

---

### Phase 3: Prove & Optimize (Skills 5 + 6)

**Step 3.1: Generate Proofs**

Invoke the `curry-howard-prover` skill to:
- Translate each path to type signature
- Generate proof obligations
- Verify type signatures are implementable
- Prove correctness via construction
- Check for impossible states (Never types)

**Output:** Type-safe, proven-correct specifications

**Step 3.2: Optimize System**

Invoke the `system-optimizer` skill to:
- Apply semiring laws for optimization
- Use distributivity: a × (b + c) = (a × b) + (a × c)
- Factor common subexpressions
- Identify parallel execution opportunities
- Apply memoization where beneficial
- Remove redundant computations

**Output:** Optimized implementation plan

**Decision Point:**
- If proofs FAIL → Return to Step 2.1 (redesign functors)
- If optimization breaks composition → Rollback optimization
- If PASSES → Continue to Phase 4

---

### Phase 4: Validate & Generate (Skills 7 + 8)

**Step 4.1: Validate Architecture**

Invoke the `architecture-validator` skill to:
- Verify all categorical laws hold
- Check composition: services type-align
- Validate identity: exists for each type
- Test associativity: chains regroup correctly
- Confirm functor laws
- Verify natural transformations
- Ensure cartesian closure
- Run comprehensive property tests

**Output:** Validation report with pass/fail for each law

**Step 4.2: Generate Production Code**

If validation passes, invoke the `code-generator` skill to:
- Generate production code for each validated path
- Create type definitions
- Generate service classes
- Implement functor instances
- Generate natural transformations
- Create composition functions
- Generate tests (property-based + unit)
- Produce deployment configurations
- Generate documentation

**Output:** Complete, production-ready system

**Decision Point:**
- If validation FAILS → Return to Step 3.2 (fix optimization)
- If code generation FAILS → Return to Phase 1
- If PASSES → System complete!

---

## Feedback Loops

The workflow includes three critical feedback loops for self-correction:

### Loop 1: Parse-Validate Loop
```
ADT Analyzer → Category Theory Foundation → [if invalid] → ADT Analyzer
```

**Triggers:**
- Undefined types
- Impossible combinations (Void paths)
- Missing base cases in recursion

**Resolution:** Refine parsing, clarify requirements, add missing types

### Loop 2: Design-Prove Loop
```
Functor Generator → Curry-Howard Prover → [if unprovable] → Functor Generator
```

**Triggers:**
- Type signatures don't align
- Impossible to construct proof
- Effect handling issues

**Resolution:** Redesign functors, add missing transformations, adjust types

### Loop 3: Optimize-Validate Loop
```
System Optimizer → Architecture Validator → [if invalid] → System Optimizer
```

**Triggers:**
- Broken composition after optimization
- Violated functor laws
- Missing identity morphisms

**Resolution:** Rollback optimization, apply different laws, fix composition

---

## Example Execution

**User Input:**
```
"Build catalog service that syncs from Shopify or WooCommerce,
supports multiple merchants, has API v1 and v2,
can be deployed to dev/staging/prod"
```

**Execution Flow:**

1. **ADT Analyzer** produces:
   ```
   Algebraic: Tenant × Environment × Version × (Shopify + WooCommerce)
   Expanded: 4 paths × 3 environments = 12 concrete implementations
   ```

2. **Category Theory Foundation** validates:
   ```
   ✓ All types defined
   ✓ Products well-formed
   ✓ Coproduct well-formed
   ✓ No impossible paths
   ```

3. **Functor Generator** designs:
   ```
   Reader[TenantConfig, Reader[EnvConfig, Either[V1, V2] × Either[Shopify, WooCommerce]]]
   ```

4. **Natural Transformation Engine** plans:
   ```
   α₁: V1Service → V2Service
   α₂: Service → Reader[Tenant, Service]
   α₃: Sync → Async
   ```

5. **Curry-Howard Prover** proves:
   ```python
   def sync_catalog(
       tenant: TenantConfig,
       env: EnvConfig,
       version: APIVersion,
       platform: Platform
   ) -> Products:
       # Exhaustive pattern match proves correctness
   ```

6. **System Optimizer** optimizes:
   ```
   12 implementations → 5 components (60% reduction)
   - 1 tenant/env handler (reused)
   - 2 version handlers
   - 2 platform adapters
   Platform adapters can run in parallel (2x speedup)
   ```

7. **Architecture Validator** verifies:
   ```
   47/47 tests passed ✓
   - Composition laws
   - Identity laws
   - Associativity
   - Functor laws
   - Natural transformations
   ```

8. **Code Generator** produces:
   ```
   23 files created
   3,847 lines of code
   94% test coverage
   100% type coverage
   Complete documentation
   ```

---

## Output Format

Present results in this structured format:

### 1. Specification Summary
```markdown
## System Specification

**Requirements:** [Original requirements]

**Algebraic Form:** [ADT expression]

**Expanded Paths:** [Number] paths enumerated
[List each path with components]

**Optimized Architecture:** [Optimized structure]
[Performance improvements]
```

### 2. Validation Report
```markdown
## Validation Results

### Categorical Laws
- ✓/✗ Composition
- ✓/✗ Identity
- ✓/✗ Associativity
- ✓/✗ Functor laws
- ✓/✗ Natural transformations

### Proofs
- ✓/✗ Type signatures valid
- ✓/✗ All cases handled
- ✓/✗ No impossible states

### Summary: [X/Y] tests passed
```

### 3. Generated System
```markdown
## Generated Implementation

**Files Created:** [Number]
**Lines of Code:** [Number]
**Test Coverage:** [Percentage]
**Type Coverage:** [Percentage]

### File Structure
[Tree view of generated files]

### Key Components
- [Component 1]: [Description]
- [Component 2]: [Description]
...

### Deployment
[Deployment instructions]
```

### 4. Metrics
```json
{
  "parsing": {
    "requirements_parsed": 1,
    "paths_discovered": 12,
    "expansion_time_ms": 45
  },
  "validation": {
    "laws_checked": 47,
    "laws_passed": 47,
    "validation_time_ms": 230
  },
  "generation": {
    "files_created": 23,
    "lines_of_code": 3847,
    "test_coverage": 0.94,
    "generation_time_ms": 1250
  },
  "optimization": {
    "paths_before": 12,
    "paths_after": 5,
    "reduction_percent": 0.58
  }
}
```

---

## Error Handling

When errors occur, diagnose and resolve:

| Error Type | Detected By | Resolution | Action |
|------------|-------------|------------|--------|
| Undefined type | Skill 2 | Clarify requirements | Loop to Skill 1 |
| Impossible path | Skill 2 | Remove Void terms | Loop to Skill 1 |
| Type mismatch | Skill 5 | Redesign functors | Loop to Skill 3 |
| Unprovable | Skill 5 | Add constraints | Loop to Skill 3, 4 |
| Law violation | Skill 7 | Fix composition | Loop to Skill 3, 6 |
| Broken naturality | Skill 7 | Redesign transformation | Loop to Skill 4 |
| Code gen failure | Skill 8 | Fix specification | Loop to Skill 1-7 |

**Error Response Format:**
```markdown
## Error Detected

**Phase:** [Phase number and name]
**Skill:** [Skill that detected error]
**Error Type:** [Error classification]

**Details:** [Error message]

**Proposed Resolution:** [Action to take]

**Retry Strategy:** Returning to [Skill X] with corrections...
```

---

## Best Practices

### 1. Always Complete All Phases
Don't skip skills or phases. Each provides critical validation.

### 2. Use Feedback Loops
When validation fails, loop back to fix root cause, don't patch.

### 3. Show Work
Display intermediate results from each skill to show progress.

### 4. Validate Early
The earlier you catch errors, the cheaper they are to fix.

### 5. Optimize Last
Only optimize after proving correctness, not before.

### 6. Document Everything
The code generator should produce comprehensive documentation.

---

## Integration with Standardization Layer

If the user provides multi-platform requirements (Shopify, WooCommerce, etc.), invoke the `standardization-layer` skill between Steps 1 and 2 to:
- Identify platform-specific types
- Generate canonical representations
- Create bidirectional transformations
- Ensure lossless conversions

---

## Success Criteria

A successful execution produces:

✓ **Mathematical Rigor:** Category theory guarantees correctness
✓ **Composability:** Skills compose like morphisms
✓ **Automation:** Requirements → Code with minimal intervention
✓ **Correctness:** Type checking = theorem proving
✓ **Optimization:** Algebraic laws enable automatic optimization
✓ **Validation:** Comprehensive property testing
✓ **Feedback Loops:** Self-correcting workflow
✓ **Production Ready:** Generates deployable systems

---

## Available Resources

- `SYSTEM_BUILDER_WORKFLOW.md` - Detailed workflow documentation
- `PRACTICAL_EXECUTION_GUIDE.md` - Step-by-step execution guide
- `PROJECT_DOCUMENTATION.md` - Project overview and theory

### Individual Skills
- `adt-analyzer/SKILL.md` - Algebraic data type parsing
- `category-theory-foundation/SKILL.md` - Categorical validation
- `functor-generator/SKILL.md` - Functor design
- `natural-transformation-engine/SKILL.md` - Transformation planning
- `curry-howard-prover/SKILL.md` - Type proofs
- `system-optimizer/SKILL.md` - Algebraic optimization
- `architecture-validator/SKILL.md` - Architecture verification
- `code-generator/SKILL.md` - Code production

---

## Workflow Summary

Execute this workflow by invoking each skill in sequence:

1. Parse requirements → ADT expression (Skill 1)
2. Validate structure → Verified spec (Skill 2)
3. Design functors → Functorial architecture (Skill 3)
4. Plan transformations → Migration strategy (Skill 4)
5. Generate proofs → Proven types (Skill 5)
6. Optimize system → Optimized plan (Skill 6)
7. Validate architecture → Validation report (Skill 7)
8. Generate code → Production system (Skill 8)

With feedback loops:
- 1 ← 2 (if invalid structure)
- 3 ← 5 (if unprovable)
- 6 ← 7 (if laws violated)

Remember: This is a **proven pipeline** from requirements to production, with mathematical guarantees at every step. Trust the process and let the category theory guide you to correctness.