Deterministic · Explainable · Geometric

Crystalline is a domain-specific language for specifying code synthesis requirements. The synthesis engine uses geometric field optimization and evolutionary transformations to generate code with explainable decision-making.

Language specification and synthesis engine

Treats program structure as a geometric field. Optimizes through:

• Golden angle phase spacing (φ = 137.5°)
• Curvature minimization
• Evolutionary transformations
• Energy-guided selection

Subproject for adaptive computational structures

Explores self-organizing computation through geometric principles. Manifolds adapt their structure based on computational demands.

📄 Read Intelligent Manifolds paper COMING SOON! 📂 View subproject → COMING SOON!

synthesize {
  task: "API integration with large dataset"
  constraints: [
    "optimize for speed",
    "low memory footprint",
    "handle errors gracefully"
  ]
  target: Python
  quality: optimal
}

Stage 1: Field Architecture

Compute optimal phase relationships using golden angle
Stage 1: QUERY      (φ=0.0°,   κ=-2.5)
Stage 2: PHYSICS    (φ=137.5°, κ=-3.247)  [API call]
Stage 3: COGNITION  (φ=225.8°, κ=-2.613)  [Parse]
Stage 4: RELATIONAL (φ=318.4°, κ=-2.089)  [Transform]
Stage 5: OUTPUT     (φ=45.0°,  κ=-1.5)

Stage 2: Computational Atoms

Decompose template into irreducible operations:
- LOAD (energy 0.5, pure, parallelizable)
- CALL (energy 2.0, impure, varies)
- TRANSFORM (energy 1.2, pure, parallelizable)
- STORE (energy 0.8, impure, sequential)

Stage 3: Evolution

Apply transformations:
✓ Loop fusion (ΔE = -5.0)
✓ Stream conversion (ΔE = -0.5n)  
✓ Async I/O (ΔE = -8.0 + parallelism)
✓ Constant folding (ΔE = -cost)

import asyncio
import aiohttp
from typing import AsyncIterator

async def fetch_and_process(url: str, batch_size: int = 100) -> AsyncIterator[dict]:
    """
    Crystalline-synthesized code
    
    Optimizations discovered:
    - Async I/O pattern
    - Streaming generator (O(1) space)
    - Parallel processing
    - Loop fusion (single pass)
    """
    async with aiohttp.ClientSession() as session:
        async with session.get(url) as response:
            buffer = []
            async for line in response.content:
                # Fused filter + transform
                if item := transform(parse(line)):
                    buffer.append(item)
                    if len(buffer) >= batch_size:
                        yield from buffer
                        buffer = []
            if buffer:
                yield from buffer

Synthesis certificate includes:

• Energy evolution graph
• Transformations applied and why
• Proof of optimization correctness
• Alternative paths considered

Program structure treated as electromagnetic field:

S = ∫[|∇Ψ|² + κΨ² + Σγⱼₖ ΨⱼΨₖ + Σαᵢⱼ⟨Ψᵢ|Ψⱼ⟩] dV

where:
  Ψ         = Program state field
  κ         = Curvature (stability)
  γⱼₖ       = Coupling coefficients
  αᵢⱼ       = Hierarchical influences

Golden angle (φ = 137.5°) creates optimal phase spacing—avoids resonances and creates uniform coverage.

56 irreducible operations with geometric properties:

Each atom has:

• Energy cost (computational expense)
• Phase (position in field)
• Purity (side effects)
• Parallelizability (can run concurrently)

Transformation rules guided by energy:

# Loop Fusion: Combine adjacent loops
for x in data:          →    for x in data:
  f(x)                       f(x)
for x in data:               g(x)  # Single pass!
  g(x)
# ΔE = -5.0 (one loop overhead eliminated)

# Stream Conversion: Lazy evaluation
result = [f(x) for x in data]  →  result = (f(x) for x in data)
# ΔE = -0.5n (memory from O(n) to O(1))

# Parallelization: Concurrent execution
for x in data:          →    with ThreadPoolExecutor() as executor:
  f(x)                         executor.map(f, data)
# ΔE = +8.0 setup, -n/cores throughput

20+ transformation rules available. Engine selects based on energy minimization.

Each generation:

1. Generate population of variants (apply transformations)
2. Compute energy for each variant
3. Select lowest energy configurations
4. Apply additional transformations
5. Repeat until convergence or energy target reached

Result: Code at local minimum of energy functional.

synthesize {
  // What to build
  task: string
  
  // Constraints
  constraints: [string, ...]
  
  // Target language
  target: "Python" | "Rust" | "C++" | "Julia"
  
  // Optimization goal
  quality: "optimal" | "fast_compile" | "balanced"
  
  // Optional: Provide seed template
  template: string?
  
  // Optional: Maximum synthesis time
  max_time: duration?
  
  // Optional: Energy target
  energy_target: float?
}

High-Performance Data Processing:

synthesize {
  task: "Process streaming sensor data"
  constraints: [
    "real-time performance",
    "handle 1M+ events/second",
    "minimal memory footprint",
    "graceful degradation under load"
  ]
  target: Rust
  quality: optimal
  max_time: 5m
}

Database Query Optimization:

synthesize {
  task: "Multi-table join with aggregation"
  constraints: [
    "optimize for large datasets",
    "minimize I/O",
    "parallel execution where safe"
  ]
  target: Python
  quality: optimal
  template: "SELECT * FROM users JOIN orders"
}

git clone https://github.com/[user]/crystalline-language
cd crystalline-language

# Core language spec
cat specification/language-spec.md

# Field theory foundation
cat specification/field-theory.md

# Computational atoms
cat specification/computational-atoms.md

# Transformation rules
cat specification/transformation-rules.md

# Synthesis algorithm
cat specification/synthesis-algorithm.md

cd implementation/python
pip install -r requirements.txt

# Quick synthesis
python crystalline_codegen_v3_1.py "API integration, optimize for speed"

# With full options
python crystalline_codegen_v3_1.py \
  --task "stream processing" \
  --constraints "low memory" "high throughput" \
  --target python \
  --quality optimal \
  --output synthesized_code.py

synthesize {
  task: "Sort array of integers"
  constraints: ["optimize for speed", "in-place if possible"]
  target: Python
}

Discovers: Quicksort with median-of-three pivot selection.

Why: Energy analysis shows partition-based algorithms minimize comparison operations for random data. Median-of-three reduces worst-case probability.

synthesize {
  task: "Scrape product data from e-commerce site"
  constraints: [
    "respect rate limits",
    "handle pagination",
    "extract structured data",
    "error recovery"
  ]
  target: Python
}

Discovers: Async scraper with adaptive rate limiting, exponential backoff, and structured extraction pipeline.

Why: Async I/O minimizes wait time (ΔE = -8.0 per request). Adaptive rate limiting prevents blocks (stability term κ).

synthesize {
  task: "Batch image resizing and filtering"
  constraints: [
    "process 1000+ images",
    "maintain quality",
    "minimal memory"
  ]
  target: Python
}

Discovers: Streaming pipeline with parallel processing, memory-mapped I/O, and incremental processing.

Why: Streaming keeps memory constant (ΔE = -0.5n). Parallel processing exploits multiple cores (ΔE = -n/cores).

• 📘 Language Specification - Full syntax and semantics
• 📙 Crystalline Book - The Crystalline Book

• 🎓 Crystalline Language Guide - GPT - Onboard quickly with GPT

• 🐍 Crystalline Codegen
• 📚 Crystalline Compiler
• 🔧 Crystalline Core
• 🧪 Example-Crystalline Dual Track

The implementation/python/ directory contains:

crystalline_core_v3_1.py - Language runtime

from crystalline_core import FieldState, Domain

# Define field architecture
field = FieldState(
    domain=Domain.PHYSICS,
    shell=2,
    phase=137.5,
    curvature=-3.247,
    amplitude=1.0,
    meaning="API_call",
    coherence=1.0
)

crystalline_codegen_v3_1.py - Code generator

from crystalline_codegen import synthesize

result = synthesize(
    task="API integration",
    constraints=["speed", "low memory"],
    target="python",
    quality="optimal"
)

print(f"Initial energy: {result.initial_energy}")
print(f"Final energy: {result.final_energy}")
print(f"Optimizations: {result.optimizations}")
print(result.code)

field_optimizer.py - Field architecture engine

from field_optimizer import optimize_field_architecture

architecture = optimize_field_architecture(
    num_stages=5,
    constraints={"speed": "high", "memory": "low"}
)

for stage in architecture.stages:
    print(f"{stage.name}: φ={stage.phase}°, κ={stage.curvature}")

synthesis_engine.py - Evolutionary optimizer

from synthesis_engine import SynthesisEngine

engine = SynthesisEngine()
result = engine.evolve(
    initial_template=template,
    energy_target=30.0,
    max_generations=50
)

print(f"Generations: {result.generations}")
print(f"Optimizations applied: {result.optimizations}")

# Basic synthesis
crystalline synthesize "API integration" --target python

# With constraints
crystalline synthesize "data pipeline" \
  --constraints "low-memory" "high-throughput" \
  --target rust \
  --output pipeline.rs

# Explain synthesis
crystalline explain synthesized_code.py
# Shows energy evolution, optimizations applied, why each decision was made

# Visualize field architecture
crystalline visualize --task "API integration" --output field.png

The synthesis engine minimizes:

E_total = E_kinetic + E_potential + E_coupling + E_interference

E_kinetic    = ∫ |∇Ψ|² dV        (computational complexity)
E_potential  = ∫ κΨ² dV          (stability cost)
E_coupling   = Σ γⱼₖ ΨⱼΨₖ        (interaction cost)
E_interference = Σ sin²(θᵢ - θⱼ) (phase mismatch)

Lower energy = more efficient code.

The golden angle φ ≈ 137.5° creates optimal distribution:

φ = 360° × (1 - 1/φ_golden)
  = 360° × (2 - (1+√5)/2)
  ≈ 137.508°

Why optimal:

• Avoids rational fraction resonances
• Maximizes phase space coverage
• Minimizes interference terms
• Found throughout nature (plant phyllotaxis)

Variational principle:

δS/δΨ = 0

Leads to:
-∇²Ψ + κΨ + Σγⱼ∂V/∂Ψⱼ = 0

Solutions are stable configurations (code at energy minima).

Q: Is this just a compiler optimizer?
A: No. Crystalline is a language for specifying synthesis requirements. It discovers novel code patterns, not just optimizes existing code.

Q: How is this different from Copilot/ChatGPT?
A: Crystalline is deterministic (same input → same output), explainable (shows why), and uses geometric optimization (not statistical prediction).

Q: Can I trust the generated code?
A: Yes. Every synthesis includes a certificate showing the energy evolution, transformations applied, and proofs of correctness.

Q: What languages can it generate?
A: Currently: Python, Rust, C++, Julia. The language is extensible—add new targets via atom mappings.

Q: Does it work for all problems?
A: Best for problems with clear optimization objectives (speed, memory, throughput). Less suited for UI code or complex business logic.

Q: How long does synthesis take?
A: Depends on complexity and quality setting. Fast mode: seconds. Optimal mode: minutes.

Q: Can I provide my own templates?
A: Yes! Templates provide starting points. Evolution discovers improvements.

Q: What about Intelligent Manifolds?
A: It's a subproject exploring self-organizing computational structures. See intelligent-manifolds/README.md.

📄 Crystalline: Physics-Guided Evolutionary Code Synthesis (25 pages)

Abstract: This paper presents the Crystalline framework, a novel computational substrate that maintains numeric values and semantic meaning as coupled invariants throughout all transformations. Unlike traditional computational models that treat performance and provenance as separate concerns, Crystalline enforces dual-track preservation where every numeric operation simultaneously updates semantic state in a mathematically rigorous and verifiable manner. This paper provides comprehensive mathematical foundations for dual-track computation , derives the coupling and superposition mechanisms, establishes coherence decay properties, and demonstrates validation criteria. The framework exhibits deep structural parallels to geometric phase calculi, particularly the Wave Pattern Encoding (WPE) and Temporal Modulation Encoding (TME) systems, while introducing unique contributions in computational provenance, observable duality without collapse, and cross-domain semantic fusion. The framework requires no specialized hardware and operates as a restricted intermediate representation within existing programming languages, making it immediately deployable for applications requiring complete computational transparency, interpretability, and semantic consistency.

Read on ResearchGate →
Download PDF →

We welcome contributions!

Areas needing help:

• Add target languages (Go, Zig, Swift)
• Implement new transformation rules
• Create synthesis patterns library
• Build IDE integrations
• Optimize synthesis engine
• Contribute to Intelligent Manifolds subproject

Good first issues:

• Add new computational atoms
• Write tutorial content
• Add language-specific code generators
• Improve visualization tools

• Rust compiler implementation
• VS Code extension with real-time synthesis
• WebAssembly target support
• Intelligent Manifolds alpha release

• Formal verification integration
• GPU code generation (CUDA, Metal)
• Distributed synthesis (cloud-based)
• Language server protocol (LSP)

• Production deployments tracking
• Academic collaborations
• Standardization efforts
• Community-driven synthesis patterns

• 💬 GitHub Discussions
• 🐛 Issues
• 📧 Email

• WPE/TME Language - Geometric calculus (shares foundation)
• BioGenerative Crystal - Biological modeling

Apache 2.0 License - see LICENSE

Code synthesis through geometric principles. Deterministic. Explainable. Systematic.

⭐ Star this repo if you believe code synthesis can be deterministic and explainable!