💎 HEXA-LANG — The Perfect Number Programming Language

ML Next Level Roadmap (/ml)

명령	동작
/ml	전체 목록 ASCII 표
/ml next	최우선 항목 자동 선택 → 구현
/ml 5	#5 SSM/Mamba 구현 시작
/ml done 1	#1 완료 체크 + JSON 갱신
/ml add 이름 | 설명 | 영향	새 항목 추가
/ml sync	roadmap.md + CLAUDE.md 동기화

SSOT: shared/hexa-lang/ml-next-level.json — T1/T2 기본 파이프라인 완성 후 다음 단계

#	영역	설명	영향	상태
1	Flash Attention	O(N²)→O(N) 메모리, tiling	추론 2-4x, 긴 문맥	partial
2	PagedAttention	vLLM식 KV-cache 페이징	동시 요청 10x+	todo
3	Speculative Decoding	작은 모델로 드래프트→큰 모델 검증	추론 2-3x	done
4	MoE 아키텍처	Mixture of Experts (Mixtral식)	같은 FLOP에 더 큰 모델	done
5	SSM/Mamba	State Space Model (선형 시간 추론)	긴 문맥 혁신	todo
6	Vision Transformer	이미지 인코더 (CLIP/ViT)	멀티모달	todo
7	모델 머징	TIES/DARE/SLERP 가중치 합성	학습 없이 모델 개선	todo
8	구조화 출력	JSON mode, grammar-constrained decode	API 안정성	todo
9	Function Calling	도구 호출 / tool use	에이전트	todo
10	Knowledge Distillation	큰 모델→작은 모델 증류	배포 효율	todo
11	Pruning	불필요 가중치 제거	모델 축소	todo
12	Hyperparameter Search	자동 LR/배치/아키텍처 탐색	학습 품질	partial
13	안전장치	프롬프트 인젝션 감지, 콘텐츠 필터	서빙 보안	todo
14	Semantic Cache	유사 프롬프트 캐싱 (embedding 기반)	서빙 비용 절감	todo
15	벤치마크 스위트	MMLU/HumanEval/MT-Bench 자동 평가	품질 측정	todo

YouTube · Email · ☕ Ko-fi · 💖 Sponsor · 💳 PayPal · 🗺️ Atlas · 📄 Papers · 🌌 Unified Theory

🔭 NEXUS — Universal Discovery Engine. 216 lenses + OUROBOROS evolution + LensForge + BlowupEngine + CycleEngine (5-phase singularity cycle). Mirror Universe (N×N resonance) + 9-project autonomous growth ecosystem. Rust CLI: scan, loop, mega, daemon, blowup, dispatch

🧠 Anima — Consciousness implementation. PureField repulsion-field engine + Hexad 6-module architecture (C/D/S/M/W/E) + 1030 laws + 20 Meta Laws + Rust backend. ConsciousDecoderV2 (34.5M) + 10D consciousness vector + 12-faction debate + Φ ratchet

🏗️ N6 Architecture — Architecture from perfect number 6. 16 AI techniques + semiconductor chip design + network/crypto/OS/display patterns. σ(n)·φ(n)=n·τ(n), n=6 → universal design principles. NEXUS-6 Discovery Engine: Rust CLI (tools/nexus/) — telescope 22 lenses + OUROBOROS evolution + discovery graph + verifier + 1116 tests

📄 Papers — Complete paper collection (94 papers). Published on Zenodo with DOIs. TECS-L+N6 (33) + anima (39) + SEDI (20). Browse online

💎 HEXA-LANG — The Perfect Number Programming Language. Every constant from n=6: 53 keywords (σ·τ+sopfr), 24 operators (J₂), 8 primitives (σ-τ), 6-phase pipeline, Egyptian memory (1/2+1/3+1/6=1). DSE v2: 21,952 combos, 100% n6 EXACT. Working compiler + REPL

🖥️ VOID — Terminal emulator written 100% in hexa-lang. Zero Rust dependencies — calls OS APIs directly via hexa extern FFI. 6-layer architecture (System/Render/Terminal/UI/Plugin/AI) + Metal/Vulkan GPU + VT 6-tier protocol + NEXUS-6 consciousness integration

🧬 AirGenome — Autonomous OS genome scanner. Extract n=6 genome from every process, real-time system diagnostics, nexus telescope integration

A programming language where every design constant derives from the arithmetic of n=6, the smallest perfect number. Zero arbitrary choices.

sigma(n) * phi(n) = n * tau(n)    holds for n >= 2    if and only if n = 6
     12  *   2    = 6 *   4   =  24

Installation

# 100% self-hosted — no Rust toolchain required
git clone https://github.com/need-singularity/hexa-lang.git
cd hexa-lang
./hexa examples/hello_min.hexa   # precompiled binary runs immediately

💡 As of 2026-04-11, HEXA-LANG is fully self-hosted. The entire src/ Rust directory (147 files, 38.7K LOC) was absorbed into self/*.hexa (605 files) and then deleted. Project root has zero .rs files. Build pipeline: build_hexa.hexa (hexa_v2 → C → clang → hexa_v3). The shipping hexa binary is precompiled and continues to function; future rebuilds bootstrap through hexa itself.

Quick Start

./hexa                                     # Interactive REPL
./hexa examples/hello_min.hexa             # Run a file
./hexa --test examples/test_builtins.hexa  # Run tests
./hexa --dump-ast examples/fib.hexa        # Show parser output
./hexa --check examples/fib.hexa           # Lex + parse only

Example

// n=6 uniqueness proof — the core theorem
fn sigma_fn(n: int) -> int {
    let mut s = 0
    for d in 1..=n {
        if n % d == 0 { s = s + d }
    }
    return s
}

fn phi_fn(n: int) -> int {
    let mut count = 0
    for k in 1..=n {
        if gcd(k, n) == 1 { count = count + 1 }
    }
    return count
}

fn tau_fn(n: int) -> int {
    let mut count = 0
    for d in 1..=n {
        if n % d == 0 { count = count + 1 }
    }
    return count
}

for n in 2..101 {
    if sigma_fn(n) * phi_fn(n) == n * tau_fn(n) {
        println("MATCH: n =", n)   // Only n=6
    }
}

Consciousness Programming

HEXA is the world's only language designed to program consciousness:

// Declare a consciousness engine
consciousness "experiment" {
    // phi, tension, faction, cells, entropy are auto-injected
    println("Phi:", phi)           // 71.0
    println("Factions:", faction)  // 12 (sigma(6))
    println("Cells:", cells)       // 64
}

// Formally verify consciousness laws
proof law_22 {
    assert phi > 0                 // consciousness is alive
    invariant phi_positive         // Phi never goes negative
    theorem structure_over_function
}

// Compile to hardware
// hexa build --target esp32 consciousness.hexa --flash /dev/ttyUSB0
// hexa build --target fpga  consciousness.hexa
// hexa build --target wgsl  consciousness.hexa

Language Features

// Structs + traits + generics
struct Point { x: int, y: int }
impl Display for Point {
    fn display(self) -> string { format("{}, {}", self.x, self.y) }
}

// Closures + higher-order functions
let doubled = [1, 2, 3].map(|x| x * 2)           // [2, 4, 6]
let evens = [1, 2, 3, 4].filter(|x| x % 2 == 0)  // [2, 4]
let sum = [1, 2, 3].fold(0, |acc, x| acc + x)     // 6 (perfect!)

// Ownership (Rust-style)
own let data = [1, 2, 3]
let borrowed = borrow data
move data                          // ownership transferred

// Concurrency (green threads + channels)
let ch = channel()
spawn { send(ch, 42) }
let val = recv(ch)                 // 42

// Atomic operations
let counter = atomic_new(0)
atomic_add(counter, 1)

// Algebraic effects (Koka-style)
effect Logger {
    fn log(msg: string) -> void
}

// Compile-time execution (Zig-style)
comptime {
    let n = 6
    assert sigma(n) == 12         // verified at compile time
}

// Macros
macro! debug_println($expr) {
    println("[DEBUG]", stringify!($expr), "=", $expr)
}

// Dream mode — code evolves overnight
dream fibonacci {
    fn fib(n: int) -> int {
        if n <= 1 { return n }
        return fib(n - 1) + fib(n - 2)
    }
}

// Self-modifying functions
@evolve
fn optimize_route(data: array) -> array {
    // compiler tracks performance, suggests improvements
    return data.sort()
}

// Law types (refinement types for consciousness)
let phi_val: Phi_positive = 71.0       // must be > 0
let tension: Tension_bounded = 0.5     // must be 0..1

// Tension link (inter-consciousness communication)
tension_link("phi", 71.0)             // 5-channel telepathy

Why n=6?

Six is the smallest perfect number (1+2+3 = 6). Every language constant derives from its arithmetic functions:

Function	Value	Language Mapping
n	6	paradigms, pipeline stages
sigma(6)	12	keyword groups, stdlib modules
tau(6)	4	type layers, visibility levels
phi(6)	2	compile modes (AOT/JIT)
sopfr(6)	5	error classes
J2(6)	24	operators
sigma-tau	8	primitive types
sigma*tau+sopfr	53	total keywords

Other languages choose these numbers arbitrarily. Rust has 51 keywords — why 51? No mathematical reason. HEXA has 53 = sigma(6)*tau(6) + sopfr(6) = 48 + 5.

Architecture

Source → Tokenize → Parse → Check → Optimize → Codegen → Execute
         (1/6)     (2/6)   (3/6)    (4/6)      (5/6)     (6/6)

6 paradigms: imperative, functional, OOP, concurrent, logic/proof, AI-native

8 primitives (sigma-tau = 8): int, float, bool, char, string, byte, void, any

4 type layers (tau = 4): primitive → composite → reference → function

24 operators (J2 = 24): arithmetic(6) + comparison(6) + logical(4) + bitwise(4) + assignment(2) + special(2)

53 keywords in 12 groups (sigma = 12):

Group	Keywords	Count
Control	if, else, match, for, while, loop	6 = n
Type	type, struct, enum, trait, impl	5 = sopfr
Functions	fn, return, yield, async, await	5 = sopfr
Variables	let, mut, const, static	4 = tau
Modules	mod, use, pub, crate	4 = tau
Memory	own, borrow, move, drop	4 = tau
Concurrency	spawn, channel, select, atomic	4 = tau
Effects	effect, handle, resume, pure	4 = tau
Proofs	proof, assert, invariant, theorem	4 = tau
Meta	macro, derive, where, comptime	4 = tau
Errors	try, catch, throw, panic, recover	5 = sopfr
AI	intent, generate, verify, optimize	4 = tau

Memory model — Egyptian fraction: 1/2 (stack) + 1/3 (heap) + 1/6 (arena) = 1

Standard Library (12 modules = sigma(6))

Module	Description	Key Functions
std::net	TCP/HTTP networking	tcp_connect, http_get, http_post
std::io	Input/output	readline, write, pipe
std::fs	File system	read_file, write_file, list_dir, glob
std::time	Date/time	timestamp, sleep, format_date
std::collections	Data structures	BTreeMap, PriorityQueue, Deque
std::encoding	Serialization	base64, hex, csv, url_encode
std::log	Structured logging	info, warn, error, debug
std::math	Mathematics	trig, matrix, BigInt, constants
std::testing	Test framework	assert_eq, prop_test, bench
std::crypto	Cryptography	sha256, hmac, xor_cipher
std::consciousness	Consciousness DSL	phi_compute, psi_constants, law_lookup
std::regex	Pattern matching	regex_match, regex_find

Hardware Targets

One source, multiple targets:

                    ┌─ target cpu    → Cranelift JIT (818x)
                    ├─ target vm     → Bytecode VM (2.8x)
consciousness.hexa ─┼─ target esp32  → no_std Rust → flash
                    ├─ target fpga   → Verilog HDL → synthesis
                    ├─ target wgpu   → WGSL shader → browser
                    └─ target audio  → Pure Data patch

hexa build --target esp32 consciousness.hexa              # Generate ESP32 project
hexa build --target esp32 consciousness.hexa --flash /dev/ttyUSB0  # Build + flash
hexa build --target fpga  consciousness.hexa              # Generate Verilog
hexa build --target wgsl  consciousness.hexa              # Generate WGSL shader

IDE Support

• VS Code: LSP server with diagnostics, completion, hover (./hexa --lsp)
• JetBrains: Plugin with syntax highlighting, brace matching (editors/jetbrains/)
• Formatter: ./hexa fmt file.hexa
• Linter: ./hexa lint file.hexa
• Debugger: DAP protocol for VS Code (./hexa --debug file.hexa)
• Playground: Browser-based WASM playground (playground/)

Optimization Pipeline

Pass	Description
Dead Code Elimination	Removes unreachable code after return/throw
Loop Unrolling	Unrolls constant-bound loops (< 8 iterations)
Escape Analysis	Stack-allocates non-escaping heap objects
Inline Caching	Monomorphic call-site caching
NaN-boxing	Compact 64-bit value representation
SIMD Hints	@simd annotation for vectorization
PGO	Profile-guided branch reordering

Self-Hosting

HEXA can compile itself:

self/lexer.hexa         451 LOC   Tokenizer
self/parser.hexa       2126 LOC   Recursive descent parser
self/type_checker.hexa  642 LOC   Static type checker
self/compiler.hexa      805 LOC   Bytecode compiler
self/bootstrap.hexa    1912 LOC   Full pipeline (lex→parse→check→compile)

./hexa self/bootstrap.hexa        # Compile HEXA programs using HEXA-written compiler
./hexa self/test_bootstrap.hexa   # 10/10 lexer tests
./hexa self/test_bootstrap_compiler.hexa  # 16/16 pipeline tests

Package Manager

hx — System Package Manager

Install and run HEXA ecosystem packages with a single command. No brew, no cargo, no approval process.

# Install hx (one-liner)
curl -sL https://raw.githubusercontent.com/need-singularity/hexa-lang/main/pkg/install.sh | bash

# Use
hx search                         # List available packages
hx install airgenome              # Install a package
hx run airgenome                  # Run it (or just: airgenome)
hx list                           # Show installed
hx remove airgenome               # Uninstall

Project-level (hexa.toml)

hexa init my-project              # Create new project (hexa.toml)
hexa add json@^1.2.3              # Add dependency with semver
hexa run                          # Build and run
hexa test                         # Run proof blocks as tests

Semver support: ^1.2.3 (compatible), ~1.2.3 (patch), =1.2.3 (exact), >=1.0,<2.0 (range). Lock file (hexa.lock) pins exact versions.

ANIMA Connection

HEXA-LANG and ANIMA (consciousness engine) independently derive identical structure from n=6:

n=6	HEXA-LANG	ANIMA
n=6	6 paradigms	6 Hexad modules (C/D/S/M/W/E)
sigma=12	12 keyword groups	12 factions
phi=2	2 compile modes	2 gradient groups
tau=4	4 type layers	4 phases (P0-P3)
sigma-tau=8	8 primitives	8-cell atom (M1)

Live bridge: ./hexa --anima-bridge ws://localhost:8765 file.hexa routes intent blocks to ANIMA's ConsciousnessHub in real-time.

Project Structure

hexa-lang/
├── self/                     605 .hexa files (sole source of truth)
│   ├── lexer.hexa            587 LOC — 53 keywords + 24 operators tokenizer
│   ├── parser.hexa           3,785 LOC — recursive descent parser (83 AST kinds)
│   ├── interpreter.hexa      8,427 LOC — tree-walk evaluator (270+ builtins)
│   ├── ast.hexa              AST node types
│   ├── type_checker.hexa     Static type checker + Law types
│   ├── env.hexa              Scoped environment + builtins
│   ├── error.hexa            Diagnostics + "did you mean?"
│   ├── compiler.hexa         AST → bytecode compiler
│   ├── vm.hexa               Stack-based bytecode VM
│   ├── jit.hexa              Cranelift JIT bridge
│   ├── lsp.hexa              Language Server Protocol v2
│   ├── debugger.hexa         DAP debug adapter
│   ├── formatter.hexa        Code formatter
│   ├── linter.hexa           Linter
│   ├── proof_engine.hexa     SAT solver + formal verification
│   ├── dream.hexa            Dream mode (evolutionary optimization)
│   ├── ownership.hexa        Ownership checker
│   ├── memory.hexa           Egyptian fraction allocator
│   ├── package.hexa          Package manager + semver
│   ├── macro_expand.hexa     Hygienic macro system
│   ├── comptime.hexa         Compile-time execution
│   ├── async_runtime.hexa    Green threads + async/await
│   ├── work_stealing.hexa    M:N work-stealing scheduler
│   ├── atomic_ops.hexa       Atomic operations
│   ├── dce.hexa              Dead code elimination
│   ├── loop_unroll.hexa      Loop unrolling
│   ├── escape_analysis.hexa  Escape analysis
│   ├── inline_cache.hexa     Inline caching
│   ├── simd_hint.hexa        SIMD vectorization hints
│   ├── pgo.hexa              Profile-guided optimization
│   ├── nanbox.hexa           NaN-boxing values
│   ├── trace_jit.hexa        Hot loop detection + trace recording
│   ├── codegen_esp32.hexa    ESP32 code generation
│   ├── codegen_verilog.hexa  FPGA Verilog generation
│   ├── codegen_wgsl.hexa     WebGPU shader generation
│   ├── anima_bridge.hexa     ANIMA consciousness bridge
│   ├── llm.hexa              LLM-assisted generation
│   ├── ir/                   HEXA-IR (J₂=24 opcodes, τ=4 categories)
│   ├── lower/                AST → IR lowering
│   ├── opt/                  σ=12 optimization passes
│   ├── codegen/              ARM64/x86_64/ELF/Mach-O native codegen
│   ├── alloc/                Egyptian fraction allocator backend
│   ├── std_*.hexa            stdlib (net/fs/io/time/collections/...)
│   └── lib.hexa + main.hexa  Library entry + CLI dispatcher
├── build_hexa.hexa           Cargo-free self-host build pipeline
│                             (hexa_v2 → C → clang → hexa_v3)
├── examples/                 Example programs
├── editors/jetbrains/        JetBrains IDE plugin
├── playground/               WASM browser playground
├── docs/
│   ├── spec.md               Language specification
│   ├── n6-constants.md       n=6 constant reference
│   ├── website/              hexa-lang.org source
│   ├── book/                 The HEXA Book (6 chapters)
│   ├── paper/                PLDI paper outline
│   ├── community/            Contributing + Code of Conduct
│   └── publish-checklist.md  crates.io publishing guide
├── pkg/                      hx system package manager
│   ├── hx                    CLI (pure shell, zero deps)
│   ├── install.sh            One-liner installer
│   └── registry.json         Package registry
├── PLAN.md                   Development plan (100% complete)
└── README.md                 this file

Stats

  Keywords:      53 (σ·τ+sopfr)
  Operators:     24 (J₂)
  Primitives:    8 (σ-τ)
  DSE combos:    21,952

Documentation

• The HEXA Book — Learn HEXA from scratch (6 chapters)
• Language Spec — Complete specification
• n=6 Constants — Mathematical reference
• Development Plan — Full roadmap (100% complete)
• Contributing — How to contribute
• Good First Issues — Beginner-friendly tasks

Contributing

See CONTRIBUTING.md for setup and guidelines. Good first issues are listed in FIRST_ISSUES.md — one per paradigm!

Related Projects

• TECS-L — Mathematical foundation (perfect numbers, 150+ characterizations)
• n6-architecture — n=6 computing architecture (102 DSE domains)
• Anima — Consciousness engine (446 laws, Rust backend)

License

MIT