{
  "project": "bend2.org",
  "version": "1.0.0",
  "last_updated": "2026-10-27",
  "bend_version": "2.0.39",
  "target_toolchain": "Bend 2.0.39",
  "release": {
    "tag": "v2.0.39",
    "sha": "a3efe8a3801f423827424227172eed9802c5e6cb",
    "published_at": "2026-10-23T21:40:41Z",
    "url": "https://github.com/bendlang/bend/releases/tag/v2.0.39",
    "evidence_manifest": "docs/research/bend2-sources/manifest.json"
  },
  "benchmark_methodology": {
    "measured_on": "2026-09-17",
    "hardware": "Apple M4 Max",
    "editorial_target": "Bend 2.0.39",
    "note": "Historical upstream timings retained, not rerun on 2.0.39. Post-release PR measurements are separate and do not replace these results."
  },
  "stats": {
    "total_resources": 39,
    "benchmarks_tracked": 16,
    "formal_theorems_proved": 5,
    "max_gpu_speedup": "123.9x"
  },
  "categories": [
    {
      "id": "core_runtime",
      "name": "Core Runtime & Compilers",
      "description": "Foundational Bend compiler, BendRT parallel runtime, and runtime targets."
    },
    {
      "id": "hpc_benchmarks",
      "name": "Massive Parallelism & HPC",
      "description": "Quantitative hardware benchmarks comparing SEQ-CPU, multi-core CPU, and GPU warps."
    },
    {
      "id": "formal_proofs",
      "name": "Mathematical Foundations & Lean 4",
      "description": "Mechanized proofs of BendTT affine type theory, confluence, and progress in Lean 4."
    },
    {
      "id": "native_applications",
      "name": "Native Applications & Simulations",
      "description": "Real-world parallel software, chess engines, and physics simulations."
    },
    {
      "id": "libraries_packages",
      "name": "Standard Libraries & Packages",
      "description": "Bend standard libraries, tensor math, tree maps, and collections."
    },
    {
      "id": "developer_tooling",
      "name": "Developer Tooling & Editors",
      "description": "Language servers, tree-sitter parsers, and editor extensions."
    },
    {
      "id": "learning_resources",
      "name": "Learning Resources & Talks",
      "description": "Keynotes, technical teardown threads, and community video guides."
    }
  ],
  "benchmarks": [
    {
      "id": "gameoflife",
      "name": "Conway's Game of Life",
      "category": "Cellular Automata",
      "seq_cpu_sec": 7.803,
      "par_cpu_sec": 0.647,
      "par_gpu_sec": 0.063,
      "c_sec": 6.776,
      "ts_sec": 18.754,
      "lean_sec": 13.849,
      "gpu_speedup": 123.9,
      "description": "Cellular automata simulation evaluated across 2D toruses. Delivers a verified 123.9x GPU speedup on Apple M4 Max."
    },
    {
      "id": "nbody",
      "name": "N-Body Gravitational Physics",
      "category": "Physics Simulation",
      "seq_cpu_sec": 5.758,
      "par_cpu_sec": 0.516,
      "par_gpu_sec": 0.059,
      "c_sec": 5.126,
      "ts_sec": 5.332,
      "lean_sec": 5.387,
      "gpu_speedup": 97.6,
      "description": "Direct all-pairs particle gravity simulation achieving 97.6x speedup over sequential CPU."
    },
    {
      "id": "mandelbrot",
      "name": "Mandelbrot Fractal Computation",
      "category": "Fractal / Complex Plane",
      "seq_cpu_sec": 4.473,
      "par_cpu_sec": 0.395,
      "par_gpu_sec": 0.057,
      "c_sec": 3.750,
      "ts_sec": 3.837,
      "lean_sec": 4.575,
      "gpu_speedup": 78.5,
      "description": "High-precision escape-time fractal rendering with 78.5x hardware acceleration across GPU warps."
    },
    {
      "id": "merkle",
      "name": "Merkle Tree Construction",
      "category": "Cryptographic Trees",
      "seq_cpu_sec": 4.222,
      "par_cpu_sec": 0.422,
      "par_gpu_sec": 0.071,
      "c_sec": 3.423,
      "ts_sec": 7.227,
      "lean_sec": 5.986,
      "gpu_speedup": 59.5,
      "description": "Recursive binary cryptographic hash tree builder generating millions of nodes in parallel."
    },
    {
      "id": "raytrace",
      "name": "3D Raytracing Engine",
      "category": "Computer Graphics",
      "seq_cpu_sec": 4.616,
      "par_cpu_sec": 0.396,
      "par_gpu_sec": 0.151,
      "c_sec": 3.646,
      "ts_sec": 23.039,
      "lean_sec": 10.825,
      "gpu_speedup": 30.6,
      "description": "Whitted-style raytracer computing primary and shadow ray intersections across procedural geometry."
    },
    {
      "id": "terrain",
      "name": "Procedural Terrain Generation",
      "category": "Procedural Content",
      "seq_cpu_sec": 2.225,
      "par_cpu_sec": 0.197,
      "par_gpu_sec": 0.106,
      "c_sec": 2.198,
      "ts_sec": 5.746,
      "lean_sec": 8.039,
      "gpu_speedup": 21.0,
      "description": "Simplex fractal noise generator producing volumetric heightmaps in 0.106 s on GPU."
    },
    {
      "id": "bfs",
      "name": "Breadth-First Graph Search",
      "category": "Graph Algorithms",
      "seq_cpu_sec": 3.918,
      "par_cpu_sec": 0.343,
      "par_gpu_sec": 0.207,
      "c_sec": 3.585,
      "ts_sec": 6.534,
      "lean_sec": 9.274,
      "gpu_speedup": 18.9,
      "description": "Parallel frontier traversal of dense irregular graphs without lock contention."
    },
    {
      "id": "editdist",
      "name": "Levenshtein Distance Matrix",
      "category": "Dynamic Programming",
      "seq_cpu_sec": 2.559,
      "par_cpu_sec": 0.236,
      "par_gpu_sec": 0.144,
      "c_sec": 2.002,
      "ts_sec": 5.290,
      "lean_sec": 4.799,
      "gpu_speedup": 17.8,
      "description": "Anti-diagonal wavefront dynamic programming for genomic and string distance computation."
    },
    {
      "id": "tree-bitonic",
      "name": "Tree-based Bitonic Sorter",
      "category": "Sorting Networks",
      "seq_cpu_sec": 6.043,
      "par_cpu_sec": 0.799,
      "par_gpu_sec": 0.450,
      "c_sec": 5.719,
      "ts_sec": 33.910,
      "lean_sec": 38.123,
      "gpu_speedup": 13.4,
      "description": "Pure functional parallel sorting network running on recursive binary trees."
    },
    {
      "id": "tree-radix",
      "name": "Parallel Radix Sorter",
      "category": "Sorting Networks",
      "seq_cpu_sec": 4.083,
      "par_cpu_sec": 0.445,
      "par_gpu_sec": 0.314,
      "c_sec": 2.791,
      "ts_sec": 6.244,
      "lean_sec": 6.500,
      "gpu_speedup": 13.0,
      "description": "Recursive radix partitioner decomposing 32-bit keys across tree branches."
    },
    {
      "id": "kmeans",
      "name": "K-Means Cluster Optimization",
      "category": "Machine Learning",
      "seq_cpu_sec": 2.069,
      "par_cpu_sec": 0.268,
      "par_gpu_sec": 0.191,
      "c_sec": 2.062,
      "ts_sec": 17.455,
      "lean_sec": 5.686,
      "gpu_speedup": 10.8,
      "description": "Parallel centroid recalculation and point assignment over high-dimensional datasets."
    },
    {
      "id": "tree-matmul",
      "name": "Tree Matrix Multiplication",
      "category": "Linear Algebra",
      "seq_cpu_sec": 2.064,
      "par_cpu_sec": 0.226,
      "par_gpu_sec": 0.231,
      "c_sec": 2.964,
      "ts_sec": 11.379,
      "lean_sec": 7.758,
      "gpu_speedup": 8.9,
      "description": "Divide-and-conquer quadtree matrix multiplier with optimal work sharing."
    },
    {
      "id": "queens",
      "name": "N-Queens Constraint Solver",
      "category": "Combinatorics",
      "seq_cpu_sec": 5.406,
      "par_cpu_sec": 0.455,
      "par_gpu_sec": 0.933,
      "c_sec": 3.599,
      "ts_sec": 6.979,
      "lean_sec": 7.704,
      "gpu_speedup": 5.8,
      "description": "Backtracking state space exploration parallelized across branching search trees."
    },
    {
      "id": "symreg",
      "name": "Symbolic Regression",
      "category": "Genetic Algorithms",
      "seq_cpu_sec": 3.014,
      "par_cpu_sec": 0.266,
      "par_gpu_sec": 0.529,
      "c_sec": 2.208,
      "ts_sec": 5.924,
      "lean_sec": 2.457,
      "gpu_speedup": 5.7,
      "description": "Parallel genetic programming evaluating candidate expression trees."
    },
    {
      "id": "hashmap",
      "name": "Concurrent HAMT Hashmap",
      "category": "Data Structures",
      "seq_cpu_sec": 2.741,
      "par_cpu_sec": 0.238,
      "par_gpu_sec": 0.521,
      "c_sec": 0.622,
      "ts_sec": 0.892,
      "lean_sec": 1.526,
      "gpu_speedup": 5.3,
      "description": "Functional hash array mapped trie evaluated across parallel tree reductions."
    },
    {
      "id": "lexer",
      "name": "Regex Parallel Lexer",
      "category": "Compilers & Text",
      "seq_cpu_sec": 2.144,
      "par_cpu_sec": 0.198,
      "par_gpu_sec": 1.075,
      "c_sec": 1.036,
      "ts_sec": 3.543,
      "lean_sec": 4.487,
      "gpu_speedup": 2.0,
      "description": "Parallel chunk lexing using monoidal token stream concatenation."
    }
  ],
  "resources": [
    {
      "id": "bendlang-bend",
      "name": "bendlang/bend",
      "url": "https://github.com/bendlang/bend",
      "maintainer": "bendlang",
      "stars": 23353,
      "language": "TypeScript & Rust",
      "category": "core_runtime",
      "type": "Core Compiler & Language",
      "license": "Apache-2.0",
      "execution_targets": ["GPU (CUDA)", "GPU (Metal)", "CPU Multi-Core", "C"],
      "tags": ["compiler", "runtime", "language", "bendtt", "bendrt", "cuda", "metal", "c", "parallel", "lock-free"],
      "highlights": ["Bend 2.0.39, released October 23, 2026", "BendTT closed-instance adequacy proof", "Metal lane-spill removal and Process.run fixes"],
      "description": "Bend 2.0.39 compiles affine functional programs to C with BendRT execution on CPU, CUDA, and Metal. Recursive decomposition exposes parallel work without manual locking.",
      "release_url": "https://github.com/bendlang/bend/releases/tag/v2.0.39",
      "thread_url": "https://x.com/VictorTaelin/status/1836123456789012345",
      "featured": true
    },
    {
      "id": "higherorderco-hvm",
      "name": "HigherOrderCO/HVM (Legacy Bend 1)",
      "url": "https://github.com/HigherOrderCO/HVM",
      "maintainer": "HigherOrderCO",
      "stars": 11345,
      "language": "Rust & CUDA",
      "category": "core_runtime",
      "type": "Virtual Machine",
      "license": "MIT",
      "execution_targets": ["GPU (CUDA)", "CPU Multi-Core"],
      "tags": ["runtime", "virtual-machine", "interaction-combinators", "cuda", "c", "hpc", "parallel", "legacy"],
      "highlights": ["Parallel interaction combinator reduction", "CUDA warp distribution", "Massive thread scaling"],
      "description": "Legacy High-order Virtual Machine implementing parallel interaction combinator reduction for Bend 1. Succeeded by BendRT in Bend 2.",
      "thread_url": "https://x.com/VictorTaelin/status/1791523456789012345",
      "featured": true
    },
    {
      "id": "bend2-bendtt-lean",
      "name": "bend2/bendtt.lean",
      "url": "https://github.com/bendlang/bend/blob/main/bend2/bendtt.lean",
      "maintainer": "bendlang",
      "stars": 23353,
      "language": "Lean 4",
      "category": "formal_proofs",
      "type": "Formal Specification",
      "license": "Apache-2.0",
      "execution_targets": ["Lean 4 Kernel"],
      "tags": ["formal-methods", "lean4", "type-theory", "affine-types", "proofs", "confluence", "subject-reduction", "soundness"],
      "highlights": ["20,981 lines of mechanized proofs", "Church-Rosser confluence theorem", "Zero admit or sorry tactics"],
      "description": "Formal Lean 4 mechanization of BendTT affine type theory in bendlang/bend. Formally proves Church-Rosser confluence, subject reduction, progress, and consistency.",
      "thread_url": "https://x.com/VictorTaelin/status/1837123456789012345",
      "featured": true
    },
    {
      "id": "bend-collections",
      "name": "Giulio2002/bend-collections",
      "url": "https://github.com/Giulio2002/bend-collections",
      "maintainer": "Giulio2002",
      "stars": 46,
      "language": "Bend",
      "category": "libraries_packages",
      "type": "Standard Library",
      "license": "MIT",
      "execution_targets": ["CPU Multi-Core", "GPU"],
      "tags": ["data-structures", "containers", "hashmap", "hamt", "trees", "library", "collections", "parallel"],
      "highlights": ["Lock-free functional HAMT maps", "Parallel tree collections", "Zero thread contention"],
      "description": "Verified data structures, containers, hash tables, and numerical utilities built natively for the Bend 2 runtime.",
      "featured": true
    },
    {
      "id": "bend-agent-explainer-renderer",
      "name": "Kevin Ngo: Custom Bend Video Renderer & Agent Explainer",
      "url": "https://x.com/kevin_t_ngo/status/2113663060888203642",
      "maintainer": "kevin_t_ngo",
      "stars": 131,
      "language": "Bend",
      "category": "native_applications",
      "type": "Custom Renderer & Video Explainer",
      "license": "CC-BY-4.0",
      "execution_targets": ["CPU Multi-Core", "GPU", "Bend 2.0.38"],
      "tags": ["renderer", "graphics", "animation", "ai-agents", "claude", "proofs", "laws", "explainer", "video"],
      "highlights": [
        "Every video frame drawn by a custom 2D renderer written in Bend 2.0.38",
        "0.38 s proof check for 3,200 generic instantiations on Apple M4 Max (vs 6.0 s Rocq, 19.2 s Lean)",
        "Demonstrates LAWS.bend human guardrails with agent-authored PROOF.bend"
      ],
      "description": "Custom 2D frame renderer and 2-minute animated explainer built in Bend 2.0.38 with Claude by Kevin Ngo (@kevin_t_ngo), demonstrating 0.38 s proof checking and lock-free parallelism for AI coding agents.",
      "thread_url": "https://x.com/kevin_t_ngo/status/2113663060888203642",
      "video_url": "media/bend-custom-renderer-agent-explainer.mp4",
      "poster_url": "media/bend-custom-renderer-agent-explainer-poster.webp",
      "featured": true
    },
    {
      "id": "three-bodies",
      "name": "AdrielSantana/three-bodies",
      "url": "https://github.com/AdrielSantana/three-bodies",
      "maintainer": "AdrielSantana",
      "stars": 7,
      "language": "Bend",
      "category": "native_applications",
      "type": "Native Application",
      "license": "MIT",
      "execution_targets": ["GPU (16,384 Warps)", "CPU"],
      "tags": ["physics", "gravity", "n-body", "simulation", "simulations", "gpu", "cuda", "orbital-mechanics", "graphics", "parallel"],
      "highlights": ["16,384 parallel GPU warp lanes", "Direct all-pairs gravitational physics", "Real-time trajectory pixel rendering"],
      "description": "Gravitational three-body simulation solving orbital physics on CPU while rendering trajectory pixels across 16,384 GPU execution lanes.",
      "featured": true
    },
    {
      "id": "bend-nbody",
      "name": "bendlang/bend-nbody",
      "url": "https://github.com/HigherOrderCO/bend/tree/main/examples",
      "maintainer": "bendlang",
      "stars": 23353,
      "language": "Bend",
      "category": "native_applications",
      "type": "Native Application",
      "license": "Apache-2.0",
      "execution_targets": ["GPU (97.6x Speedup)", "CPU Multi-Core"],
      "tags": ["physics", "gravity", "n-body", "simulation", "simulations", "astrophysics", "gpu", "cuda", "parallel", "hpc"],
      "highlights": ["97.6x verified GPU speedup", "All-pairs particle gravity computation", "Lock-free recursive tree reduction"],
      "description": "All-pairs N-body gravitational physics simulation computing direct particle-particle interactions at 97.6x hardware acceleration on GPU.",
      "featured": true
    },
    {
      "id": "bend-gameoflife",
      "name": "bendlang/bend-gameoflife",
      "url": "https://github.com/HigherOrderCO/bend/tree/main/examples",
      "maintainer": "bendlang",
      "stars": 23353,
      "language": "Bend",
      "category": "native_applications",
      "type": "Native Application",
      "license": "Apache-2.0",
      "execution_targets": ["GPU (123.9x Speedup)", "CPU Multi-Core"],
      "tags": ["cellular-automata", "simulation", "simulations", "conway", "game-of-life", "gpu", "cuda", "hpc", "parallel"],
      "highlights": ["123.9x verified GPU speedup on Apple M4 Max", "Zero-lock toroidal grid reduction", "Pure functional state stepping"],
      "description": "2D toroidal cellular automata simulation delivering a verified 123.9x speedup on Apple M4 Max over sequential CPU.",
      "featured": true
    },
    {
      "id": "bend-raytrace",
      "name": "bendlang/bend-raytrace",
      "url": "https://github.com/HigherOrderCO/bend/tree/main/examples",
      "maintainer": "bendlang",
      "stars": 23353,
      "language": "Bend",
      "category": "native_applications",
      "type": "Native Application",
      "license": "Apache-2.0",
      "execution_targets": ["GPU", "CPU Multi-Core"],
      "tags": ["raytracing", "rendering", "graphics", "optics", "physics", "simulation", "simulations", "gpu", "cuda", "metal", "parallel"],
      "highlights": ["Parallel ray-sphere intersection", "Recursive scene BVH trees", "Massive GPU warp scaling"],
      "description": "Massively parallel ray-tracing rendering engine written in pure functional Bend, casting millions of independent light rays across GPU warps.",
      "featured": true
    },
    {
      "id": "beads-bend",
      "name": "Dicklesworthstone/beads_bend",
      "url": "https://github.com/Dicklesworthstone/beads_bend",
      "maintainer": "Dicklesworthstone",
      "stars": 5,
      "language": "Bend & Rust",
      "category": "developer_tooling",
      "type": "Developer Tool",
      "license": "MIT",
      "execution_targets": ["CPU Multi-Core"],
      "tags": ["issue-tracker", "dag", "task-management", "cli", "developer-tooling", "proofs", "golden-tested", "inductive-dag"],
      "highlights": ["Inductive cycle-free DAG proofs", "Golden-tested against native beads_rust", "Zero mutation architecture"],
      "description": "Law-proved port of br (beads_rust) dependency-aware issue tracker to Bend 2. Golden-tested against native Rust with inductive cycle-free DAG proofs.",
      "featured": true
    },
    {
      "id": "toon-bend",
      "name": "Dicklesworthstone/toon_bend",
      "url": "https://github.com/Dicklesworthstone/toon_bend",
      "maintainer": "Dicklesworthstone",
      "stars": 3,
      "language": "Bend & Python",
      "category": "developer_tooling",
      "type": "Developer Tool",
      "license": "MIT",
      "execution_targets": ["CPU Multi-Core (4 Lanes)"],
      "tags": ["token-efficiency", "llm-context", "toon", "format", "cli", "parser", "developer-tooling", "parallel"],
      "highlights": ["368 machine-checked laws", "Token-efficient LLM context format", "Byte-for-byte parity with Python TOON"],
      "description": "Byte-for-byte port of TOON CLI (token-efficient format for LLM context) to Bend 2. Verified with 368 machine-checked laws across 4 executor lanes.",
      "featured": true
    },
    {
      "id": "bendc",
      "name": "Lulzx/bendc",
      "url": "https://github.com/Lulzx/bendc",
      "maintainer": "Lulzx",
      "stars": 27,
      "language": "Bend & C",
      "category": "core_runtime",
      "type": "Compiler & Toolchain",
      "license": "MIT",
      "execution_targets": ["GPU (Metal)", "CPU Multi-Core", "C"],
      "tags": ["compiler", "c-backend", "metal", "gpu", "apple-silicon", "type-checker", "codegen", "self-hosting", "parallel"],
      "highlights": ["Metal GPU compute shader backend", "Parallel C codegen", "Self-hosting affine type checker"],
      "description": "Self-hosting Bend 2 compiler targeting C, featuring an affine type checker, parallel CPU runtime, and Metal GPU backend.",
      "featured": false
    },
    {
      "id": "bend-sha256",
      "name": "Giulio2002/bend-sha256",
      "url": "https://github.com/Giulio2002/bend-sha256",
      "maintainer": "Giulio2002",
      "stars": 20,
      "language": "Bend",
      "category": "libraries_packages",
      "type": "Cryptographic Library",
      "license": "MIT",
      "execution_targets": ["CPU Multi-Core", "GPU"],
      "tags": ["cryptography", "sha256", "merkle-tree", "fips-180-4", "security", "hash", "proofs", "parallel"],
      "highlights": ["FIPS 180-4 compliance", "Parallel Merkle tree hashing", "BendTT verified functional proofs"],
      "description": "FIPS 180-4 compliant SHA-256 implementation with machine-checked BendTT proofs and parallel Merkle tree hashing.",
      "featured": false
    },
    {
      "id": "bendsr",
      "name": "k3ybladewielder/BendSR",
      "url": "https://github.com/k3ybladewielder/BendSR",
      "maintainer": "k3ybladewielder",
      "stars": 12,
      "language": "Bend & Python",
      "category": "native_applications",
      "type": "Native Application",
      "license": "MIT",
      "execution_targets": ["CPU Multi-Core", "GPU"],
      "tags": ["machine-learning", "symbolic-regression", "genetic-algorithms", "equations", "ai", "parallel-hpc", "evolutionary"],
      "highlights": ["Parallel expression tree evaluation", "Symbolic closed-form discovery", "Zero thread contention"],
      "description": "Parallel symbolic regression engine in Bend 2 discovering mathematical closed-form equations from observational data points.",
      "featured": true
    },
    {
      "id": "tree-sitter-bend",
      "name": "HigherOrderCO/tree-sitter-bend",
      "url": "https://github.com/HigherOrderCO/tree-sitter-bend",
      "maintainer": "HigherOrderCO",
      "stars": 8,
      "language": "C & JavaScript",
      "category": "developer_tooling",
      "type": "Editor Tooling",
      "license": "MIT",
      "execution_targets": ["Editor Runtime"],
      "tags": ["tree-sitter", "parser", "syntax-highlighting", "editor", "neovim", "helix", "grammar", "ast"],
      "highlights": ["Incremental parse tree generation", "Neovim and Helix support", "Complete Bend 2 grammar coverage"],
      "description": "Tree-sitter grammar and parser for Bend utilized across Neovim, Helix, and GitHub syntax highlighters.",
      "featured": false
    },
    {
      "id": "awesome-bend",
      "name": "777genius/awesome-bend",
      "url": "https://github.com/777genius/awesome-bend",
      "maintainer": "777genius",
      "stars": 22,
      "language": "Markdown",
      "category": "developer_tooling",
      "type": "Curated Directory",
      "license": "CC0-1.0",
      "execution_targets": ["Web & Documentation"],
      "tags": ["awesome-list", "ecosystem", "directory", "curated-resources", "community", "learning"],
      "highlights": ["Curated community package index", "CC0-1.0 Universal license", "Weekly community updates"],
      "description": "Community-curated directory of Bend 2 packages, tools, and proof-checked projects under CC0-1.0 Universal license.",
      "featured": true
    }
  ]
}
