Bend Docs

bend-ml-tensor-array: tensors over a flat Array<F32>, with the shape in the type.

One clock assumption, 2.5 GHz (0.4 ns per cycle), prices both vector MACs

Fixed prepared HTTP applications and bounded affine dependency bundles.

Private bounded transport accounting. Replies contain copied data, never resources.

Postgres frontend/backend protocol 3.0 messages over Bytes, and an incremental reader of backend messages.

multipart/form-data (RFC 7578): an encoder with a secure random boundary and a streaming decoder over Bytes. Source: https://github.com/paymog/bend-kit/tree/main/multipart

Redis and Valkey client: RESP3 over TCP or TLS, with pipelining and a pool. Source: https://github.com/paymog/bend-kit/tree/main/redis

RFC 7541 HPACK header blocks with a bounded dynamic table.

Parallel map and reduce over lists and arrays, a worker pool, select over channels, and timeouts.

Bounded packed-byte transfers between files and TCP/TLS sockets.

ZIP archives read over Bytes: stored and DEFLATE entries, checked against their CRC-32 and sizes. Source: https://github.com/paymog/bend-kit/tree/main/archive

DNS codec and host lookup. Source: https://github.com/paymog/bend-kit/tree/main/dns

Pure generators: each takes a Rand.Rng and returns a value beside the next state.

Leveled, structured logging: a logger value, key-value fields, and logfmt or JSON-lines output. Source: https://github.com/paymog/bend-kit/tree/main/notch

RFC 6455 WebSocket client: opening handshake, frames over packed Bytes, and messages over Wire. Source: https://github.com/paymog/bend-kit/tree/main/websocket

LLM client for the Anthropic Messages and OpenAI Chat Completions APIs, with SSE streaming. Source: https://github.com/paymog/bend-kit/tree/main/llm

JSON Web Tokens: HS256/384/512, RS256, and ES256 compact JWS sign and verify, claim checks, and JWKS keys over Hairpin. Source: https://github.com/paymog/bend-kit/tree/main/jwt

OAuth 2.0 client credentials, refresh, and authorization code with PKCE over Hairpin. Source: https://github.com/paymog/bend-kit/tree/main/oauth2

AWS Signature V4 signing and S3 object storage over Hairpin. Source: https://github.com/paymog/bend-kit/tree/main/sigv4

Webhook signatures: Standard Webhooks sign and verify, Stripe and GitHub verify, over the raw body. Source: https://github.com/paymog/bend-kit/tree/main/webhooks

DEFLATE, gzip, and zlib encoding and decoding (RFC 1951, 1952, 1950) over byte strings, plus gzip, zstd, and brotli through the C libraries. Source: https://github.com/paymog/bend-kit/tree/main/zlib

Prepared SQLite statements through libsqlite3. Source: https://github.com/paymog/bend-kit/tree/main/sqlite

Seeded pseudo-random numbers: xoshiro128**, unbiased ranges, floats and shuffles. Not for cryptography.

Hashes, HMAC, HKDF, RSA and ECDSA signatures, and secure random bytes through OpenSSL 3 libcrypto. Source: https://github.com/paymog/bend-kit/tree/main/crypto

Subprocesses and process-level OS access, with byte-exact input and output.

POSIX paths plus directory and metadata effects. Source: https://github.com/paymog/bend-kit/tree/main/files

Pure terminal text: ANSI SGR styling and Unicode 17 display width.

Byte-exact TCP, UDP, and TLS sockets. Source: https://github.com/paymog/bend-kit/tree/main/wire

Hairpin: an HTTP client with a base URL, default headers, a pool, cookies, mTLS, redirects, and proven retries. Source: https://github.com/paymog/bend-kit/tree/main/hairpin

Clocks, Duration and Instant, Gregorian dates, RFC 3339 and HTTP-date text, and TZif time zones. Source: https://github.com/paymog/bend-kit/tree/main/time

Bounded capacity pools with affine reservations: reserve, release, split, and combine.

Proved laws that relate Word and U32 arithmetic to Nat. Source: https://github.com/paymog/bend-kit/tree/main/lemmas

Pure bounded protobuf wire codec over Bytes. https://github.com/paymog/bend-kit/tree/main/protobuf

IEEE 754 binary64 add, sub, mul, and div. Source: https://github.com/paymog/bend-kit/tree/main/f64

Library correctness laws and integration obligations.

bend-mathlib/algebra.bend: abstract associativity/commutativity theorems and their Nat/Bool/List instances.

bend-ml-autograd: automatic differentiation with a proved law.

bend-ml-tensor: tensors with the shape in the TYPE. A shape error is a type error.

bend-ml-bpe-tokenizer: byte-level BPE with a proved roundtrip.

bend-ml-nat-lemmas: Nat and List lemmas, proved, that Bend's Base does not have.

JSON values, parsed and encoded as RFC 8259. Source: https://github.com/paymog/bend-kit/tree/main/json

Prepared HTTP routes with exact paths, validated registration, and path-first method selection. Source: https://github.com/paymog/bend-kit/tree/main/router

shake: a proven command-line argument parser for Bend 2, with subcommands and help.

An unofficial Anthropic SDK for Bend, with typed requests, streaming, and tool calling.

Byte buffers packed four bytes to a U32, with bounds-checked access. Source: https://github.com/paymog/bend-kit/tree/main/bytes

snap: run programs from Bend 2 with argv as a list of strings, no shell.

eztoml: TOML for Bend 2, a proven parser and renderer for TOML documents.

ezhttp: HTTP/1.1 client and server for Bend 2, with auth, cookie and CORS helpers.

bend-blas: BLAS, LAPACK and cuBLAS for Bend 2, as one def per routine

URL parsing, resolution, and percent-encoding (RFC 3986). Source: https://github.com/paymog/bend-kit/tree/main/url

Non-cryptographic hashes over Bytes: FNV-1a, xxHash, SipHash-1-3, CRC-32, and Adler-32. Source: https://github.com/paymog/bend-kit/tree/main/hash

Fixed-width integers U8, U16, U64, I32 and I64: wrapping, checked and saturating arithmetic, and text in radix 2 to 36.

Text formatting: a string builder, format, padding, and shortest F32 printing.

SQLite connections, typed values, prepared statements and transactions for C and Wasm.

UTF-8 encoding and decoding between text and Bytes. Source: https://github.com/paymog/bend-kit/tree/main/encoding

Generated by gen.py from UCD 17.0.0. Do not edit.

bendlib-kernel-list: frozen step-list permutations over List, generic over -A: Data.

ezjson: JSON for Bend 2, with a parser, a printer and a pull cursor

URL parsing, resolution, and percent-encoding (RFC 3986).

Byte-exact TCP, UDP, and TLS sockets.

JSON values, parsed and encoded as RFC 8259.

Shape specialisation: a non-tail binary recursion on a Nat depth that the leaf gives as a literal. WGSL has no

Addresses and mailboxes. An address is local@domain, a dot-atom (RFC

AMF0, the encoding of RTMP's commands (connect, play, _result...): a

AMF0, the encoding of RTMP's commands (connect, play, _result...): a

Addresses and mailboxes. An address is local@domain, a dot-atom (RFC

Library correctness laws and integration obligations.

W3C Trace Context Level 2 propagation, with its rules proved as laws. Source: https://github.com/LucasGois1/bend-trace-context

Unsga3Algorithm.Run — C# Unsga3.Algorithm.Unsga3Algorithm.

An unofficial OpenAI SDK for Bend, with typed requests, streaming, and tool calling.

Fast CSV parser with proofs

tar archives (POSIX ustar with PAX path and size records) of regular files and directories over Bytes. Source: https://github.com/paymog/bend-kit/tree/main/tar

ezx: ez, the package manager for Bend 2.

bolt: a linter, checker and language server for Bend 2.

ezaudio: audio for Bend 2, reading and writing WAV (RIFF PCM) and MP3 (MPEG-1 Layer III).

ezx: ez's ledger library for Bend 2: it parses an ez.toml into its package, dependencies and pinned tools.

ezimg: images for Bend 2, with PNG and baseline JPEG decode and encode

ezaudio: audio for Bend 2, reading and writing WAV (RIFF PCM) and MP3 (MPEG-1 Layer III).

Linear-time regular expressions: RE2 syntax, Pike VM, capture groups. Source: https://github.com/paymog/bend-kit/tree/main/regex

Arbitrary-precision signed integers: add, sub, mul, divmod, pow, modpow, gcd and decimal text.

Generic collections: maps, a vector, a deque and a priority queue. Source: https://github.com/paymog/bend-kit/tree/main/collections

IPv4 and IPv6 address values: strict parsing, RFC 5952 text, and CIDR prefixes. Source: https://github.com/paymog/bend-kit/tree/main/netip

Host entropy

CBOR (RFC 8949) values encoded and decoded over Bytes. Source: https://github.com/paymog/bend-kit/tree/main/cbor

CSV (RFC 4180) over bytes: a record cursor, a whole-document parse, and an encoder. Source: https://github.com/paymog/bend-kit/tree/main/csv

bend-sendfile: package entry for BendHub.

bend-open-under: package entry for BendHub.

base List: reverse is involutive and an insertion sort orders (dupes

Parser combinators over text, with positioned errors. Source: https://github.com/paymog/bend-kit/tree/main/parse

BendSR: Massively Parallel Symbolic Regression Engine in Bend

SPDX-License-Identifier: MIT-0

wordlib: laws about Base's fixed-width words. Word(n) is n Bools,

bendcheck: property-based testing for Bend.

wordlib: laws about Base's fixed-width words. Word(n) is n Bools,

histogram.bend: a parallel histogram of U32 keys into K buckets, with no

bolt: a linter, checker and language server for Bend 2.

ezhttp/b64: Base64 encoding for HTTP credentials (RFC 4648 §4). The

V: data structures for your Bend algorithms.

ledger/manifest: the dependency ledger. Bend's import lines carry a bare

Generic collections: an ordered map and set, a vector, a deque and a priority queue. Source: https://github.com/paymog/bend-kit/tree/main/collections

ezaudio: a Clip is a sample rate, a channel count, a sample format, and

ezimg: images for Bend 2, with PNG and baseline JPEG decode and encode

shake: CLI argument parser for Bend 2. Describe a program with `app`, `sub`,

json.bend: A production-grade, highly reusable JSON library for Bend 2.

DEFLATE, gzip, and zlib decoding (RFC 1951, 1952, 1950) over byte strings. Source: https://github.com/paymog/bend-kit/tree/main/zlib

Byte-exact TCP, UDP, and TLS sockets. Source: https://github.com/paymog/bend-kit

HTTP/1.1 client and server for http and https, with DNS and TLS. Source: https://github.com/paymog/bend-net

DNS A-record lookup over UDP. Source: https://github.com/paymog/bend-net/tree/main/dns

DEFLATE, gzip, and zlib decoding (RFC 1951, 1952, 1950) over byte strings. Source: https://github.com/paymog/bend-net/tree/main/zlib

Match an HTTP method and path to a handler. Source: https://github.com/paymog/bend-net/tree/main/router

UTF-8 and hex encoding for byte strings. Source: https://github.com/paymog/bend-net/tree/main/encoding

JSON values, parsed and encoded as RFC 8259. Source: https://github.com/paymog/bend-net/tree/main/json

URL parsing, resolution, and percent-encoding (RFC 3986). Source: https://github.com/paymog/bend-net/tree/main/url

Byte-exact TCP, UDP, and TLS sockets. Source: https://github.com/paymog/bend-net

Byte buffers packed four bytes to a U32, with bounds-checked access. Source: https://github.com/paymog/bend-net/tree/main/bytes

HTTP/1.1 client for http and https, with DNS and TLS.

DNS A-record lookup over UDP.

UTF-8 and hex encoding for byte strings.

HTTP/1.1 client for http and https, with DNS and TLS.

SPDX-License-Identifier: Apache-2.0

SPDX-License-Identifier: Apache-2.0

Byte buffers packed four bytes to a U32, with bounds-checked access.

origin-form paths and query strings, percent-encoded.

DNS A-record lookup over UDP.

DEFLATE, gzip, and zlib decoding (RFC 1951, 1952, 1950) over byte strings.

HTTP/1.1 client for http and https, with DNS and TLS.

Core module

bend_tensors: dense linear algebra with shapes in the types.

HTTP/1.1 client for http and https, with DNS and TLS.

Match an HTTP method and path to a handler.

Hex of each char as two nibbles.

DNS A-record lookup over UDP.

bend_tensors: dense linear algebra with shapes in the types.

Adding zero changes nothing: one proof, published to test the hub

bend-i64: a SIGNED 64-bit integer in pure Bend, two's complement over Word(64n).

bend-u64: package entry for BendHub.

shake: CLI argument parser for Bend 2. `parse` reads argv against a Cli;

eztoml: the TOML slice for string-valued sectioned docs. A line is blank, a

ezjson/lazy: a branch that does not run both ways. `stop` takes `a` when

Heap: a priority queue, as a skew heap ordered by a le you pass in.

Deque: a double-ended queue, as a front list and a reversed back list.

snap: program runner for Bend 2. `run` (and `exec`) run a

Base64 over byte lists (no IO, no TLS).

DNS: one IPv4 dotted quad via getaddrinfo. A numeric host is Base's

bend-init: a proven Bend project in one command.

An unofficial Anthropic SDK for Bend, with typed requests, streaming, and tool calling.

An unofficial OpenAI SDK for Bend, with typed requests, streaming, and tool calling.

bolt/args: bolt's command line, read from `IO.args()`: `bolt [lint]

List.append, List.reverse and List.length — the lemmas Base does not ship.

String.append and String.reverse — the lemmas Base does not ship.

Nat.add — the laws of Base's Nat.add, as a callable lemma set.

Nat.add — the first two lemmas: a + 0 == a, and (a + b) + c == a + (b + c).

json.bend: A production-grade, highly reusable JSON library for Bend 2.

GLIDER at scale — a soup census over the readable engine.

LAWS.bend -- the laws of tinygrad, stated for the Bend port.

bend-ml: machine learning in Bend 2. Parallel linear regression, batches, statistics, and metrics.

Lorem ipsum text

Executable laws for the strict, lowercase Hex codec.

Definitional laws for Vec2.

Definitional laws for ColorSample (concrete seeds / ranges).

Definitional laws for Prng (xorshift32 over U32).

Definitional laws for Color layer 1.

Definitional laws for Crc32's Base-only List<&2, U32> API.

Laws for Base64's Base-only List<&2, U32> API.

LAWS.bend -- the spec. A human writes this; the AI never touches it.

Art: the tile set, and the board as one Image.

The bend.how fixed-point library, as one package: `bend fixed.bend

TinyChess — the board and the way the pieces move.

Prio — foundational U32 priority bag for Bend.

Path — small Unix-style path helpers for Bend.

Deque — foundational two-list double-ended queue for Bend.

Stack — foundational LIFO stack for Bend.

Test — small Bool-check / proof-suite helper for Bend.

Bytes — foundational byte-buffer for Bend.

Json v1 — leaf-only JSON AST + encode/decode for Bend.

Parse — tiny String parser combinators for Bend.

Tree — foundational binary tree for Bend.

Queue — foundational two-list FIFO for Bend.

NonEmpty (aka NEList) — foundational non-empty list for Bend.