valgebra

A closed, irreducible Boolean algebra of schemas for Python. A schema denotes a set of Python values, and validating asks whether a value you already hold is a member — no copy, no coercion. union, intersection, complement, refinement, and fixpoints are the only primitives; they close into a lattice whose laws are property-tested, and every other pattern is derived from them by composition rather than bundled as a special combinator. The schema compiles to a Rust validator, so a check is cheap enough to run on every request.

📖 Documentation: https://ppigazzini.github.io/valgebra/

🤖 For AI assistants and coding agents: the documentation is also published as llms.txt (a curated manifest) and llms-full.txt (the full text, including the API reference) per the llmstxt.org convention.

[!WARNING] Pre-alpha. Published to PyPI; the API works today but may change before a stable 0.1.0 release.

Schemas are sets; the operators are or, and, not

The everyday case looks like any validator — a type annotation is a schema, and checking it asks whether a value belongs to the set the annotation denotes:

from valgebra import ValidationError, Validator

is_user = Validator({"name": str, "age": int})

assert is_user.is_valid({"name": "Ada", "age": 36})
assert not is_user.is_valid({"name": "Ada", "age": "unknown"})

# validate() raises a structured error pointing at the offending value
try:
    is_user.validate({"name": "Ada", "age": "unknown"})
except ValidationError as err:
    assert err.code == "int_type"
    assert err.path == ("age",)

What sets valgebra apart starts when you treat schemas as the sets they denote. Because membership is Boolean, union, intersection, and complement are exactly or, and, and not, and they compose any schema into a lattice:

from valgebra import Validator, complement, intersection, union

non_bool_int = intersection(int, complement(bool))  # an int that is not a bool
assert non_bool_int.is_valid(5)
assert not non_bool_int.is_valid(True)

# Schemas are first-class values you can compare as sets — soundly.
assert Validator(bool).is_subtype_of(int)  # subtyping is set inclusion
assert union(bool, int).is_equivalent(int)  # same set, different syntax
assert intersection(int, complement(int)).is_empty()  # provably no value

What makes it peculiar

A real, closed Boolean algebra. Schemas compose with union, intersection, and complement into a lattice with anything as top and nothing as bottom. Every Boolean law — associativity, idempotence, absorption, distributivity, De Morgan, double negation — is property-tested against the membership relation, not asserted.
Irreducible: only the generators ship. valgebra bundles no conditional, no at_least_one, no one_of. Those are derived by composition (see below). A named wrapper for a one-line composition would make a standard library, not a schema algebra.
Schemas are comparable values. is_subtype_of (inclusion), is_equivalent (mutual inclusion), and is_empty (unsatisfiable) form a sound decision procedure: a True is always correct, and the procedure decides a wide fragment completely and stays conservative beyond it — never a wrong answer. Keep is_equivalent (semantic) distinct from == (syntactic shape).
A law-justified simplifier. simplify reduces a schema to a lattice normal form that admits exactly the same values — it never changes a schema's meaning.
anything is not Any. Both admit every value at runtime, but in the algebra anything is the lattice top (it obeys the laws) while Any is the gradual dynamic type — an atom the simplifier never rewrites. "Checked: all values admitted" stays distinct from "deliberately unchecked".
Check, don't parse. validate/is_valid never copy or coerce; the proof is about the object you keep, not a reconstructed copy. ensure is the separate, explicit value-returning mode.
Typing-first. Standard annotations are the primary notation, read through the typing spec's own introspection. Union has the operator typing already uses, |; intersection and complement stay spelled out because typing has no operator for them and valgebra invents none.

from typing import Any

from valgebra import Validator, anything, complement, union

# A law-justified simplifier: a lattice normal form with the same value set.
assert repr(complement(complement(int)).simplify()) == "int"  # double negation
assert repr(union(int, int).simplify()) == "int"  # idempotence

# `anything` is the lattice top; `Any` means "deliberately unchecked".
assert repr(complement(anything).simplify()) == "nothing"  # top obeys the laws
assert repr(Validator(Any).simplify()) == "Any"  # left untouched

# Union has typing's `|`; intersection and complement stay spelled out.
assert (Validator(int) | str | None).is_equivalent(union(int, str, None))

Everything else is derived

Because the algebra is closed, the patterns other libraries ship as built-in combinators are one-line compositions here. "If it is an int, it must be non-negative" is a union of two intersections — no implies primitive exists, you derive it:

from typing import Annotated

import annotated_types as at

from valgebra import anything, complement, intersection, union


def implies(condition, then, otherwise=anything):
    return union(
        intersection(condition, then),
        intersection(complement(condition), otherwise),
    )


non_negative_if_int = implies(int, Annotated[int, at.Ge(0)])
assert non_negative_if_int.is_valid(5)
assert not non_negative_if_int.is_valid(-1)
assert non_negative_if_int.is_valid("not an int")  # not an int: admitted

The same handful of operators derives first-matching-case dispatch, key cardinality ("at least one of these keys", "exactly one", "not both"), length-bounded lists, and conditional records. The recipes — each runnable and explained — live in the Boolean algebra guide.

Recursive schemas and JSON

Recursive (recursive) schemas describe trees and JSON-like data, and JSON input is validated directly on the Rust path — parsed and checked in one pass, never materialized into an untyped object graph first:

from valgebra import Validator

assert Validator(list[int]).is_valid_json(b"[1, 2, 3]")  # parse + check in Rust

Two ways to use it

As a contract in your codebase

Reach for valgebra when you already hold a Python object — a parsed request body, a config dict, an LLM tool-call argument, a function input — and need to check it against a composable, inspectable contract on the hot path, cheaply enough to run on every request or every agent turn. Because the algebra is closed, a subsystem's contract is the intersection of its parts' contracts, an exclusion is a complement, and a migration is "old schema or new" — contracts refactor like code instead of decaying into opaque predicate functions.

Start at the tutorial; the algebra guide covers composition.

As a harness over a codebase that has none

A schema is an ordinary annotation, so valgebra reads the annotations a codebase already has and answers questions about them the interpreter cannot. Nothing is added to the code under study: the schemas live in the script asking the question, and valgebra stays a development dependency. This is the mode that suits an agent working on a codebase it did not write.

The sharpest question it can settle is whether a contract the code implies is one anything enforces. A parameter used as a divisor must not be zero; one whose attribute is read must not be None. The body states that by using the value that way, and declared ∧ ¬implied is exactly the set of values that pass the type check and break the function:

from valgebra import Validator, complement, intersection


def unenforced(declared: object, implied: object) -> list[object]:
    """Values the declaration admits and the body cannot survive."""
    breaking = intersection(Validator(declared), complement(Validator(implied)))
    return [p for p in (None, 0, "", []) if breaking.is_valid(p)]


# `def make_grid(columns: int)` whose body computes `idx // columns`:
# the annotation is correct, the code typechecks, and zero breaks it.
assert unenforced(int, complement(Validator(0))) == [0]

Others in the same shape — a branch its own annotation makes unreachable, a union arm another already covers, an annotation that admits nothing, an override that narrows its base, and which arms of a union a test run never reached:

from valgebra import Validator, intersection, union

# `if isinstance(key, bytes)` inside `def __setitem__(self, key: str, ...)`.
# The branch is dead, so the code and its annotation disagree about what arrives.
assert intersection(Validator(str), Validator(bytes)).is_empty()

# `bool | int` is `int`: bool is a subclass, so the arm adds nothing.
assert union(bool, int).is_equivalent(int)

# `except (OSError, TimeoutError)` names one class that contains the other.
assert Validator(TimeoutError).is_subtype_of(OSError)

Inspecting a codebase is the full set of recipes, with what each cannot see.

Neither mode requires the other. A codebase can adopt valgebra as a runtime contract, or never import it in its own source and still be studied with it.

How it compares

valgebra checks an object you already hold; it never coerces or constructs. That makes it different from the tools you might already use:

pydantic parses untrusted input into typed models with coercion and defaults. Use it for ingestion; use valgebra to check a value you already have.
msgspec is the fastest path for deserializing bytes into structs.
jsonschema validates against the JSON Schema standard; valgebra validates against Python types and a set-theoretic algebra instead.

On a synthetic benchmark (the PGO release wheel) a passing check is faster than a strict pydantic TypeAdapter — roughly 2× on a 50-field record and a large list[int], ~7× on deep nesting — and far faster than pure-Python jsonschema. The comparison is not apples-to-apples and is gated against regression in CI; see the performance page for the method, the matrix, and the limits.

Install

valgebra ships prebuilt wheels to PyPI, so installing it needs no Rust toolchain (Python ≥ 3.10):

pip install valgebra
# or
uv add valgebra

To build from source instead — for development or an unsupported platform — requires uv and stable Rust (edition 2024, MSRV 1.88):

git clone https://github.com/ppigazzini/valgebra && cd valgebra
uv sync                 # create .venv and install dev dependencies
uv run maturin develop  # build the Rust extension into the venv

Why valgebra (in one screen)

Schemas are sets; validation is membership. Subtyping is set inclusion and equivalence is mutual inclusion — sound, deciding a wide fragment and staying deliberately conservative beyond it (foundations, decidability, soundness argument).
A closed, irreducible algebra. Five primitives generate everything; the laws are property-tested and a law-justified simplifier exploits them.
Check, don't parse. validate/is_valid never copy or coerce; ensure is the explicit value-returning mode.
One boundary crossing. Tree walks, key lookups, and bound checks run in Rust; a comparison against a Python object — a literal, a refinement predicate, or an instance or attribute check — is the documented step into Python, never a silent fallback.
Immutable and thread-safe by design. Free-threaded (no-GIL) CPython 3.14 is supported with a dedicated cp314t wheel where the release image exposes that interpreter.

Project

Versioning follows SemVer; changes are recorded in CHANGELOG.md. Releases are dispatch-driven and published to PyPI through trusted publishing — no tag push publishes.
Contributing: CONTRIBUTING.md and AGENTS.md cover the build-health gate and the project's rules; ARCHITECTURE.md maps the components.
Security: the load-bearing property is soundness of acceptance — an accepted value really belongs to the schema's set. Report issues privately per SECURITY.md. valgebra is pre-alpha and unaudited.

License

Licensed under either of Apache License, Version 2.0 or MIT license at your option. Contributions are dual-licensed as above unless you state otherwise.

Release files for valgebra 0.0.9

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Source distribution for valgebra 0.0.9
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File	Interpreter	ABI	Platform	Reset
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valgebra-0.0.9-pp311-pypy311_pp73-musllinux_1_2_aarch64.whl 1.1 MB Aug 26, 2026	PyPy 3.11	PyPy 3.11 7.3	Linux musl 1.2+ ARM64	Details
valgebra-0.0.9-pp311-pypy311_pp73-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 932.0 kB Aug 26, 2026	PyPy 3.11	PyPy 3.11 7.3	Linux glibc 2.17+ x86-64	Details
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valgebra-0.0.9-cp314-cp314t-musllinux_1_2_x86_64.whl 1.2 MB Aug 26, 2026	CPython 3.14	CPython 3.14 free-threading	Linux musl 1.2+ x86-64	Details
valgebra-0.0.9-cp314-cp314t-musllinux_1_2_aarch64.whl 1.1 MB Aug 26, 2026	CPython 3.14	CPython 3.14 free-threading	Linux musl 1.2+ ARM64	Details
valgebra-0.0.9-cp314-cp314t-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 931.5 kB Aug 26, 2026	CPython 3.14	CPython 3.14 free-threading	Linux glibc 2.17+ x86-64	Details
valgebra-0.0.9-cp314-cp314t-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 886.6 kB Aug 26, 2026	CPython 3.14	CPython 3.14 free-threading	Linux glibc 2.17+ ARM64	Details
valgebra-0.0.9-cp314-cp314-win_arm64.whl 832.0 kB Aug 26, 2026	CPython 3.14	CPython 3.14	Windows ARM64	Details
valgebra-0.0.9-cp314-cp314-win_amd64.whl 856.1 kB Aug 26, 2026	CPython 3.14	CPython 3.14	Windows x86-64	Details
valgebra-0.0.9-cp314-cp314-musllinux_1_2_x86_64.whl 1.2 MB Aug 26, 2026	CPython 3.14	CPython 3.14	Linux musl 1.2+ x86-64	Details
valgebra-0.0.9-cp314-cp314-musllinux_1_2_aarch64.whl 1.1 MB Aug 26, 2026	CPython 3.14	CPython 3.14	Linux musl 1.2+ ARM64	Details
valgebra-0.0.9-cp314-cp314-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 930.8 kB Aug 26, 2026	CPython 3.14	CPython 3.14	Linux glibc 2.17+ x86-64	Details
valgebra-0.0.9-cp314-cp314-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 887.4 kB Aug 26, 2026	CPython 3.14	CPython 3.14	Linux glibc 2.17+ ARM64	Details
valgebra-0.0.9-cp314-cp314-macosx_11_0_arm64.whl 845.3 kB Aug 26, 2026	CPython 3.14	CPython 3.14	macOS 11.0+ ARM64	Details
valgebra-0.0.9-cp314-cp314-macosx_10_12_x86_64.whl 889.9 kB Aug 26, 2026	CPython 3.14	CPython 3.14	macOS 10.12+ x86-64	Details
valgebra-0.0.9-cp313-cp313-win_arm64.whl 832.6 kB Aug 26, 2026	CPython 3.13	CPython 3.13	Windows ARM64	Details
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valgebra-0.0.9-cp313-cp313-musllinux_1_2_x86_64.whl 1.2 MB Aug 26, 2026	CPython 3.13	CPython 3.13	Linux musl 1.2+ x86-64	Details
valgebra-0.0.9-cp313-cp313-musllinux_1_2_aarch64.whl 1.1 MB Aug 26, 2026	CPython 3.13	CPython 3.13	Linux musl 1.2+ ARM64	Details
valgebra-0.0.9-cp313-cp313-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 929.8 kB Aug 26, 2026	CPython 3.13	CPython 3.13	Linux glibc 2.17+ x86-64	Details
valgebra-0.0.9-cp313-cp313-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 885.7 kB Aug 26, 2026	CPython 3.13	CPython 3.13	Linux glibc 2.17+ ARM64	Details
valgebra-0.0.9-cp313-cp313-macosx_11_0_arm64.whl 844.2 kB Aug 26, 2026	CPython 3.13	CPython 3.13	macOS 11.0+ ARM64	Details
valgebra-0.0.9-cp313-cp313-macosx_10_12_x86_64.whl 888.4 kB Aug 26, 2026	CPython 3.13	CPython 3.13	macOS 10.12+ x86-64	Details
valgebra-0.0.9-cp312-cp312-win_arm64.whl 833.2 kB Aug 26, 2026	CPython 3.12	CPython 3.12	Windows ARM64	Details
valgebra-0.0.9-cp312-cp312-win_amd64.whl 854.3 kB Aug 26, 2026	CPython 3.12	CPython 3.12	Windows x86-64	Details
valgebra-0.0.9-cp312-cp312-musllinux_1_2_x86_64.whl 1.2 MB Aug 26, 2026	CPython 3.12	CPython 3.12	Linux musl 1.2+ x86-64	Details
valgebra-0.0.9-cp312-cp312-musllinux_1_2_aarch64.whl 1.1 MB Aug 26, 2026	CPython 3.12	CPython 3.12	Linux musl 1.2+ ARM64	Details
valgebra-0.0.9-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 930.1 kB Aug 26, 2026	CPython 3.12	CPython 3.12	Linux glibc 2.17+ x86-64	Details
valgebra-0.0.9-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 886.3 kB Aug 26, 2026	CPython 3.12	CPython 3.12	Linux glibc 2.17+ ARM64	Details
valgebra-0.0.9-cp312-cp312-macosx_11_0_arm64.whl 844.5 kB Aug 26, 2026	CPython 3.12	CPython 3.12	macOS 11.0+ ARM64	Details
valgebra-0.0.9-cp312-cp312-macosx_10_12_x86_64.whl 888.9 kB Aug 26, 2026	CPython 3.12	CPython 3.12	macOS 10.12+ x86-64	Details
valgebra-0.0.9-cp311-cp311-win_amd64.whl 855.3 kB Aug 26, 2026	CPython 3.11	CPython 3.11	Windows x86-64	Details
valgebra-0.0.9-cp311-cp311-musllinux_1_2_x86_64.whl 1.2 MB Aug 26, 2026	CPython 3.11	CPython 3.11	Linux musl 1.2+ x86-64	Details
valgebra-0.0.9-cp311-cp311-musllinux_1_2_aarch64.whl 1.1 MB Aug 26, 2026	CPython 3.11	CPython 3.11	Linux musl 1.2+ ARM64	Details
valgebra-0.0.9-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 931.0 kB Aug 26, 2026	CPython 3.11	CPython 3.11	Linux glibc 2.17+ x86-64	Details
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valgebra-0.0.9-cp311-cp311-macosx_11_0_arm64.whl 848.6 kB Aug 26, 2026	CPython 3.11	CPython 3.11	macOS 11.0+ ARM64	Details
valgebra-0.0.9-cp311-cp311-macosx_10_12_x86_64.whl 882.9 kB Aug 26, 2026	CPython 3.11	CPython 3.11	macOS 10.12+ x86-64	Details
valgebra-0.0.9-cp310-cp310-win_amd64.whl 856.2 kB Aug 26, 2026	CPython 3.10	CPython 3.10	Windows x86-64	Details
valgebra-0.0.9-cp310-cp310-musllinux_1_2_x86_64.whl 1.2 MB Aug 26, 2026	CPython 3.10	CPython 3.10	Linux musl 1.2+ x86-64	Details
valgebra-0.0.9-cp310-cp310-musllinux_1_2_aarch64.whl 1.1 MB Aug 26, 2026	CPython 3.10	CPython 3.10	Linux musl 1.2+ ARM64	Details
valgebra-0.0.9-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 931.5 kB Aug 26, 2026	CPython 3.10	CPython 3.10	Linux glibc 2.17+ x86-64	Details
valgebra-0.0.9-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 889.5 kB Aug 26, 2026	CPython 3.10	CPython 3.10	Linux glibc 2.17+ ARM64	Details
valgebra-0.0.9-cp310-cp310-macosx_10_12_x86_64.whl 883.5 kB Aug 26, 2026	CPython 3.10	CPython 3.10	macOS 10.12+ x86-64	Details

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Publishing repository: github.com/ppigazzini/valgebra
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Publishing repository: github.com/ppigazzini/valgebra
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Publishing repository: github.com/ppigazzini/valgebra
Publishing commit: github.com/ppigazzini/valgebra/tree/d6b0230d98aeb6a8bd2b26bd99f00b12580c8926

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Publishing repository: github.com/ppigazzini/valgebra
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Publishing platform: GitHub Actions
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Workflow

Publishing configuration: github.com/ppigazzini/valgebra/blob/d6b0230d98aeb6a8bd2b26bd99f00b12580c8926/.github/workflows/release.yml
Publishing logs: github.com/ppigazzini/valgebra/actions/runs/33015832290/attempts/1

Artifact

Subject: valgebra-0.0.9-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl
SHA-256 checksum: c4f6bba6acb347701332a9ddb286e7ed288fafe7887826d5b125c03754c86318 Verifying attestations

Release files / valgebra-0.0.9-cp310-cp310-macosx_10_12_x86_64.whl

Download URL	valgebra-0.0.9-cp310-cp310-macosx_10_12_x86_64.whl
Size	883.5 kB
Tags	CPython 3.10 macOS 10.12+ x86-64
SHA-256 checksum How to use checksums	`230ac786842e3786bd93ee04292f997e4d60a046ef443e929f25689bc10eff8c`
BLAKE2b-256 checksum How to use checksums	`361f7bf8e1f8984e07f8b29e78bdceef8cfbf1cf230d640840ee1b9ef8ca1d11`
Upload date	Aug 26, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/ppigazzini/valgebra
Publishing commit: github.com/ppigazzini/valgebra/tree/d6b0230d98aeb6a8bd2b26bd99f00b12580c8926

Workflow

Publishing configuration: github.com/ppigazzini/valgebra/blob/d6b0230d98aeb6a8bd2b26bd99f00b12580c8926/.github/workflows/release.yml
Publishing logs: github.com/ppigazzini/valgebra/actions/runs/33015832290/attempts/1

Artifact

Subject: valgebra-0.0.9-cp310-cp310-macosx_10_12_x86_64.whl
SHA-256 checksum: 230ac786842e3786bd93ee04292f997e4d60a046ef443e929f25689bc10eff8c Verifying attestations