# valgebra

> Fast runtime validation through a complete Boolean algebra of schemas.

Fast runtime validation through a closed Boolean algebra of schemas. A schema denotes a set of Python values; validation is membership, with no copy and no coercion. Schemas compile once into a Rust validator tree. Standard typing annotations are the primary notation; union, intersection, complement, refinement, and fixpoints compose them into a law-tested lattice.

## Getting started

- [Home](https://ppigazzini.github.io/valgebra/index.md): Overview, positioning against pydantic and msgspec, and a first example.
- [Installation](https://ppigazzini.github.io/valgebra/installation/index.md): Install the package and its build toolchain.
- [Tutorial](https://ppigazzini.github.io/valgebra/tutorial/index.md): Guided learning path from a scalar schema to an inspected failure.
- [Quickstart](https://ppigazzini.github.io/valgebra/quickstart/index.md): Condensed feature tour for readers who know the domain.

## Guides

- [Schema language](https://ppigazzini.github.io/valgebra/schema-language/index.md): Every schema form with its denotation as a set of Python values.
- [The Boolean algebra](https://ppigazzini.github.io/valgebra/algebra/index.md): The Boolean lattice — union, intersection, complement — and the law-justified simplifier.
- [Refinements](https://ppigazzini.github.io/valgebra/refinements/index.md): Constraints and predicate refinements over a base schema.
- [Recursive schemas](https://ppigazzini.github.io/valgebra/recursion/index.md): The recursive fixpoint for self-referential schemas.
- [JSON input](https://ppigazzini.github.io/valgebra/json/index.md): Parsing and validating JSON on the Rust path.
- [Error model](https://ppigazzini.github.io/valgebra/error-model/index.md): Exception type, error codes, and the violation path format.
- [Resource limits](https://ppigazzini.github.io/valgebra/limits/index.md): Resource limits and the bounds the validator enforces.
- [Performance](https://ppigazzini.github.io/valgebra/performance/index.md): Measured benchmarks, datasets, and compared versions.

## Explanation

- [Foundations](https://ppigazzini.github.io/valgebra/foundations/index.md): The denotational frame and the sourced set-theoretic and lattice theory.
- [Soundness argument](https://ppigazzini.github.io/valgebra/soundness/index.md): Why membership checking is sound on its own terms.
- [Decidability boundary](https://ppigazzini.github.io/valgebra/decidability/index.md): What subtyping, equivalence, and emptiness decide exactly versus conservatively.

## API reference

- [API reference](https://ppigazzini.github.io/valgebra/api/index.md): The full public surface, generated from the package docstrings.