Aya is a proof assistant and dependently-typed programming language. It supports advanced type-theoretic features and is designed for both theorem proving and functional programming.
The language includes dependent types, cubical type theory, pattern matching, termination checking, and literate programming capabilities.
This is free and open source software.
Key Features
- Dependent types including Π-types, Σ-types, and indexed families.
- Set-level cubical type theory.
- Support for quotient-inductive-inductive types.
- Pattern matching with first-match semantics.
- Overlapping and order-independent patterns.
- JIT compiler translating Aya code to higher-order abstract syntax in Java.
- Literate programming mode with inline code fragments.
- Binary operators with precedence specified using partial ordering.
- Termination checker capable of accepting complex recursive definitions.
Website: github.com/aya-prover/aya-dev
Support:
Developer: Aya Prover developers
License: MIT License
Aya is written in Java. Learn Java with our recommended free books and free tutorials.
Related Software
| Proof Assistants | |
|---|---|
| Rocq Prover | Formal proof management system |
| Isabelle | Generic proof assistant; express mathematical formulas in a formal language |
| Lean | Programming language and theorem prover |
| Agda | Interactive system for writing and checking proofs |
| F* | Functional language for verified programs with dependent refinement types |
| HOL4 | Interactive higher-order logic environment for rigorous theorem development |
| Aya | Dependently typed language for formalisation and certified programming |
| Lambdapi | Logical framework for defining and checking expressive type systems |
| HOL Light | Lightweight higher-order logic system with a small trusted kernel |
| PVS | Specification and verification suite for analysing complex systems |
| LISA | Scala-based platform for formal mathematics and automated reasoning |
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