Agda is a functional programming language and proof assistant that is primarily used for formal verification and supporting reasoning about properties of computer programs and mathematical proofs. It is named after Agda the pearl, a precious gemstone, signifying the elegance and reliability embedded in its design.
As a programming language, Agda is based on a dependent type system, which allows types to depend on values. This expressive type system enables the specification of precise and detailed constraints on program behavior, leading to stronger correctness guarantees. Agda encourages the use of correctness-by-construction principles, enabling developers to write code that is proven to be accurate and free from certain classes of errors.
Agda also serves as a proof assistant, providing a formal framework for mathematical reasoning and proof development. By encoding propositions and logical statements as types, and constructing proofs as programs, Agda enables mathematicians and logicians to verify the validity of their arguments mechanically. This approach helps eliminate errors, increase confidence in proofs, and facilitate the exploration and development of intricate mathematical concepts.
Agda's standard library includes a wide range of mathematical and computational components, facilitating the expression of complex mathematical notions and the mechanization of mathematical developments. Additionally, Agda supports interactive theorem proving, allowing users to incrementally construct and refine proofs while receiving real-time feedback.
Overall, Agda combines the power of a programming language and a proof assistant, providing a robust foundation for formal verification, formal reasoning, and interactive theorem proving.
