The Howdy Glossary

Gallina is a functional programming language used within the Coq proof assistant for specifying programs and mathematical proofs, combining higher-order logic with dependent types. It permits writing both specifications and executable code in a unified environment, supporting constructs like pattern matching, recursive functions, inductive data types, and modules for managing extensive projects. Developed by Thierry Coquand and Gérard Huet, Gallina enables the articulation of formal definitions and their rigorous verification via Coq's type checker.

Gallina's unique features make it a standout tool for formal verification within the Coq system. Its seamless integration of higher-order logic with dependent types allows users to write precise program specifications alongside executable code. Essential programming constructs such as pattern matching, recursive functions, inductive data types, and module support enhance its capability to handle complex concepts intuitively. The formal verification process facilitated by Coq's type checker ensures the correctness of programs and mathematical proofs.

In comparison to languages like Agda and Idris which also focus on formal verification through functional programming in proof assistants, Gallina distinguishes itself through its integration within the Coq ecosystem. Agda emphasizes minimalistic syntax with simple dependent type theory while Idris focuses on expressive type-level programming for flexible reasoning about programs. Despite these differences, all three languages cater to users who prioritize rigor in developing verified programs and mathematical proofs using higher-order logic and dependent types in an interactive theorem-proving environment.