Beluga: A Framework for Programming and Reasoning with Deductive Systems (System Description) [chapter]

Brigitte Pientka, Jana Dunfield
2010 Lecture Notes in Computer Science  
Beluga is an environment for programming and reasoning about formal systems given by axioms and inference rules. It implements the logical framework LF for specifying and prototyping formal systems via higher-order abstract syntax. It also supports reasoning: the user implements inductive proofs about formal systems as dependently typed recursive functions. A distinctive feature of Beluga is that it not only represents binders using higher-order abstract syntax, but directly supports reasoning
more » ... ith contexts. Contextual objects represent hypothetical and parametric derivations, leading to compact and elegant proofs. Our test suite includes standard examples such as the Church-Rosser theorem, type uniqueness, proofs about compiler transformations, and preservation and progress for various ML-like languages. We also implemented proofs of structural properties of expressions and paths in expressions. Stating these properties requires nesting of quantifiers and implications, demonstrating the expressive power of Beluga.
doi:10.1007/978-3-642-14203-1_2 fatcat:pcc5n6yoa5ajzds65jt6mhps4q