Streams, Calculational Proofs and Dafny

The article discusses the use of calculational proofs in the context of the programming language Dafny, particularly focusing on streams and their properties. It illustrates how to establish equality between expressions using a chain of equalities, exemplified by the lemma that shows the equivalence of appending two repeated elements. The proof leverages inductive reasoning for lists and coinductive reasoning for streams, highlighting the unique solutions to restricted stream equations. The author presents functions for creating streams, such as natural numbers and repeated elements, and demonstrates how to prove that certain stream expressions are equal by satisfying the same restricted equations. The paper emphasizes the role of Dafny in automating the proof process, allowing users to focus on formulating the necessary lemmas. It concludes with a discussion on the uniqueness of fixed points in stream equations, showcasing how to prove that specific stream constructions yield the same results.

- The article explores calculational proofs in Dafny, focusing on streams and their properties.

- It demonstrates the use of inductive and coinductive reasoning in establishing equality between stream expressions.

- The author provides examples of functions for creating and manipulating streams.

- Dafny is highlighted for its ability to automate proof processes, simplifying the proof-writing experience.

- The uniqueness of solutions to restricted stream equations is a key theme in the discussion.