Q# is a standalone domain-specific programming language from Microsoft for
writing and running quantum programs. Like most industrial languages, it was
designed without a formal specification, which can naturally lead to ambiguity
in its interpretation. We aim to provide a formal language definition for Q#,
placing the language on a solid mathematical foundation and enabling further
evolution of its design and type system. This paper presents λ-Q#, an
idealized version of Q# that illustrates how we may view Q# as a quantum Algol
(algorithmic language). We show the safety properties enforced by
λ-Q#'s type system and present its equational semantics based on a
fully complete algebraic theory by Staton.Comment: In Proceedings QPL 2022, arXiv:2311.0837