Abstract Machine Semantics for Quipper

Quipper is a domain-specific programming language for the description of quantum circuits. Because it is implemented as an embedded language in Haskell, Quipper is a very practical functional language. However, for the same reason, it lacks a formal semantics and it is limited by Haskell's type-system. In particular, because Haskell lacks linear types, it is easy to write Quipper programs that violate the non-cloning property of quantum states. In order to formalize relevant fragments of Quipper in a type-safe way, the Proto-Quipper family of research languages has been introduced over the last years. In this thesis we first introduce Quipper and Proto-Quipper-M. Proto-Quipper-M is an instance of the Proto-Quipper family based on a categorical model for quantum circuits, which features a linear type-system that guarantees that the non-cloning property holds at compile time. We then derive a tentative small-step operational semantics from the big-step semantics of Proto-Quipper-M and we prove that the two are equivalent. After proving subject reduction and progress results for the tentative semantics, we build upon it to obtain a truly small-step semantics in the style of an abstract machine, which we eventually prove to be equivalent to the original semantics.