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We give a categorical semantics to the call-by-name and call-by-value versions of Parigot's λµ-calculus with disjunction types. We introduce the class of control categories, which combine a cartesian-closed structure with a premonoidal structure in the sense of Power and Robinson. We prove, via a categorical structure theorem, that the categorical semantics… (More)

It differs from the present version in that it has been copy-edited and reformatted. Abstract Many familiar models of the untyped lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory of β-or… (More)

- Peter Selinger
- 2009

This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and others who use diagrammatic reasoning. We have opted for a somewhat informal treatment of topological notions, and have… (More)

The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a call-by-value operational semantics, and we give a type system using affine intuitionistic linear logic. The main results of… (More)

- Peter Selinger
- 2003

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to… (More)

- Peter Selinger
- 2004

The search for a semantics for higher-order quantum computation leads naturally to the study of categories of normed cones. In the first part of this paper, we develop the theory of continuous normed cones, and prove some of their basic properties, including a Hahn-Banach style theorem. We then describe two different concrete *-autonomous categories of… (More)

In this paper, we propose an adversary-centric, logical framework for formalizing cryptographic protocols. The formalism is inspired by the work of Compton and Dexter and of Cervesato et al., but we do not focus on proof search, but instead on logical validity. A novel contribution of this paper is a technique for giving very short proofs of protocol… (More)

We consider the problem of decomposing arbitrary single-qubit z-rotations into ancilla-free Clifford+T circuits, up to given epsilon. We present a new efficient algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum… (More)