arXiv subjects

Peter LeFanu Lumsdaine

Publications and source records attributed to Peter LeFanu Lumsdaine.

22 records · Page 2Linked to original sources

arXiv2013

Quipper: A Scalable Quantum Programming Language

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 program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.

cs.PL↗

arXiv2012

On the Bourbaki-Witt Principle in Toposes

The Bourbaki-Witt principle states that any progressive map on a chain-complete poset has a fixed point above every point. It is provable classically, but not intuitionistically. We study this and related principles in an intuitionistic setting. Among other things, we show that Bourbaki-Witt fails exactly when the trichotomous ordinals form a set, but does not imply that fixed points can always be found by transfinite iteration. Meanwhile, on the side of models, we see that the principle fails in realisability toposes, and does not hold in the free topos, but does hold in all cocomplete toposes.

math.CT↗

arXiv2010

Weak omega-categories from intensional type theory

We show that for any type in Martin-Löf Intensional Type Theory, the terms of that type and its higher identity types form a weak omega-category in the sense of Leinster. Precisely, we construct a contractible globular operad of definable composition laws, and give an action of this operad on the terms of any type and its identity types.

math.LO↗

arXiv2009

A Small Observation on Co-categories

Various concerns suggest looking for internal co-categories in categories with strong logical structure. It turns out that in any coherent category, all co-categories are co-equivalence relations.

math.CT↗