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Wave-Style Token Machines and Quantum Lambda Calculi (Long Version) [article]

Ugo Dal Lago, Margherita Zorzi
2013 arXiv   pre-print
Particle-style token machines are a way to interpret proofs and programs, when the latter are defined according to the principles of linear logic.  ...  In this paper, we show that token machines also make sense when the programs at hand are those of a simple linear quantum λ-calculus.  ...  gates occurring in the underlying lambda-term; • we show that also wave-style token machines are sound with respect to an operational theory of superposed type derivations; • we give evidence that wave-style  ... 
arXiv:1307.0550v3 fatcat:a243opcyyfesne7nmptfhx7t2e

Wave-Style Token Machines and Quantum Lambda Calculi

Ugo Dal Lago, Margherita Zorzi
2015 Electronic Proceedings in Theoretical Computer Science  
Particle-style token machines are a way to interpret proofs and programs, when the latter are written following the principles of linear logic.  ...  In this paper, we show that token machines also make sense when the programs at hand are those of a simple quantum lambda-calculus with implicit qubits.  ...  This is the main object of study of this paper, and is the calculus for which we will give a wave-style token machine in the coming sections.  ... 
doi:10.4204/eptcs.176.6 fatcat:vs7bmpp6unafbbyj4t36hy2khq

Measurements in Proof Nets as Higher-Order Quantum Circuits [chapter]

Akira Yoshimizu, Ichiro Hasuo, Claudia Faggian, Ugo Dal Lago
2014 Lecture Notes in Computer Science  
Specifically, we introduce a quantum lambda calculus MLLqm and define its geometry of interaction (GoI) semantics-in the style of token machines-via the translation of terms into proof nets.  ...  The calculus MLLqm attains a pleasant balance between expressivity (it is higher-order and accommodates all quantum operations) and concreteness of models (given as token machines, i.e. in the form of  ...  Use of multiple tokens is already in [4] where the style is called wave-style token machine.  ... 
doi:10.1007/978-3-642-54833-8_20 fatcat:kvgmkacuqvb6vhkxrxgijy334a

The geometry of parallelism: classical, probabilistic, and quantum effects

Ugo Dal Lago, Claudia Faggian, Benoît Valiron, Akira Yoshimizu
2017 Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017  
Our model comes with a multi-token machine, a proof net system, and a PCF-style language.  ...  We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a fully fledged quantum programming language in which entanglement, duplication, and recursion  ...  This model has been used extensively in the context of quantum lambda-calculi [11, 13, 24] , with minor variations.  ... 
doi:10.1145/3009837.3009859 fatcat:t72iddrvb5dxloldy4ccufhjo4

The Geometry of Parallelism. Classical, Probabilistic, and Quantum Effects [article]

Ugo Dal Lago, Claudia Faggian, Benoit Valiron, Akira Yoshimizu
2017 arXiv   pre-print
Our model comes with a multi-token machine, a proof net system, and a PCF-style language.  ...  We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all  ...  This model has been used extensively in the context of quantum lambda-calculi [11, 13, 24] , with minor variations.  ... 
arXiv:1610.09629v3 fatcat:esaxtrs4prgyjlpxvlcoc52foy

The geometry of parallelism: classical, probabilistic, and quantum effects

Ugo Dal Lago, Claudia Faggian, Benoît Valiron, Akira Yoshimizu
2017 SIGPLAN notices  
Our model comes with a multi-token machine, a proof net system, and a PCF-style language.  ...  We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a fully fledged quantum programming language in which entanglement, duplication, and recursion  ...  This model has been used extensively in the context of quantum lambda-calculi [11, 13, 24] , with minor variations.  ... 
doi:10.1145/3093333.3009859 fatcat:itlirwu4f5gsbphcajfc62anq4

Semantics of Higher-Order Quantum Computation via Geometry of Interaction

Ichiro Hasuo, Naohiko Hoshino
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum  ...  Keywords-quantum computation; lambda calculus; categorical semantics; geometry of interaction; realizability Kℓ(Q) we obtain the category PER Q .  ...  The examples of a TSMC C in GoI [7] are divided into two groups: the wave-style ones where C's monoidal structure is given by products ×; and the particle-style ones where it is given by coproducts +  ... 
doi:10.1109/lics.2011.26 dblp:conf/lics/HasuoH11 fatcat:xeeny4nzwbgwvjprdc6wvw2mcq

A Fresh Look at the lambda-Calculus (Invited Talk)

Beniamino Accattoli, Michael Wagner
2019 International Conference on Rewriting Techniques and Applications  
And yet -we argue here -its study is far from being over.  ...  The paper aims at inducing a new way of looking at an old topic, focussing on high-level issues and perspectives.  ...  Token-Based Abstract Machines. There is another class of abstract machines that is much less famous than those based on environments.  ... 
doi:10.4230/lipics.fscd.2019.1 dblp:conf/rta/Accattoli19 fatcat:75swok72vvb6fdfl3fx5lu5sey

Semantics of Higher-Order Quantum Computation via Geometry of Interaction [article]

Ichiro Hasuo, Naohiko Hoshino
2016 arXiv   pre-print
, based on linear lambda calculus and equipped with features like the !  ...  While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum  ...  the anonymous reviewers (for the earlier version [1] as well as for the current version) for useful discussions and comments; and to Andy Pitts for his ETAPS'07 talk that inspired the current work.  ... 
arXiv:1605.05079v1 fatcat:xwlvnvpmajejjbkzx66ykogvfa

Proceedings Third International Workshop on Linearity [article]

Sandra Alves, Iliano Cervesato (Carnegie Mellon University)
2015 pre-print
systems, quantum models of computation, and biological and chemical models of computation.  ...  The aim of this workshop was to bring together researchers who are exploring theory and applications of linear calculi, to foster their interaction and provide a forum for presenting new ideas and work  ...  Tov and Greg Morrisett 34 Ludics without Designs I: Triads Michele Basaldella 49 Wave-Style Token Machines and Quantum Lambda Calculi Ugo Dal Lago and Margherita Zorzi 64 Geometry of Resource  ... 
doi:10.4204/eptcs.176 arXiv:1502.04419v1 fatcat:v5tlnlejrnbzflchbhmotmu7fa

Geometry of Interaction and the Dynamics of Proof Reduction: A Tutorial [chapter]

E. Haghverdi, P. Scott
2010 Lecture Notes in Physics  
The kind of logics we deal with, such as Girard's linear logic, are resource sensitive and have their proof-theory intimately related to various monoidal (tensor) categories.  ...  In the context of proof theory, where one views algorithms as proofs and computation as cut-elimination, this program translates to providing a mathematical modelling of the dynamics of cut-elimination  ...  As explained in [Abr96, AHS02] , product-style traces may be thought of as passing information in a "global information wave" while sum-style traces can be modelled by streams of particles or tokens flowing  ... 
doi:10.1007/978-3-642-12821-9_5 fatcat:uo6lpvdkz5d7bclk4tis6u74ri

The early history of F#

Don Syme
2020 Proceedings of the ACM on Programming Languages (PACMPL)  
I start with the origins of strongly-typed functional programming (FP) in the 1970s, 80s and 90s. During the same period, Microsoft was founded and grew to dominate the software industry.  ...  The development of the core features of F# 1.0 happened from 2004-2007, and I describe the decision-making process that led to the łproductizationž of F# by Microsoft in 2007-10 and the release of F# 2.0  ...  This world was heavily influenced by foundational calculi, most obviously the Lambda Calculus and its variations such as System F, followed by concurrent calculi such as CCS and the Pi Calculus [Sangiorgi  ... 
doi:10.1145/3386325 fatcat:lk7zpwvyzfdc5gkscsmqmnze2e

Relevance of time‐varying properties of the first formant frequency in vowel representation

Maria‐Gabriella Di Benedetto
1985 Journal of the Acoustical Society of America  
In addition, examples such as calculi and tottoni demonstrate that stress is sensitive to etymology, a nonlocal property of the entire word.  ...  The technique has been used to determine in a machine-readable dictionary, where an entry is S6 J. Acoust. Soc. Am.  ...  machines.  ... 
doi:10.1121/1.2023018 fatcat:3lbckbce2rglzj7zx3fp4nhiui

On the performance and programming of reversible molecular computers

Amelie Hannah Earley, Apollo-University Of Cambridge Repository, Gos Micklem
2021
A result of Frank is refined and strengthened, showing that the adiabatic regime reversible computer performance is the best possible for any computer—quantum or classical.  ...  Nonetheless, scaling superior to that of irreversible computers can be preserved, and appropriate mitigations and considerations are discussed.  ...  This may be considered to ultimately originate in early mathematical models of computations such as the Turing Machine and Lambda Calculus in which overwriting and discarding, respectively, are implicit  ... 
doi:10.17863/cam.79111 fatcat:ged47nao2jdjfexz4y5d3u4u4y

Proceedings of the ESSLLI 2014 Student Session Area experts

Ronald De Haan, Philip Schulz, Universiteit Van Amsterdam, Thomas Brochhagen, Miriam Kaeshammer, Ramon Ziai, Jakub Szymanik, Michael Franke, Roger Levy, Fangzhou Zhai, Tingxiang Zou
unpublished
As in previous years, Springer-Verlag has generously offered prizes for Best Paper and Best Poster Awards, and for this we are very grateful.  ...  At the Student Session, 16 of these submissions were presented orally and 6 submissions were presented in the form of a poster.  ...  and the three anonymous reviewers for their valuable feedback.  ... 
fatcat:wvyjfv2wcjehlmzh2xd7jmxksq
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