Scalar system F for linear-algebraic λ-calculus: Towards a quantum physical logic

Electronic Notes in Theoretical Computer Science

Volumn 270, Issue 2, 2011, Pages 219-229

  Arrighi, Pablo ^a   Díaz Caro, Alejandro ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

Curry Howard; Probabilistic Lambda Calculus; Quantum Logic; Type Theory

Indexed keywords

ALGEBRA; COMPUTATIONAL MECHANICS; COMPUTER CIRCUITS; DIFFERENTIATION (CALCULUS); QUANTUM THEORY; SET THEORY;

CURRY-HOWARD; CURRY-HOWARD ISOMORPHISM; LAMBDA CALCULUS; LINEAR COMBINATIONS; LINEAR-ALGEBRAIC; PROBABILISTIC FUNCTIONS; QUANTUM LOGIC; TYPE THEORY;

CALCULATIONS;

EID: 79751485316     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2011.01.033     Document Type: Conference Paper

References (12)

1. T. Altenkirch, J.J. Grattage, J.K. Vizzotto, and A. Sabry An algebra of pure quantum programming Electronic Notes in Theoretical Computer Science 170 2007 23 47
2. P. Arrighi, and G. Dowek Linear-algebraic λ-calculus: higher-order, encodings and confluence (RTA'08) Lecture Notes in Computer Science 5117 2008 17 31
3. H.P. Barendregt Lambda calculi with types Handbook of Logic in Computer Science 2 1992 Clarendon Press Oxford
4. G. Birkhoff, and J. von Neumann The logic of quantum mechanics Annals of Mathematics 37 1936 823 843
5. A. Di Pierro, C. Hankin, and H. Wiklicky Probabilistic λ-calculus and quantitative program analysis Journal of Logic and Computation 15 2005 159 179 (Pubitemid 40860588)
6. S.J. Gay Quantum programming languages: survey and bibliography Mathematical Structures in Computer Science 16 2006 581 600 (Pubitemid 44706982)
7. J.-Y. Girard Linear logic Theoretical Computer Science 50 1987 1 102
8. J.-Y. Girard, A. Scedrov, and P.J. Scott Bounded linear logic: a modular approach to polynomial-time computability Theoretical Computer Science 97 1992 1 66
9. Grover, L.K., A fast quantum mechanical algorithm for database search, in: STOC '96: Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (1996), pp. 212-219.
10. P. Selinger A brief survey of quantum programming languages Functional and Logic Programming Lecture Notes in Computer Science 2998 2004 1 6
11. P.W. Shor Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer SIAM Journal on Computing 26 1997 1484 1509 (Pubitemid 127613100)
12. M.H. Sørensen, and P. Urzyczyn Lectures on the Curry-Howard Isomorphism Studies in Logic and the Foundations of Mathematics Volume 149 2006 Elsevier Science Inc. New York, NY, USA