Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Proceedings of the 9th International Conference on Mathematical Foundations of Programming Semantics
A Lambda Calculus for Quantum Computation
SIAM Journal on Computing
A Functional Quantum Programming Language
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Probabilistic λ-calculus and Quantitative Program Analysis
Journal of Logic and Computation
A lambda calculus for quantum computation with classical control
Mathematical Structures in Computer Science
An Algebra of Pure Quantum Programming
Electronic Notes in Theoretical Computer Science (ENTCS)
Linear-algebraic λ-calculus: higher-order, encodings, and confluence.
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
A Computational Definition of the Notion of Vectorial Space
Electronic Notes in Theoretical Computer Science (ENTCS)
Taming non-compositionality using new binders
UC'07 Proceedings of the 6th international conference on Unconventional Computation
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This paper demonstrates how to add a measurement operator to quantum @l-calculi. A proof of the consistency of the semantics is given through a proof of confluence presented in a sufficiently general way to allow this technique to be used for other languages. The method described here may be applied to probabilistic rewrite systems in general, and to add measurement to more complex languages such as QML [Grattage, J. and T. Altenkirch, A functional quantum programming language, in: LICS '05: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science (2005), pp. 249-258] or Lineal [Arrighi, P. and G. Dowek, A computational definition of the notion of vectorial space, Electronic Notes in Theoretical Computer Science 117 (2005), pp. 249-261; Arrighi, P. and G. Dowek, Linear-algebraic lambda-calculus: higher-order, encodings and confluence, in: B. Buchberger, editor, Term Rewriting and Applications, 19th International Conference, RTA-08, To appear in LNCS (2008), eprint available at arXiv:quant-ph/0612199], which is the subject of further research.