Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Theoretical Computer Science
Adding algebraic rewriting to the untyped lambda calculus (extended abstract)
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Handbook of theoretical computer science (vol. B)
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Lambda-calculi for (strict) parallel functions
Information and Computation
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Probabilistic Asynchronous pi-Calculus
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
The differential Lambda-calculus
Theoretical Computer Science
A Lambda Calculus for Quantum Computation
SIAM Journal on Computing
Towards a quantum programming language
Mathematical Structures in Computer Science
A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th 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)
Rewriting logic and probabilities
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
On linear combinations of λ-terms
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Linear-algebraic λ-calculus: higher-order, encodings, and confluence.
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
On the completeness of quantum computation models
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Measurements and Confluence in Quantum Lambda Calculi With Explicit Qubits
Electronic Notes in Theoretical Computer Science (ENTCS)
Confluence Results for a Quantum Lambda Calculus with Measurements
Electronic Notes in Theoretical Computer Science (ENTCS)
Scalar System F for Linear-Algebraic λ-Calculus: Towards a Quantum Physical Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
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We introduce a minimal language combining higher-ordercomputation and linear algebra. This language extends theλ-calculus with the possibility to make arbitrarylinear combinations of terms λ.t+β.u. We describe how to "execute" thislanguage in terms of a few rewrite rules, and justify them throughthe two fundamental requirements that the language be a language oflinear operators, and that it be higher-order. We mention theperspectives of this work in the field of quantum computation,whose circuits we show can be easily encoded in the calculus.Finally we prove the confluence of the calculus, this is our mainresult.