Theoretical Computer Science
Lambda-calculus, types and models
Lambda-calculus, types and models
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
The differential Lambda-calculus
Theoretical Computer Science
On Köthe sequence spaces and linear logic
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
Theoretical Computer Science
A Computational Definition of the Notion of Vectorial Space
Electronic Notes in Theoretical Computer Science (ENTCS)
On linear combinations of λ-terms
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Linearity, Non-determinism and Solvability
Fundamenta Informaticae - From Mathematical Beauty to the Truth of Nature: to Jerzy Tiuryn on his 60th Birthday
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We introduce an extension of the pure lambda calculus by endowing the set of terms with the structure of a vector space, or, more generally, of a module, over a fixed set of scalars. Moreover, terms are subject to identities similar to the usual pointwise definition of linear combinations of functions with values in a vector space. We then study a natural extension of beta reduction in this setting: we prove it is confluent, then discuss consistency and conservativity over the ordinary lambda calculus. We also provide normalisation results for a simple type system.