Realizability in the Unitary Sphere

  title={Realizability in the Unitary Sphere},
  author={Alejandro D{\'i}az-Caro and M. Guillermo and Alexandre Miquel and B. Valiron},
  journal={2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of typing rules for a simply-typed linear algebraic lambda-calculus, and show how it extends both to classical and quantum lambda-calculi. 
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