On dependent linear type theory (for quantum computation with classical control) with categorical semantics in indexed monoidal categories:
Matthijs Vákár, Syntax and Semantics of Linear Dependent Types (arXiv:1405.0033)
Matthijs Vákár, Splitting the Atom of Dependent Types… or Linear and Operational Dependent Type Theory, November 2014 (pdf)
Matthijs Vákár, A Categorical Semantics for Linear Logical Frameworks, In: A. Pitts (ed.), Foundations of Software Science and Computation Structures FoSSaCS 2015. Lecture Notes in Computer Science, vol 9034. Springer 2015 (arXiv:1501.05016, doi:10.1007/978-3-662-46678-0_7)
On side effects in functional programming with dependent type theory:
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