Haskell (in type theory)
Coq, Agda (in dependent type theory)
Quipper (for quantum computation)
(…)
Wikipedia, Functional programming
John Backus, Can programming be liberated from the von Neumann style? A functional style and its algebra of programs, Communications of the ACM Volume 21 Number 8, 1978 (pdf)
Erik Meijer, Maarten Fokkinga, Ross Paterson, Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire, 1991 (doi:10.1.1.41.125)
Eugenio Moggi, Notions of computations and monads, 1991 (pdf)
Discussion of aspects of quantum computing in terms of monads in functional programming are in
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