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• W2969706276 abstract "Abstract Lambda- S is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi. One is to forbid duplication of variables, while the other is to consider all lambda-terms as algebraic linear functions. The type system of Lambda- S have a constructor S such that a type A is considered as the base of a vector space while S(A) is its span. A first semantics of this calculus have been given when first presented, with such an interpretation: superposed types are interpreted as vectors spaces while non-superposed types as their basis. In this paper we give a concrete categorical semantics of Lambda- S , showing that S is interpreted as the composition of two functors in an adjunction relation between the category of sets and the category of vector spaces over C . The right adjoint is a forgetful functor U, which is hidden in the language, and plays a central role in the computational reasoning." @default.
• W2969706276 created "2019-08-29" @default.
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• W2969706276 date "2019-08-01" @default.
• W2969706276 modified "2023-10-17" @default.
• W2969706276 title "A Concrete Categorical Semantics of Lambda-S" @default.
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• W2969706276 doi "https://doi.org/10.1016/j.entcs.2019.07.006" @default.
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