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• W4366078183 abstract "Abstract Modal types—types that are derived from proof systems of modal logic—have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds to a type constructor for code types and controls free variables and their types in code values. Nanevski et al. have proposed contextual modal type theory , which has modal types with fine-grained information on free variables: modal types are explicitly indexed by contexts —the types of all free variables in code values. This paper presents $$lambda _{forall []}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mo>∀</mml:mo> <mml:mo>[</mml:mo> <mml:mo>]</mml:mo> </mml:mrow> </mml:msub> </mml:math> , a novel extension of contextual modal type theory with parametric polymorphism over contexts . Such an extension has been studied in the literature but, unlike earlier proposals, $$lambda _{forall []}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mo>∀</mml:mo> <mml:mo>[</mml:mo> <mml:mo>]</mml:mo> </mml:mrow> </mml:msub> </mml:math> is more general in that it allows multiple occurrence of context variables in a single context. We formalize $$lambda _{forall []}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mo>∀</mml:mo> <mml:mo>[</mml:mo> <mml:mo>]</mml:mo> </mml:mrow> </mml:msub> </mml:math> with its type system and operational semantics given by $$beta $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>β</mml:mi> </mml:math> -reduction and prove its basic properties including subject reduction, strong normalization, and confluence. Moreover, to demonstrate the expressive power of polymorphic contexts, we show a type-preserving embedding from a two-level fragment of Davies’ $$lambda _{bigcirc }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>λ</mml:mi> <mml:mo>◯</mml:mo> </mml:msub> </mml:math> , which is based on linear-time temporal logic, to $$lambda _{forall []}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mo>∀</mml:mo> <mml:mo>[</mml:mo> <mml:mo>]</mml:mo> </mml:mrow> </mml:msub> </mml:math> ." @default.
• W4366078183 created "2023-04-19" @default.
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• W4366078183 date "2023-01-01" @default.
• W4366078183 modified "2023-09-25" @default.
• W4366078183 title "Contextual Modal Type Theory with Polymorphic Contexts" @default.
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• W4366078183 doi "https://doi.org/10.1007/978-3-031-30044-8_11" @default.
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