
Polymorphic System I
System I is a simplytyped lambda calculus with pairs, extended with an ...
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The Vectorial Lambda Calculus Revisited
We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vec...
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Normalization by Evaluation for CallbyPushValue and Polarized LambdaCalculus
We observe that normalization by evaluation for simplytyped lambdacalc...
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Gradualizing the Calculus of Inductive Constructions
Acknowledging the ordeal of a fully formal development in a proof assist...
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IndexStratified Types (Extended Version)
We present Tores, a core language for encoding metatheoretic proofs. The...
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A Dependently Typed MultiStage Calculus
We study a dependently typed extension of a multistage programming lang...
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Explicit Auditing
The Calculus of Audited Units (CAU) is a typed lambda calculus resulting...
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Functional Pearl: The Distributive λCalculus
We introduce a simple extension of the λcalculus with pairs—called the distributive λcalculus—obtained by adding a computational interpretation of the valid distributivity isomorphism A (B∧ C) ≡ (A B) ∧ (A C) of simple types. We study the calculus both as an untyped and as a simply typed setting. Key features of the untyped calculus are confluence, the absence of clashes of constructs, that is, evaluation never gets stuck, and a leftmostoutermost normalization theorem, obtained with straightforward proofs. With respect to simple types, we show that the new rules satisfy subject reduction if types are considered up to the distributivity isomorphism. The main result is strong normalization for simple types up to distributivity. The proof is a smooth variation over the one for the λcalculus with pairs and simple types.
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