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Correct and Complete Type Checking and Certified Erasure for Coq, in Coq

In which we report on the MetaCoq project, up to its 1.2 version.

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Definitional Functoriality for Dependent (Sub)Types

In which we extend a dependent type theory with definitionally functorial operations, and use these to obtain a well-behaved coercive subtyping.

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Martin-Löf à la Coq

In which we report on a formalization, in Coq, of a fully certified type-checker for Martin-Löf Type Theory.

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A Reasonably Gradual Type Theory

In which we extend our Gradual Calculus of Inductive Constructions to internalize precision and allow for sound reasoning over gradual programs.

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Gradualizing the Calculus of Inductive Constructions

In which we investigate gradual variations on the Calculus of Inductive Construction. Presented at POPL '22.

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Complete Bidirectional Typing for the Calculus of Inductive Constructions

In which I presents a bidirectional type system for the Calculus of Inductive Constructions.

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