
Consistency of the Predicative Calculus of Cumulative Inductive Constructions (pCuIC)
In order to avoid wellknow paradoxes associated with selfreferential d...
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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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Touring the MetaCoq Project (Invited Paper)
Proof assistants are getting more widespread use in research and industr...
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Practical Sized Typing for Coq
Termination of recursive functions and productivity of corecursive funct...
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Undecidability of D_<: and Its Decidable Fragments
Dependent Object Types (DOT) is a calculus with path dependent types, in...
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Generalizing inference systems by coaxioms
After surveying classical results, we introduce a generalized notion of ...
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A BiDirectional Refinement Algorithm for the Calculus of (Co)Inductive Constructions
The paper describes the refinement algorithm for the Calculus of (Co)Ind...
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Complete Bidirectional Typing for the Calculus of Inductive Constructions
This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence of computation in types. The key property of the system is its completeness with respect to the usual undirected one, which has been formally proven in Coq as a part of the MetaCoq project. Although it plays an important role in an ongoing completeness proof for a realistic typing algorithm, the interest of bidirectionality is wider, as it gives insights and structure when trying to prove properties on CIC or design variations and extensions. In particular, we put forward constrained inference, an intermediate between the usual inference and checking judgements, to handle the presence of computation in types.
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