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Lightweight Proof by Reflection Using a Posteriori Simulation of Effectful Computation

This work proposes a novel technique for proof-by-reflection that marries, in Type Theory, an effectful language with (partial) proofs of correctness and uses simulable monads.
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Pervasive Parallelism in Highly-Trustable Interactive Theorem Proving Systems

Interactive theorem proving is a technology of fundamental importance for mathematics and computer-science and its applications include huge mathematical proofs and semi-automated verifications of complex software systems.
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Axiomatic and dual systems for constructive necessity, a formally verified equivalence

ABSTRACT We present a proof of the equivalence between two deductive systems for constructive necessity, namely an axiomatic characterisation inspired by Hakli and Negri's system of derivations from…
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Gradual typing using union typing with records

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Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach

An adequacy theorem with respect to a realizability semantics based on saturated sets and saturated-valued functions is proved and the strong normalization property for the proof-term reduction is obtained, an important feature which is absent in previous related work.
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Dual and Axiomatic Systems for Constructive S4, a Formally Verified Equivalence

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On interactive proof-search for constructive modal necessity

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Selective Memoization with Box Types

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Incrementality and effect simulation in the simply typed lambda calculus. (Incrémentalité et simulation d'effets dans le lambda calcul simplement typé)

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A Dual-Context Sequent Calculus for S4 Modal Lambda-Term Synthesis

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