8 citations · 16 across the 6 of their papers we have counts for
11 papers · 1 filter
Derivatives for Containers in Univalent Foundations
Philipp Joram, Niccolò Veltri
Containers conveniently represent a wide class of inductive data types. Their derivatives compute representations of types of one-hole contexts, useful for implementing tree-traver…
Monoid Structures on Indexed Containers
Michele De Pascalis, Tarmo Uustalu, Niccolò Veltrì
Containers represent a wide class of type constructions relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the…
Doctrinal Semantics of Directed First-Order Logic
Andrea Laretto, Fosco Loregian, Niccolò Veltri
We present a first-order logic equipped with an "asymmetric" directed notion of equality, which can be thought of as rewrites between terms, allowing for types to be interpreted as…
Semi-Substructural Logics with Additives
Niccolò Veltri, Cheng-Syuan Wan
This work concerns the proof theory of (left) skew monoidal categories and their variants (e.g. closed monoidal, symmetric monoidal), continuing the line of work initiated in recen…
Proof Theory of Skew Non-Commutative MILL
Tarmo Uustalu, Niccolò Veltri, Cheng-Syuan Wan
Monoidal closed categories naturally model NMILL, non-commutative multiplicative intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and co…
Normalization by Evaluation for the Lambek Calculus
Niccolò Veltri
The syntactic calculus of Lambek is a deductive system for the multiplicative fragment of intuitionistic non-commutative linear logic. As a fine-grained calculus of resources, it h…