4 papers
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…
Di- is for Directed: First-Order Directed Type Theory via Dinaturality
Andrea Laretto, Fosco Loregian, Niccolò Veltri
We show how dinaturality plays a central role in the interpretation of directed type theory where types are interpreted as (1-)categories and directed equality is represented by $\…
Two-dimensional transducers
Fosco Loregian
We define a bicategory whose 1-cells provide a categorification of transducers, computational devices extending finite-state automata with output capabilities. This…
Monads and limits in bicategories of circuits
Fosco Loregian
We study monads in the (pseudo-)double category where loose arrows are Mealy automata valued in an ambient monoidal category , and the cate…