69 citations · 205 across the 22 of their papers we have counts for
24 papers
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…
A Unifying Categorical View of Nondeterministic Iteration and Tests
Sergey Goncharov, Tarmo Uustalu
We study Kleene iteration in the categorical context. A celebrated completeness result by Kozen introduced Kleene algebra (with tests) as a ubiquitous tool for lightweight reasonin…
Canonical Gradings of Monads
Flavien Breuvart, Dylan McDermott, Tarmo Uustalu
We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable con…
What Makes a Strong Monad?
Dylan McDermott, Tarmo Uustalu
Strong monads are important for several applications, in particular, in the denotational semantics of effectful languages, where strength is needed to sequence computations that ha…
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…
Proof Theory of Partially Normal Skew Monoidal Categories
Tarmo Uustalu, Niccolò Veltri, Noam Zeilberger
The skew monoidal categories of Szlachányi are a weakening of monoidal categories where the three structural laws of left and right unitality and associativity are not required to…