Zobrazeno 1 - 10
of 209
pro vyhledávání: '"Uustalu, Tarmo"'
Autor:
Goncharov, Sergey, Uustalu, Tarmo
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 reasoning about program equivalence, and yet, numerous variants of it came alo
Externí odkaz:
http://arxiv.org/abs/2407.08688
Publikováno v:
EPTCS 380, 2023, pp. 1-21
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 conditions (including that M forms a factorization system), there is a ca
Externí odkaz:
http://arxiv.org/abs/2307.16558
Autor:
McDermott, Dylan, Uustalu, Tarmo
Publikováno v:
EPTCS 360, 2022, pp. 113-133
Strong monads are important for several applications, in particular, in the denotational semantics of effectful languages, where strength is needed to sequence computations that have free variables. Strength is non-trivial: it can be difficult to det
Externí odkaz:
http://arxiv.org/abs/2207.00851
Publikováno v:
EPTCS 358, 2022, pp. 118-135
Monoidal closed categories naturally model NMILL, non-commutative multiplicative intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and conjunction; the internal hom interprets linear implication. In recent y
Externí odkaz:
http://arxiv.org/abs/2204.06727
Publikováno v:
EPTCS 333, 2021, pp. 230-246
The skew monoidal categories of Szlach\'anyi are a weakening of monoidal categories where the three structural laws of left and right unitality and associativity are not required to be isomorphisms but merely transformations in a particular direction
Externí odkaz:
http://arxiv.org/abs/2101.10487
Publikováno v:
EPTCS 332, 2021, pp. 35-53
In this paper, we develop the proof theory of skew prounital closed categories. These are variants of the skew closed categories of Street where the unit is not represented. Skew closed categories in turn are a weakening of the closed categories of E
Externí odkaz:
http://arxiv.org/abs/2101.03809
Szlach\'anyi's skew monoidal categories are a well-motivated variation of monoidal categories in which the unitors and associator are not required to be natural isomorphisms, but merely natural transformations in a particular direction. We present a
Externí odkaz:
http://arxiv.org/abs/2003.05213
We introduce and study functor-functor and monad-comonad interaction laws as mathematical objects to describe interaction of effectful computations with behaviors of effect-performing machines. Monad-comonad interaction laws are monoid objects of the
Externí odkaz:
http://arxiv.org/abs/1912.13477
Autor:
Maarand, Hendrik, Uustalu, Tarmo
We provide syntactic derivative-like operations, defined by recursion on regular expressions, in the styles of both Brzozowski and Antimirov, for trace closures of regular languages. Just as the Brzozowski and Antimirov derivative operations for regu
Externí odkaz:
http://arxiv.org/abs/1908.03551
Publikováno v:
Logical Methods in Computer Science, Volume 14, Issue 4 (October 29, 2018) lmcs:4899
We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical TT-lifting. After
Externí odkaz:
http://arxiv.org/abs/1810.07972