Lax extensions of coalgebra functors and their logic

Marti, Johannes; Venema, Yde

doi:10.1016/j.jcss.2014.12.006

Cited by 21 publications

(43 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, for a weak pullback preserving functor B, the canonical lifting Rel(B) is a lax extension preserving diagonals. But the results in [MV15] also show that non-weak pullback preserving set functors have such lax extensions. In fact, any finitary functor for which an expressive logic with "monotone" modalities exist, has a suitable lifting.…”

Section: :18mentioning

confidence: 95%

“…e.g. Remark 4 in [MV15]) and the other equalities follow from the definition of reindexing. This implies that ( B, B) is a fibration map once we establish that B is a lifting of B along p : Rel → Set.…”

Section: :18mentioning

confidence: 98%

“…In order to be able to cover a larger class of functors, and move to behavioural equivalence, we use the notion of lax extension preserving diagonals. Definition 3.9 [MV15]. Let B : Set → Set be a functor.…”

Section: This Is Above the Identity Onmentioning

confidence: 99%

“…Examples include the so-called ( ) 3 2 -functor , the functor P n that maps a set X to the collection P n X of subsets of X with less than n elements and the so-called monotone neighbourhood functor (cf. Example 7 in [MV15]). The following proposition establishes that the lax lifting B fits into the fibrational framework of our paper, and that Proposition 3.8 applies.…”

Section: :18mentioning

confidence: 99%

See 3 more Smart Citations

Expressive Logics for Coinductive Predicates

Kupke¹,

Rot²

2021

Logical Methods in Computer Science

View full text Add to dashboard Cite

The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata.

show abstract

Section: :18mentioning

confidence: 95%

Section: :18mentioning

confidence: 98%

Section: This Is Above the Identity Onmentioning

confidence: 99%

Section: :18mentioning

confidence: 99%

See 2 more Smart Citations

Expressive Logics for Coinductive Predicates

Kupke¹,

Rot²

2021

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…Maps Γ : Rel(X, T Y ) → Rel(T X, T Y ) that guarantee good properties of T-corelation composition turn out to coincide with the so-called relational extensions of T [24]- [27], a notion playing an important role in topology [24], [26], [27], coalgebra [25], [28], [29], logic [30], [31], and programming language theory [32]- [37]. This correspondence allows us to develop our relational theory of monadic rewriting systems relying on a vast body of results and techniques.…”

Section: A Relational Theory Of Monadic Rewriting Systemmentioning

confidence: 99%

A Relational Theory of Monadic Rewriting Systems, Part I

Gavazzo

Faggian

2021

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

View full text Add to dashboard Cite

Motivated by the study of effectful programming languages and computations, we introduce a relational theory of monadic rewriting systems. The latter are rewriting systems whose notion of reduction is effectful, where effects are modelled as monads. Contrary to what happens in the ordinary operational semantics of monadic programming languages, defining meaningful notions of monadic rewriting turns out to problematic for several monads, including the distribution, powerset, reader, and global state monad. This raises the question of when monadic rewriting is possible. We answer that question by identifying a class of monads, known as weakly cartesian monads, that guarantee monadic rewriting to be well-behaved. In case monads are given as equational theories, as it is the case for algebraic effects, we also show that a sufficient condition to have wellbehaved notion of monadic rewriting is that all equations in the theory are linear. Finally, we apply the abstract theory of monadic rewriting systems to the call-by-value λ-calculus with algebraic effects, this way obtaining effectful (surface) standardisation and confluence theorems.

show abstract