8 research outputs found
Graph Rewriting and Relabeling with PBPO+
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting
with strong matching. Our approach, called \pbpostrong, exerts more control
over the embedding of the pattern in the host graph, which is important for a
large class of graph rewrite systems. In addition, we show that \pbpostrong is
well-suited for rewriting labeled graphs and certain classes of attributed
graphs. For this purpose, we employ a lattice structure on the label set and
use order-preserving graph morphisms. We argue that our approach is simpler and
more general than related relabeling approaches in the literature.Comment: 20 pages, accepted to the International Conference on Graph
Transformation 2021 (ICGT 2021
Graph rewriting and relabeling with PBPO+: A unifying theory for quasitoposes
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching. Our approach, called PBPO+, allows more control over the embedding of the pattern in the host graph, which is important for a large class of rewrite systems. We argue that PBPO+ can be considered a unifying theory in the general setting of quasitoposes, by demonstrating that PBPO+ can define a strict superset of the rewrite relations definable by PBPO, AGREE and DPO. Additionally, we show that PBPO+ is well suited for rewriting labeled graphs and some classes of attributed graphs, by introducing a lattice structure on the label set and requiring graph morphisms to be order-preserving
Algebraic Presentation of Semifree Monads
Monads and their composition via distributive laws have many applications in
program semantics and functional programming. For many interesting monads,
distributive laws fail to exist, and this has motivated investigations into
weaker notions. In this line of research, Petri\c{s}an and Sarkis recently
introduced a construction called the semifree monad in order to study
semialgebras for a monad and weak distributive laws. In this paper, we prove
that an algebraic presentation of the semifree monad M^s on a monad M can be
obtained uniformly from an algebraic presentation of M. This result was
conjectured by Petri\c{s}an and Sarkis. We also show that semifree monads are
ideal monads, that the semifree construction is not a monad transformer, and
that the semifree construction is a comonad on the category of monads.Comment: In Proceedings of CMCS 202
Graph Rewriting and Relabeling with PBPO +
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching. Our approach, called PBPO +, exerts more control over the embedding of the pattern in the host graph, which is important for a large class of graph rewrite systems. In addition, we show that PBPO + is well-suited for rewriting labeled graphs and certain classes of attributed graphs. For this purpose, we employ a lattice structure on the label set and use order-preserving graph morphisms. We argue that our approach is simpler and more general than related relabeling approaches in the literature
Algebraic Presentation of Semifree Monads
Monads and their composition via distributive laws have many applications in program semantics and functional programming. For many interesting monads, distributive laws fail to exist, and this has motivated investigations into weaker notions. In this line of research, Petrişan and Sarkis recently introduced a construction called the semifree monad in order to study semialgebras for a monad and weak distributive laws. In this paper, we prove that an algebraic presentation of the semifree monad Ms on a monad M can be obtained uniformly from an algebraic presentation of M. This result was conjectured by Petrişan and Sarkis. We also show that semifree monads are ideal monads, that the semifree construction is not a monad transformer, and that the semifree construction is a comonad on the category of monads