8 papers · 1 filter
Convex Biproducts, Stochastic Matrices and Tape Diagrams
Filippo Bonchi, Cipriano Junior Cioffo
Categories with finite biproducts play a central role in category theory, providing an abstract setting in which additive and linear structures can be studied uniformly. In this pa…
Tapes as Stochastic Matrices of String Diagrams
Filippo Bonchi, Cipriano Junior Cioffo
Tape diagrams provide a graphical notation for categories equipped with two monoidal products, and , where is a biproduct. Recently, they have been gener…
A Diagrammatic Basis for Computer Programming
Filippo Bonchi, Alessandro Di Giorgio, Elena Di Lavore
Tape diagrams provide a convenient graphical notation for arrows of rig categories, i.e., categories equipped with two monoidal products, and . In this work, we i…
Deriving Program Logics from Distributive Monoidal Categories
Filippo Bonchi, Elena Di Lavore, Mario Román +1
We derive multiple program logics - including correctness, incorrectness, and relational Hoare logic - from the axioms of imperative categories: uniformly traced distributive copy-…
The calculus of neo-Peircean relations
Filippo Bonchi, Alessandro Di Giorgio, Nathan Haydon +1
The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on qu…
Tape Diagrams for Monoidal Monads
Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio +1
Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, and , where dist…
A Diagrammatic Algebra for Program Logics
Filippo Bonchi, Alessandro Di Giorgio, Elena Di Lavore
Tape diagrams provide a convenient notation for arrows of rig categories, i.e., categories equipped with two monoidal products, and , where distributes…
Effectful Mealy Machines
Filippo Bonchi, Elena Di Lavore, Mario Román
Effectful Mealy machines, which we introduce, are a generalization of Mealy machines with global effects determined by an effectful triple. We provide semantics of effectful Mealy…