7 citations · 7 across the 7 of their papers we have counts for
10 papers
String Diagrams for Closed Symmetric Monoidal Categories
Callum Reader, Alessandro Di Giorgio
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bra…
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…
Parametric Iteration in Resource Theories
Alessandro Di Giorgio, Pawel Sobocinski, Niels Voorneveld
Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security pa…
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…
When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines
Filippo Bonchi, Alessandro Di Giorgio, Davide Trotta
Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and comple…
Diagrammatic Algebra of First Order Logic
Filippo Bonchi, Alessandro Di Giorgio, Nathan Haydon +1
We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and com…
Deconstructing the Calculus of Relations with Tape Diagrams
Filippo Bonchi, Alessandro Di Giorgio, Alessio Santamaria
Rig categories with finite biproducts are categories with two monoidal products, where one is a biproduct and the other distributes over it. In this work we present tape diagrams,…
Diagrammatic Polyhedral Algebra
Filippo Bonchi, Alessandro Di Giorgio, Pawel Sobocinski
We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affi…