Introduction to higher order categorical logic
Introduction to higher order categorical logic
Theoretical Computer Science
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
From proof-nets to interaction nets
Proceedings of the workshop on Advances in linear logic
Domains and lambda-calculi
Two applications of analytic functors
Theoretical Computer Science - Special issue on theories of types and proofs
What is a Categorical Model of Intuitionistic Linear Logic?
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculi
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Stable Models of Typed lambda-Calculi
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Fibrational Control Structures
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models (Extended Abstract)
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
From Action Calculi to Linear Logic
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Higher Dimensional Word Problem
Proceedings of the 4th International Conference on Category Theory and Computer Science
Glueing and orthogonality for models of linear logic
Theoretical Computer Science - Category theory and computer science
A Stability Theorem in Rewriting Theory
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Mathematical Structures in Computer Science
Categorical logic of names and abstraction in action calculi
Mathematical Structures in Computer Science
Pure bigraphs: Structure and dynamics
Information and Computation
On traced monoidal closed categories
Mathematical Structures in Computer Science
Traces for coalgebraic components
Mathematical Structures in Computer Science
A modified GoI interpretation for a linear functional programming language and its adequacy
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Functional programming in sublinear space
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
A Graphical Foundation for Schedules
Electronic Notes in Theoretical Computer Science (ENTCS)
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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String diagrams were introduced by Roger Penrose as a handy notation to manipulate morphisms in a monoidal category. In principle, this graphical notation should encompass the various pictorial systems introduced in proof-theory (like Jean-Yves Girard’s proof-nets) and in concurrency theory (like Robin Milner’s bigraphs). This is not the case however, at least because string diagrams do not accomodate boxes — a key ingredient in these pictorial systems. In this short tutorial, based on our accidental rediscovery of an idea by Robin Cockett and Robert Seely, we explain how string diagrams may be extended with a notion of functorial box depicting a functor transporting an inside world (its source category) to an outside world (its target category). We expose two elementary applications of the notation: first, we characterize graphically when a faithful balanced monoidal functor F:ℂ $\longrightarrow$$\mathbb{D}$ transports a trace operator from the category $\mathbb{D}$ to the category ℂ, and exploit this to construct well-behaved fixpoint operators in cartesian closed categories generated by models of linear logic; second, we explain how the categorical semantics of linear logic induces that the exponential box of proof-nets decomposes as two enshrined boxes.