Behavioural Analysis of Sessions Using the Calculus of Structures

  title={Behavioural Analysis of Sessions Using the Calculus of Structures},
  author={Gabriel Ciobanu and Ross Horne},
  booktitle={Ershov Memorial Conference},
This paper describes an approach to the behavioural analysis of sessions. The approach is made possible by the calculus of structures — a deep inference proof calculus, generalising the sequent calculus, where inference rules are applied in any context. The approach involves specifications of global and local sessions inspired by the Scribble language. The calculus features a novel operator that synchronises parts of a protocol that must be treated atomically. Firstly, the calculus can be used… 
Towards Proofs as Successful Executions of Processes
This work focuses on a first-order extension of the proof calculus BV featuring a de Morgan dual pair of nominal quantifiers, called BV1, and emphasises that linear implication is strictly finer than trace inclusion, providing a tight refinement semantics for processes respecting both causality and the scope of private names.
Multiparty Session Types as Coherence Proofs
A Curry–Howard correspondence between a language for programming multiparty sessions and a generalisation of Classical Linear Logic, which generalise the cut rule of CLL to a new rule for composing many processes communicating in a multiparty session is proposed.
Session Subtyping and Multiparty Compatibility Using Circular Sequents
We present a structural proof theory for multi-party sessions, exploiting the expressive power of non-commutative logic which can capture explicitly the message sequence order in sessions. The
Constructing weak simulations from linear implications for processes with private names
  • R. Horne, A. Tiu
  • Mathematics, Computer Science
    Mathematical Structures in Computer Science
  • 2019
This paper clarifies that linear implication defines a branching-time preorder, preserved in all contexts, when used to compare embeddings of process in non-commutative logic, called BV1, a first-order extension of the proof system BV featuring a de Morgan dual pair of nominal quantifiers.
Linear Logic, the π-calculus, and their Metatheory: A Recipe for Proofs as Processes
The Curry-Howard correspondence between natural deduction and the _-calculus has provided a canonical foundation for the study of typed functional languages. Initiated by Abramsky [1994], the Proofs
Predicates as processes : Linear implication is a branching-time causality-preserving precongruence
For fragments of MAV1, the soundness of implication is shown with respect to both weak simulation and pomset trace inclusion; hence implication is a branching-time causality-preserving precongruence.
Private Names in Non-Commutative Logic
An expressive but decidable first-order system defined by using the calculus of structures, a generalisation of the sequent calculus, which incorporates a pair of nominal quantifiers called `new' and `wen', distinct from the self-dual Gabbay-Pitts and Miller-Tiu nominal quantifier.
The Consistency and Complexity of Multiplicative Additive System Virtual
  • R. Horne
  • Mathematics, Computer Science
    Sci. Ann. Comput. Sci.
  • 2015
A generalised cut elimination result is proven for MAV, thereby establishing the consistency of linear implication defined in the calculus.
De Morgan Dual Nominal Quantifiers Modelling Private Names in Non-Commutative Logic
The proof theory necessary for recommending an expressive but decidable first-order system, named MAV1, featuring a De Morgan dual pair of nominal quantifiers called “new” and “wen” are explored, which is defined using the calculus of structures, a generalisation of the sequent calculus.
Prioritise the Best Variation
Priority CP (PCP) is defined, which allows cyclic-structured processes and restores deadlock freedom by using priorities and an encoding from PCP to PGV is defined and proved that the encoding preserves typing and is sound and complete with respect to the operational semantics.


Subtyping for session types in the pi calculus
The syntax, operational semantics and typing rules of an extended pi calculus are formalized, it is proved that typability guarantees absence of run-time communication errors, and the typing rules are transformed into a practical typechecking algorithm.
Global Principal Typing in Partially Commutative Asynchronous Sessions
A theory of multiparty session types for the *** -calculus through asynchronous communication subtyping is generalised, which allows a programmer to choose between a top-down and a bottom-up style of communication programming, ensuring the same desirable properties of typable processes.
Scribbling Interactions with a Formal Foundation
The proposed methodology promotes a formally founded, and highly structured, development framework for modelling and building distributed applications, from high-level models to design and implementation to static checking to runtime validation.
Session Types as Intuitionistic Linear Propositions
This paper introduces a type system for the π-calculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic, and provides the first purely logical account of all features of session types.
Linear type theory for asynchronous session types
A multithreaded functional language with session types is defined, which unifies, simplifies and extends previous work, and significantly simplifies session types in the functional setting, clarifies their essential features and provides a secure foundation for language developments such as polymorphism and object-orientation.
Types for Dyadic Interaction
A typed formalism for concurrency where types denote freely composable structure of dyadic interaction in the symmetric scheme is formulated and it is shown that typed β-equality has a clean embedding in the bisimilarity.
The Focused Calculus of Structures
The focusing theorem is transplanted from the sequent calculus to the calculus of structures in order to make it more amenable to proof search and to give a direct inductive proof of the completeness of the focused calculus ofstructures with respect to a more standard unfocused form.
Multiparty Compatibility in Communicating Automata: Characterisation and Synthesis of Global Session Types
The key property of the findings is the notion of multiparty compatibility which non-trivially extends the duality condition for binary session types.
Maude as a Platform for Designing and Implementing Deep Inference Systems
The Maude language is proposed as a means for designing and implementing dieren t deep inference deductive systems and proof strategies that work on these systems and it is argued that these ideas can be analogously carried to other deductives systems for other logics.
Typing and subtyping for mobile processes
  • B. Pierce, D. Sangiorgi
  • Computer Science
    [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science
  • 1993
The authors define the syntax, typing, subtyping, and operational semantics of their calculus, prove that the typing rules are sound, apply the system to Milner's lambda -calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.