scholarly journals A denotational semantics for the symmetric interaction combinators

2007 ◽  
Vol 17 (3) ◽  
pp. 527-562 ◽  
Author(s):  
DAMIANO MAZZA
Keyword(s):  
Linear Logic ◽  
Denotational Semantics ◽  
Distributed Computation ◽  
Higher Order ◽  
Parallel Execution ◽  
Turing Machines ◽  
Algebraic Semantics ◽  
Relational Semantics ◽  
Completeness Result ◽  
Higher Order Functions

The symmetric interaction combinators are a variant of Lafont's interaction combinators. They enjoy a weaker universality property with respect to interaction nets, but are equally expressive. They are a model of deterministic distributed computation and share the good properties of Turing machines (elementary reductions) and of the λ-calculus (higher-order functions and parallel execution). We introduce a denotational semantics for this system, which is inspired by the relational semantics for linear logic, and prove an injectivity and full completeness result for it. We also consider the algebraic semantics defined by Lafont, and prove that the two are strongly related.

scholarly journals Proofs, denotational semantics and observational equivalences in Multiplicative Linear Logic

2007 ◽  
Vol 17 (2) ◽  
pp. 341-359 ◽  
Author(s):  
MICHELE PAGANI
Keyword(s):  
Linear Logic ◽  
Denotational Semantics ◽  
Cut Elimination ◽  
Relational Semantics ◽  
Observational Equivalence ◽  
Proof Nets ◽  
General Method

We study full completeness and syntactical separability of MLL proof nets with the mix rule. The general method we use consists of first addressing these two questions in the less restrictive framework of proof structures, and then adapting the results to proof nets.At the level of proof structures, we find a semantical characterisation of their interpretations in relational semantics, and define an observational equivalence that is proved to be the equivalence induced by cut elimination. Hence, we obtain a semantical characterisation (in coherent spaces) and an observational equivalence for the proof nets with the mix rule.

scholarly journals Domain Theory for Concurrency

2003 ◽  
Vol 10 (43) ◽  
Author(s):  
Mikkel Nygaard ◽  
Glynn Winskel
Keyword(s):  
Linear Logic ◽  
Operational Semantics ◽  
Denotational Semantics ◽  
Higher Order ◽  
The Other ◽  
Domain Theory ◽  
Parallel Composition ◽  
Concurrent Computation ◽  
Contextual Equivalence

A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation. Two choices of comonad yield two expressive metalanguages for higher-order processes, both arising from canonical constructions in the model. Their denotational semantics are fully abstract with respect to contextual equivalence. One language derives from an exponential of linear logic; it supports a straightforward operational semantics with simple proofs of soundness and adequacy. The other choice of comonad yields a model of affine-linear logic, and a process language with a tensor operation to be understood as a parallel composition of independent processes. The domain theory can be generalised to presheaf models, providing a more refined treatment of nondeterministic branching. The article concludes with a discussion of a broader programme of research, towards a fully fledged domain theory for concurrency.

scholarly journals Voigt Transform and Umbral Image

2020 ◽  
Vol 25 (3) ◽  
pp. 49
Author(s):  
Silvia Licciardi ◽  
Rosa Maria Pidatella ◽  
Marcello Artioli ◽  
Giuseppe Dattoli
Keyword(s):  
Spectroscopic Studies ◽  
Higher Order ◽  
Point Of View ◽  
The Other ◽  
Pivotal Role ◽  
Umbral Calculus ◽  
Laguerre Functions ◽  
Hermite And Laguerre Functions ◽  
Higher Order Functions ◽  
Voigt Function

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

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