Authors: Ghilezan, Silvia 
Ivetić, Jelena
Lescanne, Pierre
Likavec, Silvia
Title: Structural rules and resource control in logic and computation
Journal: Logic in Computer Science
Series/Report no.: Zbornik radova
Volume: 18
Issue: 26
First page: 79
Last page: 109
Issue Date: 2015
Rank: M14
ISSN: 0351-9406
Control of resources and awareness of their usage has an important role in logic and lambda calculus as well as in programming languages, compiler design and program synthesis. Already Gentzen had the idea to control the use of formulae in structural rules of the sequent calculus, whereas the idea to control the use of variables interm calculi goes back to Church’s λI-calculus. This work provides an overview of the most important work in the field of resource control and presents the authors’ contributions in this field. The journey starts with the Resource control lambda calculus, continues with its sequent counterpart, the Resource control sequent lambda calculus, and concludes with computational inter-pretations of substructural logics, by presenting a lambda calculus without thinning, corresponding to a variant of the relevant logic.
Keywords: lambda calculus | sequent calculus | logic | resource control | structural rules | typeability | intersection types | strong normalisation
Publisher: Mathematical Institute of the SASA
Project: Representations of logical structures and formal languages and their application in computing 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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