Typing a core binary-field arithmetic in a light logic

Authors:
Emanuele Cesena;Marco Pedicini;Luca Roversi
Affiliations:
Dip. di Automatica e Informatica, Politecnico di Torino, Torino, Italy;Istituto per le Applicazioni del Calcolo "Mauro Picone", CNR, Roma, Italy,LIPN --- UMR CNRS 7030, Institut Galilée, Université Paris-Nord, France;Dip. di Informatica, Università degli Studi di Torino, Torino, Italy,Istituto per le Applicazioni del Calcolo "Mauro Picone", CNR, Roma, Italy
Venue:
FOPARA'11 Proceedings of the Second international conference on Foundational and Practical Aspects of Resource Analysis
Year:
2011

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Abstract

We design a library for binary-field arithmetic and we supply a core application programming interface (API) completely developed in a formal system we introduce: Typeable Functional Assembly (TFA) which essentially is the system Dual Light Affine Logic (DLAL) introduced by Baillot and Terui and extended with a fix-point formula. TFA is a light type assignment system, in the sense that substructural rules on types of linear logic allow just to type functional programs with polynomial evaluation cost. As a consequence, we show the core of a functional programming setting for binary-field arithmetic with built-in polynomial complexity.