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Geometry of resource interaction and Taylor–Ehrhard–Regnier expansion: a minimalist approach

Published online by Cambridge University Press:  10 November 2016

MARCO SOLIERI Open the ORCID record for MARCO SOLIERI [Opens in a new window]
MARCO SOLIERI*
Affiliation:
LIPN, UMR 7030 CNRS, Université Paris 13, Sorbonne Paris Cité, Villetaneuse, France. Email: ms@xt3.it IRIF, UMR 8243, CNRS, Université Paris 7, Sorbonne Paris Cité, Paris, France DISI, Università di Bologna, INRIA, Bologna, Italy
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Abstract

The resource λ-calculus is a variation of the λ-calculus where arguments are superpositions of terms and must be linearly used; hence, it is a model for linear and non-deterministic programming languages. Moreover, it is the target language of the Taylor–Ehrhard–Regnier expansion of λ-terms, a linearisation of the λ-calculus which develops ordinary terms into infinite series of resource terms. In a strictly typed restriction of the resource λ-calculus, we study the notion of path persistence, and define a remarkably simple geometry of resource interaction (GoRI) that characterises it. In addition, GoRI is invariant under reduction and counts addends in normal forms. We also analyse expansion on paths in ordinary terms, showing that reduction commutes with expansion and, consequently, that persistence can be transferred back and forth between a path and its expansion. Lastly, we also provide an expanded counterpart of the execution formula, which computes paths as series of objects of GoRI; thus, exchanging determinism and conciseness for linearity and simplicity.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 5: Linearity 2014 , May 2018 , pp. 667 - 709
Copyright
Copyright © Cambridge University Press 2016 

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