A Core Quantitative Coeffect Calculus

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8410)


Linear logic is well known for its resource-awareness, which has inspired the design of several resource management mechanisms in programming language design. Its resource-awareness arises from the distinction between linear, single-use data and non-linear, reusable data. The latter is marked by the so-called exponential modality, which, from the categorical viewpoint, is a (monoidal) comonad.

Monadic notions of computation are well-established mechanisms used to express effects in pure functional languages. Less well-established is the notion of comonadic computation. However, recent works have shown the usefulness of comonads to structure context dependent computations. In this work, we present a language \(\ell \mathcal{R}\) PCF inspired by a generalized interpretation of the exponential modality. In \(\ell \mathcal{R}\) PCF the exponential modality carries a label—an element of a semiring \(\mathcal{R}\)—that provides additional information on how a program uses its context. This additional structure is used to express comonadic type analysis.


Type System Natural Transformation Operational Semantic Linear Logic Observable Quantity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.CNRS, UMR 7030, LIPN, Sorbonne Paris CitéUniversité Paris 13France
  2. 2.University of DundeeUK
  3. 3.University of PennsylvaniaUSA

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