What is a model for a semantically linear λ-calculus?

@article{Gaboardi2014WhatIA,
  title={What is a model for a semantically linear $\lambda$-calculus?},
  author={Marco Gaboardi and M. Piccolo},
  journal={J. Log. Comput.},
  year={2014},
  volume={24},
  pages={557-589}
}
This paper is about a categorical approach to model a simple term calculus, named S�λ - calculus. This is the core calculus underlying the programming language SPCF that have been conceived in order to program only linear functions between Coherence Spaces. In this work, we introduce the notion of S�λ -category, which is able to describe a large class of sound models of S�λ -calculus. S�λ -category extends in the natural way Benton, Bierman, Hyland and de Paiva's Linear Category. We will define… Expand

References

SHOWING 1-10 OF 36 REFERENCES
Categorical Models for a Semantically Linear Lambda-calculus
TLDR
Sll-Category is introduced, which is able to describe a very large class of sound models of Sll-calculus, and extends in the natural way Benton, Bierman, Hyland and de Paiva's Linear Category, in order to soundly interpret all the constructs of S%calculus. Expand
Finiteness spaces
  • T. Ehrhard
  • Computer Science, Mathematics
  • Mathematical Structures in Computer Science
  • 2005
TLDR
A new denotational model of linear logic based on the purely relational model, where webs are equipped with a notion of ‘finitary’ subsets satisfying a closure condition and proofs are interpreted as finitary sets is investigated. Expand
A Simple Adequate Categorical Model for PCF
TLDR
An axiomatic approach to adequacy for PCF is presented, in the sense that categorical axioms enabling an adequate semantics to be given are introduced, which takes the point of view that partiality is the fundamental notion from which order-structure should be derived. Expand
Linearity and PCF: a semantic insight!
TLDR
A language is introduced, named SlPCF*, that increases the higher-order expressivity of a linear core of PCF by means of new operators related to exception handling and parallel evaluation, and formalizes two evaluation machineries for the language. Expand
Linear Lambda-Calculus and Categorial Models Revisited
TLDR
In this paper, multiplicative exponential linear logic (MELL) is considered, i.e. the fragment which has multiplicative conjunction or tensor, , linear implication,, and the logical operator, `!', which allows a formula to be used as many times as required (including zero). Expand
Not Enough Points Is Enough
TLDR
It is shown that any categorical model of λ-calculus can be presented as aλ-model, even when the underlying category does not have enough points. Expand
An internal language for autonomous categories
TLDR
The language proposed is the term assignment to the multiplicative fragment of Intuitionistic Linear Logic, which possesses exactly the right structure for an autonomous theory and is proved an internal language for symmetric monoidal closed (autonomous) categories. Expand
A Term Calculus for Intuitionistic Linear Logic
TLDR
This paper considers the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems and explores the relationship between these and considers their computational content. Expand
Full abstraction for a Linear PCF
We study SPCF� , namely a Turing-complete programming lan- guage inspired by a semantic notion of linearity. SPCFis based on a linear core of PCF and some operators providing basic primi- tivesExpand
A stable programming language
TLDR
In this paper, a paradigmatic programming language named St PCF is proposed, which extends the language PCF with two additional operators, although the evaluation of one of the new operators cannot be formalized in a PCF-like rewrite system. Expand
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