A Taste of Linear Logic

@inproceedings{Wadler1993ATO,
  title={A Taste of Linear Logic},
  author={Philip Wadler},
  booktitle={MFCS},
  year={1993}
}
  • P. Wadler
  • Published in MFCS 30 August 1993
  • Philosophy, Computer Science
This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types”. The presentation of linear logic is simplified by basing it on the Logic of Unity. An application to the array update problem is briefly discussed. 
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108 Citations
Highly Influential Citations
10
Background Citations
38
Methods Citations
18
Results Citations
2

108 Citations

A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models (Extended Abstract)
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From Indexed Lax Logic to Intuitionistic Logic
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This work presents translations from a logic with indexed lax modalities to first-order intuitionistic logic and intuitionistic linear logic and shows that they preserve provability of formulas.
Hanoi towers in resource oriented perspective
The features of linear predicate logic (based on propositional linear logic enriched by the first order predicate logic principles) are implemented in logic programming language called Vorvan.…
A Syntax for Linear Logic
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A new solution to the problem that arises and a standard approach to its solution is proposed, based on ideas taken from Girard's Logic of Unity, allowing for concise expression of programs.
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  • Nick Benton, P. Wadler
  • Philosophy, Computer Science
    Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
  • 1996
TLDR
Models of intuitionistic linear logic also provide models of Moggi's computational metalanguage and the adjoint presentation of these models and the associated adjoint calculus is used to show that three translations of the lambda calculus into the computational metalanguages correspond exactly to three translations, due mainly to Girard, of intuitionist logic into intuitionisticlinear logic.
Applications of Linear Logic to Computation: An Overview
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An overview of existing applications of Linear Logic LL to issues of computation and the implications of LL to functional programming logic programming concurrent and object oriented programming and some other applications of LL are discussed.
A General Adequacy Result for a Linear Functional Language
Quantum Computation, Categorical Semantics and Linear Logic
TLDR
A type theory and denotational semantics are developed and provided for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic.
An affine-intuitionistic system of types and effects: confluence and termination
TLDR
An affine-intuitionistic system of types and effects is presented which can be regarded as an extension of Barber-Plotkin Dual Intuitionsistic Linear Logic to multi-threaded programs with effects and it is shown that a discipline of region stratification guarantees termination.
The Linear Lambda Calculus
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The diierent calling mechanisms can be explained in terms of logical translations, bringing them into the scope of the Curry-Howard isomorphism.
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References

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A new solution to the problem that arises and a standard approach to its solution is proposed, based on ideas taken from Girard's Logic of Unity, allowing for concise expression of programs.
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Is there a use for linear logic
TLDR
This paper defines a sequence of languages based on linear logic that span the gap between theory and practice that can derive information about sharing in a linear type sys- tem.
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TLDR
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