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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References

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A Syntax for Linear Logic
TLDR
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.
Computational Interpretations of Linear Logic
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TLDR
This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.
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TLDR
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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 system.
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TLDR
The ultimate goal was to develop a notion of construction suitable for the interpretation of intuitionistic mathematics, so the use of the word construction is not very appropriate, but the terminology has been kept in order to preserve the original title.
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We examine three disparate views of the type structure of programming languages: Milner's type deduction system and polymorphic let construct, the theory of subtypes and generic operators, and the
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
This work is able to devise a type system that combines types and modes into a unified framework, and enables one to express directionality declaratively, and brings logic programming into the broader world of typed languages and types-as-propositions paradigm.
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