# A Taste of Linear Logic

@inproceedings{Wadler1993ATO, title={A Taste of Linear Logic}, author={Philip Wadler}, booktitle={MFCS}, year={1993} }

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.

## 108 Citations

A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models (Extended Abstract)

- Philosophy, MathematicsCSL
- 1994

Intuitionistic linear logic regains the expressive power of intuitionistic logic through the ! (‘of course’) modality and an associated notion of categorical model in which the ! modality is modelled by a comonad satisfying certain extra conditions.

From Indexed Lax Logic to Intuitionistic Logic

- Philosophy, Computer Science
- 2008

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

- Computer Science2017 IEEE 15th International Symposium on Applied Machine Intelligence and Informatics (SAMI)
- 2017

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

- Computer ScienceMFPS
- 1993

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.

Linear logic, monads and the lambda calculus

- Philosophy, Computer ScienceProceedings 11th Annual IEEE Symposium on Logic in Computer Science
- 1996

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

- Computer ScienceLog. J. IGPL
- 1994

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.

Quantum Computation, Categorical Semantics and Linear Logic

- MathematicsArXiv
- 2003

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

- Computer ScienceArXiv
- 2010

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

- Computer Science
- 1995

The diierent calling mechanisms can be explained in terms of logical translations, bringing them into the scope of the Curry-Howard isomorphism.

## 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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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.

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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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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

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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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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.