• Corpus ID: 118739437

On Intuitionistic Linear Logic

  title={On Intuitionistic Linear Logic},
  author={Gavin M. Bierman and Torben Brauner and Paul Curzon and Francis Davey},
A linear-non-linear model for a computational call-by-value lambda calculus (extended abstract)
A categorical semantics for a call-by-value linear lambda calculus, which was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation, and gives a combination of a monad and a comonad that makes the present paper interesting.
Dialectica Categories for the Lambek Calculus
The Lambek Calculus is extended with a \kappa modality, inspired by Yetter's work, which makes the calculus commutative and of-course modality ! is added, as Girard did, to re-introduce weakening and contraction for all formulas and get back the full power of intuitionistic and classical logic.
A Cointuitionistic Adjoint Logic
The dual to LNL models which are studied are shown to correspond to dual linear categories, the dual to Bierman's linear categories proposed by Bellin, and the definition of bi-LNL models is given, which are a corresponding sequent calculus, natural deduction, and term assignment for dual LNLmodels.
Multiple Conclusion Linear Logic: Cut Elimination and More
This note adopts Bellin’s proposed change to the definition of FILL and gives a direct proof of cut-elimination and a double-negation translation of linear logic into FILL that explicitly uses par in addition to tensor.
Practical programming with substructural types
This dissertation presents the design of a general purpose language with substructureural types, and discusses several language design problems that had to be solved in order to make substructural types useful in practice.
1 Quantum Lambda Calculus
The quantum lambda calculus is defined and safety invariants, such as the no-cloning property, are enforced by a static type system that is based on intuitionistic linear logic.
Sequent Calculi without Polarities for the Unity of Logic
The present work aims to establish the unity of logic in the same sense as Girard's well-known work yet without having recourse to polarities. Our motivations are to reduce various logics into a
Two Applications of Logic Programming to Coq
This paper implements in Elpi a proof checker for first-order intuitionistic logic and demonstrates how proof certificates can be supplied by external Coq provers and then elaborated into the fully detailed proof terms that can be checked by the Coq kernel.
Explicit construction of cofree precoalgebras and coalgebras
In this paper, we will explicitly construct cofree coalgebras, by first constructing cofree precoalgebras (namely those not necessarily coassociative or counital). Our approach does not impose any
Implicit automata in typed λ-calculi II: streaming transducers vs categorical semantics
A connection between a feature of streaming tree transducers and the multiplicative/additive distinction of linear logic is exhibited and generalized from strings to trees using a similar approach.


The formulae-as-types notion of construction
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.
Eds). Haskell: A non-strict, purely functional language
  • ACM SIGPLAN Notices,
  • 1992
The Collected Papers of Gerhard Gentzen
Linear Logic and Lazy Computation
Recently, J.Y. Girard discovered that usual logical connectors such as ⇒ (implication) could be broken up into more elementary linear connectors, providing a new linear logic where hypothesis are used once and only once.
A new implementation technique for applicative languages
  • D. Turner
  • Computer Science
    Softw. Pract. Exp.
  • 1979
It is shown how by using results from combinatory logic an applicative language, such as LISP, can be translated into a form from which all bound variables have been removed. A machine is described
Computational Interpretations of Linear Logic
There's No Substitute for Linear Logic
An alternative syntax is proposed, that has striking parallels to Moggi's language for monads, that eliminates some terms look like the identity that should not, and vice versa; the new syntax eliminates this awkwardness.
Linear Logic, -Autonomous Categories and Cofree Coalgebras
A brief outline of the categorical characterisation of Girard's linear logic is given, analagous to the relationship between cartesian closed categories and typed-calculus. The linear structure
Linear logic
This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.
Natural Deduction, volume 3 of Stockholm Studies in Philosophy
  • Almqvist and Wiksell,
  • 1965