Bounded Linear Logic, Revisited

Lago, Ugo Dal; Hofmann, Martin

doi:10.2168/lmcs-6(4:7)2010

Cited by 10 publications

(3 citation statements)

References 18 publications

(17 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, we could consider a graded or indexed version of the same, i.e., □ , which only takes away a set of capabilities ∈ (C) from a value. Our hope would be that this could form a model of systems like bounded linear logic [Dal Lago and Hofmann 2009;Orchard et al 2019], or other systems of coeffects [Petricek et al 2014]. This use of qualifiers on contexts to encode linear resource behaviour appeared first in [Terui 2007], and was also used in the quantitative coeffect calculus in [Brunel et al 2014].…”

Section: Typesmentioning

confidence: 99%

Recovering purity with comonads and capabilities

Choudhury

Krishnaswami

2020

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

In this paper, we take a pervasively effectful (in the style of ML) typed lambda calculus, and show how to extend it to permit capturing pure expressions with types. Our key observation is that, just as the pure simplytyped lambda calculus can be extended to support effects with a monadic type discipline, an impure typed lambda calculus can be extended to support purity with a comonadic type discipline. We establish the correctness of our type system via a simple denotational model, which we call the capability space model. Our model formalises the intuition common to systems programmers that the ability to perform effects should be controlled via access to a permission or capability, and that a program is capability-safe if it performs no effects that it does not have a runtime capability for. We then identify the axiomatic categorical structure that the capability space model validates, and use these axioms to give a categorical semantics for our comonadic type system. We then give an equational theory (substitution and the call-by-value and laws) for the imperative lambda calculus, and show its soundness relative to this semantics. Finally, we give a translation of the pure simply-typed lambda calculus into our comonadic imperative calculus, and show that any two terms which are-equal in the STLC are equal in the equational theory of the comonadic calculus, establishing that pure programs can be mapped in an equation-preserving way into our imperative calculus.

show abstract

Section: Typesmentioning

confidence: 99%

Recovering purity with comonads and capabilities

Choudhury

Krishnaswami

2020

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

show abstract

“…Bounded Linear Logic (BLL) was subsequently extended to improve its flexibility while retaining poly-time [5] and further extensions to linear dependent typing were used to completely characterize complexity of evaluation of functional programs [4].…”

Section: Resource-aware Types and Semanticsmentioning

confidence: 99%

“…some form of resource-based polymorphism (cf. [5]) then a new structural rule would be required to handle type congruences induced by the semiring theory:…”

Section: Bounded Linear Types Over a Semiringmentioning

confidence: 99%

Bounded Linear Types in a Resource Semiring

Ghica

Smith

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce a bounded linear typing discipline on a general notion of resource which can be modeled in a semiring. For this type system we provide both a general type-inference procedure, parameterized by the decision procedure of the semiring equational theory, and a (coherent) categorical semantics. This could be a useful type-theoretic and denotational framework for resource-sensitive compilation, and it represents a generalization of several existing type systems. As a nontrivial instance, motivated by hardware compilation, we present a complex new application to calculating and controlling timing of execution in a (recursion-free) higher-order functional programming language with local store.

show abstract

Unification and Logarithmic Space

Aubert

Bagnol

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction. We show how unification can be used to build a model of computation by means of specific subalgebras associated to finite permutations groups. We then prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. We also show that the construction can naturally represent pointer machines, an intuitive way of understanding logarithmic space computing

show abstract

Bounded Linear Logic, Revisited

Cited by 10 publications

References 18 publications

Recovering purity with comonads and capabilities

Recovering purity with comonads and capabilities

Bounded Linear Types in a Resource Semiring

Unification and Logarithmic Space

Contact Info

Product

Resources

About