Linear Dependent Types and Relative Completeness

Lago, Ugo Dal; Gaboardi, Marco

doi:10.2168/lmcs-8(4:11)2012

Cited by 17 publications

(21 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This allows for more flexibility, and ultimately for a better intensionality. Indeed, having the freedom of not adopting a fixed index language is known to lead towards completeness [5].…”

Section: Our Type System At a Glancementioning

confidence: 99%

“…Our type system can estimate the size of the clock in the ticked programP, and thus the runtime of the considered program P. Noteworthy, this transformation is straight forward to implement. 5 product ms ns = foldr (λ m ps. foldr (λ n. (:) (m,n)) ps ns) [] ms Figure 2: Sized type annotated program computing the cross-product of two lists.…”

Section: Polymorphic Recursion Over Sizes Type Inference In Functionmentioning

confidence: 99%

“…Estimating the size of intermediate results is crucial for complexity analysis, but up to now, the only attempt of using sized types for complexity analysis is due to Vasconcelos [10], and confined to space complexity. If one wants to be sound for time analysis, size types need to be further refined, e.g., by turning them into linear dependently types [5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Automated Sized-Type Inference and Complexity Analysis

Avanzini

Lago

2017

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking monadic transformation and a concrete tool for constraint solving. Noticeably, the presented methodology can be fully automated, and is able to analyse a series of examples which cannot be handled by most competitor methodologies. This is possible due to various key ingredients, and in particular an abstract index language and index polymorphism at higher ranks. A prototype implementation is available.Comment: In Proceedings DICE-FOPARA 2017, arXiv:1704.0516

show abstract

“…This allows for more flexibility, and ultimately for a better intensionality. Indeed, having the freedom of not adopting a fixed index language is known to lead towards completeness [5].…”

Section: Our Type System At a Glancementioning

confidence: 99%

Section: Polymorphic Recursion Over Sizes Type Inference In Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Automated Sized-Type Inference and Complexity Analysis

Avanzini

Lago

2017

Electron. Proc. Theor. Comput. Sci.

Self Cite

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%

“…The BLL type system has been already generalized by Dal Lago and collaborators to Linear Dependent Types (LDT) [4,6]. This greatly increases the expressiveness of the type system but at the expense of losing decidability.…”

Section: Related Workmentioning

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

Types for Complexity of Parallel Computation in Pi-Calculus

Ghyselen

2021

Programming Languages and Systems

View full text Add to dashboard Cite

Type systems as a technique to analyse or control programs have been extensively studied for functional programming languages. In particular some systems allow to extract from a typing derivation a complexity bound on the program. We explore how to extend such results to parallel complexity in the setting of the pi-calculus, considered as a communication-based model for parallel computation. Two notions of time complexity are given: the total computation time without parallelism (the work) and the computation time under maximal parallelism (the span). We define operational semantics to capture those two notions, and present two type systems from which one can extract a complexity bound on a process. The type systems are inspired both by size types and by input/output types, with additional temporal information about communications.

show abstract

Linear Dependent Types and Relative Completeness

Cited by 17 publications

References 37 publications

Automated Sized-Type Inference and Complexity Analysis

Automated Sized-Type Inference and Complexity Analysis

Bounded Linear Types in a Resource Semiring

Types for Complexity of Parallel Computation in Pi-Calculus

Contact Info

Product

Resources

About