# Quantitative Types for the Linear Substitution Calculus

@inproceedings{Kesner2014QuantitativeTF, title={Quantitative Types for the Linear Substitution Calculus}, author={Delia Kesner and Daniel Lima Ventura}, booktitle={IFIP TCS}, year={2014} }

We define two non-idempotent intersection type systems for the linear substitution calculus, a calculus with partial substitutions acting at a distance that is a computational interpretation of linear logic proof-nets. The calculus naturally express linear-head reduction, a notion of evaluation of proof nets that is strongly related to abstract machines. We show that our first (resp. second) quantitave type system characterizes linear-head, head and weak (resp. strong) normalizing sets of terms…

## 28 Citations

### A resource aware semantics for a focused intuitionistic calculus

- Computer ScienceMathematical Structures in Computer Science
- 2017

A new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics is investigated and a type system based on non-idempotent intersection types is associated to Herbelin's syntax.

### Proof Nets and the Linear Substitution Calculus

- Computer Science, MathematicsICTAC
- 2018

It is shown that the linear substitution calculus, a simple refinement of the \(\lambda \)-calculus with sharing, is isomorphic to proof nets at the operational level.

### Proof Nets and the Linear Substitution Calculus Beniamino Accattoli

- Computer Science, Mathematics
- 2019

It is shown that the linear substitution calculus, a simple refinement of the λ-calculus with sharing, is isomorphic to proof nets at the operational level and suggests a new, abstract notion of proof net, based on rewriting considerations and not necessarily of a graphical nature.

### A Resource Aware Computational Interpretation for Herbelin's Syntax

- Computer ScienceICTAC
- 2015

A new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics is investigated and typability and the corresponding strong normalization characterization in the reduction calculus obtained from the former one are studied by projecting the explicit substitutions.

### Types as Resources for Classical Natural Deduction

- MathematicsFSCD
- 2017

Two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types are defined and typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences.

### 32 : 2 Types as Resources for Classical Natural Deduction

- Mathematics
- 2017

We define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments –based…

### Linear logic, type assignment systems and implicit computational complexity. (Logique linéaire, systèmes de types et complexité implicite)

- Computer Science
- 2015

In this thesis we explore the linear logic approach to implicit computational complexity, through the design of type assignment systems based on light linear logic, or heavily inspired by them, with…

### Non-idempotent intersection types for the Lambda-Calculus

- MathematicsLog. J. IGPL
- 2017

This article explores the use of non-idempotent intersection types in the framework of the λ-calculus by replacing the reducibility technique with trivial combinatorial arguments.

### A Strong Call-By-Need Calculus

- MathematicsFSCD
- 2021

A call-by-need λ-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once is presented and shown to be normalizing in a strong sense.

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