DeepAI

# Linear Rank Intersection Types

Non-idempotent intersection types provide quantitative information about typed programs, and have been used to obtain time and space complexity measures. Intersection type systems characterize termination, so restrictions need to be made in order to make typability decidable. One such restriction consists in using a notion of finite rank for the idempotent intersection types. In this work, we define a new notion of rank for the non-idempotent intersection types. We then define a novel type system and a type inference algorithm for the lambda-calculus, using the new notion of rank 2. In the second part of this work, we extend the type system and the type inference algorithm to use the quantitative properties of the non-idempotent intersection types to infer quantitative information related to resource usage.

• 1 publication
• 8 publications
• 6 publications
02/15/2019

### Types by Need (Extended Version)

A cornerstone of the theory of lambda-calculus is that intersection type...
04/26/2022

### Structural Rules and Algebraic Properties of Intersection Types

In this paper we define several notions of term expansion, used to defin...
11/05/2019

### Non-idempotent intersection types in logical form

Intersection types are an essential tool in the analysis of operational ...
03/06/2013

### Inference Algorithms for Similarity Networks

We examine two types of similarity networks each based on a distinct not...
04/23/2019

### Intersection Types for Unboundedness Problems

Intersection types have been originally developed as an extension of sim...
07/18/2022

### Multi Types and Reasonable Space (Long Version)

Accattoli, Dal Lago, and Vanoni have recently proved that the space used...
12/04/2019

### A Quantitative Understanding of Pattern Matching

This paper shows that the recent approach to quantitative typing systems...