DeepAI AI Chat
Log In Sign Up

The Bang Calculus Revisited

02/10/2020
by   Antonio Bucciarelli, et al.
0

Call-by-Push-Value (CBPV) is a programming paradigm subsuming both Call-by-Name (CBN) and Call-by-Value (CBV) semantics. The paradigm was recently modelled by means of the Bang Calculus, a term language connecting CBPV and Linear Logic. This paper presents a revisited version of the Bang Calculus, called λ !, enjoying some important properties missing in the original system. Indeed, the new calculus integrates commutative conversions to unblock value redexes while being confluent at the same time. A second contribution is related to non-idempotent types. We provide a quantitative type system for our λ !-calculus, and we show that the length of the (weak) reduction of a typed term to its normal form plus the size of this normal form is bounded by the size of its type derivation. We also explore the properties of this type system with respect to CBN/CBV translations. We keep the original CBN translation from λ-calculus to the Bang Calculus, which preserves normal forms and is sound and complete with respect to the (quantitative) type system for CBN. However, in the case of CBV, we reformulate both the translation and the type system to restore two main properties: preservation of normal forms and completeness. Last but not least, the quantitative system is refined to a tight one, which transforms the previous upper bound on the length of reduction to normal form plus its size into two independent exact measures for them.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/02/2021

The Power of Tightness for Call-By-Push-Value

We propose tight type systems for Call-by-Name (CBN) and Call-by-Value (...
02/07/2022

Call-by-Value Solvability and Multi Types

This paper provides a characterization of call-by-value solvability usin...
12/04/2019

A Quantitative Understanding of Pattern Matching

This paper shows that the recent approach to quantitative typing systems...
12/27/2018

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus (Long Version)

We investigate the possibility of a semantic account of the execution ti...
03/15/2023

Quantitative Global Memory

We show that recent approaches of static analysis based on quantitative ...
04/26/2019

A certifying extraction with time bounds from Coq to call-by-value λ-calculus

We provide a plugin extracting Coq functions of simple polymorphic types...
02/15/2018

Non-idempotent types for classical calculi in natural deduction style

In the first part of this paper, we define two resource aware typing sys...