Types of Fireballs

Beniamino Accattoli, Giulio Guerrieri

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

21 Citations (SciVal)


The good properties of Plotkin’s call-by-value lambda-calculus crucially rely on the restriction to weak evaluation and closed terms. Open call-by-value is the more general setting where evaluation is weak but terms may be open. Such an extension is delicate and the literature contains a number of proposals. Recently, we provided operational and implementative studies of these proposals, showing that they are equivalent with respect to termination, and also at the level of time cost models. This paper explores the denotational semantics of open call-by-value, adapting de Carvalho’s analysis of call-by-name via multi types (aka non-idempotent intersection types). Our type system characterises normalisation and thus provides an adequate relational semantics. Moreover, type derivations carry quantitative information about the cost of evaluation: their size bounds the number of evaluation steps and the size of the normal form, and we also characterise derivations giving exact bounds. The study crucially relies on a new, refined presentation of the fireball calculus, the simplest proposal for open call-by-value, that is more apt to denotational investigations.

Original languageEnglish
Title of host publicationProgramming Languages and Systems - 16th Asian Symposium, APLAS 2018, Proceedings
EditorsSukyoung Ryu
PublisherSpringer Verlag
Number of pages22
ISBN (Print)9783030027674
Publication statusPublished - 15 Nov 2018
Event16th Asian Symposium on Programming Languages and Systems, APLAS 2018 - Wellington, New Zealand
Duration: 2 Dec 20186 Dec 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11275 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th Asian Symposium on Programming Languages and Systems, APLAS 2018
Country/TerritoryNew Zealand

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


Dive into the research topics of 'Types of Fireballs'. Together they form a unique fingerprint.

Cite this