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Hybrid Intersection Types for PCF

17 pagesPublished: May 26, 2024


Intersection type systems have been independently applied to different evaluation strate- gies, such as call-by-name (CBN) and call-by-value (CBV). These type systems have been then generalized to different subsuming paradigms being able, in particular, to encode CBN and CBV in a unique unifying framework. However, there are no intersection type systems that explicitly enable CBN and CBV to cohabit together, without making use of an encoding into a common target framework.
This work proposes an intersection type system for a specific notion of evaluation for PCF, called PCFH. Evaluation in PCFH actually has a hybrid nature, in the sense that CBN and CBV operational behaviors cohabit together. Indeed, PCFH combines a CBV- like behavior for function application with a CBN-like behavior for recursion. This hybrid nature is reflected in the type system, which turns out to be sound and complete with respect to PCFH: not only typability implies normalization, but also the converse holds. Moreover, the type system is quantitative, in the sense that the size of typing derivations provides upper bounds for the length of the reduction sequences to normal form. This first type system is then refined to a tight one, offering exact information regarding the length of normalization sequences. This is the first time that a sound and complete quantitative type system has been designed for a hybrid computational model.

Keyphrases: call-by-name, call-by-value, evaluation strategies, intersection types, lambda calculus, quantitative models

In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 181--197

BibTeX entry
  author    = {Pablo Barenbaum and Delia Kesner and Mariana Milicich},
  title     = {Hybrid Intersection Types for PCF},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bj\{\textbackslash{}o\}rner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  pages     = {181--197},
  year      = {2024},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/gvzx}}
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