Principal typings for explicit substitutions calculi

Daniel Lima Ventura, Mauricio Ayala-Rincón, Fairouz Kamareddine

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Having principal typings (for short PT) is an important property of type systems. In simply typed systems, this property guarantees the possibility of a complete and terminating type inference mechanism. It is well-known that the simply typed ?-calculus has this property but recently J.B. Wells has introduced a system-independent definition of PT, which allows to prove that some type systems, e.g. the Hindley/Milner type system, do not satisfy PT. Explicit substitutions address a major computational drawback of the ?-calculus and allow the explicit treatment of the substitution operation to formally correspond to its implementation. Several extensions of the ?-calculus with explicit substitution have been given but some of which do not preserve basic properties such as the preservation of strong normalization. We consider two systems of explicit substitutions (?s e and ?s) and show that they can be accommodated with an adequate notion of PT. Specifically, our results are as follows: We introduce PT notions for the simply typed versions of the ?s e - and the ?s-calculi and prove that they agree with Wells' notion of PT. We show that these versions satisfy PT by revisiting previously introduced type inference algorithms. © 2008 Springer-Verlag Berlin Heidelberg.

Original languageEnglish
Title of host publicationLogic and Theory of Algorithms - 4th Conference on Computability in Europe, CiE 2008, Proceedings
Number of pages12
Volume5028 LNCS
Publication statusPublished - 2008
Event4th Conference on Computability in Europ - Athens, Greece
Duration: 15 Jun 200820 Jun 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5028 LNCS
ISSN (Print)0302-9743


Conference4th Conference on Computability in Europ
Abbreviated titleCiE 2008


  • Explicit substitution
  • Lambda-calculus
  • Principal typings


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