Dependent types from counterexamples

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

30 Citations (Scopus)

Abstract

Motivated by recent research in abstract model checking, we present a new approach to inferring dependent types. Unlike many of the existing approaches, our approach does not rely on programmers to supply the candidate (or the correct) types for the recursive functions and instead does counterexample- guided refinement to automatically generate the set of candidate dependent types. The main idea is to extend the classical fixed-point type inference routine to return a counterexample if the program is found untypable with the current set of candidate types. Then, an interpolating theorem prover is used to validate the counterexample as a real type error or generate additional candidate dependent types to refute the spurious counterexample. The process is repeated until either a real type error is found or sufficient candidates are generated to prove the program typable. Our system makes non-trivial use of "linear" intersection types in the refinement phase. The paper presents the type inference system and reports on the experience with a prototype implementation that infers dependent types for a subset of the Ocaml language. The implementation infers dependent types containing predicates from the quantifier-free theory of linear arithmetic and equality with uninterpreted function symbols.

Original languageEnglish
Title of host publicationPOPL'10 - Proceedings of the 37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Pages119-130
Number of pages12
DOIs
Publication statusPublished - 2010 Apr 20
Externally publishedYes
Event37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL'10 - Madrid, Spain
Duration: 2010 Jan 172010 Jan 23

Publication series

NameConference Record of the Annual ACM Symposium on Principles of Programming Languages
ISSN (Print)0730-8566

Other

Other37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL'10
CountrySpain
CityMadrid
Period10/1/1710/1/23

Keywords

  • Counterexamples
  • Dependent types
  • Interpolation
  • Intersection types
  • Type inference

ASJC Scopus subject areas

  • Software

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