Towards extracting explicit proofs from totality checking in twelf

Yuting Wang, Gopalan Nadathur

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

5 Scopus citations

Abstract

The Edinburgh Logical Framework (LF) is a dependently type λ-calculus that can be used to encode formal systems. The versatility of LF allows specifications to be constructed also about the encoded systems. The Twelf system exploits the correspondence between formulas and types to give specifications in LF a logic programming interpretation. By interpreting particular arguments as input and others as output, specifications can be seen as describing non-deterministic functions. We can then prove meta-theorems about the encoded systems by showing particular such functions to be total. Twelf provides tools for establishing totality. However, the resulting proofs of meta-theorems are implicit in that they do not yield a certificate that can be given to a proof checker. We begin the process here of making these proofs explicit. We treat the restricted situation in Twelf where context definitions (regular worlds), mutually recursive definitions and lemmas are not used. In this setting we describe and prove correct a translation of the steps in totality checking into an actual proof in the companion logic M2.

Original languageEnglish (US)
Title of host publicationLFMTP 2013 - Proceedings of the 2013 ACM SIGPLAN Workshop on Logical Frameworks and Meta-Languages
Subtitle of host publicationTheory and Practice, Co-located with ICFP 2013
Pages55-66
Number of pages12
DOIs
StatePublished - Oct 21 2013
Event8th International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, LFMTP 2013 - Co-located with the 18th ACM SIGPLAN International Conference on Functional Programming, ICFP 2013 - Boston, MA, United States
Duration: Sep 23 2013Sep 23 2013

Publication series

NameProceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP

Other

Other8th International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, LFMTP 2013 - Co-located with the 18th ACM SIGPLAN International Conference on Functional Programming, ICFP 2013
Country/TerritoryUnited States
CityBoston, MA
Period9/23/139/23/13

Keywords

  • Dependently typed λ-calculi
  • Proof certificates
  • Specification and reasoning
  • Totality checking

Fingerprint

Dive into the research topics of 'Towards extracting explicit proofs from totality checking in twelf'. Together they form a unique fingerprint.

Cite this