The Delta-Framework

Authors Furio Honsell, Luigi Liquori, Claude Stolze, Ivan Scagnetto

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Furio Honsell
  • Dept. of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze, 206, 33100 Udine, Italy
Luigi Liquori
  • Université Côte d'Azur, INRIA Sophia Antipolis - Méditerranée 2004 Route des Lucioles - BP 93 FR-06902 Sophia Antipolis, France
Claude Stolze
  • Université Côte d'Azur, INRIA Sophia Antipolis - Méditerranée 2004 Route des Lucioles - BP 93 FR-06902 Sophia Antipolis, France
Ivan Scagnetto
  • Dept. of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze, 206, 33100 Udine, Italy

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Furio Honsell, Luigi Liquori, Claude Stolze, and Ivan Scagnetto. The Delta-Framework. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 37:1-37:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We introduce the Delta-framework, LF_Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union. Strong proof-functional connectives take into account the shape of logical proofs, thus reflecting polymorphic features of proofs in formulae. This is in contrast to classical or intuitionistic connectives where the meaning of a compound formula depends only on the truth value or the provability of its subformulae. Our framework encompasses a wide range of type disciplines. Moreover, since relevant implication permits to express subtyping, LF_Delta subsumes also Pfenning's refinement types. We discuss the design decisions which have led us to the formulation of LF_Delta, study its metatheory, and provide various examples of applications. Our strong proof-functional type theory can be plugged in existing common proof assistants.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Logic of programs
  • type theory
  • lambda-calculus


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