Tridirectional Typechecking (TR version)

Technical report CMU-CS-04-117

Joshua Dunfield and Frank Pfenning

Abstract

In prior work we introduced a pure type assignment system that encompasses a rich set of property types, including intersections, unions, and universally and existentially quantified dependent types. This system was shown sound with respect to a call-by-value operational semantics with effects, yet is inherently undecidable.

In this paper we provide a decidable formulation for this system based on bidirectional checking, combining type synthesis and analysis following logical principles. The presence of unions and existential quantification requires the additional ability to visit subterms in evaluation position before the context in which they occur, leading to a tridirectional type system. While soundness with respect to the type assignment system is immediate, completeness requires the novel concept of contextual type annotations, introducing a notion from the study of principal typings into the source program.

Reader’s guide

This is the technical report version of our POPL paper. It contains full proofs, as well as some remarks omitted from the paper due to space constraints.

Official version (March 2004)

BibTeX entry

   @TechReport{ Dunfield04:TridirectionalTR,
      author =      {Joshua Dunfield and Frank Pfenning},
      title =       {Tridirectional Typechecking},
      institution = {Carnegie Mellon University},
      year =        {2004},
      number =      {CMU-CS-04-117},
      month =       mar,
      note =        {Extended version of \cite{Dunfield04:Tridirectional}}
    }
  

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