@Article{         StatmanDowek,
  Author        = "Statman, Richard and Dowek, Gilles",
  Abstract      = "We give a complete self-contained proof of Statman's finite completeness theoremand of a corollary of this theorem stating that the -definability conjectureimplies the higher-order matching conjecture.Keywords: simply typed lambda-calculus, finite model, lambda-definability,higher-order matchingThe purpose of this note is to give a complete self-contained proof ofStatman's finite completeness theorem and of a corollary of this theoremstating that the -definability conjecture implies the higher-order matchingconjecture. Both results are proved in {$[$}8{$]$} (theorem 2 and 5). Although, since{$[$}8{$]$} assumes some familiarity with typed -calculus model theory and presentsseveral results in short space, it may be not very accessible to readers notfamiliar with this subject.Section 1 gives the basic notations used in the paper. The reader notfamiliar with simply typed -calculus should consult Hindley and Seldin {$[$}3{$]$}.Section 2 presents standard models for simply typed -calculus, it is...",
  Address       = "School of Computer Science; Carnegie Mellon University",
  date-added    = "2013-02-15 16:53:38 +0000",
  date-modified = "2013-02-15 16:53:46 +0000",
  Keywords      = "lambda calculus",
  Title         = "On Statman's Finite Completeness Theorem",
  ty            = "JOUR",
  URL           = "http://europepmc.org/abstract/CIT/227814",
  bdsk-url-1    = "http://europepmc.org/abstract/CIT/227814",
  File          = "On Statman's Finite Completeness Theorem - Statman, Dowek (0) (0) - a - a - u.pdf"
}

@Article{ StatmanDowek, Author = "Statman, Richard and Dowek, Gilles", Abstract = "We give a complete self-contained proof of Statman's finite completeness theoremand of a corollary of this theorem stating that the -definability conjectureimplies the higher-order matching conjecture.Keywords: simply typed lambda-calculus, finite model, lambda-definability,higher-order matchingThe purpose of this note is to give a complete self-contained proof ofStatman's finite completeness theorem and of a corollary of this theoremstating that the -definability conjecture implies the higher-order matchingconjecture. Both results are proved in {$[$}8{$]$} (theorem 2 and 5). Although, since{$[$}8{$]$} assumes some familiarity with typed -calculus model theory and presentsseveral results in short space, it may be not very accessible to readers notfamiliar with this subject.Section 1 gives the basic notations used in the paper. The reader notfamiliar with simply typed -calculus should consult Hindley and Seldin {$[$}3{$]$}.Section 2 presents standard models for simply typed -calculus, it is...", Address = "School of Computer Science; Carnegie Mellon University", date-added = "2013-02-15 16:53:38 +0000", date-modified = "2013-02-15 16:53:46 +0000", Keywords = "lambda calculus", Title = "On Statman's Finite Completeness Theorem", ty = "JOUR", URL = "http://europepmc.org/abstract/CIT/227814", bdsk-url-1 = "http://europepmc.org/abstract/CIT/227814", File = "On Statman's Finite Completeness Theorem - Statman, Dowek (0) (0) - a - a - u.pdf" }