Defining λ-typed λ-calculi by axiomatizing the typing relation

  • Philippe de Groote
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


We present a uniform framework for defining different gl-typed λ-calculi in terms of systems to derive typing judgements, akin to Barendregt's Pure Type Systems [3]. We first introduce a calculus called λλ and study its abstract properties. These are, among others, the property of Church-Rosser, the property of subject reduction, and the one of strong normalization. Then we show how to extend λλ to obtain an inferential definition. of Nederpelt's Λ [20]. One may also extend λλ to get inferential definitions of van Daalen Λ β [24], and de Bruijn's ΛΔ [9] and we argue that these new inferential definitions are well suited for language-theoretic investigations.


Logical Framework Typing Context Annual IEEE Symposium Applicability Condition Strong Normalization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Philippe de Groote
    • 1
  1. 1.INRIA-Lorraine-CRIN-CNRSVandœuvre-lès-Nancy CedexFrance

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