The calculus λπ

  • L. M. G. Feijs
Part II The Design Language COLD
Part of the Lecture Notes in Computer Science book series (LNCS, volume 394)


We introduce a special version of lambda calculus called λπ, which is defined for any algebraic system with preorder. We do not have lambda terms λx.X, but we have terms λxR.X, where R is a parameter restriction. The effect of the parameter restrictions is formalised by the rules of the calculus. Instead of the rule β there is a rule called π. This calculus has been used to give a meaning to the parameterisation and design constructs of COLD-K.


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  1. [1]
    W.E. BAATS, L.M.G. FEIJS, J.H.A. Gelissen. A Formal Specification of INGRES, this volume.Google Scholar
  2. [2]
    H. BARENDREGT. The Lambda Calculus, its Syntax and Semantics, (Revised Edition), North-Holland, Amsterdam, (1984).Google Scholar
  3. [3]
    H. BARENDREGT, M. COPPO, M. DEZANI-CIANCAGLINI. A Filter Lambda Model and the Completeness of Type Assignment, Journal of Symbolic Logic, 48 (1983), 931–940.Google Scholar
  4. [4]
    L.M.G. Feijs. A Formalisation of Design Structures. Proceedings of CompEuro 88, Brussels, April 1988. Computer Society IEEE.Google Scholar
  5. [5]
    L.M.G. Feijs, H.B.M. Jonkers, C.P.J. Koymans, G.R. Renardel de Lavalette. Formal definition of the design language COLD-K, Preliminary edition. ESPRIT document METEOR/t7/PRLE/7.Google Scholar
  6. [6]
    H.B.M. Jonkers. Description Algebra, this volume.Google Scholar
  7. [7]
    C.P.J. Koymans, G.R. Renardel de Lavalette. The Logic MPL ω. this volume.Google Scholar
  8. [8]
    M. WIRSING. Structured Algebraic Specifications: a Kernel Language, Habilitation thesis, Technische Universität München (1983).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • L. M. G. Feijs
    • 1
  1. 1.Philips Research Laboratories EindhovenEindhovenThe Netherlands

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