Higher order data structures

Cartesian closure versus λ-calculus
  • Axel Poigné
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)


We discuss connections of typed λ-calculus and cartesian closure and prove equivalence of the theories ‘up to abstraction’. This is a working out of ideas of Scott and Lambeck but in an abstract data type environment. The results serve as a basis for the discussion of higher order specifications. We demonstrate that higher order equations based on λ-calculus are more appropriate if the equivalence of λ-calculus and cartesian closure is to be preserved. We construct higher order theories for higher order specifications. For higher order models we discuss existence of initial models and completeness of higher order theories.


Axiom Scheme High Order Theory Denotational Semantic High Order Equation Abstract Data Type 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Axel Poigné
    • 1
  1. 1.Informatik IIUniversität DortmundDortmund 50Germany

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