Logic of Programs 1985: Logics of Programs pp 225-236 | Cite as

Second-order logical relations

Extended abstract
  • John C. Mitchell
  • Albert R. Meyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 193)


Logical relations are a generalization of homomorphisms between models of typed lambda calculus. We define logical relations for second-order typed lambda calculus and use these relations to give a semantic characterization of second-order lambda definability. Logical relations are also used to state and prove a general representation independence theorem. Representation independence implies that the meanings of expressions do not depend on whether true is represented by 1 and false by 0, as long as all the functions that manipulate truth values are represented correctly.


Inference Rule Fundamental Theorem Logical Relation Type Expression Type Inference 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • John C. Mitchell
    • 1
  • Albert R. Meyer
    • 2
  1. 1.AT&T Bell LaboratoriesMurray Hill
  2. 2.MIT Laboratory for Computer ScienceCambridge

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