Syntactic equivalences inducing semantic equivalences

  • P-L. Curien
Constructive And Combinatory Logic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


Following the idea behind algebraic theories we define a fairly general notion of equivalence between two many-sorted equational presentations s.t. an equivalence is induced on the corresponding categories of models. This definition allows to bring down to a symbolic level some equivalences known to model theorists. We illustrate this for the known connection between λ-calculus and cartesian closed categories. We present a syntactic equivalence between an "untyped" version of cartesian closed categories (i.e. where objects are dropped), and cartesian closed categories with a universal object, isomorphic to its product and function spaces, thus relating at a purely syntactic level an untyped calculus and a typed calculus. Direct syntactic equivalences between λ-calculus and cartesian closed categories are explored in companion papers: the direction from cartesian closed categories may be used for an elegant solution of the word problem of cartesian closed categories, whereas the direction to cartesian closed categories offer simple and efficient techniques for implementing functional programming languages, well suited for special VLSI design.


Word Problem Companion Paper Combinatory Logic Source Language Symbolic Level 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • P-L. Curien
    • 1
  1. 1.Tour 55-56 1er étageCNRS-Université Paris VII, LITPParis Cedex 05

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