Combinatorial problems, combinator equations and normal forms

  • Corrado Böhm
  • Mariangiola Dezani-Ciancaglini
Tuesday Morning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 14)


Some cases of solvability of the convertibility equation MX=N, where M,N and X are normal forms of the λ-K-β-calculus are considered and their relationship to pattern-matching problems is discussed. In particular, the solvability of such an equation is decided in the cases:
  1. i)

    N ≡ I and M = BF

  2. ii)

    N ≡ I and M = CBF where F is a normal form

  3. iii)

    N is an arbitrary normal form.


For this purpose, a polynomial representation and subsequently a tree representation of normal forms are introduced.


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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Corrado Böhm
    • 1
  • Mariangiola Dezani-Ciancaglini
    • 1
  1. 1.Istituto di Scienza dell'Informazione dell'Università di TorinoTorino

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