Lambda representation of operations between different term algebras

  • Marek Zaionc
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 933)


There is a natural isomorphism identifying second order types of the simple typed λ calculus with free homogeneous term algebras. Let τA and τB be types representing algebras A and B respectively. Any closed term of the type τAτB represents a computable function between algebras A and B. The problem investigated in the paper is to find and characterize the set of all λ definable functions between structures A and B. The problem is presented in a more general setting. If algebrasA1,..., A n ,B are represented respectively by second order types \(\tau ^{A_l } ,...,\tau ^{A_n } \), τB then \(\tau ^{A_l } \)→ (...(\(\tau ^{A_n } \)τB...) is a type of functions from the product A1×...xAn into algebra B. Any closed term of this type is a representation of algorithm which transforms the tuple of terms of types \(\tau ^{A_l } ,...,\tau ^{A_n } \) respectively into a term of type τB, which represents an object in algebra B (see [BöB85]). The problem investigated in the paper is to find an effective computational characteristic of the λ definable functions between arbitrary free algebras and the expressiveness of such transformations. As an example we will consider λ definability between well known free structures such as: numbers, words and trees. The result obtained in the paper is an extension of the results concerning λ definability in various free structures described in [Sch75] [Sta79] [Lei89] [Zai87] [Zai90] and [Zai91]


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Marek Zaionc
    • 1
  1. 1.Instytut InformatykiUniwersytet JagiellońskiKrakowPoland

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