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Linearity and iterator types for Gödel’s System

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Higher-Order and Symbolic Computation

Abstract

System is a linear λ-calculus with numbers and an iterator, which, although imposing linearity restrictions on terms, has all the computational power of Gödel’s System . System owes its power to two features: the use of a closed reduction strategy (which permits the construction of an iterator on an open function, but only iterates the function after it becomes closed), and the use of a liberal typing rule for iterators based on iterative types. In this paper, we study these new types, and show how they relate to intersection types. We also give a sound and complete type reconstruction algorithm for System .

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Authors and Affiliations

  1. Department of Computer Science & LIACC, University of Porto, R. do Campo Alegre 1021/1055, 4169-007, Porto, Portugal

    Sandra Alves & Mário Florido

  2. Department of Computer Science, King’s College London, Strand, London, WC2R 2LS, UK

    Maribel Fernández

  3. LIX, École Polytechnique, 91128, Palaiseau Cedex, France

    Ian Mackie

Authors
  1. Sandra Alves
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  2. Maribel Fernández
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  3. Mário Florido
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  4. Ian Mackie
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Correspondence to Ian Mackie.

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Alves, S., Fernández, M., Florido, M. et al. Linearity and iterator types for Gödel’s System . Higher-Order Symb Comput 23, 1–27 (2010). https://doi.org/10.1007/s10990-010-9060-x

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