Linearity and iterator types for Gödel's System

Authors:
Sandra Alves;Maribel Fernández;Mário Florido;Ian Mackie
Affiliations:
Department of Computer Science & LIACC, University of Porto, Porto, Portugal 4169-007;Department of Computer Science, King's College London, London, UK WC2R 2LS;Department of Computer Science & LIACC, University of Porto, Porto, Portugal 4169-007;LIX, École Polytechnique, Palaiseau Cedex, France 91128
Venue:
Higher-Order and Symbolic Computation
Year:
2010

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Abstract

System is a linear 驴-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 .