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Computation by Prophecy

  • Ana Bove
  • Venanzio Capretta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4583)

Abstract

We describe a new method to represent (partial) recursive functions in type theory. For every recursive definition, we define a co-inductive type of prophecies that characterises the traces of the computation of the function. The structure of a prophecy is a possibly infinite tree, which is coerced by linearisation to a type of partial results defined by applying the delay monad to the co-domain of the function. Using induction on a weight relation defined on the prophecies, we can reason about them and prove that the formal type-theoretic version of the recursive function, resulting from the present method, satisfies the recursive equations of the original function. The advantages of this technique over the method previously developed by the authors via a special-purpose accessibility (domain) predicate are: there is no need of extra logical arguments in the definition of the recursive function; the function can be applied to any element in its domain, regardless of termination properties; we obtain a type of partial recursive functions between any two given types; and composition of recursive functions can be easily defined.

Keywords

Type Theory Recursive Function Recursive Call Recursive Equation Proof Assistant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Ana Bove
    • 1
  • Venanzio Capretta
    • 2
  1. 1.Department of Computer Science and Engineering, Chalmers University of Technology, 412 96 GöteborgSweden
  2. 2.Computer Science Institute (iCIS), Radboud University Nijmegen 

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