Type-Based Homeomorphic Embedding and Its Applications to Online Partial Evaluation

  • Authors:
  • Elvira Albert;John Gallagher;Miguel Gómez-Zamalloa;Germán Puebla

  • Affiliations:
  • DSIC, Complutense University of Madrid, Madrid, Spain E-28040;CBIT, Roskilde University, Roskilde, Denmark DK-4000;DSIC, Complutense University of Madrid, Madrid, Spain E-28040;CLIP, Technical University of Madrid, Madrid, Spain E-28660

  • Venue:
  • Logic-Based Program Synthesis and Transformation
  • Year:
  • 2008

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Abstract

Homeomorphic Embedding(HEm) has proven to be very powerful for supervising termination of computations, provided that such computations are performed over a finite signature, i.e., the number of constants and function symbols involved is finite. However, there are situations, for example numeric computations, which involve an infinite (or too large) signature, in which HEmdoes not guarantee termination. Some extensions to HEmfor the case of infinite signatures have been proposed which guarantee termination, but they either do not provide systematic means for generating such extensions or the extensions are too simplistic and do not produce the expected results in practice. We introduce Type-based Homeomorphic Embedding(TbHEm) as an extension of the standard, untyped HEmto deal with infinite signatures. In the paper, we show how TbHEmcan be used to improve the accuracy of online partial evaluation. For this purpose, we propose an approach to constructing suitable types for partial evaluation automatically based on existing analysis tools for constraint logic programs. We also present useful properties of types which allow us to take full advantage of TbHEmin practice. Experimental results are reported which show that our work improves the state of the practice of online partial evaluation.