Leftmost outside-in narrowing calculi

  • Authors:

  • Tetsuo Ida;Koichi Nakahara

  • Affiliations:

  • Institute of Information Sciences and Electronics and Center for Tsukuba Advanced Research Alliance University of Tsukuba, Tsukuba 305, Japan;Canon Inc., Shimomaruko, Ohta-ku, Tokyo 146, Japan

  • Venue:
  • Journal of Functional Programming
  • Year:
  • 1997

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Abstract

We present narrowing calculi that are computation models of functional-logic programming languages. The narrowing calculi are based on the notion of the leftmost outside-in reduction of Huet and Lévy. We note the correspondence between the narrowing and reduction derivations, and define the leftmost outside-in narrowing derivation. We then give a narrowing calculus OINC that generates the leftmost outside-in narrowing derivations. It consists of several inference rules that perform the leftmost outside-in narrowing. We prove the completeness of OINC using an ordering defined over a narrowing derivation space. To use the calculus OINC as a model of computation of functional-logic programming, we extend OINC to incorporate strict equality. The extension results in a new narrowing calculus, s-OINC. We show also that s-OINC enjoys the same completeness property as OINC.