Blanqui, Frédéric and Jouannaud, Jean-Pierre and Rubio, Albert - The computability path ordering

lmcs:1604 - Logical Methods in Computer Science, October 26, 2015, Volume 11, Issue 4
The computability path ordering

Authors: Blanqui, Frédéric and Jouannaud, Jean-Pierre and Rubio, Albert

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by lifting a precedence on function symbols. A first version, core CPO, is essentially obtained from the higher-order recursive path ordering (HORPO) by eliminating type checks from some recursive calls and by incorporating the treatment of bound variables as in the com-putability closure. The well-foundedness proof shows that core CPO captures the essence of computability arguments \'a la Tait and Girard, therefore explaining its name. We further show that no further type check can be eliminated from its recursive calls without loosing well-foundedness, but for one for which we found no counterexample yet. Two extensions of core CPO are then introduced which allow one to consider: the first, higher-order inductive types; the second, a precedence in which some function symbols are smaller than application and abstraction.


Source : oai:arXiv.org:1506.03943
DOI : 10.2168/LMCS-11(4:3)2015
Volume: Volume 11, Issue 4
Published on: October 26, 2015
Submitted on: March 6, 2014
Keywords: Computer Science - Logic in Computer Science


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