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Journal Articles Logical Methods in Computer Science Year : 2015

The Computability Path Ordering


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 so-called computability closure. The well-foundedness proof shows that core CPO captures the essence of computability arguments à la Tait and Girard, therefore explaining its name. We further show that no more type check can be eliminated from its recursive calls without loosing well-foundedness, but 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.
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Dates and versions

hal-01163091 , version 1 (12-06-2015)
hal-01163091 , version 2 (16-11-2015)



Frédéric Blanqui, Jean-Pierre Jouannaud, Albert Rubio. The Computability Path Ordering. Logical Methods in Computer Science, 2015, ⟨10.2168/LMCS-11(4:3)2015⟩. ⟨hal-01163091v2⟩
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