Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be understood coinductively. Cycle detection is a popular method to capture a small subset of such derivations. We show that in fact cycle detection is a restricted form of coinductive proof, in which the atomic formula forming the cycle plays the rôle of coinductive hypothesis. This paper introduces a heuristic method for obtaining richer coinductive hypotheses in the form of Horn formulas. Our approach subsumes cycle detection and gives coinductive meaning to a larger class of derivations. For this purpose we extend resolution with Horn formula resolvents and corecursive evidence generation. We illustrate our method on nonterminating type class resolution problems.
Fe and N-co-doped hollow carbon nanospheres have been fabricated via a simple pyrolysis method using poly(aniline-co-pyrrole) copolymer hollow nanospheres as precursors. The resulting catalyst displayed potential application as a cathode in a MFC.
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