A lactone ring confers unusual stability to a diphenylmethyl-like radical that is virtually unreactive toward oxygen. Thus, the radical derived from HP-136 is about 10,000 times less reactive than typical carbon-centered radicals. A reversible reaction with oxygen is proposed by analogy with triphenylmethyl; however, the association constant is about 1000 times smaller for HP-136 than for triphenylmethyl. While the lactone ring greatly influences the reactivity, the spectroscopy of the HP-136-derived radical is in line with that expected for a substituted diphenylmethyl radical.

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Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding operator that is constructed definitionally from a de Bruijn index representation. In this paper we make a variety of improvements to Hybrid, culminating in an abstract interface that on one hand makes Hybrid a more mathematically satisfactory theory, and on the other hand has important practical benefits. We start with a modification of Hybrid's type of terms that better hides its implementation in terms of de Bruijn indices, by excluding at the type level terms with dangling indices. We present an improved set of definitions, and a series of new lemmas that provide a complete characterization of Hybrid's primitives in terms of properties stated at the HOAS level. Benefits of this new package include a new proof of adequacy and improvements to reasoning about object logics. Such proofs are carried out at the higher level with no involvement of the lower level de Bruijn syntax.