Axiomatizing the Quote

Andrew Polonsky
We study reflection in the Lambda Calculus from an axiomatic point of view. Specifically, we consider various properties that the quote operator must satisfy as a function on lambda terms. The most important of these is the existence of a definable left inverse, a so-called evaluator for the quote operator. Usually the quote operator encodes the syntax of a given term, and the evaluator proceeds by analyzing the syntax and reifying all constructors by their...