 Lambda quotation

For an effective Gödel numbering $M\mapsto \#M$, the quotation $d(M)=c_{\#M}$ is a Church numeral coding the syntax of $M$. It is not a code of a beta equivalence class. The operations taking syntax codes to the code of an application, or to the code of the numeral itself, are total computable functions and hence lambda-definable functions.