The Proto-Quipper family of programming languages aims to provide a formal foundation for the Quipper quantum programming language. Unfortunately, Proto-Quipper languages have complex operational semantics: they are inherently effectful, and they rely on set-theoretic operations and fresh name generation to manipulate quantum circuits. This makes them difficult to reason about using standard programming language techniques and, ultimately, to mechanize. We introduce Proto-Quipper-A, a rational reconstruction of Proto-Quipper languages for static circuit generation. It uses a linear $\lambda$-calculus to describe quantum circuits with normal forms that closely correspond to box-and-wire circuit diagrams. Adjoint-logical foundations integrate this circuit language with a linear/non-linear functional language and let us reconstruct Proto-Quipper’s circuit programming abstractions using more primitive adjoint-logical operations. Proto-Quipper-A has a simple call-by-value reduction semantics. To illustrate its tractability as a foundation for Proto-Quipper languages, we prove and mechanize metatheoretic results using standard techniques. We give a logical relations technique to prove normalization of substructural systems, thus avoiding the complexity of existing linear logical relations.