TL;DR: This paper develops and presents MacroML, an extension of ML that supports inlining, recursive macros, and the definition of new binding constructs, and shows that MacroML is stage- and type-safe: macro expansion does not depend on runtime evaluation, and both stages do not "go wrong".
Abstract: With few exceptions, macros have traditionally been viewed as operations on syntax trees or even on plain strings. This view makes macros seem ad hoc, and is at odds with two desirable features of contemporary typed functional languages: static typing and static scoping. At a deeper level, there is a need for a simple, usable semantics for macros. This paper argues that these problems can be addressed by formally viewing macros as multi-stage computations. This view eliminates the need for freshness conditions and tests on variable names, and provides a compositional interpretation that can serve as a basis for designing a sound type system for languages supporting macros, or even for compilation. To illustrate our approach, we develop and present MacroML, an extension of ML that supports inlining, recursive macros, and the definition of new binding constructs. The latter is subtle, and is the most novel addition in a statically typed setting. The semantics of a core subset of MacroML is given by an interpretation into MetaML, a statically-typed multi-stage programming language. It is then easy to show that MacroML is stage- and type-safe: macro expansion does not depend on runtime evaluation, and both stages do not "go wrong.
TL;DR: It is shown that defining the semantics of macros in this manner helps in developing and verifying not only type systems for macro languages but also equational reasoning principles.
Abstract: Recent work proposed defining type-safe macros via interpretation into a multi-stage language. The utility of this approach was illustrated with a language called MacroML, in which all type checking is carried out before macro expansion. Building on this work, the goal of this paper is to develop a macro language that makes it easy for programmers to reason about terms locally. We show that defining the semantics of macros in this manner helps in developing and verifying not only type systems for macro languages but also equational reasoning principles. Because the MacroML calculus is sensetive to renaming of (what appear locally to be) bound variables, we present a calculus of staged notational definitions (SND) that eliminates the renaming problem but retains MacroML's phase distinction. Additionally, SND incorporates the generality of Griffin's account of notational definitions. We exhibit a formal equational theory for SND and prove its soundness.