Tradeoffs in Metaprogramming

TL;DR

This paper explores the inherent tradeoffs in metaprogramming language design, analyzing the decidability of safety properties and the implications of language restrictions using computability theory.

Contribution

It provides a formal analysis of tradeoffs in metaprogramming languages, establishing conditions for capturing safety properties and demonstrating the complexity of translating between languages.

Findings

Safety properties are generally undecidable, e.g., halting and type correctness.

Restricted languages can sometimes capture safety properties, but not all.

Translating metaprograms between languages relates directly to the properties being verified.

Abstract

The design of metaprogramming languages requires appreciation of the tradeoffs that exist between important language characteristics such as safety properties, expressive power, and succinctness. Unfortunately, such tradeoffs are little understood, a situation we try to correct by embarking on a study of metaprogramming language tradeoffs using tools from computability theory. Safety properties of metaprograms are in general undecidable; for example, the property that a metaprogram always halts and produces a type-correct instance is $\Pi^0_2$-complete. Although such safety properties are undecidable, they may sometimes be captured by a restricted language, a notion we adapt from complexity theory. We give some sufficient conditions and negative results on when languages capturing properties can exist: there can be no languages capturing total correctness for metaprograms, and no `functional' safety properties above $\Sigma^0_3$ can be captured. We prove that translating a metaprogram from a general-purpose to a restricted metaprogramming language capturing a property is tantamount to proving that property for the metaprogram. Surprisingly, when one shifts perspective from programming to metaprogramming, the corresponding safety questions do not become substantially harder -- there is no `jump' of Turing degree for typical safety properties.