Tradeoffs in Metaprogramming

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.