2005/12/15 by Todd L. Veldhuizen, Veldhuizen, Todd L.
Computer Science · #Formal Methods in Verification #Logic, programming, and type systems #Software Engineering Research #cs.PL
paper · pdf · doi:10.48550/arxiv.cs/0512065
2006 ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation (PEPM 2006)
arxiv created 2005/12/15 · arxiv updated 2009/12/01
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 Π02-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 Σ03 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.