Knowing When to Ask

Arjen Rouvoet, Hendrik van Antwerpen, Casper Bach Poulsen,
Robbert Krebbers, and Eelco Visser


AThere is a large gap between the specification of type systems and the implementation of their type checkers, which impedes reasoning about the soundness of the type checker with respect to the specification. A vision to close this gap involves automatically obtaining type checkers from declarative programming language specifications. This moves the burden of proving correctness from a case-by-case basis for concrete languages, to a single correctness proof for the specification language. This vision is obstructed by an aspect common to all programming languages: name resolution. Naming and scoping are pervasive and complex aspects of the static semantics of programming languages. Implementations of type checkers for languages with name binding features such as modules, imports, classes, and inheritance interleave collection of binding information (i.e., declarations, scoping structure, and imports) and querying that information. This requires scheduling those two aspects in such a way that query answers are stable—i.e., they are computed only after all relevant binding structure has been collected. Type checkers for concrete languages accomplish stability using language-specific knowledge about the type system.

In this paper we give a language independent characterization of necessary and sufficient conditions to guarantee stability of name and type queries during type checking in terms of critical edges in an incomplete scope graph. We use critical edges to give a formal small-step operational semantics to a declarative specification language for type systems, delaying queries that may depend on missing information. This yields type checkers for the specified languages that are safe-by-construction—i.e., they safely schedule queries and only accept programs that are name- and type-correct according to the declarative language specification. We implement this approach, and evaluate it against specifications of a small module and record language, as well as subsets of Java and Scala.