A Correspondence between Type Checking via Reduction and Type Checking via Evaluation

Ilya Sergey and Dave Clarke

Katholieke Universiteit Leuven

DistriNet,   Dept. Computer Science

This work describes a derivational approach to proving the equivalence of different representations of a type system. Different ways of representing type assignments are convenient for particular applications such as reasoning or implementation, but some kind of correspondence between them should be proven. In this paper we deal with two such semantics for type checking: one, due to Kuan et al., in the form of a term rewriting system and another in the form of a traditional set of derivation rules. By employing a set of techniques investigated by Danvy et al., we mechanically derive the correspondence between a reduction-based semantics for type-checking and a traditional one in the form of derivation rules, implemented as a recursive descent. The correspondence is established through a series of semantics-preserving functional program transformations.

Sources

• Available from GitHub

Technical report

• A Correspondence between Type Checking via Reduction and Type Checking via Evaluation  

  Technical report with the accompanying code overview, Ilya Sergey and Dave Clarke, Report CW 617, Katholieke Universiteit Leuven, January 2012