A Sound Reduction Semantics for Untyped CBN Multi-Stage Computation. Or, the Theory of MetaML is Non-trivial

A multi-stage computation is one involving more than one stage of execution. MetaML is a language for programming multi-stage computations. Previous studies presented big-step semantics, categorical semantics, and sound type systems for MetaML. In this paper, we report on a confluent and sound reduction semantics for untyped call-by name (CBN) MetaML. The reduction semantics can be used to formally justify some optimization performed by a CBN MetaML implementation. The reduction semantics demonstrates that non-trivial equalities hold for object-code, even in the untyped setting. The paper also emphasizes that adding intensional analysis (that is, taking-apart object programs) to MetaML remains an interesting open problem.