1ML – Core and modules united

Abstract

AbstractML is two languages in one: there is the core, with types and expressions, and there are modules, with signatures, structures, and functors. Modules form a separate, higher-order functional language on top of the core. There are both practical and technical reasons for this stratification; yet, it creates substantial duplication in syntax and semantics, and it imposes seemingly unnecessary limits on expressiveness because it makes modules second-class citizens of the language. For example, selecting one among several possible modules implementing a given interface cannot be made a dynamic decision. Language extensions allowing modules to be packaged up as first-class values have been proposed and implemented in different variations. However, they remedy expressiveness only to some extent and tend to be even more syntactically heavyweight than using second-class modules alone. We propose a redesign of ML in which modules are truly first-class values, and core and module layers are unified into one language. In this “1ML”, functions, functors, and even type constructors are one and the same construct; likewise, no distinction is needed between structures, records, or tuples. Or viewed the other way round, everything is just (“a mode of use of”) modules. Yet, 1ML does not require dependent types: its type structure is expressible in terms of plain System Fω, with a minor variation of our F-ing modules approach. We introduce both an explicitly typed version of 1ML and an extension with Damas–Milner-style implicit quantification. Type inference for this language is not complete, but, we argue, not substantially worse than for Standard ML.