1ML – core and modules united (F-ing first-class modules)

ABSTRACT

ML 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 reduces expressiveness. For example, selecting a module 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, are syntactically cumbersome, and do not alleviate redundancy. We propose a redesign of ML in which modules are truly first-class values, and core and module layer are unified into one language. In this "1ML", functions, functors, and even type constructors are one and the same construct; likewise, no distinction is made 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, and its type structure is expressible in terms of plain System Fω, in 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. An alternative view is that 1ML is a user-friendly surface syntax for System Fω that allows combining term and type abstraction in a more compositional manner than the bare calculus.

References

1. H. Barendregt. Lambda calculi with types. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science, vol. 2, chapter 2, pages 117–309. Oxford University Press, 1992.
2. S. K. Biswas. Higher-order functors with transparent signatures. In POPL, 1995.
3. L. Damas and R. Milner. Principal type-schemes for functional programs. In POPL, 1982.
4. D. Dreyer. Understanding and Evolving the ML Module System. PhD thesis, CMU, 2005.
5. D. Dreyer and M. Blume. Principal type schemes for modular programs. In ESOP, 2007.
6. D. Dreyer, K. Crary, and R. Harper. A type system for higher-order modules. In POPL, 2003.
7. J. Garrigue and A. Frisch. First-class modules and composable signatures in Objective Caml 3.12. In ML, 2010.
8. J. Garrigue and D. Rémy. Semi-explicit first-class polymorphism for ML. Information and Computation, 155(1-2), 1999.
9. R. Harper and M. Lillibridge. A type-theoretic approach to higherorder modules with sharing. In POPL, 1994.
10. R. Harper and J. C. Mitchell. On the type structure of Standard ML. In ACM TOPLAS, volume 15(2), 1993.
11. R. Harper, J. C. Mitchell, and E. Moggi. Higher-order modules and the phase distinction. In POPL, 1990.
12. R. Harper and B. Pierce. Design considerations for ML-style module systems. In B. C. Pierce, editor, Advanced Topics in Types and Programming Languages, chapter 8, pages 293–346. MIT Press, 2005.
13. R. Harper and C. Stone. A type-theoretic interpretation of Standard ML. In Proof, Language, and Interaction: Essays in Honor of Robin Milner. MIT Press, 2000.
14. D. Le Botlan and D. Rémy. MLF: Raising ML to the power of System F. In ICFP, 2003.
15. X. Leroy. Applicative functors and fully transparent higher-order modules. In POPL, 1995.
16. M. Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, CMU, 1997.
17. D. MacQueen. Using dependent types to express modular structure. In POPL, 1986.
18. R. Milner. A theory of type polymorphism in programming languages. JCSS, 17:348–375, 1978.
19. R. Milner, M. Tofte, R. Harper, and D. MacQueen. The Definition of Standard ML (Revised). MIT Press, 1997.
20. J. C. Mitchell and G. D. Plotkin. Abstract types have existential type. ACM TOPLAS, 10(3):470–502, July 1988.
21. D. Rémy. Records and variants as a natural extension of ML. In POPL, 1989.
22. A. Rossberg. The Missing Link – Dynamic components for ML. In ICFP, 2006.
23. A. Rossberg. 1ML – Core and modules united (Technical Appendix), 2015. mpi-sws.org/˜rossberg/1ml/.
24. A. Rossberg and D. Dreyer. Mixin’ up the ML module system. ACM TOPLAS, 35(1), 2013.
25. A. Rossberg, C. Russo, and D. Dreyer. F-ing modules. JFP, 24(5):529–607, 2014.
26. C. Russo. Non-dependent types for Standard ML modules. In PPDP, 1999.
27. C. Russo. First-class structures for Standard ML. Nordic Journal of Computing, 7(4):348–374, 2000.
28. C. Russo. Types for Modules. ENTCS, 60, 2003.
29. C. Russo and D. Vytiniotis. QML: Explicit first-class polymorphism for ML. In ML, 2009.
30. Z. Shao. Transparent modules with fully syntactic signatures. In ICFP, 1999.
31. C. A. Stone and R. Harper. Extensional equivalence and singleton types. ACM TOCL, 7(4):676–722, 2006.
32. J.-P. Talpin and P. Jouvelot. Polymorphic type, region and effect inference. JFP, 2(3):245271, 1992.
33. D. Vytiniotis, S. Weirich, and S. Peyton Jones. FPH: First-class polymorphism for Haskell. In ICFP, 2008.
34. P. Wadler and S. Blott. How to make ad-hoc polymorphism less ad hoc. In POPL, 1989.
35. A. Wright. Simple imperative polymorphism. LASC,8:343–356, 1995.

Index Terms

• Software and its engineering

  • Software notations and tools

    • Formal language definitions

    • General programming languages

      • Language features

• Theory of computation

  • Formal languages and automata theory

  • Semantics and reasoning

    • Program constructs