There are a few fundamental differences that you cannot overcome easily:
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ML signatures are structural types, Scala traits are nominal: an ML signature can be matched by any appropriate module after the fact, for Scala objects you need to declare the relation at definition time. Likewise, subtyping between ML signatures is fully structural. Scala refinements are closer to structural types, but have some rather severe limitations (e.g., they cannot reference their own local type definitions, nor contain free references to abstract types outside their scope).
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ML signatures can be composed structurally using
includeandwhere. The resulting signature is equivalent to the inline expansion of the respective signature expression or type equation. Scala’s mixin composition, while more powerful in many ways, again is nominal, and creates an inequivalent type. Even the order of composition matters for type equivalence. -
ML functors are parameterised by structures, and thereby by both types and values, Scala’s generic classes are only parameterised by types. To encode a functor, you would need to turn it into a generic function, that takes the types and the values separately. In general, this transformation — called phase-splitting in the ML module literature — cannot be limited to just definitions and uses of functors, because at their call-sites it has to be applied recursively to nested structure arguments; this ultimately requires that all structures are consistently phase-split, which is not a style you want to program in manually. (Neither is it possible to map functors to plain functions in Scala, since functions cannot express the necessary type dependencies between parameter and result types. Edit: since 2.10, Scala has support for dependent methods, which can encode some examples of SML’s first-order generative functors, although it does not seem possible in the general case.)
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ML has a general theory of refining and propagating “translucent” type information. Scala uses a weaker equational theory of “path-dependent” types, where paths denote objects. Scala thereby trades ML’s more expressive type equivalences for the ability to use objects (with type members) as first-class values. You cannot easily have both without quickly running into decidability or soundness issues.
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Edit: ML can naturally express abstract type constructors (i.e., types of higher kind), which often arise with functors. For Scala, higher kinds have to be activated explicitly, which are more challenging for its type system, and apparently lead to undecidable type checking.
The differences become even more interesting when you move beyond SML, to higher-order, first-class, or recursive modules. We briefly discuss a few issues in Section 10.1 of our MixML paper.