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Asked: 2026-05-28T07:38:53+00:00

Can anyone explain why these both compile happily : data A a b =

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Can anyone explain why these both compile happily :

data A a b = A { a :: a, b :: b }
newtype B a = B (A a (B a))
newtype C = C (A Int C)

But I cannot create a similarly recursively defined types via type synonyms?

type B a = A a (B a)
type C = A Int C

Although obviously data B a = A { a :: a, b :: B a } works just fine.

Is there any way to avoid dealing with that extra constructor X everywhere I want the type recursive? I’m mostly passing in accessor functions that pick out the b anyways, so I’m mostly okay, but if an easy circumvention mechanism exists I’d like to know about it.

Any pragmas I should be using to improve performance with the specialized data type C? Just specialize stuff?

Any clever trick for copying between A a b and A c d defining only the a -> b and c -> d mapping without copying over the record twice? I’m afraid that A‘s fields will change in future. Template Haskell perhaps?

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1 Answer

  1. Editorial Team

    This has to do with Equi-recursive types versus iso-recursive types. Haskell implements recursive types using iso-recursive types, which require the programmer to tell the type-checker when type recursion is happening. The way you mark it is with a specific constructor, which a simple type-synonym doesn’t allow you to have.

    Equi-recursive types allow the compiler to infer where recursion is happening, but it leads to a much more complicated type-checker and in some seemingly simple cases the problem is undecidable.

    If you’d like a good discussion of equi vs. iso recursive types, check out Benjamin Pierce’s excellent Types and Programming Languages

    Short answer: because type synonyms don’t introduce constructors, and haskell needs constructors to explicitly mark recursion at the type-level, you can’t use recursive type synonyms.

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