Version 5 (modified by 5 years ago) (diff) | ,
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We use a family of singleton types to relate type-level naturals to runtime values.

In our design, we chose to provide as primitive an overloaded "smart" constructor and a polymorphic elimination construct:

newtype Sing n = Sing (SingRep n) class SingI n where sing :: Sing n instance SingI 0 where sing = Sing 0 instance SingI 1 where sing = Sing 1 ... fromSing :: Sing n -> SingRep n fromSing (Sing n) = n

It is also possible to make the dual choice, where we provide a polymorphic constructor and an overloaded elimination construct:

data Sing n = Sing class SingE n where fromSing :: Sing n -> SingRep n instance NatE 0 where fromSing Sing = 0 instance NatE 1 where fromSing Sing = 1 ...

We made this choice, at least in part, because it made the implementation simpler: with our choice the evidence for class `SingI`

is just an integer or a string. Note that our choice does not loose any generality because we can define the alternative design in terms of it:

data Sing1 = Sing1 fromSing1 :: SingI n => Sing1 n -> SingRep n fromSing1 = fromSing . cast where cast :: SingI n => Sing1 n -> Sing n cast Sing1 = sing