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Hi Gershom, This is a good question, and often overlooked. Bob Harper taught me to think of these things as abstract types, and I agree — so the thing that makes two different datatype declarations different is the existing abstraction mechanism of your language. When you think of it this way, you think of the pattern-matching forms as being elaborated to some kinds of destructors or combinators — which are themselves part of the abstract interface of the type. I cannot confirm because I don't remember the code, but it may be that the TILT compiler actually worked this way. Probably Bob will have a fresher recollection of this. Best, Jon On Fri, Jan 26, 2024, at 10:18 PM, Gershom B wrote: > [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ] > > In typical treatments of languages with recursive types, we present a > syntax with either isorecursive or equirecursive types. But we do not > have a syntax for introduction of type declarations. > > This is to say that we assemble types out of constructors for e.g., > polymorphism, recursion, sum, product, unit, exponential (give or > take). > > But we do not have the equivalent of a "data" declaration in Haskell > that lets us explicitly say > > data Bool = True | False > > or > > data List a = Nil | Cons a > > It is, I suppose, expected that readers of these papers can think > through how to translate any given data datatypes in languages with > explicit declaration into the underlying fixed type calculus. > > However, I am curious if there is any reference for *explicit* > treatment of the syntax for datatype declarations and semantic > modeling of such? > > One reason for such would be that in the calculi I described above, > there's of course no way to distinguish between the above `data Bool` > and e.g. `1 + 1`, while it might be desirable to maintain that strict > distinction between actual equality and merely observable isomorphism. > > Thanks, > Gershom
