Comments on: GADTs in Haskell 98

By: Bob Atkey

Bob Atkey — Fri, 13 Nov 2009 12:28:15 +0000

Unfortunately, not all GADTs can be expressed faithfully in this way, due to “leakage” between the types used for representation and the type parameters in the constructors. An example is given in Section 4 of the paper “Unembedding domain-specific languages” (available from my home page), where we called them “exotically typed terms”. The example in the paper involves Higher-Order Abstract Syntax, but it still happens when you have no negative occurrences of the type variable: a simple example is a GADT for representing typed S and K combinators with application. The problem seems to occur when there is a type parameter inside a GADT term that does not appear on the outside of the term.

Fortunately, all is not lost (if you allow yourself Haskell98 + Rank-2 polymorphism + existential types). One can still represent the Equality GADT as a type class (with single method refl :: f a a), and then use Neil Ghani and Patty Johann’s decomposition of GADTs into normal algebraic datatypes plus the equality GADT. Oleg did this in OCaml in a post to the OCaml mailing list. A disadvantage of this approach is that you have to apply the type equalities by hand.

By: Chung-chieh Shan

Chung-chieh Shan — Fri, 13 Nov 2009 08:45:36 +0000

Jacques Carette and Oleg Kiselyov and I wrote up some more things that one can do (and have been done) in this way: “Finally
tagless, partially evaluated: Tagless staged interpreters for simpler
typed languages.” Journal of Functional Programming 19(5):509-543.

By: Brent Yorgey

Brent Yorgey — Thu, 12 Nov 2009 17:58:08 +0000

Aha, I never realized you could encode GADTs as type classes like this! Simple once you see it. Thanks for sharing!

By: jj

jj — Thu, 12 Nov 2009 14:08:10 +0000

What I like about GADTs is not what they let us do, but what they stop us from doing. The standard GADT example you show makes it impossible to produce an ill-typed Term (not term, Term) without using error or naughty recursion. Using the type class TermC, you have to either give up pattern matching or type safety.