It's valid Haskell 98 with a type constructor: http://r6.ca/blog/20060919T084800Z.html. But in GHC I think the first code snippet without NOINLINE still crashes, it's a perma-bug: https://downloads.haskell.org/~ghc/latest/docs/html/users_gu...

Some type systems do support equi-recursive types without the type constructor, e.g. Whiley (http://whiley.org/2013/04/21/iso-recursive-versus-equi-recur...). Maybe there you could implement Y without a type signature and have the recursive type inferred.

The main problem is speed. Using the Y combinator is going to mess up whatever code flow analysis the compiler has, unless it's using some cutting edge optimization research that I haven't been able to find.

There is a strongly-typed definition of Y here:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3418003

Some enterprising hacker should research who should be credited for the strongly-typed recursive def of Y.