#12564: Type family in type pattern kind -------------------------------------+------------------------------------- Reporter: int-index | Owner: goldfire Type: bug | Status: new Priority: high | Milestone: 8.4.1 Component: Compiler (Type | Version: 8.0.1 checker) | Keywords: TypeInType, Resolution: | TypeFamilies Operating System: Unknown/Multiple | Architecture: Type of failure: GHC rejects | Unknown/Multiple valid program | Test Case: Blocked By: 14119 | Blocking: Related Tickets: | Differential Rev(s): Wiki Page: | -------------------------------------+------------------------------------- Comment (by goldfire): I have an approach here worth documenting. In brief: flatten equations' left-hand sides, emitting constraints during reduction. Here is how the example in the OP would work. Original equation: {{{#!hs At (x ': _) FZ = x }}} with implicit things made explicit: {{{#!hs At @a ((:) @a x _1) (FZ @(Len @a _1)) = x }}} But now, we ''flatten''. By this, I mean we take all type family applications on the LHS and convert them into variables, and assert equality constraints that the variables equal the original type family applications. To wit: {{{#!hs (m ~ Len @a _1) => At @a ((:) @a x _1) (FZ @m) = x }}} This yields a ''constrained'' type family equation. (Note: this is mostly unrelated to [https://repository.brynmawr.edu/cgi/viewcontent.cgi?article=1075&context=compsci_pubs Constrained Type Families]) During reduction, this equation would match a target regardless of the (implicit) argument to `FZ`, but the matcher would then emit a constraint asserting that this argument equals `Len @a _1`. It's quite like how class instance matching works: we match against the head, emitting any instance constraints. Type family equations give rise to axioms in Core. To keep type safety, we would need these axioms to take the evidence of the equality match as arguments. Continuing our example, we would get this axiom: {{{ axAt :: forall (a :: Type) (x :: a) (_1 :: [a]) (m :: Nat). forall (cv :: m ~ Len @a _1). At @a ((:) @a x _1) (FZ @m) ~ x }}} Note that there are two `forall`s: the first binds type variables and the second binds coercion variables. In this case, the coercion variable `cv` is unused in the RHS, but it might potentially be mentioned. This equation could be used to reduce `At ["a", "b", "c"] FZ` to `"a"`. We would use the instantiated axiom {{{ axAt Symbol "a" ["b", "c"] 2 coLen :: At ["a", "b", "c"] FZ ~ "a" }}} where `coLen :: 2 ~ Len ["b", "c"]` is built from the axioms that describe the behavior of `Len`. Note that there is already some infrastructure for this: the `cvs` in `CoAxBranch` (and a few other places nearby) are exactly these coercion variables. What's remaining to do is to perform the flattening pass that inserts the cvs and to teach the type-family reduction mechanism (in `TcFlatten`) to emit the constraints. One challenge is that sometimes (`normaliseType`) we reduce type families without the ability to solve constraints, so some care must be taken there. However, these cases are outside our usual pipeline and can be special-cased. (While implementing `-XTypeInType`, I did this once upon a time, so I know it's possible.) -- Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/12564#comment:13 GHC http://www.haskell.org/ghc/ The Glasgow Haskell Compiler