Adding kind equalities to GHC
This page  a description of the first phase of integrating full dependent types into GHC  has two main parts:
 The first stretch describes userfacing changes in GHC 8.
 The second is notes I put together for discussion with other implementors, chiefly Simon PJ.
See also the parent page DependentHaskell.
Status
Use Keyword = TypeInType
to ensure that a ticket ends up on these lists.
Open Tickets:
 #7503
 Bug with PolyKinds, type synonyms & GADTs
 #10141
 CUSK mysteries
 #11196
 TypeInType performance regressions
 #11197
 Overeager deferred type errors
 #11198
 TypeInType error message regressions
 #11719
 Cannot use higherrank kinds with type families
 #11962
 Support induction recursion
 #12045
 Visible kind application
 #12088
 Type/data family instances in kind checking
 #12102
 “Constraints in kinds” illegal family application in instance (+ documentation issues?)
 #12564
 Type family in type pattern kind
 #12612
 Allow kinds of associated types to depend on earlier associated types
 #12766
 Allow runtimerepresentation polymorphic data families
 #12928
 Too easy to trigger CUSK condition using TH
 #13365
 Notify user when adding a CUSK might help fix a type error
 #13650
 Implement KPush in types
 #13933
 Support Typeable instances for types with coercions
 #14040
 Typed holes regression in GHC 8.0.2: No skolem info: z_a1sY[sk:2]
 #14119
 Refactor type patterns
 #14155
 GHC mentions unlifted types out of the blue (to me anyway)
 #14180
 Strange/bad error message binding unboxed type variable
 #14230
 Gruesome kind mismatch errors for associated data family instances
 #14319
 Stuck type families can lead to lousy error messages
 #14366
 Type family equation refuses to unify wildcard type patterns
 #14419
 Check kinds for ambiguity
 #14451
 Need proper SCC analysis of type declarations, taking account of CUSKs
 #14514
 Error messages: suggest annotating with higherrank kind
 #14645
 Allow type family in data family return kind
 #14668
 Ordering of declarations can cause typechecking to fail
 #14847
 Inferring dependent kinds for nonrecursive types
 #14873
 The wellkinded type invariant (in TcType)
 #14880
 GHC panic: updateRole
 #14887
 Explicitly quantifying a kind variable causes a telescope to fail to kindcheck
 #15076
 Typed hole with higherrank kind causes GHC to panic (No skolem info)
 #15515
 Bogus "No instance" error when type families appear in kinds
Closed Tickets:
 #11241
 Kindlevel PartialTypeSignatures causes internal error
 #11246
 Regression typechecking type synonym which includes `Any`.
 #11252
 :kind command hides the explicit kind
 #11266
 Can't :browse some modules with GHCi 7.11
 #11334
 GHC panic when calling typeOf on a promoted data constructor
 #11356
 GHC panic
 #11357
 Regression when deriving Generic1 on polykinded data family
 #11362
 T6137 doesn't pass with reversed uniques
 #11399
 Illkinded instance head involving XTypeInType can invoke GHC panic
 #11400
 * is not an indexed type family
 #11401
 No match in record selector ctev_dest
 #11404
 The type variable used in a kind is still used
 #11405
 Incorrect failure of typelevel skolem escape check
 #11407
 XTypeInType uses up all memory when used in data family instance
 #11410
 Quantification over unlifted type variable
 #11416
 GHC mistakenly believes datatype with type synonym in its type can't be etareduced
 #11453
 Kinds in type synonym/data declarations can unexpectedly unify
 #11463
 Template Haskell applies too many arguments to kind synonym
 #11471
 Kind polymorphism and unboxed types: bad things are happening
 #11473
 Levity polymorphism checks are inadequate
 #11484
 Type synonym using XTypeInType can't be spliced with TH
 #11485
 Very unhelpful message resulting from kind mismatch
 #11519
 Inferring nontau kinds
 #11520
 GHC falls into a hole if given incorrect kind signature
 #11548
 Absolutely misleading error message on kind error
 #11549
 Add fshowruntimerep
 #11554
 Self quantification in GADT data declarations
 #11560
 panic: isInjectiveTyCon sees a TcTyCon
 #11592
 Selfkinded type variable accepted
 #11614
 document TypeInType
 #11635
 Higherrank kind in datatype definition rejected
 #11642
 Heterogeneous type equality evidence ignored
 #11648
 assertPprPanic, called at compiler/types/TyCoRep.hs:1932
 #11672
 Poor error message
 #11699
 Type families mistakingly report kind variables as unbound type variables
 #11716
 Make TypeInType stress test work
 #11732
 Deriving Generic1 interacts poorly with TypeInType
 #11785
 Merge types and kinds in Template Haskell
 #11811
 GHC sometimes misses a CUSK
 #11821
 Internal error: not in scope during type checking, but it passed the renamer
 #11963
 GHC introduces kind equality without TypeInType
 #11964
 Without TypeInType, inconsistently accepts Data.Kind.Type but not type synonym
 #11966
 Surprising behavior with higherrank quantification of kind variables
 #11995
 Can't infer type
 #12029
 Notify user to import * from Data.Kind with TypeInType on
 #12030
 GHCi Proposal: Display (Data.Kind.)Type instead of *
 #12081
 TypeInType Compiletime Panic
 #12174
 Recursive use of typeintype results in infinite loop
 #12176
 Failure of bidirectional type inference at the kind level
 #12239
 Dependent type family does not reduce
 #12369
 data families shouldn't be required to have return kind *, data instances should
 #12442
 Pure unifier usually doesn't need to unify kinds
 #12503
 Template Haskell regression: GHC erroneously thinks a type variable is also a kind
 #12534
 GHC 8.0 accepts recursive kind signature that GHC 7.10 rejects
 #12553
 Reference kind in a type instance declaration defined in another instance declaration
 #12742
 Instantiation of invisible type family arguments is too eager
 #12919
 Equality not used for substitution
 #12922
 Kind classes compile with PolyKinds
 #12931
 tc_infer_args does not set inscope set correctly
 #12933
 Wrong class instance selection with Data.Kind.Type
 #12938
 Polykinded associated type family rejected on false pretenses
 #13109
 CUSK improvements
 #13333
 Typeable regression in GHC HEAD
 #13337
 GHC doesn't think a type is of kind *, despite having evidence for it
 #13364
 Remove checkValidTelescope
 #13391
 PolyKinds is more permissive in GHC 8
 #13399
 Location of `forall` matters with higherrank kind polymorphism
 #13407
 Fix printing of higherrank kinds
 #13408
 Consider inferring a higherrank kind for type synonyms
 #13409
 Data types with higherrank kinds are prettyprinted strangely
 #13530
 Horrible error message due to TypeInType
 #13546
 Kind error with type equality
 #13549
 GHC 8.2.1's typechecker rejects code generated by singletons that 8.0 accepts
 #13555
 Typechecker regression when combining PolyKinds and MonoLocalBinds
 #13585
 ala from Control.Lens.Wrapped panics
 #13601
 GHC errors but hangs
 #13603
 Can't resolve levity polymorphic superclass
 #13625
 GHC internal error: ‘Y’ is not in scope during type checking, but it passed the renamer
 #13643
 Core lint error with TypeInType and TypeFamilyDependencies
 #13674
 Poor error message which masks occurscheck failure
 #13761
 Can't create polykinded GADT with TypeInType enabled, but can without
 #13762
 TypeInType is not documented in the users' guide flag reference
 #13777
 Poor error message around CUSKs
 #13780
 Nightmarish prettyprinting of equality type in GHC 8.2 error message
 #13781
 (a :: (k :: Type)) is too exotic for Template Haskell
 #13790
 GHC doesn't reduce type family in kind signature unless its arm is twisted
 #13822
 GHC not using injectivity?
 #13871
 GHC panic in 8.2 only: typeIsTypeable(Coercion)
 #13872
 Strange Typeable error message involving TypeInType
 #13879
 Strange interaction between higherrank kinds and type synonyms
 #13895
 "Illegal constraint in a type" error  is it fixable?
 #13909
 Misleading error message when partially applying a data type with a visible quantifier in its kind
 #13910
 Inlining a definition causes GHC to panic (repSplitTyConApp_maybe)
 #13915
 GHC 8.2 regression: "Can't find interfacefile declaration" for promoted data family instance
 #13929
 GHC panic with levity polymorphism
 #13938
 Iface type variable out of scope: k1
 #13963
 Runtime representation confusingly displayed
 #13972
 GHC 8.2 error message around indexes for associated type instances is baffling
 #13988
 GADT constructor with kind equality constraint quantifies unused existential type variables
 #14042
 Datatypes cannot use a type family in their return kind
 #14086
 Empty case does not detect kinds
 #14091
 When PolyKinds is on, suggested type signatures seem to require TypeInType
 #14139
 Kind signature not accepted (singletons)
 #14162
 Core Lint error
 #14174
 GHC panic with TypeInType and type family
 #14175
 Panic repSplitTyConApp_maybe
 #14203
 GHCinferred type signature doesn't actually typecheck
 #14207
 Levity polymorphic GADT requires extra type signatures
 #14209
 GHC 8.2.1 regression involving telescoping kind signature
 #14238
 `:kind` suppresses visible dependent quantifiers by default in GHCi 8.2.1
 #14350
 Infinite loop when typechecking incorrect implementation (GHC HEAD only)
 #14352
 Higherrank kind ascription oddities
 #14394
 Inferred type for pattern synonym has redundant equality constraint
 #14441
 GHC HEAD regression involving type families in kinds
 #14450
 GHCi spins forever
 #14507
 Core Lint error with Type.Reflection and pattern synonyms
 #14515
 "Same" higherrank kind synonyms behave differently
 #14520
 GHC panic (TypeInType)
 #14552
 GHC panic on pattern synonym
 #14554
 Core Lint error mixing
 #14555
 GHC Panic with TypeInType / levity polymorphism
 #14556
 Core Lint error: Illkinded result in coercion
 #14563
 GHC Panic with TypeInType / levity polymorphism
 #14580
 GHC panic (TypeInType) (the 'impossible' happened)
 #14584
 Core Lint error
 #14605
 Core Lint error
 #14607
 Core Lint error
 #14720
 GHC 8.4.1alpha regression with TypeInType
 #14749
 T13822 fails
 #14764
 Make $! representationpolymorphic
 #14795
 Data type return kinds don't obey the forallornothing rule
 #14845
 TypeInType, index GADT by constraint witness
 #14846
 Renamer hangs (because of XInstanceSigs?)
 #14904
 Compiler panic (piResultTy)
 #14938
 Pattern matching on GADT does not refine type family parameters
 #14991
 GHC HEAD regression involving TYPEs in type families
 #15039
 Bizarre prettyprinting of inferred Coercible constraint in partial type signature
 #15079
 GHC HEAD regression: cannot instantiate higherrank kind
 #15116
 GHC internal error when GADT return type mentions its own constructor name
 #15122
 GHC HEAD typechecker regression
 #15142
 GHC HEAD regression: tcTyVarDetails
 #15170
 GHC HEAD panic (dischargeFmv)
 #15195
 Merge XPolyKinds with XTypeInType
 #15245
 Data family promotion is possible
 #15282
 Document how equalitybearing constructors are promoted in Core
 #15308
 Error message prints explicit kinds when it shouldn't
 #15330
 Error message prints invisible kind arguments in a visible matter
 #15343
 Implicitly quantifying a kind variable causes GHC 8.6 to panic (coercionKind)
 #15346
 Core Lint error in GHC 8.6.1: Fromtype of Cast differs from type of enclosed expression
 #15370
 Typed hole panic on GHC 8.6 (tcTyVarDetails)
 #15380
 Infinite typechecker loop in GHC 8.6
 #15419
 GHC 8.6.1 regression (buildKindCoercion)
 #15428
 Oversaturated type family application panicks GHC (piResultTys2)
 #15472
 GHC HEAD type inference regression post"Remove decideKindGeneralisationPlan"
Userfacing changes
The changes described below are intended to be controlled by a new extension XTypeInType
, which will imply XPolyKinds
and XDataKinds
. But in some cases, it would be quite hard for GHC to know that the new features are being used. These cases all fall under the use of XPolyKinds
. So the XPolyKinds
language will become modestly more expressive under this proposal. But Haskell98 and Haskell2010 modes remain as standardscompliant as they are today.
Kinds and types are the same
There will be no distinction in the language between kinds and types. (Error messages will, however, do their best to use the words "type" and "kind" much like they do now. I take nondegradation of error messages very seriously.)
This means that inhabited kinds have type *
. In particular, *
has type *
. Though this causes inconsistency in other dependentlytyped languages, it does not in Haskell, essentially because equality proofs are written in a different sublanguage than ordinary terms. See our paper for more details.
Essentially, this is the one master change coming with Phase 1. But there are many consequences, as I draw out below.
Kind variables may be explicit
This will work:
data Proxy k (a :: k) = Proxy data Proxy2 :: forall k. k > * where Proxy2 :: forall k (a :: k). Proxy2 a
Note that we're dealing with kind variables explicitly here. Explicit kind variables will work everywhere that explicit type variables do  after all, kinds and types are the same. For backward compatibility and convenience, kind variables may be implicitly quantified, just like today.
All types can be promoted to kinds
Actually, promotion from type to kind is a noop. So this holds quite easily. Note that this means we now effectively have kind families.
All data constructors can be promoted to types
This includes GADT constructors and constructors that use type families.
GADTs may be GADTlike in kind parameters
But of course, because kinds and types are the same. Here are two examples:
data (a :: k1) :~~: (b :: k2) where HRefl :: forall k (a :: k). a :~~: a  explicit forall there unnecessary but informative data TypeRep (a :: k) where TInt :: TypeRep Int TMaybe :: TypeRep Maybe
*
is hard to parse, will become Type
Say the phrase Foo * Int
appears in a type. Is that the type operator *
applied to Foo
and Int
or the the type Foo
applied to the kind *
and Int
? It's impossible to know. So we have to do something strange here.
Without XTypeInType
, GHC will continue to use its knowledge of whether you are in a type or a kind to distinguish between the type operator *
and the kind *
. So all existing code will continue to work, quite conveniently.
With XTypeInType
, GHC will treat the kind *
as an identifier exported from the Prelude
(and also from GHC.Exts
). Currently, GHC must parse expressions with operators essentially as a spaceseparated list of tokens, because it can't know fixities until it figures out where all the operators have been imported from. Thus, when sorting out fixities, the kind *
will just have a magical fixity which instructs the renamer to treat it like an alphanumeric identifier, not a symbol. This should all work out fine in most code. The only problem is when a user has both the kind *
and some type operator *
in scope, such as from GHC.TypeLits
. Using *
in this scenario will be a straightforward ambiguous identifier and is an error. Note that XTypeInType XNoImplicitPrelude
will then mean that you cannot use the kind *
in your program without importing it from somewhere.
In addition to the above treatment, some standard library module (probably Data.Kind
, if that's not taken) will export Type
, which will have the same meaning as *
, as requested by several people in the community. The eventual plan is to deprecate and remove *
as a parsing oddity. Type
, naturally, will work both with and without XTypeInType
. Type
does conflict with existing code, but the choice is backward compatible because it's not exported from the Prelude
. Type
will be a normal identifier in every way, and it can be aliased through a normal type synonym definition if necessary to avoid naming conflicts.
QUESTION: Should *
just be disabled in XTypeInType
code? This is backward compatible but creates a terrible migration story for someone who wants to use XTypeInType
in GHC 8.0 but not in previous versions.
Visible type application
With all the type variables floating around, it will be very convenient to sometimes specify a type variable visibly in source code.
So, if id :: forall a. a > a
, then id @Int :: Int > Int
. See also a draft paper on the subject.
Type family equations can be constrained
Did not make it for 8.0.
Consider the following mess:
type family F a type family Blah (x :: k) :: F k data Foo :: forall k. k > F k > * > * type family G a type instance (F k ~ *) => G (Foo @k a (Blah a) (Blah a)) = Int
Note that there is no way to write the equation for G
without assuming that F k ~ *
. So we allow this with the syntax above. This will work quite similar to class instances, in that the patterns are matched first and the constraints examined only after an equation is chosen. This is likely not what you want out of constrained type family equations, but it seems the only way forward that plays nicely with the rest of GHC.
This feature will not carry over to data families (which for reasons beyond the scope of this post require full dependent types), though it will work for closed type families.
Design questions
Visibility changes in types
GHC tracks three different levels of visibility: Invisible
binders are never userwritten, Specified
ones are available for visible type applications, and Visible
ones are always userwritten. See Note [TyBinders and VisibilityFlags]
in TyCoRep.
The problem is what to do in higherrank kind situations. Consider these definitions:
data P1 k (a :: k)  P1 :: forall k > k > *  P1 * Int is OK  P1 _ Int is OK  P1 @* Int is NOT OK  P1 Int is NOT OK data P2 (a :: k)  P2 :: forall k. k > *  P2 @* Int is OK  P2 @_ Int is OK  P2 Int is OK  P2 * Int is NOT OK data P3 a  P3 :: forall {k}. k > *  P3 Int is OK  P3 @* Int is NOT OK  P3 @_ Int is NOT OK  P3 * Int is NOT OK data X (a :: forall k. k > *)  X :: (forall k. k > *) > *
A few notes on these definitions:
 The notation
forall {k}. k > *
onP3
's type says that thek
isInvisible
and is not available for visible type application,  We say that
P2 @* Int
is OK, but visible type application is not yet implemented in types. This is just an implementation detail, and for the purposes of this discussion, we'll assume that this feature is available.  It's quite likely
@*
parses as a single lexeme. Let's ignore that fact.  Note that GHC does not currently parse the type
forall k > k > *
. But it does prettyprint that type.
The question before the house is: which of the following are accepted?
X P1
X P2
X P3
Before delving into possible answers, we should note that any of these are sound to accept. The types of P1
, P2
, and P3
are all identical, except for the visibility of the binder for k
. So it's not silly to consider this question. It comes down to how we'd like the language to behave.
There seem to be three defensible choices for which of these to accept.

 YES
 YES
 YES
This version simply ignores visibility flags on binders when doing an equality check  very easy to implement.
 Simon advocated for this design in a call on Apr 1 2016. It is the simplest.
 Richard was concerned about what an equality between
forall k > k > *
andforall k. k > *
might mean. But we don't need these to betcEqType
, we just need a coercion between them. As long as the types areeqType
, thenRefl (forall k. k > *)
does nicely.  Richard was also concerned that if we consider these types equal, it means that we can replace one with the other willynilly, in thinking about a declarative specification of the type system. But with visible type application rules, we have two subtyping relations (and hence two typeequivalence relations) one to use when both types to compare are known and one to use otherwise. (See the paper.) So having one of these relations accept a connection between these two types is OK.
 Conor finds it abhorrent to think about a system that equates (under any equivalence relation) types that have different uservisible arities, as do
forall k > k > *
(arity 2) andforall k. k > *
(arity 1).  Consider now the expression
X (P1 k :: forall k. k > *)
. Is that accepted? By the kind signature,X
's argument has the right kind. Note that the signature bringsk
into scope and then checksP1 k
againstk > *
. It indeed has this type, so it certainly seems like(P1 k :: forall k. k > *)
should be accepted. (If you're dubious, think about what happens in terms.) Sadly, this desugars into a situation where we need a typelevel lambda. We don't have this yet. But we should be futureproof against a language that does have typelevel lambda.  The bullet above argues that
X (P1 k :: forall k. k > *)
should be accepted. But plan (A) says thatX P1
should be accepted. It surely can't hurt to add a type signature, so that means thatX (P1 :: forall k. k > *)
should be accepted. And this is quite bizarre to accept that last one alongside the first one.  In the termlevel type inference rules for a polytype type annotation, the first thing that happens is skolemization. It would be a bit odd for the typelevel type inference rules to be different, yet such a difference is required if we are to accept
P1 :: forall k. k > *
.

 NO
 YES
 YES
This version is a bit harder to implement, discerning between visible/not visible but not among specified and fully invisible.
 Stephanie and Conor like this one the most.
 It distinguishes between visible and not. Whether or not a binder is visible is easy to specify, but the user has less obvious control over whether a binder is specified or invisible.
 This plan (as does plan (A)) fails source level substitution. Specifically, if
a
(the variable of typeforall k. k > *
bound in the declaration forX
) is used asa @* Int
in the definition ofX
, thenX P3
would expand to mentionP3 @* Int
, which is disallowed. Substitution is restored if we substitute along with a type annotation, thus:(P3 :: forall k. k > *) @* Int
.  This one seems most similar to the termlevel treatment. It's hard to fully compare, because case (1) does not exist in terms.

 NO
 YES
 NO
This is what Richard originally implemented, having type equality depend closely on visibility.
 This version leads to obnoxious error messages if
fprintexplicitforalls
is off, saying onX P3
thatforall k. k > *
does not matchforall k. k > *
.  This version has the advantage of allowing substitution without type annotations. However, we already don't have this property in the termlevel language due to the specified/invisible variable distinction.
 This is really quite limiting.
Taking this all into account, Richard advocates for (B), but not all that strongly.
Implementation notes
The new type system
The new type system adheres rather closely to what is proposed in the original "FC with Kind Equality" paper, available here, with the addition of NoSubKinds. The type system, as implemented, is in the Core Specification document. Here are the highlights of the changes:
 Two new constructors for
Type
:CastTy :: Type > Coercion > Type
(which performs a kind cast) andCoercionTy :: Coercion > Type
which embeds coercions into types. The former eliminates kind coercions (that's the whole point of this change!) and the latter allows for the promotion of GADT data constructors, which will promote to a type taking a coercion argument.
 Forallcoercions now take a
ForAllCoBndr
:data ForAllCoBndr = ForAllCoBndr Coercion TyCoVar TyCoVar (Maybe CoVar)
Supposeg :: forall a1:k1.t1 ~ forall a2:k2.t2
. Unlike previously,k1
andk2
can be different. This necessitates storing botha1
anda2
in the forallcoercion. TheCoercion
datum is a proof thatk1 ~ k2
, and theMaybe CoVar
proves thata1 ~ a2
, whena1
anda2
are type variables. (When they're coercion variables, we can just use proofirrelevance, described below.)
 New coercion forms:
CoherenceCo
(which proves equality between a type and that type with a cast on it) andKindCo
(which extracts a kind coercion from a heterogeneous type coercion).
UnivCo
provenances are now a datatype instead of a string:data UnivCoProvenance = UnsafeCoerceProv  ^ From @unsafeCoerce#@  PhantomProv  ^ From the need to create a phantom coercion;  the UnivCo must be Phantom.  ProofIrrelProv  ^ From the fact that any two coercions are  considered equivalent
AProofIrrelProv
UnivCo
requires that the two types in theUnivCo
are both just coercions. Proofs are irrelevant in FC. APhantomProv
UnivCo
requires that the role of theUnivCo
bePhantom
. These checks are part of CoreLint.
 Roles on kind coercions, as described in my recent ICFP submission here.
 The new mutual recursion between types and coercions means that TypeRep has been renamed TyCoRep. There is also a nontrivial Coercion.hsboot file.
Changes to the typechecker
Typechecking types (that is, the functions in TcHsType) can now emit constraints deferred to the solver. This means that every call of these functions must be in a context that can deal with emitted constraints. For types that appear within expressions, this is automatic. For toplevel declarations, though, it was necessary to add calls to captureConstraints
. This is mostly done via the new function TcSimplify.solveTopConstraints :: TcM a > TcM (a, Bag EvBind)
which captures constraints and then solves them. The "top" in there is because there are no givens or skolems.
The resulting EvBind
s then must be dealt with. However, there is often no place to put them. (For example, consider a data
declaration.) So, I convert the EvBind
s to a coercion substitution (see TcEvidence.evBindsSubst
and TcEvidence.evBindsCvSubstEnv
) and inline the coercions. This operation doesn't work as expected if the EvTerm
s in the EvBind
s can't be converted cleanly to Coercion
s. (This will happen with superclass equalities and with deferred type errors.) Currently, my implementation just fails in this case, often with an unbound variable during CoreLint. We obviously need a better story here, but I'm not quite sure of the best approach.
(I am confident that some solution exists here. As a strawman, it is easy to detect when the EvTerm
> Coercion
conversion fails and we could issue an error. These errors would happen only with superclass equalities and deferred type errors, so they would be predictable and could be reasonably dealt with by programmers. Of course, I'd like to do better, but not having a solution to this particular problem isn't a dire situation.)
 TcCanonical didn't change all that much. It now must canonicalize casts (see
TcCanonical.canEqCast
), but that's straightforward. The biggest wrinkle is that I retain the invariant that canonical equalities are still homogeneous. So, before producing theCTyEqCan
, we must homogenize the kind. This is done inTcCanonical.homogeniseRhsKind
, the implementation of which is unsurprising.
 TcFlatten has a bit of a sorry story. It seems the following is a nice invariant to have: a flattened type always has a flattened kind. However, flattening now (even in HEAD) takes roles into account. Because the role of a kind coercion is representation, no matter the role of the type coercion, it only makes sense to say that a flattened type's kind is flattened with respect to representational equality.
If we have
newtype Age = MkAge Int
anddata Proxy k (a :: k) = P
(where the kind parameter is explicit), flatteningProxy Age
(w.r.t. nominal equality) gives us(Proxy Age) > (axAge > <*>) :: Int > *
, which is generally not what we want. SeeNote [Kinds when flattening an AppTy]
in TcFlatten. This problem is surmountable, but this wrinkle demands more thought. There are several comments throughout TcFlatten about issues emanating from this one that will need to get fixed.
 Final zonking (in TcHsSyn) now works with a
CvSubstEnv
extracted from theEvBind
s. This is so that the zonked types used inTyCon
definitions have their coercion variables inlined. It wouldn't work just to do zonking as before and then substitute, because we would need to zonk again, and then substitute again, etc. (Plus, we're sometimes in the typechecking knot, when we're forced to do it all in one pass.)
 See
Note [Bidirectional type checking]
in TcHsType. In brief, I now support higherrank kinds via a simple bidirectional type checking algorithm.
 Dealing with
LHsTyVarBndrs
has become more challenging, because there can be dependency between the variables: we must bring a variable into scope before checking any subsequent variables. See{kt}cHsTyVarBndrs
andsplitTelescopeTvs
in TcHsType. See alsoNote [Typechecking telescopes]
.
 Gobs of code dealing exclusively with kinds has been removed from TcHsType.
 In HEAD, GHC is not as good as it could be keeping proper
TyVar
s out of the typechecker and keeping skolems in. HEAD's kindlevelTyVar
s, in particular, may be encountered in the typechecker. This problem is worse in my branch, meaning thatTyVar
s can be encountered in types and in kinds. My solution is to just allow this to happen, callingTyVar
s vanilla skolems:tcTyVarDetails
no longer requires aTcTyVar
. An alternate solution is to do a better job instantiating, etc.
SLPJ. A project I have in the back of my mind is to separate TcType
from Type
. The former have unification variables, and perhaps other clutter (e.g. evidence bindings perhaps). The latter do not. Desugaring woudl convert TcType
to Type
.
TcMType.quantifyTyCoVars
may deserve special attention. It now usesquantifyPred
(taken fromdecideQuantification
) to figure out what to do with covars. I believe it works as written, but it's a substantial change from before.
 Just like we sometimes have to promote tyvars in
simplifyInfer
, we now have to promote covars. Promoting a covar is simply reemitting it as a Wanted in a larger context.
 We should discuss
simplifyRule
. I'm still a little mystified about how RULES are typechecked.
 In general, TcSimplify may deserve a little extra attention, as there are a lot of nontrivial and nonobvious changes there.
rejigConRes
has become more complicated. As it (at least at one point) had quite a lot of faffing about with coercions, I moved the tricky bits toCoercion.mkGADTVars
. See the comments around that function. Once nondependent equalities are eliminated fully, some aspects of this will get slightly simpler.
Points of interest
TyVar
> TyCoVar
In many functions and datatypes throughout GHC, I changed names including
TyVar
to names include TyCoVar
. These functions/types now may contain
coercion variables as well as type variables. The name change does two
things: it calls my attention to these functions when something changes
during a merge, and the new name reminds me (and, potentially, others
someday) to handle both type variables and coercion variables.
SLPJ type/kind variable are erased, but coercion variables are valuelevel and are not erased. So a TyCoVar
is a bit of a mysterious beast.
Similarly, a TvSubst
without a coercion substitution just doesn't make sense. So, TvSubst
and CvSubst
have been combined to TCvSubst
.
A pervasive effect is that mkTyVarTy
has been split into mkOnlyTyVarTy
, which works only on type variables, and mkTyCoVarTy
, which works on both type and coercion variables. The latter checks what it's given and behaves accordingly.
All coercion variables are Pibound
What is the type of \ (c :: Int ~# Bool). 5 > c
? In theory, it could be
(Int ~# Bool) > Bool
or forall (c :: Int ~# Bool). Bool
. I always choose
the latter, to make exprType
sane. That forall
should really be spelled pi
.
Binder
Type
now has merged FunTy
and ForAllTy
. Here is the declaration for the
new ForAllTy
:
 ForAllTy Binder Type  ^ A ? type.
with
  A 'Binder' represents an argument to a function. Binders can be dependent  ('Named') or nondependent ('Anon'). They may also be visible or not. data Binder = Named Var VisibilityFlag  Anon Type  visibility is determined by the type (Constraint vs. *)
SLPJ So ForAllTy (Anon ty1) ty2
is ty1 > ty2
. Worth saying this! And presumably it's prettyprinted like that too.
The Binder
type is meant to be abstract throughout the codebase. The only substantive difference between the combined ForAllTy
and the separate FunTy
/ForAllTy
is that we now store visibility information. This allows use to distinguish between, for example
data Proxy1 (a :: k) = P1
and
data Proxy2 k (a :: k) = P2
Proxy1
's kind argument is Invisible
and Proxy2
's is Visible
. SLPJ Don't understand. Is this some new sourceHaskell feature?
Currently, any Named
ForAllTy
s classifying terms are all Invisible
.
This design change has a number of knockon effects. In particular, splitForAllTys
now splits regular functions, too. In some cases, this actually simplified code. In others, the code had to use the new splitNamedForAllTys
, which is equivalent to the old splitForAllTys
.
SLPJ: Do you really mean splitNamedForAllTys
here, or do you mean splitTypeLevelForAlls
? That is, are you trying to split on visibilty or on erasibility? And why?
Another knockon effect is that mkForAllTy
now takes a Binder
. To make this easier for callers, there is a new mkInvForAllTy :: TyCoVar > Type > Type
which makes a Named
, Invisible
Binder
for the ForAllTy
.
In general, I've been happy with this new design. In some preliminary work toward Pi, Binder
has added a few more bits, making this redesign even better going forward.
Previously, we've thought about adding visibility information to the anonymous case. I still think this is a good idea. I just haven't done it yet.
Coercion
and TcCoercion
The impedance mismatch between Coercion
and TcCoercion
has become more painful. This is chiefly because TcType
s and Type
s are the same, and Type
s have Coercion
s inside, not TcCoercion
s. Recently, we have injected Coercion
into TcCoercion
, and this helped my branch considerably. In particular, this means that many algorithms that previously returned a TcCoercion
now return a Coercion
, which is more flexible: Coercion
s can be used in types or can be easily converted to a TcCoercion
, if required. (In particular, TcUnify.uType
now returns a Coercion
. unifyType
, the exported function, still returns a TcCoercion
.)
It is also sometimes necessary to convert a TcCoercion
into a Coercion
. This happens in the solver, when the witness of an equality constraint must be used in a type. On the surface, this conversion seems harder, but there's a trick that makes it easy: to convert a TcCoercion
into a Coercion
, emit a new bound EvVar c
whose value is the TcCoercion
in question. Then, your Coercion
is CoVarCo c
. Works like a charm. See TcSMonad.dirtyTcCoToCo
. (I actually don't think this trick is all that dirty anymore. It felt wrong at first.)
SLPJ I'm still struggling with the idea that a term (the result of deaugaring a TcCoercion
) can appear in a type (admittedly via its name). What if it is bottom? When is it evaluated?
Due to some eager inlining of coercions, the function DsBinds.ds_tc_coercion
 the function that converts a zonked TcCoercion
to a Coercion
 is now TcEvidence.tcCoercionToCoercion
.
All of this has gotten me thinking: I think we can do away with TcCoercion
s altogether. The only reason to have TcCoercion
is to support TcLetCo
. However, it seems that this can be done with a new EvLet :: TcEvBinds > EvTerm > EvTerm
constructor for EvTerm
. If a let
is needed deep within some coercion, just bind a new EvVar to an EvLet
and use CoVarCo
. Getting rid of TcCoercion
would be a vast simplification, unless I'm missing some critical detail.
SLPJ But TcCoercion
represents a lifted equality, whereas Coercion
represents an unlifted one.
Moreover I don't think you can float out those coercions. What if it looks like
forall a. let g = ...a... in ...
where the forall
is a TcForAllCo
and the let
is a TcLetCo
. Look at TcSMonad.deferTcSForAllEq
.
Lifted vs.~unlifted equality predicates
Now, both a ~ b
and a ~# b
are considered predicates. This means that the solver deals with both lifted and unlifted equality. This is suboptimal, and the plan is to have the solver work only with unlifted equality, defining class a ~# b => a ~ b
to make lifted equality unmagical. See this page for more discussion. Because of the two forms of equality, there are some extra steps in a few places within the typechecker.
Kind equalities and data constructors
Universal variables are type variables; existentials might be coercion variables
A type constructor's type variables are just that: they are sure to be proper type variables. There doesn't seem to be anything wrong, in theory, with including coercion variables here, but there also doesn't seem to be a need. However, a data constructor's existential variables might be coercions. Indeed, this is how all GADTs are currently encoded. For example:
data G1 a where MkG1 :: Int > G1 Bool data G2 (a :: k) where MkG2 :: Char > G2 Double
The rejigged types look like this:
MkG1 :: forall (a :: *). forall (gadt :: a ~# Bool). Int > G1 a MkG2 :: forall (k :: *) (a :: k). forall (gadt1 :: k ~# *) (gadt2 :: a > gadt1 ~# Double). Char > G2 k a
Thus, a TyCon
can have coercionvariable arguments, but only if that
TyCon
is really a promoted datacon.
SLPJ How does promotion work now? What is the kind of 'MkG2
?
Separation between dependent and nondependent equalities
Various bits of code refer to dependent vs. nondependent equalities. A "dependent equality" is a coercion that is used in a type; a nondependent equality is not used in a type. At one point, I was thinking that a GADT datacon should be careful to distinguish between dependent equalities and nondependent ones. That way, we could defer type errors for nondependent equalities by using a lifted coercion instead of an unlifted one there. But, now I think everything should just use unlifted equality and that we should remove this distinction. Bottom line: don't worry about this too much.
GADT coercions are now existential variables
In accordance with the two points above, all GADTinduced coercions are now considered existential variables. This causes a little work around datacon signatures, because a signature includes a separate field for existential variables as it does for GADT equalities. This could be cleaned up somewhat, now that I've decided that all GADT equalities really should be existentials.
SLPJ Given an example. GADTs have the eqSpec
stuff...
Parsing is just wrong
I've removed the kind parser, in favor of just using the type parser. This is wrong, if only because of the type *
. See proposed solution here, under "UPDATE".
tryTcS
is now really pure
In HEAD, tryTcS
claims to "throw away all evidence generated". This isn't quite true. tryTcS
can still set metavariables and may twiddle EvBindsVar
s inside of implications. With kind equalities, this won't do. The problem is that solving may invent new coercion variables; these variables may end up in types. If a metavariable is then set to point to a type with a fresh coercion variable in it, we have a problem: after throwing away the evidence, that coercion variable is unbound. (This actually happens in practice.) So, tryTcS
must be very careful to be properly pure. It does this by maintaining the set of filledin metavariables and a way to roll back any changes to nested EvBindsVar
s. After the inner TcS
action is complete, tryTcS
rolls back the changes.
This works nicely in practice, but one does have to be careful when reading a ddumptctrace
, because a writeMetaTyVar
might not be the final word. (If that's an issue, it's easy to fix. The TcS
monad could know whether it's pure or not and print out accordingly.)
SLPJ Ha ha. tryTcS
is no longer used. It's dead code. (It was always only used for defaulting, in very restricted way, and I got rid of that part, but forgot to remove tryTcS
itself.)
CUSKs
I have a sinking feeling that a type has a CUSK now only when all types and kinds have known types. But I can't come up with an example that shows this clearly. However, we can say that anything to the right of a ::
is known to have type *
, so this doesn't bite hard in practice. Thus data T (a :: k)
has a CUSK, but data S (a :: Proxy k)
does not. Does data U (a :: Maybe k)
? I think it does, but that's not quite as obvious. What's the easytoarticulate rule here? (Now, it's this nice rule: a type has a CUSK iff all of its type variables are annotated; if it's a closed type family, the result kind must be annotated, too.)
Datacon wrappers are now rejigged
In HEAD, a datacon worker differs from a datacon wrapper in two distinct ways: the worker's types are UNPACK
ed as requested, and the worker's type is rejigged, la
rejigConRes
. The wrapper has the datacon's original type.
This design caused endless headaches for me. (Sadly, I can't recall exactly what the problem was  something to do with applying kind substitutions to variables. I can easily recall going round and round trying to figure out the right datacon design, though!) So, I changed wrappers to have a rejigged type. (Workers are unchanged.) This was actually a nice simplification in several places  specifically in GADT record update. The only annoying bit is that we have to be careful to print out the right userfacing type, which is implemented in DataCon.dataConUserType
.
SLPJ so :t K
, where K
is a GADT data constructor, will show... ah maybe it's ok. And :info K
knows to use dataConUserType
. Need a Note
about this. Pattern matching may need care.
Bad GADT return types cause panic
Writing a bogus GADT return type causes a panic. The problem is that
checkValidDataCon
is supposed to check if rejigConRes
was valid. To do
this, checkValidDataCon
needs the userspecified result type. Normally,
this is retrieved from dataConOrigResTy
. The problem is that, now,
the dataConOrigResTy
is substed by the kind substitution produced in
rejigConRes
. This is an ugly circular dependency. We could (1) store the
original, unsubsted result ty in the DataCon
for just this reason, or
(2) install lots of ugly plumbing in TcTyClsDecls to carry the unsubsted
result ty, or (3) do something else. I want your input, as both (1)
and (2) are terrible.
SLPJ We'd better discuss this. It can't be that hard.
liftCoSubst
The lifting operation has become subtler. Happily, it is well described in Section 5 of this paper. The actual, implemented, roleaware version of lifting is included in Appendix B of this paper.
New eqType
SLPJ I'm also worried about the typelevel equivalent of CoreSubst.exprIsConApp_maybe
. This is a complicated function! Do we need to do something similar when trying to persuade a type to look like a TyConApp
? In general there are lots of functions in Type
and every one of them must be adjusted to handle casts. Is it clear how?
Is Int
the same as Int > <*>
? In the formalism: no. This is OK, because we have a coercion form (CoherenceCo
) that proves Int ~ (Int > <*>)
. But, in practice, this is very very annoying. It's tempting to write eqType
simply to ignore casts... but that would be wrong, because it can equate two types with different kinds. So, the solution is to have an "erased equality check" that compares types ignoring coercions, but to use that check on the types in question and their kinds. This is all implemented in eqType
. The upshot is that two types are equal when they have the same kinds and the types are the same, ignoring coercions. Nice and simple.
There are, of course, wrinkles:
 We wish to avoid ever comparing coercions. So, I removed
eqCoercion
and replaced it with a check looking at a coercion's type. After all, if two proofs prove the same thing, they should be interchangeable. This change includes a vast simplification toCoercionMap
in TrieMap.
SLPJ good idea! But it should still be called eqCoercion
shouldn't it? It just has a better implementation. RAE Yes,
that's entirely unclear above. It still is called eqCoercion
.
 There is a bizarre wrinkle around unification. We want unification to succeed whenever a unifying substitution exists. Take this example:
type family Bool2 where Bool2 = Bool data T :: Bool > *
Now, we wish to unify
T True
witha b
, wherea :: Bool2 > *
andb :: Bool2
. A solution exists:[a > T > (sym axBool2 > *), b > True > sym axBool2]
. But the substitution requiresaxBool2
, which isn't mentioned in the input. Figuring out this kind of unification is beyond the scope of the unifier. (It gets even harder to justify with open type families.)
My solution is to say that
(T > (axBool2 > *)) (True > sym axBool)
is not equal toT True
. When doing the erased equality check, we also check the kind of every application argument. Because the kind ofTrue > sym axBool
differs from the kind ofTrue
, the types above differ. With this change, unification is complete. Note that the issue comes up only withAppTy
s, neverTyConApp
s, because aTyCon
's kind is always closed. If there is a difference in the kind of an argument, that difference must show up earlier in a kind argument. See alsoNote [Nontrivial definitional equality]
in TyCoRep.
 We need a
TypeMap
now to treat alleqType
types equally. This takes some work, implemented in TrieMap.
 Instance lookup now returns a matching instance along with a coercion witnessing the equality between the found instance and the desired instance. This is because, say, a lookup of
Foo (Int > co)
should find the instanceFoo Int
. Similarly, unification returns a unifying substitution and a coercion.
Substitution in the desugarer
Solving may produce toplevel unlifted coercions. Of course, we can't have toplevel unlifted things. So, the desugarer inlines these as it works. This causes a lot of line changes, but it's all very straightforward.
SLPJ How do we know they are nonrecursive?
evBindsCvSubstEnv
There are several scenarios (in particular, in TcTyClsDecls) where we need to extract a coercion substitution from a Bag EvBind
. This happens when we don't have a convenient place to bind coercion variables.
SLPJ eh?
Error messages
Now that kind errors in types can be deferred to the solver, all the errormessage generating machinery in TcHsType is gone. Instead, I've had to add a lot of adhoc processing in TcErrors in an attempt to recreate the errors just as before. (We can debate whether the messages should be reformatted, but I wanted to ensure there was no degradation in the quality of errors.) The changes to TcErrors are mostly terrible, and the whole lot needs refactoring. This state of affairs is somewhat intentional, because I was really unsure what was going to be necessary to get good errors. As I get closer to 0 testsuite failures, the picture is becoming clearer. Soon, I'll be able to figure out a better way to do TcErrors and will refactor. In the meantime, we deal with the mess.
One particular step I had to take is to include extra information in the TypeEqOrigin
CtOrigin
. Previously, it had fields for "expected type" and "actual type". It now includes a flag whether the error message should say "type" or "kind", along with the thing that has the actual type. This "thing with actual type" is not used in termlevel error message printing, in order to avoid spurious testsuite failures, but it could (and should) be. See TcRnTypes.CtOrigin
.
Unboxed tuples are more parameterized
Because an unboxed tuple can contain both boxed bits and unboxed bits, it is necessary to parameterize the type and data constructors over levity variables. For example:
(#,,#) :: forall (v1 :: Levity) (v2 :: Levity) (v3 :: Levity) TYPE v1 > TYPE v2 > TYPE v3 > *
Renaming in LHsTyVarBndrs
The salient difference between the two fields of LHsTyVarBndrs
is no longer that one is kinds and one is types, but how the bits are declared. What was hsq_kvs
is now hsq_implicit
(for implicitlydeclared) and what was hsq_tvs
is now hsq_explicit
.
SLPJ we could do with nailing down terminology
 implicit vs explicit
 visible vs invisible
 erased vs nonerased
and use it consistently.
Refactoring in iface/
There's a bunch of changes to the iface
code, but it's all rather boring.
Fewer optimizations in zonking
There are a few little optimizations in TcHsSyn around zonking. For example, after finding a filledin metavariable, its contents are zonked and then the variable is reset to the zonked contents. This is problematic now.
The zonking algorithm in TcHsSyn knotties Id
s. Of course, coercion variables are Id
s, and so these knottied bits can appear in types. We thus must be very careful never, ever to look at a zonked type, which these optimizations do. So, I removed them.
I have not yet reexamined to see if there is a way to restore this behavior. There probably is, as coercion variables can't be recursive!
Overring visibility assumptions
My limited experience in programming in the enhanced language tells me that we really
need ways to override a visibility specification. That is, we need to allow _
to have
GHC infer a normallyvisible argument, and we need a way of specifying an invisible
argument at call sites. Currently, because there is no override, there is no syntax
for providing a role annotation to an invisible argument. Thus, all invisible arguments
default to having a nominal role, in order to preserve abstraction.
SLPJ Don't understand.
MaybeNew
is back
In Simon's refactoring in fall 2014, the MaybeNew
type disappeared from the solver infrastructure. I found this type useful, so I brought it back. It seemed like a better way to structure my algorithm than working without it.
Lots more "OrCoVar
" functions in Id
module
A CoVar
is now a distinct flavour of an Id
, with its own IdDetails
. This is necessary because we often want to see  quickly  whether or not a var is a covar. However, there are many places in the code that creates an Id
, without really knowing if the Id
should be a plain old Id
or really a CoVar
. There are also a bunch of places where we're sure it's really not a CoVar
. The OrCoVar
functions allow call sites to distinguish when the CoVar
check (done by looking at a var's type) should be made. This is not just an optimization: in one obscure scenario (in the simplifier, if I recall), the type is actually a panic.
This could stand some cleaning up, but it was hard for me to figure out when we're sure an Id
isn't a CoVar
.
No more instance Eq Type
Somewhere along the way (I think in wildcard implementation?), an instance Eq Type
slipped in. I removed it.
analyzeType
Once upon a time, I embarked on a mission to reduce imports of TyCoRep
, instead aiming to export functions to make exposing Type
's innards unnecessary. This effort became analyzeType
and mapType
, both in Type.hs
. mapType
is a clear win, removing gobs of zonking code and making a relatively clean interface. See simplifications in TcHsSyn and TcMType. It's not clear if analyzeType
is paying its weight though. I could easily undo this change.
Tasks
 Fully remove nondependent GADT equalities.
 Try to restore optimizations in zonking. (Could be after merging)
 Check kind variables when determining whether or not a declaration has a CUSK.
 Sort out the debugger. It's scary, so I've ignored it. Any help/advice appreciated.
 Fix parser.
 Remove
TcCoercion
. (Could be after merging)
 Refactor TcErrors. (Could be after merging)
 Remove lifted equality predicates from the solver.
 Figure out what to do about superclass equalities. (Could be after merging)
 Figure out what to do about deferred kind errors. (Could be after merging)
 Fix flattening. See comments in TcFlatten.
 Fix pattern synonyms.
 Use
pushRefl
when splitting a coercion. Unless we're guaranteed that the input is nonRefl. And then ASSERT.
 Document the new weird type equality (which ignores casts)
Questions
 What to do about bad GADT return types
 Clarify typechecking RULES
 How to expose levity polymorphism to users
 Keep
analyzeType
?
 How to deal with superclass equalities and deferred kind errors
 What concrete syntax to use for overriding visibility specifications?
Answers
 Proposal: remove dependent coercion quantification.
 That is, not allow
forall (c::a~b). ...(ty > c)....
. Instead only allow anonymous quantification, thus(a~b) => ....
.
 Another way to say this: coercion variables are only bound by terms, not in types.
 We do not lose any kindindexed GADTs, because we have hererogeneous equality. The prototypical example is
data Eq (a::k1) (b::k2) where EQ :: forall (c::k). Eq c c  EQ :: forall k1 k2 (a::k1) (b::k2). (a ~ b) => Eq k1 k2 a b
 Richard has an exotic example of what is lost. We could not write this type:
foo :: forall k (a::k). (c: F k ~ G k) => Proxy [H1 a > c, H2 a] where H1 :: forall k. k > F k H2 :: forall k. k > G k
But you can write this without using dependent coercions:foo :: forall (a::k) (b :: F k). (b ~ H2 a) => Proxy [H1 a, b]
But what aboutforall (c: t1~t2). K c where K :: (t1~t2) => *
 That is, not allow
 Coercion equalities solved by
TcCoVars
, not via theEvBinds
stuff. Enables getting rid ofTcLetCo
and hence collapseCoercion
andTcCoercion
. Deferred type errors collected by zonker when zonking coercions.
 Give up on deferred kind errors.
 Nominal roles only in kinds. Yay.
More minor
 Remove
SubCo
in favour of implicit subroling. Do this in HEAD.  Simon: make
GivenCt
containEvVar
only. In HEAD.