True of FlatSkol skolems only

True of both given and wanted flatten-skolems (fak and usk)

Make a representational equality predicate

Make an equality predicate at a given role. The role must not be Phantom.

Similar to coreView, but for the type checker, which just looks through synonyms

Does the AppTy split as in splitAppTy_maybe, but assumes that any Core view stuff is already done

What is the role assigned to the next parameter of this type? Usually, this will be Nominal, but if the type is a TyConApp, we may be able to do better. The type does *not* have to be well-kinded when applied for this to work!

Type equality on source types. Does not look through newtypes or PredTypes, but it does look through type synonyms. Watch out for horrible hack: See Note [Comparison with OpenTypeKind]

Does the given tyvar appear in the given type outside of any non-newtypes? Assume we're looking for a. Says "yes" for a, N a, b a, a b, b (N a). Says "no" for [a], Maybe a, T a, where N is a newtype and T is a datatype.

Finds outermost type-family applications occuring in a type, after expanding synonyms.

The key type representing kinds in the compiler. Invariant: a kind is always in one of these forms:

FunTy k1 k2
TyConApp PrimTyCon [...]
TyVar kv   -- (during inference only)
ForAll ... -- (for top-level coercions)

See Type for details of the distinction between these Kinds

See Type for details of the distinction between these Kinds

See Type for details of the distinction between these Kinds

See Type for details of the distinction between these Kinds

Given two kinds k1 and k2, creates the Kind k1 -> k2

Iterated application of mkArrowKind

See Type for details of the distinction between these Kinds

True of any sub-kind of OpenTypeKind

Essentially splitFunTys on kinds

The key representation of types within the compiler

A type of the form p of kind Constraint represents a value whose type is the Haskell predicate p, where a predicate is what occurs before the => in a Haskell type.

We use PredType as documentation to mark those types that we guarantee to have this kind.

It can be expanded into its representation, but:

• The type checker must treat it as opaque
• The rest of the compiler treats it as transparent

Consider these examples:

f :: (Eq a) => a -> Int
g :: (?x :: Int -> Int) => a -> Int
h :: (r\l) => {r} => {l::Int | r}

Here the Eq a and ?x :: Int -> Int and rl are all called "predicates"

A collection of PredTypes

Wraps foralls over the type using the provided TyVars from left to right

Creates a function type from the given argument and result type

Splits off argument types from the given type and associating them with the things in the input list from left to right. The final result type is returned, along with the resulting pairs of objects and types, albeit with the list of pairs in reverse order. Panics if there are not enough argument types for the input list.

A key function: builds a TyConApp or FunTy as appropriate to its arguments. Applies its arguments to the constructor from left to right.

Applies a type to another, as in e.g. k a

Instantiate a forall type with one or more type arguments. Used when we have a polymorphic function applied to type args:

f t1 t2

We use applyTys type-of-f [t1,t2] to compute the type of the expression. Panics if no application is possible.

This function is interesting because:

1. The function may have more for-alls than there are args

   1. Less obviously, it may have fewer for-alls

For case 2. think of:

applyTys (forall a.a) [forall b.b, Int]

This really can happen, but only (I think) in situations involving undefined. For example: undefined :: forall a. a Term: undefined (forall b. b->b) Int This term should have type (Int -> Int), but notice that there are more type args than foralls in undefineds type.

Create the plain type constructor type which has been applied to no type arguments at all.

Creates a type equality predicate

Type substitution

The following invariants must hold of a TvSubst:

1. The in-scope set is needed only to guide the generation of fresh uniques
2. In particular, the kind of the type variables in the in-scope set is not relevant
3. The substitution is only applied ONCE! This is because in general such application will not reached a fixed point.

A substitution of Types for TyVars and Kinds for KindVars

Generates the in-scope set for the TvSubst from the types in the incoming environment, hence "open"

Generates the in-scope set for the TvSubst from the types in the incoming environment, hence "open"

Called when doing top-level substitutions. Here we expect that the free vars of the range of the substitution will be empty.

Substitute within a Type

Substitute within several Types

Type substitution making use of an TvSubst that is assumed to be open, see zipOpenTvSubst

Substitute within a ThetaType

See Type for what an unlifted type is

Returns true of types that are opaque to Haskell.

NB: for type synonyms tyVarsOfType does not expand the synonym tyVarsOfType returns only the free variables of a type For example, tyVarsOfType (a::k) returns {a}, not including the kind variable {k}