A global typecheckable-thing, essentially anything that has a name. Not to be confused with a TcTyThing, which is also a typecheckable thing but in the *local* context. See TcEnv for how to retrieve a TyThing given a Name.

Argument Flag

Is something required to appear in source Haskell (Required), permitted by request (Specified) (visible type application), or prohibited entirely from appearing in source Haskell (Inferred)? See Note [TyBinders and ArgFlags] in TyCoRep

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

Variable

Essentially a typed Name, that may also contain some additional information about the Var and it's use sites.

Type or kind Variable

Type or Coercion Variable

A TyBinder represents an argument to a function. TyBinders can be dependent (Named) or nondependent (Anon). They may also be visible or not. See Note [TyBinders]

Type Variable Binder

A TyVarBinder is the binder of a ForAllTy It's convenient to define this synonym here rather its natural home in TyCoRep, because it's used in DataCon.hs-boot

Attempts to obtain the type variable underlying a Type, and panics with the given message if this is not a type variable type. See also getTyVar_maybe

Attempts to obtain the type variable underlying a Type

Attempts to obtain the type variable underlying a Type, without any expansion

If the type is a tyvar, possibly under a cast, returns it, along with the coercion. Thus, the co is :: kind tv ~R kind type

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

Attempts to take a type application apart, as in splitAppTy_maybe, and panics if this is not possible

Recursively splits a type as far as is possible, leaving a residual type being applied to and the type arguments applied to it. Never fails, even if that means returning an empty list of type applications.

Like splitAppTys, but doesn't look through type synonyms

Attempt to take a type application apart, whether it is a function, type constructor, or plain type application. Note that type family applications are NEVER unsaturated by this!

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

Does the AppTy split as in tcSplitAppTy_maybe, but assumes that any coreView stuff is already done. Refuses to look through (c => t)

Make an arrow type

Make nested arrow types

Attempts to extract the argument and result types from a type, and panics if that is not possible. See also splitFunTy_maybe

Attempts to extract the argument and result types from a type

Extract the function result type and panic if that is not possible

Extract the function argument type and panic if that is not possible

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

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

The same as fst . splitTyConApp

Retrieve the tycon heading this type, if there is one. Does not look through synonyms.

The same as snd . splitTyConApp

Attempts to tease a type apart into a type constructor and the application of a number of arguments to that constructor

Attempts to tease a type apart into a type constructor and the application of a number of arguments to that constructor. Panics if that is not possible. See also splitTyConApp_maybe

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!

Like tcSplitTyConApp_maybe but doesn't look through type synonyms.

Split a type constructor application into its type constructor and applied types. Note that this may fail in the case of a FunTy with an argument of unknown kind FunTy (e.g. FunTy (a :: k) Int. since the kind of a isn't of the form TYPE rep). Consequently, you may need to zonk your type before using this function.

If you only need the TyCon, consider using tcTyConAppTyCon_maybe.

Attempts to tease a list type apart and gives the type of the elements if successful (looks through type synonyms)

Like splitTyConApp_maybe, but doesn't look through synonyms. This assumes the synonyms have already been dealt with.

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

Like mkForAllTys, but assumes all variables are dependent and Inferred, a common case

Like mkForAllTys, but assumes all variables are dependent and specified, a common case

Like mkForAllTys, but assumes all variables are dependent and visible

Make a dependent forall over an Inferred (as opposed to Specified) variable

Take a ForAllTy apart, returning the list of tyvars and the result type. This always succeeds, even if it returns only an empty list. Note that the result type returned may have free variables that were bound by a forall.

Like splitPiTys but split off only named binders.

Attempts to take a forall type apart, but only if it's a proper forall, with a named binder

Take a forall type apart, or panics if that is not possible.

Attempts to take a forall type apart; works with proper foralls and functions

Takes a forall type apart, or panics

Split off all TyBinders to a type, splitting both proper foralls and functions

Given a list of type-level vars and a result type, makes TyBinders, preferring anonymous binders if the variable is, in fact, not dependent. All binders are visible.

Makes a (->) type or an implicit forall type, depending on whether it is given a type variable or a term variable. This is used, for example, when producing the type of a lambda. Always uses Inferred binders.

mkLamType for multiple type or value arguments

(piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn) where f :: f_ty piResultTys is interesting because: 1. f_ty may have more for-alls than there are args 2. Less obviously, it may have fewer for-alls For case 2. think of: piResultTys (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.

Drops all ForAllTys

Is this a numeric literal. We also look through type synonyms.

Is this a symbol literal. We also look through type synonyms.

Extract the RuntimeRep classifier of a type. For instance, getRuntimeRep_maybe Int = LiftedRep. Returns Nothing if this is not possible.

Extract the RuntimeRep classifier of a type from its kind. For example, getRuntimeRepFromKind * = LiftedRep; Returns Nothing if this is not possible.

Make a CastTy. The Coercion must be nominal. This function looks at the entire structure of the type and coercion in an attempt to maintain representation invariance (that is, any two types that are eqType look the same). Be very wary of calling this in a loop.

Is this type a custom user error? If so, give us the kind and the error message.

Render a type corresponding to a user type error into a SDoc.

Get the type on the LHS of a coercion induced by a type/data family instance.

Try to split up a coercion type into the types that it coerces

Given a tycon and its arguments, filters out any invisible arguments

Like filterOutInvisibles, but works on TyVars

Given a tycon and a list of things (which correspond to arguments), partitions the things into Inferred or Specified ones and Required ones The callback function is necessary for this scenario:

T :: forall k. k -> k
partitionInvisibles T [forall m. m -> m -> m, S, R, Q]

After substituting, we get

T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n

Thus, the first argument is invisible, S is visible, R is invisible again, and Q is visible.

If you're absolutely sure that your tycon's kind doesn't end in a variable, it's OK if the callback function panics, as that's the only time it's consulted.

Find the result Kind of a type synonym, after applying it to its arity number of type variables Actually this function works fine on data types too, but they'd always return *, so we never need to ask

This describes how a "map" operation over a type/coercion should behave

Unwrap one layer of newtype on a type constructor and its arguments, using an eta-reduced version of the newtype if possible. This requires tys to have at least newTyConInstArity tycon elements.

Given a family instance TyCon and its arg types, return the corresponding family type. E.g:

data family T a
data instance T (Maybe b) = MkT b

Where the instance tycon is :RTL, so:

mkFamilyTyConApp :RTL Int  =  T (Maybe Int)

Creates a primitive type equality predicate. Invariant: the types are not Coercions

Makes a lifted equality predicate at the given role

Creates a primite type equality predicate with explicit kinds

Creates a primitive representational type equality predicate with explicit kinds

A choice of equality relation. This is separate from the type Role because Phantom does not define a (non-trivial) equality relation.

Get the equality relation relevant for a pred type.

Do these denote the same level of visibility? Required arguments are visible, others are not. So this function equates Specified and Inferred. Used for printing.

Make a named binder

Make many named binders

Make an anonymous binder

Does this binder bind a variable that is not erased? Returns True for anonymous binders.

Extract a relevant type, if there is one.

Like maybe, but for binders.

Does this ArgFlag classify an argument that is written in Haskell?

Does this ArgFlag classify an argument that is not written in Haskell?

Does this binder bind a visible argument?

Does this binder bind an invisible argument?

Manufacture a new TyConBinder from a TyBinder. Anonymous TyBinders are still assigned names as TyConBinders, so we need the extra gunk with which to construct a Name. Used when producing tyConTyVars from a datatype kind signature. Defined here to avoid module loops.

The (->) type constructor.

(->) :: forall (rep1 :: RuntimeRep) (rep2 :: RuntimeRep).
        TYPE rep1 -> TYPE rep2 -> *

Is the type suitable to classify a given/wanted in the typechecker?

Does this type classify a core (unlifted) Coercion? At either role nominal or representational (t1 ~ t2)

Checks whether this is a proper forall (with a named binder)

Is this a function or forall?

Determine whether a type could be the type of a join point of given total arity, according to the polymorphism rule. A join point cannot be polymorphic in its return type, since given join j a b x y z = e1 in e2, the types of e1 and e2 must be the same, and a and b are not in scope for e2. (See Note [The polymorphism rule of join points] in CoreSyn.) Returns False also if the type simply doesn't have enough arguments.

Note that we need to know how many arguments (type *and* value) the putative join point takes; for instance, if j :: forall a. a -> Int then j could be a binary join point returning an Int, but it could *not* be a unary join point returning a -> Int.

TODO: See Note [Excess polymorphism and join points]

Returns Just True if this type is surely lifted, Just False if it is surely unlifted, Nothing if we can't be sure (i.e., it is levity polymorphic), and panics if the kind does not have the shape TYPE r.

See Type for what an unlifted type is. Panics on levity polymorphic types.

See Type for what an algebraic type is. Should only be applied to types, as opposed to e.g. partially saturated type constructors

See Type for what an algebraic type is. Should only be applied to types, as opposed to e.g. partially saturated type constructors. Closed type constructors are those with a fixed right hand side, as opposed to e.g. associated types

Check whether a type is a data family type

Returns true of types that are opaque to Haskell.

Computes whether an argument (or let right hand side) should be computed strictly or lazily, based only on its type. Currently, it's just isUnliftedType. Panics on levity-polymorphic types.

Is this the type RuntimeRep?

Is a tyvar of type RuntimeRep?

Is this a type of kind RuntimeRep? (e.g. LiftedRep)

Drops prefix of RuntimeRep constructors in TyConApps. Useful for e.g. dropping 'LiftedRep arguments of unboxed tuple TyCon applications:

dropRuntimeRepArgs [ 'LiftedRep, 'IntRep , String, Int]

Extract the RuntimeRep classifier of a type. For instance, getRuntimeRep_maybe Int = LiftedRep. Panics if this is not possible.

Extract the RuntimeRep classifier of a type from its kind. For example, getRuntimeRepFromKind * = LiftedRep; Panics if this is not possible.

The key type representing kinds in the compiler.

Returns True if a type is levity polymorphic. Should be the same as (isKindLevPoly . typeKind) but much faster. Precondition: The type has kind (TYPE blah)

Looking past all pi-types, is the end result potentially levity polymorphic? Example: True for (forall r (a :: TYPE r). String -> a) Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type)

The worker for tyVarsOfType and tyVarsOfTypeList. The previous implementation used unionVarSet which is O(n+m) and can make the function quadratic. It's exported, so that it can be composed with other functions that compute free variables. See Note [FV naming conventions] in FV.

Eta-expanded because that makes it run faster (apparently) See Note [FV eta expansion] in FV for explanation.

Returns free variables of a type, including kind variables as a non-deterministic set. For type synonyms it does not expand the synonym.

Returns free variables of types, including kind variables as a non-deterministic set. For type synonyms it does not expand the synonym.

tyVarsOfType that returns free variables of a type in a deterministic set. For explanation of why using VarSet is not deterministic see Note [Deterministic FV] in FV.

Add the kind variables free in the kinds of the tyvars in the given set. Returns a non-deterministic set.

Add the kind variables free in the kinds of the tyvars in the given set. Returns a deterministically ordered list.

Returns True if this type has no free variables. Should be the same as isEmptyVarSet . tyCoVarsOfType, but faster in the non-forall case.

Retrieve the free variables in this type, splitting them based on whether they are used visibly or invisibly. Invisible ones come first.

Expand out all type synonyms. Actually, it'd suffice to expand out just the ones that discard type variables (e.g. type Funny a = Int) But we don't know which those are currently, so we just expand all.

expandTypeSynonyms only expands out type synonyms mentioned in the type, not in the kinds of any TyCon or TyVar mentioned in the type.

Keep this synchronized with synonymTyConsOfType

Extract a well-scoped list of variables from a deterministic set of variables. The result is deterministic. NB: There used to exist varSetElemsWellScoped :: VarSet -> [Var] which took a non-deterministic set and produced a non-deterministic well-scoped list. If you care about the list being well-scoped you also most likely care about it being in deterministic order.

Do a topological sort on a list of tyvars, so that binders occur before occurrences E.g. given [ a::k, k::*, b::k ] it'll return a well-scoped list [ k::*, a::k, b::k ]

This is a deterministic sorting operation (that is, doesn't depend on Uniques).

Get the free vars of a type in scoped order

Get the free vars of types in scoped order

Type equality on source types. Does not look through newtypes or PredTypes, but it does look through type synonyms. This first checks that the kinds of the types are equal and then checks whether the types are equal, ignoring casts and coercions. (The kind check is a recursive call, but since all kinds have type Type, there is no need to check the types of kinds.) See also Note [Non-trivial definitional equality] in TyCoRep.

Compare types with respect to a (presumably) non-empty RnEnv2.

Type equality on lists of types, looking through type synonyms but not newtypes.

Compare two TyCons. NB: This should never see the "star synonyms", as recognized by Kind.isStarKindSynonymTyCon. See Note [Kind Constraint and kind *] in Kind. See Note [nonDetCmpType nondeterminism]

This function Strips off the top layer only of a type synonym application (if any) its underlying representation type. Returns Nothing if there is nothing to look through. This function considers Constraint to be a synonym of TYPE LiftedRep.

By being non-recursive and inlined, this case analysis gets efficiently joined onto the case analysis that the caller is already doing

Gives the typechecker view of a type. This unwraps synonyms but leaves Constraint alone. c.f. coreView, which turns Constraint into TYPE LiftedRep. Returns Nothing if no unwrapping happens. See also Note [coreView vs tcView] in Type.

All type constructors occurring in the type; looking through type synonyms, but not newtypes. When it finds a Class, it returns the class TyCon.

A substitution of Types for TyVars and Kinds for KindVars

Type & coercion substitution

The following invariants must hold of a TCvSubst:

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 reach a fixed point.

Generates the in-scope set for the TCvSubst from the types in the incoming environment. No CoVars, please!

Generates the in-scope set for the TCvSubst from the types in the incoming environment. No CoVars, please!

Returns the free variables of the types in the range of a substitution as a non-deterministic set.

(compose env1 env2)(x) is env1(env2(x)); i.e. apply env2 then env1. It assumes that both are idempotent. Typically, env1 is the refinement to a base substitution env2

Composes two substitutions, applying the second one provided first, like in function composition.

Substitute within a Type The substitution has to satisfy the invariants described in Note [The substitution invariant].

Substitute within several Types The substitution has to satisfy the invariants described in Note [The substitution invariant].

Type substitution, see zipTvSubst

Type substitution, see zipTvSubst

Substitute within a ThetaType The substitution has to satisfy the invariants described in Note [The substitution invariant].

Substitute within a Type after adding the free variables of the type to the in-scope set. This is useful for the case when the free variables aren't already in the in-scope set or easily available. See also Note [The substitution invariant].

Substitute within a Type disabling the sanity checks. The problems that the sanity checks in substTy catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substTyUnchecked to substTy and remove this function. Please don't use in new code.

Substitute within several Types disabling the sanity checks. The problems that the sanity checks in substTys catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substTysUnchecked to substTys and remove this function. Please don't use in new code.

Substitute within a ThetaType disabling the sanity checks. The problems that the sanity checks in substTys catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substThetaUnchecked to substTheta and remove this function. Please don't use in new code.

Type substitution, see zipTvSubst. Disables sanity checks. The problems that the sanity checks in substTy catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substTyUnchecked to substTy and remove this function. Please don't use in new code.

Substitute within a Coercion disabling sanity checks. The problems that the sanity checks in substCo catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substCoUnchecked to substCo and remove this function. Please don't use in new code.

Coercion substitution, see zipTvSubst. Disables sanity checks. The problems that the sanity checks in substCo catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substCoUnchecked to substCo and remove this function. Please don't use in new code.

Print a user-level forall; see Note [When to print foralls]

Pretty prints a TyCon, using the family instance in case of a representation tycon. For example:

data T [a] = ...

In that case we want to print T [a], where T is the family TyCon

Grabs the free type variables, tidies them and then uses tidyType to work over the type itself

This tidies up a type for printing in an error message, or in an interface file.

It doesn't change the uniques at all, just the print names.

Add the free TyVars to the env in tidy form, so that we can tidy the type they are free in

Treat a new TyCoVar as a binder, and give it a fresh tidy name using the environment if one has not already been allocated. See also tidyTyCoVarBndr

Calls tidyType on a top-level type (i.e. with an empty tidying environment)