A type which has a syntactically fixed RuntimeRep as per Note [Fixed RuntimeRep] in GHC.Tc.Utils.Concrete.

A TcSigmaTypeFRR is a TcSigmaType which has a syntactically fixed RuntimeRep in the sense of Note [Fixed RuntimeRep] in GHC.Tc.Utils.Concrete.

In particular, this means that:

• typePrimRep does not panic,
• typeLevity_maybe does not return Nothing.

This property is important in functions such as matchExpectedFunTys, where we want to provide argument types which have a known runtime representation. See Note [Return arguments with a fixed RuntimeRep.

Type variable that might be a metavariable

A type labeled KnotTied might have knot-tied tycons in it. See Note [Type checking recursive type and class declarations] in GHC.Tc.TyCl

An expected type to check against during type-checking. See Note [ExpType] in GHC.Tc.Utils.TcMType, where you'll also find manipulators.

An ExpType which has a fixed RuntimeRep.

For a Check ExpType, the stored TcType must have a fixed RuntimeRep. For an Infer ExpType, the ir_frr field must be of the form Just frr_orig.

Like TcSigmaTypeFRR, but for an expected type.

See ExpTypeFRR.

Make an ExpType suitable for checking.

Returns the expected type when in checking mode.

Returns the expected type when in checking mode. Panics if in inference mode.

What to expect for an argument to a rebindable-syntax operator. Quite like Type, but allows for holes to be filled in by tcSyntaxOp. The callback called from tcSyntaxOp gets a list of types; the meaning of these types is determined by a left-to-right depth-first traversal of the SyntaxOpType tree. So if you pass in

SynAny `SynFun` (SynList `SynFun` SynType Int) `SynFun` SynAny

you'll get three types back: one for the first SynAny, the element type of the list, and one for the last SynAny. You don't get anything for the SynType, because you've said positively that it should be an Int, and so it shall be.

You'll also get three multiplicities back: one for each function arrow. See also Note [Linear types] in Multiplicity.

This is defined here to avoid defining it in GHC.Tc.Gen.Expr boot file.

Like SynType but accepts a regular TcType

Like mkFunTys but for SyntaxOpType

What restrictions are on this metavariable around unification? These are checked in GHC.Tc.Utils.Unify.checkTopShape

What caused us to create a ConcreteTv metavariable? See Note [ConcreteTv] in GHC.Tc.Utils.Concrete.

Is this type variable a concrete type variable, i.e. it is a metavariable with ConcreteTv MetaInfo?

Returns the ConcreteTvOrigin stored in the type variable if so, or Nothing otherwise.

Is this type variable a concrete type variable, i.e. it is a metavariable with ConcreteTv MetaInfo?

Is this type concrete type variable, i.e. a metavariable with ConcreteTv MetaInfo?

Is this type a concrete type variable? If so, return the associated TcTyVar and ConcreteTvOrigin.

A mapping from skolem type variable Name to concreteness information,

See Note [Representation-polymorphism checking built-ins] in GHC.Tc.Gen.Head.

The Id has no outer forall'd type variables which must be instantiated to concrete types.

Make a sigma ty where all type variables are Inferred. That is, they cannot be used with visible type application.

Make a sigma ty where all type variables are "specified". That is, they can be used with visible type application

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

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

Like tcSplitPiTys, but splits off only named binders, returning just the tyvars.

Like tcSplitForAllTyVars, but only splits ForAllTys with Invisible type variable binders.

Like tcSplitForAllTyVars, but only splits a ForAllTy if argf_pred argf is True, where argf is the visibility of the ForAllTy's binder and argf_pred is a predicate over visibilities provided as an argument to this function.

Like tcSplitForAllTyVars, but only splits ForAllTys with Required type variable binders. All split tyvars are annotated with ().

Like tcSplitForAllTyVars, but only splits ForAllTys with Invisible type variable binders. All split tyvars are annotated with their Specificity.

Splits a forall type into a list of PiTyVarBinders and the inner type. Always succeeds, even if it returns an empty list.

Splits a type into a PiTyVarBinder and a body, if possible.

Like tcSplitForAllTyVars, but splits off only named binders.

Strips off n *visible* arguments and returns the resulting type

Split off exactly the specified number argument types Returns (Left m) if there are m missing arrows in the type (Right (tys,res)) if the type looks like t1 -> ... -> tn -> res

tcSplitTyConApp_maybe splits a type constructor application into its type constructor and applied types.

Differs from splitTyConApp_maybe in that it does *not* split types headed with (=>), as that's not a TyCon in the type-checker.

Note that this may fail (in funTyConAppTy_maybe) 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`. This isn't usually a problem but may be temporarily the case during canonicalization: see Note [Decomposing FunTy] in GHC.Tc.Solver.Equality and Note [The Purely Kinded Type Invariant (PKTI)] in GHC.Tc.Gen.HsType, Wrinkle around FunTy

Consequently, you may need to zonk your type before using this function.

Like tcRepSplitTyConApp_maybe, but only returns the TyCon.

Just like splitAppTyNoView_maybe, but does not split (c => t) See Note [Decomposing fat arrow c=>t]

Split a sigma type into its parts. This only splits invisible type variable binders, as these are the only forms of binder that the typechecker will implicitly instantiate.

Split a sigma type into its parts, going underneath as many arrows and foralls as possible. See Note [tcSplitNestedSigmaTys]

Like isRhoTy, but also says True for Infer types

Is the type inhabited by machine floating-point numbers?

Used to check that we don't use floating-point literal patterns in Core.

See #9238 and Note [Rules for floating-point comparisons] in GHC.Core.Opt.ConstantFold.

Is a type String?

Check whether the type is of the form Any :: k, returning the kind k.

Type equality on source types. Does not look through newtypes, PredTypes or type families, 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 GHC.Core.TyCo.Rep.

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

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

Like pickyEqTypeVis, but returns a Bool for convenience

tcEqType implements typechecker equality It behaves just like eqType, but is implemented differently (for now)

Just like tcEqType, but will return True for types of different kinds as long as their non-coercion structure is identical.

Like tcEqType, but returns True if the visible part of the types are equal, even if they are really unequal (in the invisible bits)

Check whether two TyConApps are the same; if the number of arguments are different, just checks the common prefix of arguments.

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.

Returns the (kind, type) variables in a type that are as-yet-unknown: metavariables and RuntimeUnks

Finds outermost type-family applications occurring in a type, after expanding synonyms. In the list (F, tys) that is returned we guarantee that tys matches F's arity. For example, given type family F a :: * -> * (arity 1) calling tcTyFamInsts on (Maybe (F Int Bool) will return (F, [Int]), not (F, [Int,Bool])

This is important for its use in deciding termination of type instances (see #11581). E.g. type instance G [Int] = ...(F Int <big type>)... we don't need to take <big type> into account when asking if the calls on the RHS are smaller than the LHS

Like tcTyFamInsts, except that the output records whether the type family and its arguments occur as an invisible argument in some type application. This information is useful because it helps GHC know when to turn on -fprint-explicit-kinds during error reporting so that users can actually see the type family being mentioned.

As an example, consider:

class C a
data T (a :: k)
type family F a :: k
instance C (T @(F Int) (F Bool))

There are two occurrences of the type family F in that C instance, so tcTyFamInstsAndVis (C (T @(F Int) (F Bool))) will return:

[ (True,  F, [Int])
, (False, F, [Bool]) ]

F Int is paired with True since it appears as an invisible argument to C, whereas F Bool is paired with False since it appears an a visible argument to C.

See also Note [Kind arguments in error messages] in GHC.Tc.Errors.

In an application of a TyCon to some arguments, find the outermost occurrences of type family applications within the arguments. This function will not consider the TyCon itself when checking for type family applications.

See tcTyFamInstsAndVis for more details on how this works (as this function is called inside of tcTyFamInstsAndVis).

Check that a type does not contain any type family applications.

The Paterson size of a given type, in the sense of Note [Paterson conditions] in GHC.Tc.Validity

• after expanding synonyms,
• ignoring coercions (as they are not user written).

Why did the Paterson conditions fail; that is, why was the context P not Paterson-smaller than the head H?

See Note [Paterson conditions] in GHC.Tc.Validity.

Indicates whether a Paterson condition failure occurred in an instance declaration or a type family equation. Useful for differentiating context in error messages.

ltPatersonSize ps1 ps2 returns:

• Nothing iff ps1 is definitely strictly smaller than ps2,
• Just ps_fail otherwise; ps_fail says what went wrong.

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).

It is also meant to be stable: that is, variables should not be reordered unnecessarily. This is specified in Note [ScopedSort] See also Note [Ordering of implicit variables] in GHC.Rename.HsType

When this says True, ignore this class constraint during a termination check See (PS1) in Note [The PatersonSize of a type]

The key type representing kinds in the compiler.

Returns True if the argument is (lifted) Type or Constraint See Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim

Returns True if the kind classifies unlifted types (like 'Int#') and False otherwise. Note that this returns False for representation-polymorphic kinds, which may be specialized to a kind that classifies unlifted types.

Does this classify a type allowed to have values? Responds True to things like *, TYPE Lifted, TYPE IntRep, TYPE v, Constraint.

True of a kind `TYPE _` or `CONSTRAINT _`

A type of the form p of constraint kind 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

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

ForAllTyFlag

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 [VarBndrs, ForAllTyBinders, TyConBinders, and visibility] in GHC.Core.TyCo.Rep

The non-dependent version of ForAllTyFlag. See Note [FunTyFlag] Appears here partly so that it's together with its friends ForAllTyFlag and ForallVisFlag, but also because it is used in IfaceType, rather early in the compilation chain

Like mkTyCoForAllTy, but does not check the occurrence of the binder See Note [Unused coercion variable in ForAllTy]

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

Wraps foralls over the type using the provided InvisTVBinders 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

Make a dependent forall over an Inferred variable

Like mkTyCoInvForAllTy, but tv should be a tyvar

Like mkTyCoInvForAllTys, but tvs should be a list of tyvar

Make nested arrow types | Special, common, case: Arrow type with mult Many

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

(mkTyConTy tc) returns (TyConApp tc []) but arranges to share that TyConApp among all calls See Note [Sharing nullary TyConApps] So it's just an alias for tyConNullaryTy!

Is a tyvar of type RuntimeRep?

Checks that a kind of the form Type, Constraint or 'TYPE r is concrete. See isConcreteType.

Precondition: The type has kind `TYPE blah` or `CONSTRAINT blah`

Does this binder bind a visible argument?

Does this binder bind an invisible argument?

Type & coercion & id substitution

The Subst data type defined in this module contains substitution for tyvar, covar and id. However, operations on IdSubstEnv (mapping from Id to CoreExpr) that require the definition of the Expr data type are defined in GHC.Core.Subst to avoid circular module dependency.

A substitution of Types for TyVars and Kinds for KindVars

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

Generates the in-scope set for the TCvSubst from the types in the incoming environment. No CoVars, please! The InScopeSet is just a thunk so with a bit of luck it'll never be evaluated

Find the in-scope set: see Note [The substitution invariant]

Add the Var to the in-scope set

Add the Vars to the in-scope set: see also extendInScope

Add the Vars to the in-scope set: see also extendInScope

Add a substitution for a TyVar to the Subst The TyVar *must* be a real TyVar, and not a CoVar You must ensure that the in-scope set is such that Note [The substitution invariant] holds after extending the substitution like this.

Make a TCvSubst with specified tyvar subst and empty covar subst

The InScopeSet is just a thunk so with a bit of luck it'll never be evaluated

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

Substitute covars within a type

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.

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

Is the given type definitely unlifted? See Type for what an unlifted type is.

Panics on representation-polymorphic types; See mightBeUnliftedType for a more approximate predicate that behaves better in the presence of representation polymorphism.

Returns true of types that are opaque to Haskell.

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 does not look through type family applications.

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

The worker for tyCoFVsOfType and tyCoFVsOfTypeList. 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 GHC.Utils.FV.

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

tyCoFVsOfType 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 GHC.Utils.FV.

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

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

tyCoFVsOfType that returns free variables of a type in deterministic order. For explanation of why using VarSet is not deterministic see Note [Deterministic FV] in GHC.Utils.FV.

Returns free variables of types, including kind variables as a deterministically ordered list. For type synonyms it does not expand the synonym.

For every arg a tycon can take, the returned list says True if the argument is taken visibly, and False otherwise. Ends with an infinite tail of Trues to allow for oversaturation.

If the tycon is applied to the types, is the next argument visible?

Should this type be applied to a visible argument? E.g. (s t): is t a visible argument of s?