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

Make an ExpType suitable for checking.

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.

This is defined here to avoid defining it in TcExpr.hs-boot.

Like SynType but accepts a regular TcType

Like mkFunTys but for SyntaxOpType

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

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

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

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

Splits a type into a TyBinder and a body, if possible. Panics otherwise

Like tcSplitForAllTys, 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

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.

Like tcSplitTyConApp_maybe but doesn't look through type synonyms.

Like tcRepSplitTyConApp_maybe, but returns Nothing if,

1. the type is structurally not a type constructor application, or
2. the type is a function type (e.g. application of funTyCon), but we currently don't even enough information to fully determine its RuntimeRep variables. For instance, FunTy (a :: k) Int.

By contrast tcRepSplitTyConApp_maybe panics in the second case.

The behavior here is needed during canonicalization; see Note [FunTy and decomposing tycon applications] in TcCanonical for details.

Like tcRepSplitTyConApp_maybe, but only returns the TyCon.

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

Returns the number of arguments in the given type, without looking through synonyms. This is used only for error reporting. We don't look through synonyms because of #11313.

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

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!

Split a sigma type into its parts.

Split a sigma type into its parts, going underneath as many ForAllTys as possible. For example, given this type synonym:

type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t

if you called tcSplitSigmaTy on this type:

forall s t a b. Each s t a b => Traversal s t a b

then it would return ([s,t,a,b], [Each s t a b], Traversal s t a b). But if you instead called tcSplitNestedSigmaTys on the type, it would return ([s,t,a,b,f], [Each s t a b, Applicative f], (a -> f b) -> s -> f t).

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.

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

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 information about whether the difference is visible in the case of a mismatch. Nothing : the types are equal Just True : the types differ, and the point of difference is visible Just False : the types differ, and the point of difference is invisible

Like isRhoTy, but also says True for Infer types

Does a type represent a floating-point number?

Is a type String?

Is a type a CallStack?

Is a PredType a CallStack implicit parameter?

If so, return the name of the parameter.

Is this a ForAllTy with a named binder?

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

Does the given tyvar appear at the head of a chain of applications (a t1 ... tn)

Is the equality a ~r ...a.... definitely insoluble or not? a ~r Maybe a -- Definitely insoluble a ~N ...(F a)... -- Not definitely insoluble -- Perhaps (F a) reduces to Int a ~R ...(N a)... -- Not definitely insoluble -- Perhaps newtype N a = MkN Int See Note [Occurs check error] in TcCanonical for the motivation for this function.

When inferring types, should we quantify over a given predicate? Generally true of classes; generally false of equality constraints. Equality constraints that mention quantified type variables and implicit variables complicate the story. See Notes [Inheriting implicit parameters] and [Quantifying over equality constraints]

Finds outermost type-family applications occuring 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 Trac #11581). E.g. type instance G [Int] = ...(F Int type)... we don't need to take type into account when asking if the calls on the RHS are smaller than the LHS

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

Worker for splitDepVarsOfType. This might output the same var in both sets, if it's used in both a type and a kind. See Note [CandidatesQTvs determinism and order] See Note [Dependent type variables]

Like splitDepVarsOfType, but over a list of types

Find all variables bound anywhere in a type. See also Note [Scope-check inferred kinds] in TcHsType

The key type representing kinds in the compiler.

This version considers Constraint to be distinct from *. Returns True if the argument is equivalent to Type and False otherwise.

Returns True if the kind classifies unlifted types and False otherwise. Note that this returns False for levity-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 v, Constraint.

True of any sub-kind of OpenTypeKind

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

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]

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 [TyVarBndrs, TyVarBinders, TyConBinders, and visibility] in TyCoRep

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

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

Make an arrow type

Make nested arrow types

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

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

Is a tyvar of type RuntimeRep?

Tests whether the given kind (which should look like TYPE x) is something other than a constructor tree (that is, constructors at every node).

Does this binder bind a visible argument?

Does this binder bind an invisible argument?

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.

A substitution of Types for TyVars and Kinds for KindVars

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!

Make a TCvSubst with specified tyvar subst and empty covar subst

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].

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

Returns true of types that are opaque to Haskell.

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.

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

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.

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

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 FV.

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

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

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

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).

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?