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 [VarBndrs, TyCoVarBinders, TyConBinders, and visibility] in TyCoRep

The non-dependent version of ArgFlag.

Is a forall invisible (e.g., forall a b. {...}, with a dot) or visible (e.g., forall a b -> {...}, with an arrow)?

The key representation of types within the compiler

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

Variable

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

Type or kind Variable

Is this a type-level (i.e., computationally irrelevant, thus erasable) variable? Satisfies isTyVar = not . isId.

Type or Coercion Variable

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

Variable Binder

A TyCoVarBinder 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

A TyVarBinder is a binder with only TyVar

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

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 ~N kind ty

The type or kind of the Var in question

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 nested arrow types

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

Just like piResultTys but for a single argument Try not to iterate piResultTy, because it's inefficient to substitute one variable at a time; instead use 'piResultTys"

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

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.

Moreover, for a FunTy, it only succeeds if the argument types have enough info to extract the runtime-rep arguments that the funTyCon requires. This will usually be true; but may be temporarily false during canonicalization: see Note [FunTy and decomposing tycon applications] in TcCanonical

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

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

Like mkForAllTy, but assumes the variable is dependent and Specified, 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 variable

Like mkTyCoInvForAllTy, but tv should be a tyvar

Like mkTyCoInvForAllTys, but tvs should be a list of tyvar

Take a ForAllTy apart, returning the list of tycovars 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 splitForAllTys, but only splits a ForAllTy if sameVis argf supplied_argf is True, where argf is the visibility of the ForAllTy's binder and supplied_argf is the visibility provided as an argument to this function.

Like splitPiTys but split off only named binders and returns TyCoVarBinders rather than TyCoBinders

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.

Like splitForAllTy_maybe, but only returns Just if it is a tyvar binder.

Like splitForAllTy_maybe, but only returns Just if it is a covar binder.

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

Takes a forall type apart, or panics

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

Given a list of type-level vars and the free vars of a result kind, makes TyCoBinders, preferring anonymous binders if the variable is, in fact, not dependent. e.g. mkTyConBindersPreferAnon (k:*),(b:k),(c:k) We want (k:*) Named, (b:k) Anon, (c:k) Anon

All non-coercion 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

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)

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

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

Is this a type literal (symbol or numeric).

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

Given a kind (TYPE rr), extract its RuntimeRep classifier rr. For example, kindRep_maybe * = Just LiftedRep Returns Nothing if the kind is not of form (TYPE rr) Treats * and Constraint as the same

Extract the RuntimeRep classifier of a type from its kind. For example, kindRep * = LiftedRep; Panics if this is not possible. Treats * and Constraint as the same

Make a CastTy. The Coercion must be nominal. Checks the Coercion for reflexivity, dropping it if it's reflexive. See Note [Respecting definitional equality] in TyCoRep

Drop the cast on a type, if any. If there is no cast, just return the original type. This is rarely what you want. The CastTy data constructor (in TyCoRep) has the invariant that another CastTy is not inside. See the data constructor for a full description of this invariant. Since CastTy cannot be nested, the result of discardCast cannot be a CastTy.

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.

Given a TyCon and a list of argument types, filter out any invisible (i.e., Inferred or Specified) arguments.

Given a TyCon and a list of argument types, filter out any Inferred arguments.

Given a TyCon and a list of argument types, partition the arguments into:

1. Inferred or Specified (i.e., invisible) arguments and
2. Required (i.e., visible) arguments

Given a list of things paired with their visibilities, partition the things into (invisible things, visible things).

Given a TyCon and a list of argument types to which the TyCon is applied, determine each argument's visibility (Inferred, Specified, or Required).

Wrinkle: consider the following scenario:

T :: forall k. k -> k
tyConArgFlags 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.

Given a Type and a list of argument types to which the Type is applied, determine each argument's visibility (Inferred, Specified, or Required).

Most of the time, the arguments will be Required, but not always. Consider f :: forall a. a -> Type. In f Type Bool, the first argument (Type) is Specified and the second argument (Bool) is Required. It is precisely this sort of higher-rank situation in which appTyArgFlags comes in handy, since f Type Bool would be represented in Core using AppTys. (See also #15792).

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.

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 many named binders Input vars should be type variables

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.

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?

The (->) type constructor.

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

Is this a function?

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

Like isForAllTy, but returns True only if it is a tyvar binder

Like isForAllTy, but returns True only if it is a covar binder

Is this a function or forall?

Does this type classify a core (unlifted) Coercion? At either role nominal or representational (t1 ~ t2) See Note [Types for coercions, predicates, and evidence] in TyCoRep

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]

Does a TyCon (that is applied to some number of arguments) need to be ascribed with an explicit kind signature to resolve ambiguity if rendered as a source-syntax type? (See Note [When does a tycon application need an explicit kind signature?] for a full explanation of what this function checks for.)

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.

This version considers Constraint to be the same as *. Returns True if the argument is equivalent to Type/Constraint and False otherwise. See Note [Kind Constraint and kind Type]

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.

See Type for what an unlifted type is. Panics on levity polymorphic types; See mightBeUnliftedType for a more approximate predicate that behaves better in the presence of levity polymorphism.

Returns:

• False if the type is guaranteed lifted or
• True if it is unlifted, OR we aren't sure (e.g. in a levity-polymorphic case)

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

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.

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)

Is this kind equivalent to *?

This considers Constraint to be distinct from *. For a version that treats them as the same type, see isLiftedTypeKind.

Is this kind equivalent to TYPE r (for some unknown r)?

This considers Constraint to be distinct from *.

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.

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

Given a list of tyvars returns a deterministic FV computation that returns the given tyvars with the kind variables free in the kinds of the given tyvars.

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

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

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

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 RnTypes

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 Constraint (as recognized by Kind.isConstraintKindCon) which is considered a synonym for Type in Core. See Note [Kind Constraint and kind Type] 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]

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.

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 tidyVarBndr

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

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

Tests whether the given kind (which should look like TYPE x) is something other than a constructor tree (that is, constructors at every node). E.g. True of TYPE k, TYPE (F Int) False of TYPE 'LiftedRep