GHC.Core.TyCo.FVs

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.

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 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.

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

Get a deterministic set of the vars free in a coercion

Given a covar and a coercion, returns True if covar is almost devoid in the coercion. That is, covar can only appear in Refl and GRefl. See (FC6) in Note [ForAllCo] in GHC.Core.TyCo.Rep

Returns the free variables of a Type that are in injective positions. Specifically, it finds the free variables while:

• Expanding type synonyms

• Ignoring the coercion in (ty |> co)

• Ignoring the non-injective fields of a TyConApp

For example, if F is a non-injective type family, then:

injectiveTyVarsOf( Either c (Maybe (a, F b c)) ) = {a,c}

If injectiveVarsOfType ty = itvs, then knowing ty fixes itvs. More formally, if a is in injectiveVarsOfType ty and S1(ty) ~ S2(ty), then S1(a) ~ S2(a), where S1 and S2 are arbitrary substitutions.

See Note [When does a tycon application need an explicit kind signature?].

Returns the free variables of a Type that are in injective positions. Specifically, it finds the free variables while:

• Expanding type synonyms

• Ignoring the coercion in (ty |> co)

• Ignoring the non-injective fields of a TyConApp

See Note [When does a tycon application need an explicit kind signature?].

Returns the set of variables that are used invisibly anywhere within the given type. A variable will be included even if it is used both visibly and invisibly. An invisible use site includes: * In the kind of a variable * In the kind of a bound variable in a forall * In a coercion * In a Specified or Inferred argument to a function See Note [VarBndrs, ForAllTyBinders, TyConBinders, and visibility] in GHC.Core.TyCo.Rep

Like invisibleVarsOfType, but for many types.

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

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

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

Get the free vars of a type in scoped order

Get the free vars of types in scoped order

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

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

The monoid of endomorphisms under composition.

Endo f <> Endo g == Endo (f . g)

Examples

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>> appEndo computation "Haskell""Hello, Haskell!"

>>> let computation = Endo (*3) <> Endo (+1)>>> appEndo computation 16