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.

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