A Coercion is concrete evidence of the equality/convertibility of two types.

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

If it is the case that

 c :: (t1 ~ t2)

i.e. the kind of c relates t1 and t2, then coercionKind c = Pair t1 t2.

Apply coercionKind to multiple Coercions

Makes a coercion type from two types: the types whose equality is proven by the relevant Coercion

Create a symmetric version of the given Coercion that asserts equality between the same types but in the other direction, so a kind of t1 ~ t2 becomes the kind t2 ~ t1.

Create a new Coercion by composing the two given Coercions transitively.

Instantiates a Coercion with a Type argument.

Apply a Coercion to another Coercion.

Apply a type constructor to a list of coercions.

Make a function Coercion between two other Coercions

Make a Coercion which binds a variable within an inner Coercion

Manufacture a coercion from thin air. Needless to say, this is not usually safe, but it is used when we know we are dealing with bottom, which is one case in which it is safe. This is also used to implement the unsafeCoerce# primitive. Optimise by pushing down through type constructors.

Create a coercion constructor (axiom) suitable for the given newtype TyCon. The Name should be that of a new coercion CoAxiom, the TyVars the arguments expected by the newtype and the type the appropriate right hand side of the newtype, with the free variables a subset of those TyVars.

Create a coercion identifying a data, newtype or type representation type and its family instance. It has the form Co tvs :: F ts ~ R tvs, where Co is the coercion constructor built here, F the family tycon and R the (derived) representation tycon.

Sometimes we want to look through a newtype and get its associated coercion. This function only strips *one layer* of newtype off, so the caller will usually call itself recursively. Furthermore, this function should only be applied to types of kind *, hence the newtype is always saturated. If co : ty ~ ty' then:

 splitNewTypeRepCo_maybe ty = Just (ty', co)

The function returns Nothing for non-newtypes or fully-transparent newtypes.

If co :: T ts ~ rep_ty then:

 instNewTyCon_maybe T ts = Just (rep_ty, co)

This breaks a Coercion with type T A B C ~ T D E F into a list of Coercions of kinds A ~ D, B ~ E and E ~ F. Hence:

 decomposeCo 3 c = [nth 0 c, nth 1 c, nth 2 c]

Attempts to obtain the type variable underlying a Coercion

Attempts to tease a coercion apart into a type constructor and the application of a number of coercion arguments to that constructor

Attempt to take a coercion application apart.

A substitution of Coercions for CoVars (OR TyVars, when doing a "lifting" substitution)

Substitute within a Coercion

Substitute within several Coercions

liftCoMatch is sort of inverse to liftCoSubst. In particular, if liftCoMatch vars ty co == Just s, then tyCoSubst s ty == co. That is, it matches a type against a coercion of the same shape, and returns a lifting substitution which could have been used to produce the given coercion from the given type.

Determines syntactic equality of coercions