Safe Haskell | None |
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Coercion
Contents
Description
Module for (a) type kinds and (b) type coercions,
as used in System FC. See Expr
for
more on System FC and how coercions fit into it.
- data Coercion
- data Var
- type CoVar = Id
- coVarKind :: CoVar -> (Type, Type)
- coercionType :: Coercion -> Type
- coercionKind :: Coercion -> Pair Type
- coercionKinds :: [Coercion] -> Pair [Type]
- isReflCo :: Coercion -> Bool
- isReflCo_maybe :: Coercion -> Maybe Type
- mkCoercionType :: Type -> Type -> Type
- mkReflCo :: Type -> Coercion
- mkCoVarCo :: CoVar -> Coercion
- mkAxInstCo :: CoAxiom -> [Type] -> Coercion
- mkPiCo :: Var -> Coercion -> Coercion
- mkPiCos :: [Var] -> Coercion -> Coercion
- mkSymCo :: Coercion -> Coercion
- mkTransCo :: Coercion -> Coercion -> Coercion
- mkNthCo :: Int -> Coercion -> Coercion
- mkInstCo :: Coercion -> Type -> Coercion
- mkAppCo :: Coercion -> Coercion -> Coercion
- mkTyConAppCo :: TyCon -> [Coercion] -> Coercion
- mkFunCo :: Coercion -> Coercion -> Coercion
- mkForAllCo :: Var -> Coercion -> Coercion
- mkUnsafeCo :: Type -> Type -> Coercion
- mkNewTypeCo :: Name -> TyCon -> [TyVar] -> Type -> CoAxiom
- mkFamInstCo :: Name -> [TyVar] -> TyCon -> [Type] -> TyCon -> CoAxiom
- splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)
- instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion)
- decomposeCo :: Arity -> Coercion -> [Coercion]
- getCoVar_maybe :: Coercion -> Maybe CoVar
- splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion])
- splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion)
- splitForAllCo_maybe :: Coercion -> Maybe (TyVar, Coercion)
- mkCoVar :: Name -> Type -> CoVar
- isCoVar :: Var -> Bool
- isCoVarType :: Type -> Bool
- coVarName :: CoVar -> Name
- setCoVarName :: CoVar -> Name -> CoVar
- setCoVarUnique :: CoVar -> Unique -> CoVar
- tyCoVarsOfCo :: Coercion -> VarSet
- tyCoVarsOfCos :: [Coercion] -> VarSet
- coVarsOfCo :: Coercion -> VarSet
- coercionSize :: Coercion -> Int
- type CvSubstEnv = VarEnv Coercion
- emptyCvSubstEnv :: CvSubstEnv
- data CvSubst = CvSubst InScopeSet TvSubstEnv CvSubstEnv
- emptyCvSubst :: CvSubst
- lookupTyVar :: CvSubst -> TyVar -> Maybe Type
- lookupCoVar :: CvSubst -> Var -> Maybe Coercion
- isEmptyCvSubst :: CvSubst -> Bool
- zapCvSubstEnv :: CvSubst -> CvSubst
- getCvInScope :: CvSubst -> InScopeSet
- substCo :: CvSubst -> Coercion -> Coercion
- substCos :: CvSubst -> [Coercion] -> [Coercion]
- substCoVar :: CvSubst -> CoVar -> Coercion
- substCoVars :: CvSubst -> [CoVar] -> [Coercion]
- substCoWithTy :: InScopeSet -> TyVar -> Type -> Coercion -> Coercion
- substCoWithTys :: InScopeSet -> [TyVar] -> [Type] -> Coercion -> Coercion
- cvTvSubst :: CvSubst -> TvSubst
- tvCvSubst :: TvSubst -> CvSubst
- mkCvSubst :: InScopeSet -> [(Var, Coercion)] -> CvSubst
- zipOpenCvSubst :: [Var] -> [Coercion] -> CvSubst
- substTy :: CvSubst -> Type -> Type
- extendTvSubst :: CvSubst -> TyVar -> Type -> CvSubst
- extendCvSubstAndInScope :: CvSubst -> CoVar -> Coercion -> CvSubst
- substTyVarBndr :: CvSubst -> TyVar -> (CvSubst, TyVar)
- substCoVarBndr :: CvSubst -> CoVar -> (CvSubst, CoVar)
- liftCoMatch :: TyVarSet -> Type -> Coercion -> Maybe LiftCoSubst
- liftCoSubstTyVar :: LiftCoSubst -> TyVar -> Maybe Coercion
- liftCoSubstWith :: [TyVar] -> [Coercion] -> Type -> Coercion
- coreEqCoercion :: Coercion -> Coercion -> Bool
- coreEqCoercion2 :: RnEnv2 -> Coercion -> Coercion -> Bool
- seqCo :: Coercion -> ()
- pprCo :: Coercion -> SDoc
- pprParendCo :: Coercion -> SDoc
- pprCoAxiom :: CoAxiom -> SDoc
- applyCo :: Type -> Coercion -> Type
Main data type
A Coercion
is concrete evidence of the equality/convertibility
of two types.
Functions over coercions
coercionType :: Coercion -> TypeSource
coercionKind :: Coercion -> Pair TypeSource
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
.
coercionKinds :: [Coercion] -> Pair [Type]Source
Apply coercionKind
to multiple Coercion
s
mkCoercionType :: Type -> Type -> TypeSource
Makes a coercion type from two types: the types whose equality
is proven by the relevant Coercion
Constructing coercions
mkAxInstCo :: CoAxiom -> [Type] -> CoercionSource
mkTyConAppCo :: TyCon -> [Coercion] -> CoercionSource
Apply a type constructor to a list of coercions.
mkForAllCo :: Var -> Coercion -> CoercionSource
mkUnsafeCo :: Type -> Type -> CoercionSource
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.
Arguments
:: Name | Unique name for the coercion tycon |
-> [TyVar] | Type parameters of the coercion ( |
-> TyCon | Family tycon ( |
-> [Type] | Type instance ( |
-> TyCon | Representation tycon ( |
-> CoAxiom | Coercion constructor ( |
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.
Decomposition
splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)Source
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 newtype
s.
instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion)Source
If co :: T ts ~ rep_ty
then:
instNewTyCon_maybe T ts = Just (rep_ty, co)
decomposeCo :: Arity -> Coercion -> [Coercion]Source
getCoVar_maybe :: Coercion -> Maybe CoVarSource
Attempts to obtain the type variable underlying a Coercion
splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion])Source
Attempts to tease a coercion apart into a type constructor and the application of a number of coercion arguments to that constructor
splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion)Source
Attempt to take a coercion application apart.
Coercion variables
isCoVarType :: Type -> BoolSource
setCoVarName :: CoVar -> Name -> CoVarSource
setCoVarUnique :: CoVar -> Unique -> CoVarSource
Free variables
tyCoVarsOfCo :: Coercion -> VarSetSource
tyCoVarsOfCos :: [Coercion] -> VarSetSource
coVarsOfCo :: Coercion -> VarSetSource
coercionSize :: Coercion -> IntSource
Substitution
type CvSubstEnv = VarEnv CoercionSource
isEmptyCvSubst :: CvSubst -> BoolSource
substCoVar :: CvSubst -> CoVar -> CoercionSource
substCoVars :: CvSubst -> [CoVar] -> [Coercion]Source
substCoWithTy :: InScopeSet -> TyVar -> Type -> Coercion -> CoercionSource
substCoWithTys :: InScopeSet -> [TyVar] -> [Type] -> Coercion -> CoercionSource
zipOpenCvSubst :: [Var] -> [Coercion] -> CvSubstSource
Lifting
liftCoMatch :: TyVarSet -> Type -> Coercion -> Maybe LiftCoSubstSource
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.
liftCoSubstTyVar :: LiftCoSubst -> TyVar -> Maybe CoercionSource
Comparison
coreEqCoercion :: Coercion -> Coercion -> BoolSource
Determines syntactic equality of coercions
Forcing evaluation of coercions
Pretty-printing
pprParendCo :: Coercion -> SDocSource
pprCoAxiom :: CoAxiom -> SDocSource