Safe Haskell | None |
---|---|
Language | Haskell2010 |
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
- = Refl Role Type
- | TyConAppCo Role TyCon [Coercion]
- | AppCo Coercion Coercion
- | ForAllCo TyVar Coercion
- | CoVarCo CoVar
- | AxiomInstCo (CoAxiom Branched) BranchIndex [Coercion]
- | UnivCo FastString Role Type Type
- | SymCo Coercion
- | TransCo Coercion Coercion
- | AxiomRuleCo CoAxiomRule [Type] [Coercion]
- | NthCo Int Coercion
- | LRCo LeftOrRight Coercion
- | InstCo Coercion Type
- | SubCo Coercion
- data Var
- type CoVar = Id
- data LeftOrRight
- pickLR :: LeftOrRight -> (a, a) -> a
- data Role
- ltRole :: Role -> Role -> Bool
- coVarKind :: CoVar -> (Type, Type)
- coVarRole :: CoVar -> Role
- coercionType :: Coercion -> Type
- coercionKind :: Coercion -> Pair Type
- coercionKinds :: [Coercion] -> Pair [Type]
- isReflCo :: Coercion -> Bool
- isReflCo_maybe :: Coercion -> Maybe Type
- coercionRole :: Coercion -> Role
- coercionKindRole :: Coercion -> (Pair Type, Role)
- mkCoercionType :: Role -> Type -> Type -> Type
- mkReflCo :: Role -> Type -> Coercion
- mkCoVarCo :: CoVar -> Coercion
- mkAxInstCo :: Role -> CoAxiom br -> BranchIndex -> [Type] -> Coercion
- mkUnbranchedAxInstCo :: Role -> CoAxiom Unbranched -> [Type] -> Coercion
- mkAxInstLHS :: CoAxiom br -> BranchIndex -> [Type] -> Type
- mkAxInstRHS :: CoAxiom br -> BranchIndex -> [Type] -> Type
- mkUnbranchedAxInstRHS :: CoAxiom Unbranched -> [Type] -> Type
- mkPiCo :: Role -> Var -> Coercion -> Coercion
- mkPiCos :: Role -> [Var] -> Coercion -> Coercion
- mkCoCast :: Coercion -> Coercion -> Coercion
- mkSymCo :: Coercion -> Coercion
- mkTransCo :: Coercion -> Coercion -> Coercion
- mkNthCo :: Int -> Coercion -> Coercion
- mkNthCoRole :: Role -> Int -> Coercion -> Coercion
- mkLRCo :: LeftOrRight -> Coercion -> Coercion
- mkInstCo :: Coercion -> Type -> Coercion
- mkAppCo :: Coercion -> Coercion -> Coercion
- mkAppCoFlexible :: Coercion -> Role -> Coercion -> Coercion
- mkTyConAppCo :: Role -> TyCon -> [Coercion] -> Coercion
- mkFunCo :: Role -> Coercion -> Coercion -> Coercion
- mkForAllCo :: Var -> Coercion -> Coercion
- mkUnsafeCo :: Type -> Type -> Coercion
- mkUnivCo :: FastString -> Role -> Type -> Type -> Coercion
- mkSubCo :: Coercion -> Coercion
- mkPhantomCo :: Coercion -> Coercion
- mkNewTypeCo :: Name -> TyCon -> [TyVar] -> [Role] -> Type -> CoAxiom Unbranched
- downgradeRole :: Role -> Role -> Coercion -> Coercion
- mkAxiomRuleCo :: CoAxiomRule -> [Type] -> [Coercion] -> Coercion
- instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion)
- type NormaliseStepper = RecTcChecker -> TyCon -> [Type] -> NormaliseStepResult
- data NormaliseStepResult
- composeSteppers :: NormaliseStepper -> NormaliseStepper -> NormaliseStepper
- modifyStepResultCo :: (Coercion -> Coercion) -> NormaliseStepResult -> NormaliseStepResult
- unwrapNewTypeStepper :: NormaliseStepper
- topNormaliseNewType_maybe :: Type -> Maybe (Coercion, Type)
- topNormaliseTypeX_maybe :: NormaliseStepper -> Type -> Maybe (Coercion, Type)
- decomposeCo :: Arity -> Coercion -> [Coercion]
- getCoVar_maybe :: Coercion -> Maybe CoVar
- splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion)
- splitForAllCo_maybe :: Coercion -> Maybe (TyVar, Coercion)
- nthRole :: Role -> TyCon -> Int -> Role
- tyConRolesX :: Role -> TyCon -> [Role]
- setNominalRole_maybe :: Coercion -> Maybe 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
- extendTvSubstAndInScope :: CvSubst -> TyVar -> Type -> CvSubst
- substTyVarBndr :: CvSubst -> TyVar -> (CvSubst, TyVar)
- substCoVarBndr :: CvSubst -> CoVar -> (CvSubst, CoVar)
- liftCoMatch :: TyVarSet -> Type -> Coercion -> Maybe LiftCoSubst
- liftCoSubstTyVar :: LiftCoSubst -> Role -> TyVar -> Maybe Coercion
- liftCoSubstWith :: Role -> [TyVar] -> [Coercion] -> Type -> Coercion
- coreEqCoercion :: Coercion -> Coercion -> Bool
- coreEqCoercion2 :: RnEnv2 -> Coercion -> Coercion -> Bool
- seqCo :: Coercion -> ()
- pprCo :: Coercion -> SDoc
- pprParendCo :: Coercion -> SDoc
- pprCoAxiom :: CoAxiom br -> SDoc
- pprCoAxBranch :: TyCon -> CoAxBranch -> SDoc
- pprCoAxBranchHdr :: CoAxiom br -> BranchIndex -> SDoc
- tidyCo :: TidyEnv -> Coercion -> Coercion
- tidyCos :: TidyEnv -> [Coercion] -> [Coercion]
- applyCo :: Type -> Coercion -> Type
Main data type
A Coercion
is concrete evidence of the equality/convertibility
of two types.
data LeftOrRight Source
pickLR :: LeftOrRight -> (a, a) -> a Source
Functions over coercions
coercionType :: Coercion -> Type Source
coercionKind :: Coercion -> Pair Type Source
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
isReflCo_maybe :: Coercion -> Maybe Type Source
coercionRole :: Coercion -> Role Source
Retrieve the role from a coercion.
coercionKindRole :: Coercion -> (Pair Type, Role) Source
Get a coercion's kind and role. Why both at once? See Note [Computing a coercion kind and role]
mkCoercionType :: Role -> Type -> Type -> Type Source
Makes a coercion type from two types: the types whose equality
is proven by the relevant Coercion
Constructing coercions
mkAxInstCo :: Role -> CoAxiom br -> BranchIndex -> [Type] -> Coercion Source
mkUnbranchedAxInstCo :: Role -> CoAxiom Unbranched -> [Type] -> Coercion Source
mkAxInstLHS :: CoAxiom br -> BranchIndex -> [Type] -> Type Source
mkAxInstRHS :: CoAxiom br -> BranchIndex -> [Type] -> Type Source
mkUnbranchedAxInstRHS :: CoAxiom Unbranched -> [Type] -> Type Source
mkSymCo :: Coercion -> Coercion Source
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
.
mkLRCo :: LeftOrRight -> Coercion -> Coercion Source
mkTyConAppCo :: Role -> TyCon -> [Coercion] -> Coercion Source
Apply a type constructor to a list of coercions. It is the caller's responsibility to get the roles correct on argument coercions.
mkForAllCo :: Var -> Coercion -> Coercion Source
mkUnsafeCo :: Type -> Type -> Coercion Source
Manufacture an unsafe coercion from thin air.
Currently (May 14) this is used only to implement the
unsafeCoerce#
primitive. Optimise by pushing
down through type constructors.
mkPhantomCo :: Coercion -> Coercion Source
mkNewTypeCo :: Name -> TyCon -> [TyVar] -> [Role] -> Type -> CoAxiom Unbranched Source
mkAxiomRuleCo :: CoAxiomRule -> [Type] -> [Coercion] -> Coercion Source
Decomposition
instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion) Source
If co :: T ts ~ rep_ty
then:
instNewTyCon_maybe T ts = Just (rep_ty, co)
Checks for a newtype, and for being saturated
type NormaliseStepper = RecTcChecker -> TyCon -> [Type] -> NormaliseStepResult Source
A function to check if we can reduce a type by one step. Used
with topNormaliseTypeX_maybe
.
data NormaliseStepResult Source
The result of stepping in a normalisation function.
See topNormaliseTypeX_maybe
.
composeSteppers :: NormaliseStepper -> NormaliseStepper -> NormaliseStepper Source
Try one stepper and then try the next, if the first doesn't make progress.
unwrapNewTypeStepper :: NormaliseStepper Source
A NormaliseStepper
that unwraps newtypes, careful not to fall into
a loop. If it would fall into a loop, it produces NS_Abort
.
topNormaliseNewType_maybe :: Type -> Maybe (Coercion, Type) Source
Sometimes we want to look through a newtype
and get its associated coercion.
This function strips off newtype
layers enough to reveal something that isn't
a newtype
, or responds False to ok_tc. Specifically, here's the invariant:
topNormaliseNewType_maybe ty = Just (co, ty')
then (a) co : ty0 ~ ty'
.
(b) ty' is not a newtype.
The function returns Nothing
for non-newtypes
,
or unsaturated applications
This function does *not* look through type families, because it has no access to the type family environment. If you do have that at hand, consider to use topNormaliseType_maybe, which should be a drop-in replacement for topNormaliseNewType_maybe
topNormaliseTypeX_maybe :: NormaliseStepper -> Type -> Maybe (Coercion, Type) Source
A general function for normalising the top-level of a type. It continues
to use the provided NormaliseStepper
until that function fails, and then
this function returns. The roles of the coercions produced by the
NormaliseStepper
must all be the same, which is the role returned from
the call to topNormaliseTypeX_maybe
.
decomposeCo :: Arity -> Coercion -> [Coercion] Source
getCoVar_maybe :: Coercion -> Maybe CoVar Source
Attempts to obtain the type variable underlying a Coercion
splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion) Source
Attempt to take a coercion application apart.
tyConRolesX :: Role -> TyCon -> [Role] Source
Coercion variables
isCoVarType :: Type -> Bool Source
setCoVarName :: CoVar -> Name -> CoVar Source
setCoVarUnique :: CoVar -> Unique -> CoVar Source
Free variables
tyCoVarsOfCo :: Coercion -> VarSet Source
tyCoVarsOfCos :: [Coercion] -> VarSet Source
coVarsOfCo :: Coercion -> VarSet Source
coercionSize :: Coercion -> Int Source
Substitution
type CvSubstEnv = VarEnv Coercion Source
isEmptyCvSubst :: CvSubst -> Bool Source
zapCvSubstEnv :: CvSubst -> CvSubst Source
getCvInScope :: CvSubst -> InScopeSet Source
substCoVar :: CvSubst -> CoVar -> Coercion Source
substCoVars :: CvSubst -> [CoVar] -> [Coercion] Source
substCoWithTy :: InScopeSet -> TyVar -> Type -> Coercion -> Coercion Source
substCoWithTys :: InScopeSet -> [TyVar] -> [Type] -> Coercion -> Coercion Source
zipOpenCvSubst :: [Var] -> [Coercion] -> CvSubst Source
Lifting
liftCoMatch :: TyVarSet -> Type -> Coercion -> Maybe LiftCoSubst Source
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.
Comparison
coreEqCoercion :: Coercion -> Coercion -> Bool Source
Determines syntactic equality of coercions
Forcing evaluation of coercions
Pretty-printing
pprParendCo :: Coercion -> SDoc Source
pprCoAxiom :: CoAxiom br -> SDoc Source
pprCoAxBranch :: TyCon -> CoAxBranch -> SDoc Source
pprCoAxBranchHdr :: CoAxiom br -> BranchIndex -> SDoc Source