{-# LANGUAGE DeriveDataTypeable #-} {-# OPTIONS_HADDOCK not-home #-} {- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 1998 \section[GHC.Core.TyCo.Rep]{Type and Coercion - friends' interface} Note [The Type-related module hierarchy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ GHC.Core.Class GHC.Core.Coercion.Axiom GHC.Core.TyCon imports GHC.Core.{Class, Coercion.Axiom} GHC.Core.TyCo.Rep imports GHC.Core.{Class, Coercion.Axiom, TyCon} GHC.Core.TyCo.Ppr imports GHC.Core.TyCo.Rep GHC.Core.TyCo.FVs imports GHC.Core.TyCo.Rep GHC.Core.TyCo.Subst imports GHC.Core.TyCo.{Rep, FVs, Ppr} GHC.Core.TyCo.Tidy imports GHC.Core.TyCo.{Rep, FVs} GHC.Builtin.Types.Prim imports GHC.Core.TyCo.Rep ( including mkTyConTy ) GHC.Core.Coercion imports GHC.Core.Type -} -- We expose the relevant stuff from this module via the Type module module GHC.Core.TyCo.Rep ( -- * Types Type(..), TyLit(..), KindOrType, Kind, RuntimeRepType, LevityType, KnotTied, PredType, ThetaType, FRRType, -- Synonyms ForAllTyFlag(..), FunTyFlag(..), -- * Coercions Coercion(..), CoSel(..), FunSel(..), UnivCoProvenance(..), CoercionHole(..), coHoleCoVar, setCoHoleCoVar, CoercionN, CoercionR, CoercionP, KindCoercion, MCoercion(..), MCoercionR, MCoercionN, -- * Functions over types mkNakedTyConTy, mkTyVarTy, mkTyVarTys, mkTyCoVarTy, mkTyCoVarTys, mkFunTy, mkNakedFunTy, mkVisFunTy, mkScaledFunTys, mkInvisFunTy, mkInvisFunTys, tcMkVisFunTy, tcMkInvisFunTy, tcMkScaledFunTys, mkForAllTy, mkForAllTys, mkInvisForAllTys, mkPiTy, mkPiTys, mkVisFunTyMany, mkVisFunTysMany, nonDetCmpTyLit, cmpTyLit, -- * Functions over coercions pickLR, -- ** Analyzing types TyCoFolder(..), foldTyCo, noView, -- * Sizes typeSize, coercionSize, provSize, -- * Multiplicities Scaled(..), scaledMult, scaledThing, mapScaledType, Mult ) where import GHC.Prelude import {-# SOURCE #-} GHC.Core.TyCo.Ppr ( pprType, pprCo, pprTyLit ) import {-# SOURCE #-} GHC.Builtin.Types import {-# SOURCE #-} GHC.Core.Type( chooseFunTyFlag, typeKind, typeTypeOrConstraint ) -- Transitively pulls in a LOT of stuff, better to break the loop -- friends: import GHC.Types.Var import GHC.Core.TyCon import GHC.Core.Coercion.Axiom -- others import GHC.Builtin.Names import GHC.Types.Basic ( LeftOrRight(..), pickLR ) import GHC.Utils.Outputable import GHC.Data.FastString import GHC.Utils.Misc import GHC.Utils.Panic import GHC.Utils.Binary -- libraries import qualified Data.Data as Data hiding ( TyCon ) import Data.IORef ( IORef ) -- for CoercionHole import Control.DeepSeq {- ********************************************************************** * * Type * * ********************************************************************** -} -- | The key representation of types within the compiler type KindOrType = Type -- See Note [Arguments to type constructors] -- | The key type representing kinds in the compiler. type Kind = Type -- | Type synonym used for types of kind RuntimeRep. type RuntimeRepType = Type -- | Type synonym used for types of kind Levity. type LevityType = Type -- A type with a syntactically fixed RuntimeRep, in the sense -- of Note [Fixed RuntimeRep] in GHC.Tc.Utils.Concrete. type FRRType = Type -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in GHC.Core.Lint data Type -- See Note [Non-trivial definitional equality] = TyVarTy Var -- ^ Vanilla type or kind variable (*never* a coercion variable) | AppTy Type Type -- ^ Type application to something other than a 'TyCon'. Parameters: -- -- 1) Function: must /not/ be a 'TyConApp' or 'CastTy', -- must be another 'AppTy', or 'TyVarTy' -- See Note [Respecting definitional equality] \(EQ1) about the -- no 'CastTy' requirement -- -- 2) Argument type | TyConApp TyCon [KindOrType] -- ^ Application of a 'TyCon', including newtypes /and/ synonyms. -- Invariant: saturated applications of 'FunTyCon' must -- use 'FunTy' and saturated synonyms must use their own -- constructors. However, /unsaturated/ 'FunTyCon's -- do appear as 'TyConApp's. -- Parameters: -- -- 1) Type constructor being applied to. -- -- 2) Type arguments. Might not have enough type arguments -- here to saturate the constructor. -- Even type synonyms are not necessarily saturated; -- for example unsaturated type synonyms -- can appear as the right hand side of a type synonym. | ForAllTy {-# UNPACK #-} !ForAllTyBinder Type -- ^ A Π type. -- Note [When we quantify over a coercion variable] -- INVARIANT: If the binder is a coercion variable, it must -- be mentioned in the Type. See -- Note [Unused coercion variable in ForAllTy] | FunTy -- ^ FUN m t1 t2 Very common, so an important special case -- See Note [Function types] { Kind -> FunTyFlag ft_af :: FunTyFlag -- Is this (->/FUN) or (=>) or (==>)? -- This info is fully specified by the kinds in -- ft_arg and ft_res -- Note [FunTyFlag] in GHC.Types.Var , Kind -> Kind ft_mult :: Mult -- Multiplicity; always Many for (=>) and (==>) , Kind -> Kind ft_arg :: Type -- Argument type , Kind -> Kind ft_res :: Type } -- Result type | LitTy TyLit -- ^ Type literals are similar to type constructors. | CastTy Type KindCoercion -- ^ A kind cast. The coercion is always nominal. -- INVARIANT: The cast is never reflexive \(EQ2) -- INVARIANT: The Type is not a CastTy (use TransCo instead) \(EQ3) -- INVARIANT: The Type is not a ForAllTy over a tyvar \(EQ4) -- See Note [Respecting definitional equality] | CoercionTy Coercion -- ^ Injection of a Coercion into a type -- This should only ever be used in the RHS of an AppTy, -- in the list of a TyConApp, when applying a promoted -- GADT data constructor deriving Typeable Kind Typeable Kind => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Kind -> c Kind) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Kind) -> (Kind -> Constr) -> (Kind -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Kind)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Kind)) -> ((forall b. Data b => b -> b) -> Kind -> Kind) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r) -> (forall u. (forall d. Data d => d -> u) -> Kind -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> Kind -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Kind -> m Kind) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind) -> Data Kind Kind -> Constr Kind -> DataType (forall b. Data b => b -> b) -> Kind -> Kind forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> Kind -> u forall u. (forall d. Data d => d -> u) -> Kind -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Kind -> m Kind forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Kind forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Kind -> c Kind forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Kind) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Kind) $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Kind -> c Kind gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Kind -> c Kind $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Kind gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Kind $ctoConstr :: Kind -> Constr toConstr :: Kind -> Constr $cdataTypeOf :: Kind -> DataType dataTypeOf :: Kind -> DataType $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Kind) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Kind) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Kind) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Kind) $cgmapT :: (forall b. Data b => b -> b) -> Kind -> Kind gmapT :: (forall b. Data b => b -> b) -> Kind -> Kind $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r $cgmapQ :: forall u. (forall d. Data d => d -> u) -> Kind -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> Kind -> [u] $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Kind -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Kind -> u $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Kind -> m Kind gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Kind -> m Kind $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind Data.Data instance Outputable Type where ppr :: Kind -> SDoc ppr = Kind -> SDoc pprType -- NOTE: Other parts of the code assume that type literals do not contain -- types or type variables. data TyLit = NumTyLit Integer | StrTyLit FastString | CharTyLit Char deriving (TyLit -> TyLit -> Bool (TyLit -> TyLit -> Bool) -> (TyLit -> TyLit -> Bool) -> Eq TyLit forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a $c== :: TyLit -> TyLit -> Bool == :: TyLit -> TyLit -> Bool $c/= :: TyLit -> TyLit -> Bool /= :: TyLit -> TyLit -> Bool Eq, Typeable TyLit Typeable TyLit => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyLit -> c TyLit) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyLit) -> (TyLit -> Constr) -> (TyLit -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyLit)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyLit)) -> ((forall b. Data b => b -> b) -> TyLit -> TyLit) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r) -> (forall u. (forall d. Data d => d -> u) -> TyLit -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> TyLit -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit) -> Data TyLit TyLit -> Constr TyLit -> DataType (forall b. Data b => b -> b) -> TyLit -> TyLit forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> TyLit -> u forall u. (forall d. Data d => d -> u) -> TyLit -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyLit forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyLit -> c TyLit forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyLit) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyLit) $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyLit -> c TyLit gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyLit -> c TyLit $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyLit gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyLit $ctoConstr :: TyLit -> Constr toConstr :: TyLit -> Constr $cdataTypeOf :: TyLit -> DataType dataTypeOf :: TyLit -> DataType $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyLit) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyLit) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyLit) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyLit) $cgmapT :: (forall b. Data b => b -> b) -> TyLit -> TyLit gmapT :: (forall b. Data b => b -> b) -> TyLit -> TyLit $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r $cgmapQ :: forall u. (forall d. Data d => d -> u) -> TyLit -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> TyLit -> [u] $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> TyLit -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> TyLit -> u $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit Data.Data) -- Non-determinism arises due to uniqCompareFS nonDetCmpTyLit :: TyLit -> TyLit -> Ordering nonDetCmpTyLit :: TyLit -> TyLit -> Ordering nonDetCmpTyLit = (FastString -> NonDetFastString) -> TyLit -> TyLit -> Ordering forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith FastString -> NonDetFastString NonDetFastString -- Slower than nonDetCmpTyLit but deterministic cmpTyLit :: TyLit -> TyLit -> Ordering cmpTyLit :: TyLit -> TyLit -> Ordering cmpTyLit = (FastString -> LexicalFastString) -> TyLit -> TyLit -> Ordering forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith FastString -> LexicalFastString LexicalFastString {-# INLINE cmpTyLitWith #-} cmpTyLitWith :: Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith :: forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith FastString -> r _ (NumTyLit Integer x) (NumTyLit Integer y) = Integer -> Integer -> Ordering forall a. Ord a => a -> a -> Ordering compare Integer x Integer y cmpTyLitWith FastString -> r w (StrTyLit FastString x) (StrTyLit FastString y) = r -> r -> Ordering forall a. Ord a => a -> a -> Ordering compare (FastString -> r w FastString x) (FastString -> r w FastString y) cmpTyLitWith FastString -> r _ (CharTyLit Char x) (CharTyLit Char y) = Char -> Char -> Ordering forall a. Ord a => a -> a -> Ordering compare Char x Char y cmpTyLitWith FastString -> r _ TyLit a TyLit b = Int -> Int -> Ordering forall a. Ord a => a -> a -> Ordering compare (TyLit -> Int tag TyLit a) (TyLit -> Int tag TyLit b) where tag :: TyLit -> Int tag :: TyLit -> Int tag NumTyLit{} = Int 0 tag StrTyLit{} = Int 1 tag CharTyLit{} = Int 2 instance Outputable TyLit where ppr :: TyLit -> SDoc ppr = TyLit -> SDoc pprTyLit {- Note [Function types] ~~~~~~~~~~~~~~~~~~~~~~~~ FunTy is the constructor for a function type. Here are the details: * The primitive function type constructor FUN has kind FUN :: forall (m :: Multiplicity) -> forall {r1 :: RuntimeRep} {r2 :: RuntimeRep}. TYPE r1 -> TYPE r2 -> Type mkTyConApp ensures that we convert a saturated application TyConApp FUN [m,r1,r2,t1,t2] into FunTy FTF_T_T m t1 t2 dropping the 'r1' and 'r2' arguments; they are easily recovered from 't1' and 't2'. The FunTyFlag is always FTF_T_T, because we build constraint arrows (=>) with e.g. mkPhiTy and friends, never `mkTyConApp funTyCon args`. * For the time being its RuntimeRep quantifiers are left inferred. This is to allow for it to evolve. * Because the RuntimeRep args came first historically (that is, the arrow type constructor gained these arguments before gaining the Multiplicity argument), we wanted to be able to say type (->) = FUN Many which we do in library module GHC.Types. This means that the Multiplicity argument must precede the RuntimeRep arguments -- and it means changing the name of the primitive constructor from (->) to FUN. * The multiplicity argument is dependent, because Typeable does not support a type such as `Multiplicity -> forall {r1 r2 :: RuntimeRep}. ...`. There is a plan to change the argument order and make the multiplicity argument nondependent in #20164. * Re the ft_af field: see Note [FunTyFlag] in GHC.Types.Var See Note [Types for coercions, predicates, and evidence] This visibility info makes no difference in Core; it matters only when we regard the type as a Haskell source type. Note [Types for coercions, predicates, and evidence] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We treat differently: (a) Predicate types Test: isPredTy Binders: DictIds Kind: Constraint Examples: (Eq a), and (a ~ b) (b) Coercion types are primitive, unboxed equalities Test: isCoVarTy Binders: CoVars (can appear in coercions) Kind: TYPE (TupleRep []) Examples: (t1 ~# t2) or (t1 ~R# t2) (c) Evidence types is the type of evidence manipulated by the type constraint solver. Test: isEvVarType Binders: EvVars Kind: Constraint or TYPE (TupleRep []) Examples: all coercion types and predicate types Coercion types and predicate types are mutually exclusive, but evidence types are a superset of both. When treated as a user type, - Predicates (of kind Constraint) are invisible and are implicitly instantiated - Coercion types, and non-pred evidence types (i.e. not of kind Constrain), are just regular old types, are visible, and are not implicitly instantiated. In a FunTy { ft_af = af } and af = FTF_C_T or FTF_C_C, the argument type is always a Predicate type. Note [Weird typing rule for ForAllTy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Here are the typing rules for ForAllTy: tyvar : Type inner : TYPE r tyvar does not occur in r ------------------------------------ ForAllTy (Bndr tyvar vis) inner : TYPE r inner : TYPE r ------------------------------------ ForAllTy (Bndr covar vis) inner : Type Note that the kind of the result depends on whether the binder is a tyvar or a covar. The kind of a forall-over-tyvar is the same as the kind of the inner type. This is because quantification over types is erased before runtime. By contrast, the kind of a forall-over-covar is always Type, because a forall-over-covar is compiled into a function taking a 0-bit-wide erased coercion argument. Because the tyvar form above includes r in its result, we must be careful not to let any variables escape -- thus the last premise of the rule above. Note [Constraints in kinds] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Do we allow a type constructor to have a kind like S :: Eq a => a -> Type No, we do not. Doing so would mean would need a TyConApp like S @k @(d :: Eq k) (ty :: k) and we have no way to build, or decompose, evidence like (d :: Eq k) at the type level. But we admit one exception: equality. We /do/ allow, say, MkT :: (a ~ b) => a -> b -> Type a b Why? Because we can, without much difficulty. Moreover we can promote a GADT data constructor (see TyCon Note [Promoted data constructors]), like data GT a b where MkGT : a -> a -> GT a a so programmers might reasonably expect to be able to promote MkT as well. How does this work? * In GHC.Tc.Validity.checkConstraintsOK we reject kinds that have constraints other than (a~b) and (a~~b). * In Inst.tcInstInvisibleTyBinder we instantiate a call of MkT by emitting [W] co :: alpha ~# beta and producing the elaborated term MkT @alpha @beta (Eq# alpha beta co) We don't generate a boxed "Wanted"; we generate only a regular old /unboxed/ primitive-equality Wanted, and build the box on the spot. * How can we get such a MkT? By promoting a GADT-style data constructor, written with an explicit equality constraint. data T a b where MkT :: (a~b) => a -> b -> T a b See DataCon.mkPromotedDataCon and Note [Promoted data constructors] in GHC.Core.TyCon * We support both homogeneous (~) and heterogeneous (~~) equality. (See Note [The equality types story] in GHC.Builtin.Types.Prim for a primer on these equality types.) * How do we prevent a MkT having an illegal constraint like Eq a? We check for this at use-sites; see GHC.Tc.Gen.HsType.tcTyVar, specifically dc_theta_illegal_constraint. * Notice that nothing special happens if K :: (a ~# b) => blah because (a ~# b) is not a predicate type, and is never implicitly instantiated. (Mind you, it's not clear how you could creates a type constructor with such a kind.) See Note [Types for coercions, predicates, and evidence] * The existence of promoted MkT with an equality-constraint argument is the (only) reason that the AnonTCB constructor of TyConBndrVis carries an FunTyFlag. For example, when we promote the data constructor MkT :: forall a b. (a~b) => a -> b -> T a b we get a PromotedDataCon with tyConBinders Bndr (a :: Type) (NamedTCB Inferred) Bndr (b :: Type) (NamedTCB Inferred) Bndr (_ :: a ~ b) (AnonTCB FTF_C_T) Bndr (_ :: a) (AnonTCB FTF_T_T)) Bndr (_ :: b) (AnonTCB FTF_T_T)) * One might reasonably wonder who *unpacks* these boxes once they are made. After all, there is no type-level `case` construct. The surprising answer is that no one ever does. Instead, if a GADT constructor is used on the left-hand side of a type family equation, that occurrence forces GHC to unify the types in question. For example: data G a where MkG :: G Bool type family F (x :: G a) :: a where F MkG = False When checking the LHS `F MkG`, GHC sees the MkG constructor and then must unify F's implicit parameter `a` with Bool. This succeeds, making the equation F Bool (MkG @Bool <Bool>) = False Note that we never need unpack the coercion. This is because type family equations are *not* parametric in their kind variables. That is, we could have just said type family H (x :: G a) :: a where H _ = False The presence of False on the RHS also forces `a` to become Bool, giving us H Bool _ = False The fact that any of this works stems from the lack of phase separation between types and kinds (unlike the very present phase separation between terms and types). Once we have the ability to pattern-match on types below top-level, this will no longer cut it, but it seems fine for now. Note [Arguments to type constructors] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Because of kind polymorphism, in addition to type application we now have kind instantiation. We reuse the same notations to do so. For example: Just (* -> *) Maybe Right * Nat Zero are represented by: TyConApp (PromotedDataCon Just) [* -> *, Maybe] TyConApp (PromotedDataCon Right) [*, Nat, (PromotedDataCon Zero)] Important note: Nat is used as a *kind* and not as a type. This can be confusing, since type-level Nat and kind-level Nat are identical. We use the kind of (PromotedDataCon Right) to know if its arguments are kinds or types. This kind instantiation only happens in TyConApp currently. Note [Non-trivial definitional equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Is Int |> <*> the same as Int? YES! In order to reduce headaches, we decide that any reflexive casts in types are just ignored. (Indeed they must be. See Note [Respecting definitional equality].) More generally, the `eqType` function, which defines Core's type equality relation, ignores casts and coercion arguments, as long as the two types have the same kind. This allows us to be a little sloppier in keeping track of coercions, which is a good thing. It also means that eqType does not depend on eqCoercion, which is also a good thing. Why is this sensible? That is, why is something different than α-equivalence appropriate for the implementation of eqType? Anything smaller than ~ and homogeneous is an appropriate definition for equality. The type safety of FC depends only on ~. Let's say η : τ ~ σ. Any expression of type τ can be transmuted to one of type σ at any point by casting. The same is true of expressions of type σ. So in some sense, τ and σ are interchangeable. But let's be more precise. If we examine the typing rules of FC (say, those in https://richarde.dev/papers/2015/equalities/equalities.pdf) there are several places where the same metavariable is used in two different premises to a rule. (For example, see Ty_App.) There is an implicit equality check here. What definition of equality should we use? By convention, we use α-equivalence. Take any rule with one (or more) of these implicit equality checks. Then there is an admissible rule that uses ~ instead of the implicit check, adding in casts as appropriate. The only problem here is that ~ is heterogeneous. To make the kinds work out in the admissible rule that uses ~, it is necessary to homogenize the coercions. That is, if we have η : (τ : κ1) ~ (σ : κ2), then we don't use η; we use η |> kind η, which is homogeneous. The effect of this all is that eqType, the implementation of the implicit equality check, can use any homogeneous relation that is smaller than ~, as those rules must also be admissible. A more drawn out argument around all of this is presented in Section 7.2 of Richard E's thesis (http://richarde.dev/papers/2016/thesis/eisenberg-thesis.pdf). What would go wrong if we insisted on the casts matching? See the beginning of Section 8 in the unpublished paper above. Theoretically, nothing at all goes wrong. But in practical terms, getting the coercions right proved to be nightmarish. And types would explode: during kind-checking, we often produce reflexive kind coercions. When we try to cast by these, mkCastTy just discards them. But if we used an eqType that distinguished between Int and Int |> <*>, then we couldn't discard -- the output of kind-checking would be enormous, and we would need enormous casts with lots of CoherenceCo's to straighten them out. Would anything go wrong if eqType looked through type families? No, not at all. But that makes eqType rather hard to implement. Thus, the guideline for eqType is that it should be the largest easy-to-implement relation that is still smaller than ~ and homogeneous. The precise choice of relation is somewhat incidental, as long as the smart constructors and destructors in Type respect whatever relation is chosen. Another helpful principle with eqType is this: (EQ) If (t1 `eqType` t2) then I can replace t1 by t2 anywhere. This principle also tells us that eqType must relate only types with the same kinds. Interestingly, it must be the case that the free variables of t1 and t2 might be different, even if t1 `eqType` t2. A simple example of this is if we have both cv1 :: k1 ~ k2 and cv2 :: k1 ~ k2 in the environment. Then t1 = t |> cv1 and t2 = t |> cv2 are eqType; yet cv1 is in the free vars of t1 and cv2 is in the free vars of t2. Unless we choose to implement eqType to be just α-equivalence, this wrinkle around free variables remains. Yet not all is lost: we can say that any two equal types share the same *relevant* free variables. Here, a relevant variable is a shallow free variable (see Note [Shallow and deep free variables] in GHC.Core.TyCo.FVs) that does not appear within a coercion. Note that type variables can appear within coercions (in, say, a Refl node), but that coercion variables cannot appear outside a coercion. We do not (yet) have a function to extract relevant free variables, but it would not be hard to write if the need arises. Note [Respecting definitional equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Note [Non-trivial definitional equality] introduces the property (EQ). How is this upheld? Any function that pattern matches on all the constructors will have to consider the possibility of CastTy. Presumably, those functions will handle CastTy appropriately and we'll be OK. More dangerous are the splitXXX functions. Let's focus on splitTyConApp. We don't want it to fail on (T a b c |> co). Happily, if we have (T a b c |> co) `eqType` (T d e f) then co must be reflexive. Why? eqType checks that the kinds are equal, as well as checking that (a `eqType` d), (b `eqType` e), and (c `eqType` f). By the kind check, we know that (T a b c |> co) and (T d e f) have the same kind. So the only way that co could be non-reflexive is for (T a b c) to have a different kind than (T d e f). But because T's kind is closed (all tycon kinds are closed), the only way for this to happen is that one of the arguments has to differ, leading to a contradiction. Thus, co is reflexive. Accordingly, by eliminating reflexive casts, splitTyConApp need not worry about outermost casts to uphold (EQ). Eliminating reflexive casts is done in mkCastTy. This is (EQ1) below. Unfortunately, that's not the end of the story. Consider comparing (T a b c) =? (T a b |> (co -> <Type>)) (c |> co) These two types have the same kind (Type), but the left type is a TyConApp while the right type is not. To handle this case, we say that the right-hand type is ill-formed, requiring an AppTy never to have a casted TyConApp on its left. It is easy enough to pull around the coercions to maintain this invariant, as done in Type.mkAppTy. In the example above, trying to form the right-hand type will instead yield (T a b (c |> co |> sym co) |> <Type>). Both the casts there are reflexive and will be dropped. Huzzah. This idea of pulling coercions to the right works for splitAppTy as well. However, there is one hiccup: it's possible that a coercion doesn't relate two Pi-types. For example, if we have @type family Fun a b where Fun a b = a -> b@, then we might have (T :: Fun Type Type) and (T |> axFun) Int. That axFun can't be pulled to the right. But we don't need to pull it: (T |> axFun) Int is not `eqType` to any proper TyConApp -- thus, leaving it where it is doesn't violate our (EQ) property. In order to detect reflexive casts reliably, we must make sure not to have nested casts: we update (t |> co1 |> co2) to (t |> (co1 `TransCo` co2)). This is (EQ2) below. One other troublesome case is ForAllTy. See Note [Weird typing rule for ForAllTy]. The kind of the body is the same as the kind of the ForAllTy. Accordingly, ForAllTy tv (ty |> co) and (ForAllTy tv ty) |> co are `eqType`. But only the first can be split by splitForAllTy. So we forbid the second form, instead pushing the coercion inside to get the first form. This is done in mkCastTy. In sum, in order to uphold (EQ), we need the following invariants: (EQ1) No decomposable CastTy to the left of an AppTy, where a decomposable cast is one that relates either a FunTy to a FunTy or a ForAllTy to a ForAllTy. (EQ2) No reflexive casts in CastTy. (EQ3) No nested CastTys. (EQ4) No CastTy over (ForAllTy (Bndr tyvar vis) body). See Note [Weird typing rule for ForAllTy] These invariants are all documented above, in the declaration for Type. Note [Equality on FunTys] ~~~~~~~~~~~~~~~~~~~~~~~~~ A (FunTy vis mult arg res) is just an abbreviation for a TyConApp funTyCon [mult, arg_rep, res_rep, arg, res] where arg :: TYPE arg_rep res :: TYPE res_rep Note that the vis field of a FunTy appears nowhere in the equivalent TyConApp. In Core, this is OK, because we no longer care about the visibility of the argument in a FunTy (the vis distinguishes between arg -> res and arg => res). In the type-checker, we are careful not to decompose FunTys with an invisible argument. See also Note [Decomposing fat arrow c=>t] in GHC.Core.Type. In order to compare FunTys while respecting how they could expand into TyConApps, we must check the kinds of the arg and the res. Note [When we quantify over a coercion variable] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The ForAllTyBinder in a ForAllTy can be (most often) a TyVar or (rarely) a CoVar. We support quantifying over a CoVar here in order to support a homogeneous (~#) relation (someday -- not yet implemented). Here is the example: type (:~~:) :: forall k1 k2. k1 -> k2 -> Type data a :~~: b where HRefl :: a :~~: a Assuming homogeneous equality (that is, with (~#) :: forall k. k -> k -> TYPE (TupleRep '[]) ) after rejigging to make equalities explicit, we get a constructor that looks like HRefl :: forall k1 k2 (a :: k1) (b :: k2). forall (cv :: k1 ~# k2). (a |> cv) ~# b => (:~~:) k1 k2 a b Note that we must cast `a` by a cv bound in the same type in order to make this work out. See also https://gitlab.haskell.org/ghc/ghc/-/wikis/dependent-haskell/phase2 which gives a general road map that covers this space. Having this feature in Core does *not* mean we have it in source Haskell. See #15710 about that. Note [Unused coercion variable in ForAllTy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have \(co:t1 ~# t2). e What type should we give to the above expression? (1) forall (co:t1 ~# t2) -> t (2) (t1 ~# t2) -> t If co is used in t, (1) should be the right choice. if co is not used in t, we would like to have (1) and (2) equivalent. However, we want to keep eqType simple and don't want eqType (1) (2) to return True in any case. We decide to always construct (2) if co is not used in t. Thus in mkLamType, we check whether the variable is a coercion variable (of type (t1 ~# t2), and whether it is un-used in the body. If so, it returns a FunTy instead of a ForAllTy. There are cases we want to skip the check. For example, the check is unnecessary when it is known from the context that the input variable is a type variable. In those cases, we use mkForAllTy. Note [Weird typing rule for ForAllTy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Here is the (truncated) typing rule for the dependent ForAllTy: inner : TYPE r tyvar is not free in r ---------------------------------------- ForAllTy (Bndr tyvar vis) inner : TYPE r Note that the kind of `inner` is the kind of the overall ForAllTy. This is necessary because every ForAllTy over a type variable is erased at runtime. Thus the runtime representation of a ForAllTy (as encoded, via TYPE rep, in the kind) must be the same as the representation of the body. We must check for skolem-escape, though. The skolem-escape would prevent a definition like undefined :: forall (r :: RuntimeRep) (a :: TYPE r). a because the type's kind (TYPE r) mentions the out-of-scope r. Luckily, the real type of undefined is undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a and that HasCallStack constraint neatly sidesteps the potential skolem-escape problem. If the bound variable is a coercion variable: inner : TYPE r covar is free in inner ------------------------------------ ForAllTy (Bndr covar vis) inner : Type Here, the kind of the ForAllTy is just Type, because coercion abstractions are *not* erased. The "covar is free in inner" premise is solely to maintain the representation invariant documented in Note [Unused coercion variable in ForAllTy]. Though there is surface similarity between this free-var check and the one in the tyvar rule, these two restrictions are truly unrelated. -} -- | A type labeled 'KnotTied' might have knot-tied tycons in it. See -- Note [Type checking recursive type and class declarations] in -- "GHC.Tc.TyCl" type KnotTied ty = ty {- ********************************************************************** * * PredType * * ********************************************************************** -} -- | A type of the form @p@ of constraint kind represents a value whose type is -- the Haskell predicate @p@, where a predicate is what occurs before -- the @=>@ in a Haskell type. -- -- We use 'PredType' as documentation to mark those types that we guarantee to -- have this kind. -- -- It can be expanded into its representation, but: -- -- * The type checker must treat it as opaque -- -- * The rest of the compiler treats it as transparent -- -- Consider these examples: -- -- > f :: (Eq a) => a -> Int -- > g :: (?x :: Int -> Int) => a -> Int -- > h :: (r\l) => {r} => {l::Int | r} -- -- Here the @Eq a@ and @?x :: Int -> Int@ and @r\l@ are all called \"predicates\" type PredType = Type -- | A collection of 'PredType's type ThetaType = [PredType] {- (We don't support TREX records yet, but the setup is designed to expand to allow them.) A Haskell qualified type, such as that for f,g,h above, is represented using * a FunTy for the double arrow * with a type of kind Constraint as the function argument The predicate really does turn into a real extra argument to the function. If the argument has type (p :: Constraint) then the predicate p is represented by evidence of type p. %************************************************************************ %* * Simple constructors %* * %************************************************************************ These functions are here so that they can be used by GHC.Builtin.Types.Prim, which in turn is imported by Type -} mkTyVarTy :: TyVar -> Type mkTyVarTy :: TyVar -> Kind mkTyVarTy TyVar v = Bool -> SDoc -> Kind -> Kind forall a. HasCallStack => Bool -> SDoc -> a -> a assertPpr (TyVar -> Bool isTyVar TyVar v) (TyVar -> SDoc forall a. Outputable a => a -> SDoc ppr TyVar v SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> SDoc dcolon SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Kind -> SDoc forall a. Outputable a => a -> SDoc ppr (TyVar -> Kind tyVarKind TyVar v)) (Kind -> Kind) -> Kind -> Kind forall a b. (a -> b) -> a -> b $ TyVar -> Kind TyVarTy TyVar v mkTyVarTys :: [TyVar] -> [Type] mkTyVarTys :: [TyVar] -> [Kind] mkTyVarTys = (TyVar -> Kind) -> [TyVar] -> [Kind] forall a b. (a -> b) -> [a] -> [b] map TyVar -> Kind mkTyVarTy -- a common use of mkTyVarTy mkTyCoVarTy :: TyCoVar -> Type mkTyCoVarTy :: TyVar -> Kind mkTyCoVarTy TyVar v | TyVar -> Bool isTyVar TyVar v = TyVar -> Kind TyVarTy TyVar v | Bool otherwise = KindCoercion -> Kind CoercionTy (TyVar -> KindCoercion CoVarCo TyVar v) mkTyCoVarTys :: [TyCoVar] -> [Type] mkTyCoVarTys :: [TyVar] -> [Kind] mkTyCoVarTys = (TyVar -> Kind) -> [TyVar] -> [Kind] forall a b. (a -> b) -> [a] -> [b] map TyVar -> Kind mkTyCoVarTy infixr 3 `mkFunTy`, `mkInvisFunTy`, `mkVisFunTyMany` mkNakedFunTy :: FunTyFlag -> Kind -> Kind -> Kind -- See Note [Naked FunTy] in GHC.Builtin.Types -- Always Many multiplicity; kinds have no linearity mkNakedFunTy :: FunTyFlag -> Kind -> Kind -> Kind mkNakedFunTy FunTyFlag af Kind arg Kind res = FunTy { ft_af :: FunTyFlag ft_af = FunTyFlag af, ft_mult :: Kind ft_mult = Kind manyDataConTy , ft_arg :: Kind ft_arg = Kind arg, ft_res :: Kind ft_res = Kind res } mkFunTy :: HasDebugCallStack => FunTyFlag -> Mult -> Type -> Type -> Type mkFunTy :: (() :: Constraint) => FunTyFlag -> Kind -> Kind -> Kind -> Kind mkFunTy FunTyFlag af Kind mult Kind arg Kind res = Bool -> SDoc -> Kind -> Kind forall a. HasCallStack => Bool -> SDoc -> a -> a assertPpr (FunTyFlag af FunTyFlag -> FunTyFlag -> Bool forall a. Eq a => a -> a -> Bool == (() :: Constraint) => Kind -> Kind -> FunTyFlag Kind -> Kind -> FunTyFlag chooseFunTyFlag Kind arg Kind res) ([SDoc] -> SDoc forall doc. IsDoc doc => [doc] -> doc vcat [ String -> SDoc forall doc. IsLine doc => String -> doc text String "af" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> FunTyFlag -> SDoc forall a. Outputable a => a -> SDoc ppr FunTyFlag af , String -> SDoc forall doc. IsLine doc => String -> doc text String "chooseAAF" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> FunTyFlag -> SDoc forall a. Outputable a => a -> SDoc ppr ((() :: Constraint) => Kind -> Kind -> FunTyFlag Kind -> Kind -> FunTyFlag chooseFunTyFlag Kind arg Kind res) , String -> SDoc forall doc. IsLine doc => String -> doc text String "arg" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Kind -> SDoc forall a. Outputable a => a -> SDoc ppr Kind arg SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> SDoc dcolon SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Kind -> SDoc forall a. Outputable a => a -> SDoc ppr ((() :: Constraint) => Kind -> Kind Kind -> Kind typeKind Kind arg) , String -> SDoc forall doc. IsLine doc => String -> doc text String "res" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Kind -> SDoc forall a. Outputable a => a -> SDoc ppr Kind res SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> SDoc dcolon SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> Kind -> SDoc forall a. Outputable a => a -> SDoc ppr ((() :: Constraint) => Kind -> Kind Kind -> Kind typeKind Kind res) ]) (Kind -> Kind) -> Kind -> Kind forall a b. (a -> b) -> a -> b $ FunTy { ft_af :: FunTyFlag ft_af = FunTyFlag af , ft_mult :: Kind ft_mult = Kind mult , ft_arg :: Kind ft_arg = Kind arg , ft_res :: Kind ft_res = Kind res } mkInvisFunTy :: HasDebugCallStack => Type -> Type -> Type mkInvisFunTy :: (() :: Constraint) => Kind -> Kind -> Kind mkInvisFunTy Kind arg Kind res = (() :: Constraint) => FunTyFlag -> Kind -> Kind -> Kind -> Kind FunTyFlag -> Kind -> Kind -> Kind -> Kind mkFunTy (TypeOrConstraint -> FunTyFlag invisArg ((() :: Constraint) => Kind -> TypeOrConstraint Kind -> TypeOrConstraint typeTypeOrConstraint Kind res)) Kind manyDataConTy Kind arg Kind res mkInvisFunTys :: HasDebugCallStack => [Type] -> Type -> Type mkInvisFunTys :: (() :: Constraint) => [Kind] -> Kind -> Kind mkInvisFunTys [Kind] args Kind res = (Kind -> Kind -> Kind) -> Kind -> [Kind] -> Kind forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr ((() :: Constraint) => FunTyFlag -> Kind -> Kind -> Kind -> Kind FunTyFlag -> Kind -> Kind -> Kind -> Kind mkFunTy FunTyFlag af Kind manyDataConTy) Kind res [Kind] args where af :: FunTyFlag af = TypeOrConstraint -> FunTyFlag invisArg ((() :: Constraint) => Kind -> TypeOrConstraint Kind -> TypeOrConstraint typeTypeOrConstraint Kind res) tcMkVisFunTy :: Mult -> Type -> Type -> Type -- Always TypeLike, user-specified multiplicity. -- Does not have the assert-checking in mkFunTy: used by the typechecker -- to avoid looking at the result kind, which may not be zonked tcMkVisFunTy :: Kind -> Kind -> Kind -> Kind tcMkVisFunTy Kind mult Kind arg Kind res = FunTy { ft_af :: FunTyFlag ft_af = FunTyFlag visArgTypeLike, ft_mult :: Kind ft_mult = Kind mult , ft_arg :: Kind ft_arg = Kind arg, ft_res :: Kind ft_res = Kind res } tcMkInvisFunTy :: TypeOrConstraint -> Type -> Type -> Type -- Always TypeLike, invisible argument -- Does not have the assert-checking in mkFunTy: used by the typechecker -- to avoid looking at the result kind, which may not be zonked tcMkInvisFunTy :: TypeOrConstraint -> Kind -> Kind -> Kind tcMkInvisFunTy TypeOrConstraint res_torc Kind arg Kind res = FunTy { ft_af :: FunTyFlag ft_af = TypeOrConstraint -> FunTyFlag invisArg TypeOrConstraint res_torc, ft_mult :: Kind ft_mult = Kind manyDataConTy , ft_arg :: Kind ft_arg = Kind arg, ft_res :: Kind ft_res = Kind res } mkVisFunTy :: HasDebugCallStack => Mult -> Type -> Type -> Type -- Always TypeLike, user-specified multiplicity. mkVisFunTy :: (() :: Constraint) => Kind -> Kind -> Kind -> Kind mkVisFunTy = (() :: Constraint) => FunTyFlag -> Kind -> Kind -> Kind -> Kind FunTyFlag -> Kind -> Kind -> Kind -> Kind mkFunTy FunTyFlag visArgTypeLike -- | Make nested arrow types -- | Special, common, case: Arrow type with mult Many mkVisFunTyMany :: HasDebugCallStack => Type -> Type -> Type -- Always TypeLike, multiplicity Many mkVisFunTyMany :: (() :: Constraint) => Kind -> Kind -> Kind mkVisFunTyMany = (() :: Constraint) => Kind -> Kind -> Kind -> Kind Kind -> Kind -> Kind -> Kind mkVisFunTy Kind manyDataConTy mkVisFunTysMany :: [Type] -> Type -> Type -- Always TypeLike, multiplicity Many mkVisFunTysMany :: [Kind] -> Kind -> Kind mkVisFunTysMany [Kind] tys Kind ty = (Kind -> Kind -> Kind) -> Kind -> [Kind] -> Kind forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr (() :: Constraint) => Kind -> Kind -> Kind Kind -> Kind -> Kind mkVisFunTyMany Kind ty [Kind] tys --------------- mkScaledFunTy :: HasDebugCallStack => FunTyFlag -> Scaled Type -> Type -> Type mkScaledFunTy :: (() :: Constraint) => FunTyFlag -> Scaled Kind -> Kind -> Kind mkScaledFunTy FunTyFlag af (Scaled Kind mult Kind arg) Kind res = (() :: Constraint) => FunTyFlag -> Kind -> Kind -> Kind -> Kind FunTyFlag -> Kind -> Kind -> Kind -> Kind mkFunTy FunTyFlag af Kind mult Kind arg Kind res mkScaledFunTys :: HasDebugCallStack => [Scaled Type] -> Type -> Type -- All visible args -- Result type can be TypeLike or ConstraintLike -- Example of the latter: dataConWrapperType for the data con of a class mkScaledFunTys :: (() :: Constraint) => [Scaled Kind] -> Kind -> Kind mkScaledFunTys [Scaled Kind] tys Kind ty = (Scaled Kind -> Kind -> Kind) -> Kind -> [Scaled Kind] -> Kind forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr ((() :: Constraint) => FunTyFlag -> Scaled Kind -> Kind -> Kind FunTyFlag -> Scaled Kind -> Kind -> Kind mkScaledFunTy FunTyFlag af) Kind ty [Scaled Kind] tys where af :: FunTyFlag af = TypeOrConstraint -> FunTyFlag visArg ((() :: Constraint) => Kind -> TypeOrConstraint Kind -> TypeOrConstraint typeTypeOrConstraint Kind ty) tcMkScaledFunTys :: [Scaled Type] -> Type -> Type -- All visible args -- Result type must be TypeLike -- No mkFunTy assert checking; result kind may not be zonked tcMkScaledFunTys :: [Scaled Kind] -> Kind -> Kind tcMkScaledFunTys [Scaled Kind] tys Kind ty = (Scaled Kind -> Kind -> Kind) -> Kind -> [Scaled Kind] -> Kind forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr Scaled Kind -> Kind -> Kind mk Kind ty [Scaled Kind] tys where mk :: Scaled Kind -> Kind -> Kind mk (Scaled Kind mult Kind arg) Kind res = Kind -> Kind -> Kind -> Kind tcMkVisFunTy Kind mult Kind arg Kind res --------------- -- | Like 'mkTyCoForAllTy', but does not check the occurrence of the binder -- See Note [Unused coercion variable in ForAllTy] mkForAllTy :: ForAllTyBinder -> Type -> Type mkForAllTy :: ForAllTyBinder -> Kind -> Kind mkForAllTy = ForAllTyBinder -> Kind -> Kind ForAllTy -- | Wraps foralls over the type using the provided 'TyCoVar's from left to right mkForAllTys :: [ForAllTyBinder] -> Type -> Type mkForAllTys :: [ForAllTyBinder] -> Kind -> Kind mkForAllTys [ForAllTyBinder] tyvars Kind ty = (ForAllTyBinder -> Kind -> Kind) -> Kind -> [ForAllTyBinder] -> Kind forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr ForAllTyBinder -> Kind -> Kind ForAllTy Kind ty [ForAllTyBinder] tyvars -- | Wraps foralls over the type using the provided 'InvisTVBinder's from left to right mkInvisForAllTys :: [InvisTVBinder] -> Type -> Type mkInvisForAllTys :: [InvisTVBinder] -> Kind -> Kind mkInvisForAllTys [InvisTVBinder] tyvars = [ForAllTyBinder] -> Kind -> Kind mkForAllTys ([InvisTVBinder] -> [ForAllTyBinder] forall a. [VarBndr a Specificity] -> [VarBndr a ForAllTyFlag] tyVarSpecToBinders [InvisTVBinder] tyvars) mkPiTy :: PiTyBinder -> Type -> Type mkPiTy :: PiTyBinder -> Kind -> Kind mkPiTy (Anon Scaled Kind ty1 FunTyFlag af) Kind ty2 = (() :: Constraint) => FunTyFlag -> Scaled Kind -> Kind -> Kind FunTyFlag -> Scaled Kind -> Kind -> Kind mkScaledFunTy FunTyFlag af Scaled Kind ty1 Kind ty2 mkPiTy (Named ForAllTyBinder bndr) Kind ty = ForAllTyBinder -> Kind -> Kind mkForAllTy ForAllTyBinder bndr Kind ty mkPiTys :: [PiTyBinder] -> Type -> Type mkPiTys :: [PiTyBinder] -> Kind -> Kind mkPiTys [PiTyBinder] tbs Kind ty = (PiTyBinder -> Kind -> Kind) -> Kind -> [PiTyBinder] -> Kind forall a b. (a -> b -> b) -> b -> [a] -> b forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr PiTyBinder -> Kind -> Kind mkPiTy Kind ty [PiTyBinder] tbs -- | 'mkNakedTyConTy' creates a nullary 'TyConApp'. In general you -- should rather use 'GHC.Core.Type.mkTyConTy', which picks the shared -- nullary TyConApp from inside the TyCon (via tyConNullaryTy. But -- we have to build the TyConApp tc [] in that TyCon field; that's -- what 'mkNakedTyConTy' is for. mkNakedTyConTy :: TyCon -> Type mkNakedTyConTy :: TyCon -> Kind mkNakedTyConTy TyCon tycon = TyCon -> [Kind] -> Kind TyConApp TyCon tycon [] {- %************************************************************************ %* * Coercions %* * %************************************************************************ -} -- | A 'Coercion' is concrete evidence of the equality/convertibility -- of two types. -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in GHC.Core.Lint data Coercion -- Each constructor has a "role signature", indicating the way roles are -- propagated through coercions. -- - P, N, and R stand for coercions of the given role -- - e stands for a coercion of a specific unknown role -- (think "role polymorphism") -- - "e" stands for an explicit role parameter indicating role e. -- - _ stands for a parameter that is not a Role or Coercion. -- These ones mirror the shape of types = -- Refl :: _ -> N -- A special case reflexivity for a very common case: Nominal reflexivity -- If you need Representational, use (GRefl Representational ty MRefl) -- not (SubCo (Refl ty)) Refl Type -- See Note [Refl invariant] -- GRefl :: "e" -> _ -> Maybe N -> e -- See Note [Generalized reflexive coercion] | GRefl Role Type MCoercionN -- See Note [Refl invariant] -- Use (Refl ty), not (GRefl Nominal ty MRefl) -- Use (GRefl Representational _ _), not (SubCo (GRefl Nominal _ _)) -- These ones simply lift the correspondingly-named -- Type constructors into Coercions -- TyConAppCo :: "e" -> _ -> ?? -> e -- See Note [TyConAppCo roles] | TyConAppCo Role TyCon [Coercion] -- lift TyConApp -- The TyCon is never a synonym; -- we expand synonyms eagerly -- But it can be a type function -- TyCon is never a saturated (->); use FunCo instead | AppCo Coercion CoercionN -- lift AppTy -- AppCo :: e -> N -> e -- See Note [Forall coercions] | ForAllCo TyCoVar KindCoercion Coercion -- ForAllCo :: _ -> N -> e -> e | FunCo -- FunCo :: "e" -> N/P -> e -> e -> e -- See Note [FunCo] for fco_afl, fco_afr { KindCoercion -> Role fco_role :: Role , KindCoercion -> FunTyFlag fco_afl :: FunTyFlag -- Arrow for coercionLKind , KindCoercion -> FunTyFlag fco_afr :: FunTyFlag -- Arrow for coercionRKind , KindCoercion -> KindCoercion fco_mult :: CoercionN , KindCoercion -> KindCoercion fco_arg, KindCoercion -> KindCoercion fco_res :: Coercion } -- (if the role "e" is Phantom, the first coercion is, too) -- the first coercion is for the multiplicity -- These are special | CoVarCo CoVar -- :: _ -> (N or R) -- result role depends on the tycon of the variable's type -- AxiomInstCo :: e -> _ -> ?? -> e | AxiomInstCo (CoAxiom Branched) BranchIndex [Coercion] -- See also [CoAxiom index] -- The coercion arguments always *precisely* saturate -- arity of (that branch of) the CoAxiom. If there are -- any left over, we use AppCo. -- See [Coercion axioms applied to coercions] -- The roles of the argument coercions are determined -- by the cab_roles field of the relevant branch of the CoAxiom | AxiomRuleCo CoAxiomRule [Coercion] -- AxiomRuleCo is very like AxiomInstCo, but for a CoAxiomRule -- The number coercions should match exactly the expectations -- of the CoAxiomRule (i.e., the rule is fully saturated). | UnivCo UnivCoProvenance Role Type Type -- :: _ -> "e" -> _ -> _ -> e | SymCo Coercion -- :: e -> e | TransCo Coercion Coercion -- :: e -> e -> e | SelCo CoSel Coercion -- See Note [SelCo] | LRCo LeftOrRight CoercionN -- Decomposes (t_left t_right) -- :: _ -> N -> N | InstCo Coercion CoercionN -- :: e -> N -> e -- See Note [InstCo roles] -- Extract a kind coercion from a (heterogeneous) type coercion -- NB: all kind coercions are Nominal | KindCo Coercion -- :: e -> N | SubCo CoercionN -- Turns a ~N into a ~R -- :: N -> R | HoleCo CoercionHole -- ^ See Note [Coercion holes] -- Only present during typechecking deriving Typeable KindCoercion Typeable KindCoercion => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c KindCoercion) -> (KindCoercion -> Constr) -> (KindCoercion -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c KindCoercion)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c KindCoercion)) -> ((forall b. Data b => b -> b) -> KindCoercion -> KindCoercion) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r) -> (forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> KindCoercion -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion) -> Data KindCoercion KindCoercion -> Constr KindCoercion -> DataType (forall b. Data b => b -> b) -> KindCoercion -> KindCoercion forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> KindCoercion -> u forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c KindCoercion forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c KindCoercion) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c KindCoercion) $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> KindCoercion -> c KindCoercion $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c KindCoercion gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c KindCoercion $ctoConstr :: KindCoercion -> Constr toConstr :: KindCoercion -> Constr $cdataTypeOf :: KindCoercion -> DataType dataTypeOf :: KindCoercion -> DataType $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c KindCoercion) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c KindCoercion) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c KindCoercion) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c KindCoercion) $cgmapT :: (forall b. Data b => b -> b) -> KindCoercion -> KindCoercion gmapT :: (forall b. Data b => b -> b) -> KindCoercion -> KindCoercion $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> KindCoercion -> r $cgmapQ :: forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> KindCoercion -> [u] $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> KindCoercion -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> KindCoercion -> u $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> KindCoercion -> m KindCoercion Data.Data data CoSel -- See Note [SelCo] = SelTyCon Int Role -- Decomposes (T co1 ... con); zero-indexed -- Invariant: Given: SelCo (SelTyCon i r) co -- we have r == tyConRole (coercionRole co) tc -- and tc1 == tc2 -- where T tc1 _ = coercionLKind co -- T tc2 _ = coercionRKind co -- See Note [SelCo] | SelFun FunSel -- Decomposes (co1 -> co2) | SelForAll -- Decomposes (forall a. co) deriving( CoSel -> CoSel -> Bool (CoSel -> CoSel -> Bool) -> (CoSel -> CoSel -> Bool) -> Eq CoSel forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a $c== :: CoSel -> CoSel -> Bool == :: CoSel -> CoSel -> Bool $c/= :: CoSel -> CoSel -> Bool /= :: CoSel -> CoSel -> Bool Eq, Typeable CoSel Typeable CoSel => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CoSel -> c CoSel) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CoSel) -> (CoSel -> Constr) -> (CoSel -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c CoSel)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel)) -> ((forall b. Data b => b -> b) -> CoSel -> CoSel) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r) -> (forall u. (forall d. Data d => d -> u) -> CoSel -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel) -> Data CoSel CoSel -> Constr CoSel -> DataType (forall b. Data b => b -> b) -> CoSel -> CoSel forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u forall u. (forall d. Data d => d -> u) -> CoSel -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CoSel forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CoSel -> c CoSel forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c CoSel) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel) $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CoSel -> c CoSel gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CoSel -> c CoSel $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CoSel gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CoSel $ctoConstr :: CoSel -> Constr toConstr :: CoSel -> Constr $cdataTypeOf :: CoSel -> DataType dataTypeOf :: CoSel -> DataType $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c CoSel) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c CoSel) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoSel) $cgmapT :: (forall b. Data b => b -> b) -> CoSel -> CoSel gmapT :: (forall b. Data b => b -> b) -> CoSel -> CoSel $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoSel -> r $cgmapQ :: forall u. (forall d. Data d => d -> u) -> CoSel -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> CoSel -> [u] $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CoSel -> u $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> CoSel -> m CoSel Data.Data ) data FunSel -- See Note [SelCo] = SelMult -- Multiplicity | SelArg -- Argument of function | SelRes -- Result of function deriving( FunSel -> FunSel -> Bool (FunSel -> FunSel -> Bool) -> (FunSel -> FunSel -> Bool) -> Eq FunSel forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a $c== :: FunSel -> FunSel -> Bool == :: FunSel -> FunSel -> Bool $c/= :: FunSel -> FunSel -> Bool /= :: FunSel -> FunSel -> Bool Eq, Typeable FunSel Typeable FunSel => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> FunSel -> c FunSel) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c FunSel) -> (FunSel -> Constr) -> (FunSel -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c FunSel)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel)) -> ((forall b. Data b => b -> b) -> FunSel -> FunSel) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r) -> (forall u. (forall d. Data d => d -> u) -> FunSel -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel) -> Data FunSel FunSel -> Constr FunSel -> DataType (forall b. Data b => b -> b) -> FunSel -> FunSel forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u forall u. (forall d. Data d => d -> u) -> FunSel -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c FunSel forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> FunSel -> c FunSel forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c FunSel) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel) $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> FunSel -> c FunSel gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> FunSel -> c FunSel $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c FunSel gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c FunSel $ctoConstr :: FunSel -> Constr toConstr :: FunSel -> Constr $cdataTypeOf :: FunSel -> DataType dataTypeOf :: FunSel -> DataType $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c FunSel) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c FunSel) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunSel) $cgmapT :: (forall b. Data b => b -> b) -> FunSel -> FunSel gmapT :: (forall b. Data b => b -> b) -> FunSel -> FunSel $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunSel -> r $cgmapQ :: forall u. (forall d. Data d => d -> u) -> FunSel -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> FunSel -> [u] $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> FunSel -> u $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> FunSel -> m FunSel Data.Data ) type CoercionN = Coercion -- always nominal type CoercionR = Coercion -- always representational type CoercionP = Coercion -- always phantom type KindCoercion = CoercionN -- always nominal instance Outputable Coercion where ppr :: KindCoercion -> SDoc ppr = KindCoercion -> SDoc pprCo instance Outputable CoSel where ppr :: CoSel -> SDoc ppr (SelTyCon Int n Role _r) = String -> SDoc forall doc. IsLine doc => String -> doc text String "Tc" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <> SDoc -> SDoc forall doc. IsLine doc => doc -> doc parens (Int -> SDoc forall doc. IsLine doc => Int -> doc int Int n) ppr CoSel SelForAll = String -> SDoc forall doc. IsLine doc => String -> doc text String "All" ppr (SelFun FunSel fs) = String -> SDoc forall doc. IsLine doc => String -> doc text String "Fun" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <> SDoc -> SDoc forall doc. IsLine doc => doc -> doc parens (FunSel -> SDoc forall a. Outputable a => a -> SDoc ppr FunSel fs) instance Outputable FunSel where ppr :: FunSel -> SDoc ppr FunSel SelMult = String -> SDoc forall doc. IsLine doc => String -> doc text String "mult" ppr FunSel SelArg = String -> SDoc forall doc. IsLine doc => String -> doc text String "arg" ppr FunSel SelRes = String -> SDoc forall doc. IsLine doc => String -> doc text String "res" instance Binary CoSel where put_ :: BinHandle -> CoSel -> IO () put_ BinHandle bh (SelTyCon Int n Role r) = do { BinHandle -> Word8 -> IO () putByte BinHandle bh Word8 0; BinHandle -> Int -> IO () forall a. Binary a => BinHandle -> a -> IO () put_ BinHandle bh Int n; BinHandle -> Role -> IO () forall a. Binary a => BinHandle -> a -> IO () put_ BinHandle bh Role r } put_ BinHandle bh CoSel SelForAll = BinHandle -> Word8 -> IO () putByte BinHandle bh Word8 1 put_ BinHandle bh (SelFun FunSel SelMult) = BinHandle -> Word8 -> IO () putByte BinHandle bh Word8 2 put_ BinHandle bh (SelFun FunSel SelArg) = BinHandle -> Word8 -> IO () putByte BinHandle bh Word8 3 put_ BinHandle bh (SelFun FunSel SelRes) = BinHandle -> Word8 -> IO () putByte BinHandle bh Word8 4 get :: BinHandle -> IO CoSel get BinHandle bh = do { Word8 h <- BinHandle -> IO Word8 getByte BinHandle bh ; case Word8 h of Word8 0 -> do { Int n <- BinHandle -> IO Int forall a. Binary a => BinHandle -> IO a get BinHandle bh; Role r <- BinHandle -> IO Role forall a. Binary a => BinHandle -> IO a get BinHandle bh; CoSel -> IO CoSel forall a. a -> IO a forall (m :: * -> *) a. Monad m => a -> m a return (Int -> Role -> CoSel SelTyCon Int n Role r) } Word8 1 -> CoSel -> IO CoSel forall a. a -> IO a forall (m :: * -> *) a. Monad m => a -> m a return CoSel SelForAll Word8 2 -> CoSel -> IO CoSel forall a. a -> IO a forall (m :: * -> *) a. Monad m => a -> m a return (FunSel -> CoSel SelFun FunSel SelMult) Word8 3 -> CoSel -> IO CoSel forall a. a -> IO a forall (m :: * -> *) a. Monad m => a -> m a return (FunSel -> CoSel SelFun FunSel SelArg) Word8 _ -> CoSel -> IO CoSel forall a. a -> IO a forall (m :: * -> *) a. Monad m => a -> m a return (FunSel -> CoSel SelFun FunSel SelRes) } instance NFData CoSel where rnf :: CoSel -> () rnf (SelTyCon Int n Role r) = Int n Int -> () -> () forall a b. a -> b -> b `seq` Role r Role -> () -> () forall a b. a -> b -> b `seq` () rnf CoSel SelForAll = () rnf (SelFun FunSel fs) = FunSel fs FunSel -> () -> () forall a b. a -> b -> b `seq` () -- | A semantically more meaningful type to represent what may or may not be a -- useful 'Coercion'. data MCoercion = MRefl -- A trivial Reflexivity coercion | MCo Coercion -- Other coercions deriving Typeable MCoercionN Typeable MCoercionN => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercionN) -> (MCoercionN -> Constr) -> (MCoercionN -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercionN)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercionN)) -> ((forall b. Data b => b -> b) -> MCoercionN -> MCoercionN) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r) -> (forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> MCoercionN -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN) -> Data MCoercionN MCoercionN -> Constr MCoercionN -> DataType (forall b. Data b => b -> b) -> MCoercionN -> MCoercionN forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> MCoercionN -> u forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercionN forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercionN) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercionN) $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercionN -> c MCoercionN $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercionN gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercionN $ctoConstr :: MCoercionN -> Constr toConstr :: MCoercionN -> Constr $cdataTypeOf :: MCoercionN -> DataType dataTypeOf :: MCoercionN -> DataType $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercionN) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercionN) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercionN) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercionN) $cgmapT :: (forall b. Data b => b -> b) -> MCoercionN -> MCoercionN gmapT :: (forall b. Data b => b -> b) -> MCoercionN -> MCoercionN $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercionN -> r $cgmapQ :: forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> MCoercionN -> [u] $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MCoercionN -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MCoercionN -> u $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercionN -> m MCoercionN Data.Data type MCoercionR = MCoercion type MCoercionN = MCoercion instance Outputable MCoercion where ppr :: MCoercionN -> SDoc ppr MCoercionN MRefl = String -> SDoc forall doc. IsLine doc => String -> doc text String "MRefl" ppr (MCo KindCoercion co) = String -> SDoc forall doc. IsLine doc => String -> doc text String "MCo" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> KindCoercion -> SDoc forall a. Outputable a => a -> SDoc ppr KindCoercion co {- Note [Refl invariant] ~~~~~~~~~~~~~~~~~~~~~~~~ Invariant 1: Refl lifting Refl (similar for GRefl r ty MRefl) is always lifted as far as possible. For example (Refl T) (Refl a) (Refl b) is normalised (by mkAppCo) to (Refl (T a b)). You might think that a consequences is: Every identity coercion has Refl at the root But that's not quite true because of coercion variables. Consider g where g :: Int~Int Left h where h :: Maybe Int ~ Maybe Int etc. So the consequence is only true of coercions that have no coercion variables. Invariant 2: TyConAppCo An application of (Refl T) to some coercions, at least one of which is NOT the identity, is normalised to TyConAppCo. (They may not be fully saturated however.) TyConAppCo coercions (like all coercions other than Refl) are NEVER the identity. Note [Generalized reflexive coercion] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ GRefl is a generalized reflexive coercion (see #15192). It wraps a kind coercion, which might be reflexive (MRefl) or any coercion (MCo co). The typing rules for GRefl: ty : k1 ------------------------------------ GRefl r ty MRefl: ty ~r ty ty : k1 co :: k1 ~ k2 ------------------------------------ GRefl r ty (MCo co) : ty ~r ty |> co Consider we have g1 :: s ~r t s :: k1 g2 :: k1 ~ k2 and we want to construct a coercions co which has type (s |> g2) ~r t We can define co = Sym (GRefl r s g2) ; g1 It is easy to see that Refl == GRefl Nominal ty MRefl :: ty ~n ty A nominal reflexive coercion is quite common, so we keep the special form Refl to save allocation. Note [SelCo] ~~~~~~~~~~~~ The Coercion form SelCo allows us to decompose a structural coercion, one between ForallTys, or TyConApps, or FunTys. There are three forms, split by the CoSel field inside the SelCo: SelTyCon, SelForAll, and SelFun. * SelTyCon: co : (T s1..sn) ~r0 (T t1..tn) T is a data type, not a newtype, nor an arrow type r = tyConRole tc r0 i i < n (i is zero-indexed) ---------------------------------- SelCo (SelTyCon i r) : si ~r ti "Not a newtype": see Note [SelCo and newtypes] "Not an arrow type": see SelFun below See Note [SelCo Cached Roles] * SelForAll: co : forall (a:k1).t1 ~r0 forall (a:k2).t2 ---------------------------------- SelCo SelForAll : k1 ~N k2 NB: SelForAll always gives a Nominal coercion. * The SelFun form, for functions, has three sub-forms for the three components of the function type (multiplicity, argument, result). co : (s1 %{m1}-> t1) ~r0 (s2 %{m2}-> t2) r = funRole r0 SelMult ---------------------------------- SelCo (SelFun SelMult) : m1 ~r m2 co : (s1 %{m1}-> t1) ~r0 (s2 %{m2}-> t2) r = funRole r0 SelArg ---------------------------------- SelCo (SelFun SelArg) : s1 ~r s2 co : (s1 %{m1}-> t1) ~r0 (s2 %{m2}-> t2) r = funRole r0 SelRes ---------------------------------- SelCo (SelFun SelRes) : t1 ~r t2 Note [FunCo] ~~~~~~~~~~~~ Just as FunTy has a ft_af :: FunTyFlag field, FunCo (which connects two function types) has two FunTyFlag fields: funco_afl, funco_afr :: FunTyFlag In all cases, the FunTyFlag is recoverable from the kinds of the argument and result types/coercions; but experiments show that it's better to cache it. Why does FunCo need /two/ flags? If we have a single method class, implemented as a newtype class C a where { op :: [a] -> a } then we can have a coercion co :: C Int ~R ([Int]->Int) So now we can define FunCo co <Bool> : (C Int => Bool) ~R (([Int]->Int) -> Bool) Notice that the left and right arrows are different! Hence two flags, one for coercionLKind and one for coercionRKind. Note [Coercion axioms applied to coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The reason coercion axioms can be applied to coercions and not just types is to allow for better optimization. There are some cases where we need to be able to "push transitivity inside" an axiom in order to expose further opportunities for optimization. For example, suppose we have C a : t[a] ~ F a g : b ~ c and we want to optimize sym (C b) ; t[g] ; C c which has the kind F b ~ F c (stopping through t[b] and t[c] along the way). We'd like to optimize this to just F g -- but how? The key is that we need to allow axioms to be instantiated by *coercions*, not just by types. Then we can (in certain cases) push transitivity inside the axiom instantiations, and then react opposite-polarity instantiations of the same axiom. In this case, e.g., we match t[g] against the LHS of (C c)'s kind, to obtain the substitution a |-> g (note this operation is sort of the dual of lifting!) and hence end up with C g : t[b] ~ F c which indeed has the same kind as t[g] ; C c. Now we have sym (C b) ; C g which can be optimized to F g. Note [CoAxiom index] ~~~~~~~~~~~~~~~~~~~~ A CoAxiom has 1 or more branches. Each branch has contains a list of the free type variables in that branch, the LHS type patterns, and the RHS type for that branch. When we apply an axiom to a list of coercions, we must choose which branch of the axiom we wish to use, as the different branches may have different numbers of free type variables. (The number of type patterns is always the same among branches, but that doesn't quite concern us here.) The Int in the AxiomInstCo constructor is the 0-indexed number of the chosen branch. Note [Forall coercions] ~~~~~~~~~~~~~~~~~~~~~~~ Constructing coercions between forall-types can be a bit tricky, because the kinds of the bound tyvars can be different. The typing rule is: kind_co : k1 ~ k2 tv1:k1 |- co : t1 ~ t2 ------------------------------------------------------------------- ForAllCo tv1 kind_co co : all tv1:k1. t1 ~ all tv1:k2. (t2[tv1 |-> tv1 |> sym kind_co]) First, the TyCoVar stored in a ForAllCo is really an optimisation: this field should be a Name, as its kind is redundant. Thinking of the field as a Name is helpful in understanding what a ForAllCo means. The kind of TyCoVar always matches the left-hand kind of the coercion. The idea is that kind_co gives the two kinds of the tyvar. See how, in the conclusion, tv1 is assigned kind k1 on the left but kind k2 on the right. Of course, a type variable can't have different kinds at the same time. So, we arbitrarily prefer the first kind when using tv1 in the inner coercion co, which shows that t1 equals t2. The last wrinkle is that we need to fix the kinds in the conclusion. In t2, tv1 is assumed to have kind k1, but it has kind k2 in the conclusion of the rule. So we do a kind-fixing substitution, replacing (tv1:k1) with (tv1:k2) |> sym kind_co. This substitution is slightly bizarre, because it mentions the same name with different kinds, but it *is* well-kinded, noting that `(tv1:k2) |> sym kind_co` has kind k1. This all really would work storing just a Name in the ForAllCo. But we can't add Names to, e.g., VarSets, and there generally is just an impedance mismatch in a bunch of places. So we use tv1. When we need tv2, we can use setTyVarKind. Note [Predicate coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have g :: a~b How can we coerce between types ([c]~a) => [a] -> c and ([c]~b) => [b] -> c where the equality predicate *itself* differs? Answer: we simply treat (~) as an ordinary type constructor, so these types really look like ((~) [c] a) -> [a] -> c ((~) [c] b) -> [b] -> c So the coercion between the two is obviously ((~) [c] g) -> [g] -> c Another way to see this to say that we simply collapse predicates to their representation type (see Type.coreView and Type.predTypeRep). This collapse is done by mkPredCo; there is no PredCo constructor in Coercion. This is important because we need Nth to work on predicates too: SelCo (SelTyCon 1) ((~) [c] g) = g See Simplify.simplCoercionF, which generates such selections. Note [Roles] ~~~~~~~~~~~~ Roles are a solution to the GeneralizedNewtypeDeriving problem, articulated in #1496. The full story is in docs/core-spec/core-spec.pdf. Also, see https://gitlab.haskell.org/ghc/ghc/wikis/roles-implementation Here is one way to phrase the problem: Given: newtype Age = MkAge Int type family F x type instance F Age = Bool type instance F Int = Char This compiles down to: axAge :: Age ~ Int axF1 :: F Age ~ Bool axF2 :: F Int ~ Char Then, we can make: (sym (axF1) ; F axAge ; axF2) :: Bool ~ Char Yikes! The solution is _roles_, as articulated in "Generative Type Abstraction and Type-level Computation" (POPL 2010), available at http://www.seas.upenn.edu/~sweirich/papers/popl163af-weirich.pdf The specification for roles has evolved somewhat since that paper. For the current full details, see the documentation in docs/core-spec. Here are some highlights. We label every equality with a notion of type equivalence, of which there are three options: Nominal, Representational, and Phantom. A ground type is nominally equivalent only with itself. A newtype (which is considered a ground type in Haskell) is representationally equivalent to its representation. Anything is "phantomly" equivalent to anything else. We use "N", "R", and "P" to denote the equivalences. The axioms above would be: axAge :: Age ~R Int axF1 :: F Age ~N Bool axF2 :: F Age ~N Char Then, because transitivity applies only to coercions proving the same notion of equivalence, the above construction is impossible. However, there is still an escape hatch: we know that any two types that are nominally equivalent are representationally equivalent as well. This is what the form SubCo proves -- it "demotes" a nominal equivalence into a representational equivalence. So, it would seem the following is possible: sub (sym axF1) ; F axAge ; sub axF2 :: Bool ~R Char -- WRONG What saves us here is that the arguments to a type function F, lifted into a coercion, *must* prove nominal equivalence. So, (F axAge) is ill-formed, and we are safe. Roles are attached to parameters to TyCons. When lifting a TyCon into a coercion (through TyConAppCo), we need to ensure that the arguments to the TyCon respect their roles. For example: data T a b = MkT a (F b) If we know that a1 ~R a2, then we know (T a1 b) ~R (T a2 b). But, if we know that b1 ~R b2, we know nothing about (T a b1) and (T a b2)! This is because the type function F branches on b's *name*, not representation. So, we say that 'a' has role Representational and 'b' has role Nominal. The third role, Phantom, is for parameters not used in the type's definition. Given the following definition data Q a = MkQ Int the Phantom role allows us to say that (Q Bool) ~R (Q Char), because we can construct the coercion Bool ~P Char (using UnivCo). See the paper cited above for more examples and information. Note [TyConAppCo roles] ~~~~~~~~~~~~~~~~~~~~~~~ The TyConAppCo constructor has a role parameter, indicating the role at which the coercion proves equality. The choice of this parameter affects the required roles of the arguments of the TyConAppCo. To help explain it, assume the following definition: type instance F Int = Bool -- Axiom axF : F Int ~N Bool newtype Age = MkAge Int -- Axiom axAge : Age ~R Int data Foo a = MkFoo a -- Role on Foo's parameter is Representational TyConAppCo Nominal Foo axF : Foo (F Int) ~N Foo Bool For (TyConAppCo Nominal) all arguments must have role Nominal. Why? So that Foo Age ~N Foo Int does *not* hold. TyConAppCo Representational Foo (SubCo axF) : Foo (F Int) ~R Foo Bool TyConAppCo Representational Foo axAge : Foo Age ~R Foo Int For (TyConAppCo Representational), all arguments must have the roles corresponding to the result of tyConRoles on the TyCon. This is the whole point of having roles on the TyCon to begin with. So, we can have Foo Age ~R Foo Int, if Foo's parameter has role R. If a Representational TyConAppCo is over-saturated (which is otherwise fine), the spill-over arguments must all be at Nominal. This corresponds to the behavior for AppCo. TyConAppCo Phantom Foo (UnivCo Phantom Int Bool) : Foo Int ~P Foo Bool All arguments must have role Phantom. This one isn't strictly necessary for soundness, but this choice removes ambiguity. The rules here dictate the roles of the parameters to mkTyConAppCo (should be checked by Lint). Note [SelCo and newtypes] ~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have newtype N a = MkN Int type role N representational This yields axiom NTCo:N :: forall a. N a ~R Int We can then build co :: forall a b. N a ~R N b co = NTCo:N a ; sym (NTCo:N b) for any `a` and `b`. Because of the role annotation on N, if we use SelCo, we'll get out a representational coercion. That is: SelCo (SelTyCon 0 r) co :: forall a b. a ~r b Yikes! Clearly, this is terrible. The solution is simple: forbid SelCo to be used on newtypes if the internal coercion is representational. See the SelCo equation for GHC.Core.Lint.lintCoercion. This is not just some corner case discovered by a segfault somewhere; it was discovered in the proof of soundness of roles and described in the "Safe Coercions" paper (ICFP '14). Note [SelCo Cached Roles] ~~~~~~~~~~~~~~~~~~~~~~~~~ Why do we cache the role of SelCo in the SelCo constructor? Because computing role(Nth i co) involves figuring out that co :: T tys1 ~ T tys2 using coercionKind, and finding (coercionRole co), and then looking at the tyConRoles of T. Avoiding bad asymptotic behaviour here means we have to compute the kind and role of a coercion simultaneously, which makes the code complicated and inefficient. This only happens for SelCo. Caching the role solves the problem, and allows coercionKind and coercionRole to be simple. See #11735 Note [InstCo roles] ~~~~~~~~~~~~~~~~~~~ Here is (essentially) the typing rule for InstCo: g :: (forall a. t1) ~r (forall a. t2) w :: s1 ~N s2 ------------------------------- InstCo InstCo g w :: (t1 [a |-> s1]) ~r (t2 [a |-> s2]) Note that the Coercion w *must* be nominal. This is necessary because the variable a might be used in a "nominal position" (that is, a place where role inference would require a nominal role) in t1 or t2. If we allowed w to be representational, we could get bogus equalities. A more nuanced treatment might be able to relax this condition somewhat, by checking if t1 and/or t2 use their bound variables in nominal ways. If not, having w be representational is OK. %************************************************************************ %* * UnivCoProvenance %* * %************************************************************************ A UnivCo is a coercion whose proof does not directly express its role and kind (indeed for some UnivCos, like PluginProv, there /is/ no proof). The different kinds of UnivCo are described by UnivCoProvenance. Really each is entirely separate, but they all share the need to represent their role and kind, which is done in the UnivCo constructor. -} -- | For simplicity, we have just one UnivCo that represents a coercion from -- some type to some other type, with (in general) no restrictions on the -- type. The UnivCoProvenance specifies more exactly what the coercion really -- is and why a program should (or shouldn't!) trust the coercion. -- It is reasonable to consider each constructor of 'UnivCoProvenance' -- as a totally independent coercion form; their only commonality is -- that they don't tell you what types they coercion between. (That info -- is in the 'UnivCo' constructor of 'Coercion'. data UnivCoProvenance = PhantomProv KindCoercion -- ^ See Note [Phantom coercions]. Only in Phantom -- roled coercions | ProofIrrelProv KindCoercion -- ^ From the fact that any two coercions are -- considered equivalent. See Note [ProofIrrelProv]. -- Can be used in Nominal or Representational coercions | PluginProv String -- ^ From a plugin, which asserts that this coercion -- is sound. The string is for the use of the plugin. | CorePrepProv -- See Note [Unsafe coercions] in GHC.Core.CoreToStg.Prep Bool -- True <=> the UnivCo must be homogeneously kinded -- False <=> allow hetero-kinded, e.g. Int ~ Int# deriving Typeable UnivCoProvenance Typeable UnivCoProvenance => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance) -> (UnivCoProvenance -> Constr) -> (UnivCoProvenance -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance)) -> ((forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r) -> (forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance) -> Data UnivCoProvenance UnivCoProvenance -> Constr UnivCoProvenance -> DataType (forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance) $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance $ctoConstr :: UnivCoProvenance -> Constr toConstr :: UnivCoProvenance -> Constr $cdataTypeOf :: UnivCoProvenance -> DataType dataTypeOf :: UnivCoProvenance -> DataType $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance) $cgmapT :: (forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance gmapT :: (forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r $cgmapQ :: forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u] $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance Data.Data instance Outputable UnivCoProvenance where ppr :: UnivCoProvenance -> SDoc ppr (PhantomProv KindCoercion _) = String -> SDoc forall doc. IsLine doc => String -> doc text String "(phantom)" ppr (ProofIrrelProv KindCoercion _) = String -> SDoc forall doc. IsLine doc => String -> doc text String "(proof irrel.)" ppr (PluginProv String str) = SDoc -> SDoc forall doc. IsLine doc => doc -> doc parens (String -> SDoc forall doc. IsLine doc => String -> doc text String "plugin" SDoc -> SDoc -> SDoc forall doc. IsLine doc => doc -> doc -> doc <+> SDoc -> SDoc forall doc. IsLine doc => doc -> doc brackets (String -> SDoc forall doc. IsLine doc => String -> doc text String str)) ppr (CorePrepProv Bool _) = String -> SDoc forall doc. IsLine doc => String -> doc text String "(CorePrep)" -- | A coercion to be filled in by the type-checker. See Note [Coercion holes] data CoercionHole = CoercionHole { CoercionHole -> TyVar ch_co_var :: CoVar -- See Note [CoercionHoles and coercion free variables] , CoercionHole -> IORef (Maybe KindCoercion) ch_ref :: IORef (Maybe Coercion) } coHoleCoVar :: CoercionHole -> CoVar coHoleCoVar :: CoercionHole -> TyVar coHoleCoVar = CoercionHole -> TyVar ch_co_var setCoHoleCoVar :: CoercionHole -> CoVar -> CoercionHole setCoHoleCoVar :: CoercionHole -> TyVar -> CoercionHole setCoHoleCoVar CoercionHole h TyVar cv = CoercionHole h { ch_co_var = cv } instance Data.Data CoercionHole where -- don't traverse? toConstr :: CoercionHole -> Constr toConstr CoercionHole _ = String -> Constr abstractConstr String "CoercionHole" gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CoercionHole gunfold forall b r. Data b => c (b -> r) -> c r _ forall r. r -> c r _ = String -> Constr -> c CoercionHole forall a. HasCallStack => String -> a error String "gunfold" dataTypeOf :: CoercionHole -> DataType dataTypeOf CoercionHole _ = String -> DataType mkNoRepType String "CoercionHole" instance Outputable CoercionHole where ppr :: CoercionHole -> SDoc ppr (CoercionHole { ch_co_var :: CoercionHole -> TyVar ch_co_var = TyVar cv }) = SDoc -> SDoc forall doc. IsLine doc => doc -> doc braces (TyVar -> SDoc forall a. Outputable a => a -> SDoc ppr TyVar cv) instance Uniquable CoercionHole where getUnique :: CoercionHole -> Unique getUnique (CoercionHole { ch_co_var :: CoercionHole -> TyVar ch_co_var = TyVar cv }) = TyVar -> Unique forall a. Uniquable a => a -> Unique getUnique TyVar cv {- Note [Phantom coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider data T a = T1 | T2 Then we have T s ~R T t for any old s,t. The witness for this is (TyConAppCo T Rep co), where (co :: s ~P t) is a phantom coercion built with PhantomProv. The role of the UnivCo is always Phantom. The Coercion stored is the (nominal) kind coercion between the types kind(s) ~N kind (t) Note [Coercion holes] ~~~~~~~~~~~~~~~~~~~~~~~~ During typechecking, constraint solving for type classes works by - Generate an evidence Id, d7 :: Num a - Wrap it in a Wanted constraint, [W] d7 :: Num a - Use the evidence Id where the evidence is needed - Solve the constraint later - When solved, add an enclosing let-binding let d7 = .... in .... which actually binds d7 to the (Num a) evidence For equality constraints we use a different strategy. See Note [The equality types story] in GHC.Builtin.Types.Prim for background on equality constraints. - For /boxed/ equality constraints, (t1 ~N t2) and (t1 ~R t2), it's just like type classes above. (Indeed, boxed equality constraints *are* classes.) - But for /unboxed/ equality constraints (t1 ~R# t2) and (t1 ~N# t2) we use a different plan For unboxed equalities: - Generate a CoercionHole, a mutable variable just like a unification variable - Wrap the CoercionHole in a Wanted constraint; see GHC.Tc.Utils.TcEvDest - Use the CoercionHole in a Coercion, via HoleCo - Solve the constraint later - When solved, fill in the CoercionHole by side effect, instead of doing the let-binding thing The main reason for all this is that there may be no good place to let-bind the evidence for unboxed equalities: - We emit constraints for kind coercions, to be used to cast a type's kind. These coercions then must be used in types. Because they might appear in a top-level type, there is no place to bind these (unlifted) coercions in the usual way. - A coercion for (forall a. t1) ~ (forall a. t2) will look like forall a. (coercion for t1~t2) But the coercion for (t1~t2) may mention 'a', and we don't have let-bindings within coercions. We could add them, but coercion holes are easier. - Moreover, nothing is lost from the lack of let-bindings. For dictionaries want to achieve sharing to avoid recomputing the dictionary. But coercions are entirely erased, so there's little benefit to sharing. Indeed, even if we had a let-binding, we always inline types and coercions at every use site and drop the binding. Other notes about HoleCo: * INVARIANT: CoercionHole and HoleCo are used only during type checking, and should never appear in Core. Just like unification variables; a Type can contain a TcTyVar, but only during type checking. If, one day, we use type-level information to separate out forms that can appear during type-checking vs forms that can appear in core proper, holes in Core will be ruled out. * See Note [CoercionHoles and coercion free variables] * Coercion holes can be compared for equality like other coercions: by looking at the types coerced. Note [CoercionHoles and coercion free variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Why does a CoercionHole contain a CoVar, as well as reference to fill in? Because we want to treat that CoVar as a free variable of the coercion. See #14584, and Note [What prevents a constraint from floating] in GHC.Tc.Solver, item (4): forall k. [W] co1 :: t1 ~# t2 |> co2 [W] co2 :: k ~# * Here co2 is a CoercionHole. But we /must/ know that it is free in co1, because that's all that stops it floating outside the implication. Note [ProofIrrelProv] ~~~~~~~~~~~~~~~~~~~~~ A ProofIrrelProv is a coercion between coercions. For example: data G a where MkG :: G Bool In core, we get G :: * -> * MkG :: forall (a :: *). (a ~ Bool) -> G a Now, consider 'MkG -- that is, MkG used in a type -- and suppose we want a proof that ('MkG a1 co1) ~ ('MkG a2 co2). This will have to be TyConAppCo Nominal MkG [co3, co4] where co3 :: co1 ~ co2 co4 :: a1 ~ a2 Note that co1 :: a1 ~ Bool co2 :: a2 ~ Bool Here, co3 = UnivCo (ProofIrrelProv co5) Nominal (CoercionTy co1) (CoercionTy co2) where co5 :: (a1 ~ Bool) ~ (a2 ~ Bool) co5 = TyConAppCo Nominal (~#) [<*>, <*>, co4, <Bool>] -} {- ********************************************************************* * * foldType and foldCoercion * * ********************************************************************* -} {- Note [foldType] ~~~~~~~~~~~~~~~~~~ foldType is a bit more powerful than perhaps it looks: * You can fold with an accumulating parameter, via TyCoFolder env (Endo a) Recall newtype Endo a = Endo (a->a) * You can fold monadically with a monad M, via TyCoFolder env (M a) provided you have instance .. => Monoid (M a) Note [mapType vs foldType] ~~~~~~~~~~~~~~~~~~~~~~~~~~ We define foldType here, but mapType in module Type. Why? * foldType is used in GHC.Core.TyCo.FVs for finding free variables. It's a very simple function that analyses a type, but does not construct one. * mapType constructs new types, and so it needs to call the "smart constructors", mkAppTy, mkCastTy, and so on. These are sophisticated functions, and can't be defined here in GHC.Core.TyCo.Rep. Note [Specialising foldType] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We inline foldType at every call site (there are not many), so that it becomes specialised for the particular monoid *and* TyCoFolder at that site. This is just for efficiency, but walking over types is done a *lot* in GHC, so worth optimising. We were worried that TyCoFolder env (Endo a) might not eta-expand. Recall newtype Endo a = Endo (a->a). In particular, given fvs :: Type -> TyCoVarSet fvs ty = appEndo (foldType tcf emptyVarSet ty) emptyVarSet tcf :: TyCoFolder enf (Endo a) tcf = TyCoFolder { tcf_tyvar = do_tv, ... } where do_tvs is tv = Endo do_it where do_it acc | tv `elemVarSet` is = acc | tv `elemVarSet` acc = acc | otherwise = acc `extendVarSet` tv we want to end up with fvs ty = go emptyVarSet ty emptyVarSet where go env (TyVarTy tv) acc = acc `extendVarSet` tv ..etc.. And indeed this happens. - Selections from 'tcf' are done at compile time - 'go' is nicely eta-expanded. We were also worried about deep_fvs :: Type -> TyCoVarSet deep_fvs ty = appEndo (foldType deep_tcf emptyVarSet ty) emptyVarSet deep_tcf :: TyCoFolder enf (Endo a) deep_tcf = TyCoFolder { tcf_tyvar = do_tv, ... } where do_tvs is tv = Endo do_it where do_it acc | tv `elemVarSet` is = acc | tv `elemVarSet` acc = acc | otherwise = deep_fvs (varType tv) `unionVarSet` acc `extendVarSet` tv Here deep_fvs and deep_tcf are mutually recursive, unlike fvs and tcf. But, amazingly, we get good code here too. GHC is careful not to mark TyCoFolder data constructor for deep_tcf as a loop breaker, so the record selections still cancel. And eta expansion still happens too. -} data TyCoFolder env a = TyCoFolder { forall env a. TyCoFolder env a -> Kind -> Maybe Kind tcf_view :: Type -> Maybe Type -- Optional "view" function -- E.g. expand synonyms , forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_tyvar :: env -> TyVar -> a -- Does not automatically recur , forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_covar :: env -> CoVar -> a -- into kinds of variables , forall env a. TyCoFolder env a -> env -> CoercionHole -> a tcf_hole :: env -> CoercionHole -> a -- ^ What to do with coercion holes. -- See Note [Coercion holes] in "GHC.Core.TyCo.Rep". , forall env a. TyCoFolder env a -> env -> TyVar -> ForAllTyFlag -> env tcf_tycobinder :: env -> TyCoVar -> ForAllTyFlag -> env -- ^ The returned env is used in the extended scope } {-# INLINE foldTyCo #-} -- See Note [Specialising foldType] foldTyCo :: Monoid a => TyCoFolder env a -> env -> (Type -> a, [Type] -> a, Coercion -> a, [Coercion] -> a) foldTyCo :: forall a env. Monoid a => TyCoFolder env a -> env -> (Kind -> a, [Kind] -> a, KindCoercion -> a, [KindCoercion] -> a) foldTyCo (TyCoFolder { tcf_view :: forall env a. TyCoFolder env a -> Kind -> Maybe Kind tcf_view = Kind -> Maybe Kind view , tcf_tyvar :: forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_tyvar = env -> TyVar -> a tyvar , tcf_tycobinder :: forall env a. TyCoFolder env a -> env -> TyVar -> ForAllTyFlag -> env tcf_tycobinder = env -> TyVar -> ForAllTyFlag -> env tycobinder , tcf_covar :: forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_covar = env -> TyVar -> a covar , tcf_hole :: forall env a. TyCoFolder env a -> env -> CoercionHole -> a tcf_hole = env -> CoercionHole -> a cohole }) env env = (env -> Kind -> a go_ty env env, env -> [Kind] -> a go_tys env env, env -> KindCoercion -> a go_co env env, env -> [KindCoercion] -> a go_cos env env) where go_ty :: env -> Kind -> a go_ty env env Kind ty | Just Kind ty' <- Kind -> Maybe Kind view Kind ty = env -> Kind -> a go_ty env env Kind ty' go_ty env env (TyVarTy TyVar tv) = env -> TyVar -> a tyvar env env TyVar tv go_ty env env (AppTy Kind t1 Kind t2) = env -> Kind -> a go_ty env env Kind t1 a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> Kind -> a go_ty env env Kind t2 go_ty env _ (LitTy {}) = a forall a. Monoid a => a mempty go_ty env env (CastTy Kind ty KindCoercion co) = env -> Kind -> a go_ty env env Kind ty a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env KindCoercion co go_ty env env (CoercionTy KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_ty env env (FunTy FunTyFlag _ Kind w Kind arg Kind res) = env -> Kind -> a go_ty env env Kind w a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> Kind -> a go_ty env env Kind arg a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> Kind -> a go_ty env env Kind res go_ty env env (TyConApp TyCon _ [Kind] tys) = env -> [Kind] -> a go_tys env env [Kind] tys go_ty env env (ForAllTy (Bndr TyVar tv ForAllTyFlag vis) Kind inner) = let !env' :: env env' = env -> TyVar -> ForAllTyFlag -> env tycobinder env env TyVar tv ForAllTyFlag vis -- Avoid building a thunk here in env -> Kind -> a go_ty env env (TyVar -> Kind varType TyVar tv) a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> Kind -> a go_ty env env' Kind inner -- Explicit recursion because using foldr builds a local -- loop (with env free) and I'm not confident it'll be -- lambda lifted in the end go_tys :: env -> [Kind] -> a go_tys env _ [] = a forall a. Monoid a => a mempty go_tys env env (Kind t:[Kind] ts) = env -> Kind -> a go_ty env env Kind t a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> [Kind] -> a go_tys env env [Kind] ts go_cos :: env -> [KindCoercion] -> a go_cos env _ [] = a forall a. Monoid a => a mempty go_cos env env (KindCoercion c:[KindCoercion] cs) = env -> KindCoercion -> a go_co env env KindCoercion c a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> [KindCoercion] -> a go_cos env env [KindCoercion] cs go_co :: env -> KindCoercion -> a go_co env env (Refl Kind ty) = env -> Kind -> a go_ty env env Kind ty go_co env env (GRefl Role _ Kind ty MCoercionN MRefl) = env -> Kind -> a go_ty env env Kind ty go_co env env (GRefl Role _ Kind ty (MCo KindCoercion co)) = env -> Kind -> a go_ty env env Kind ty a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env KindCoercion co go_co env env (TyConAppCo Role _ TyCon _ [KindCoercion] args) = env -> [KindCoercion] -> a go_cos env env [KindCoercion] args go_co env env (AppCo KindCoercion c1 KindCoercion c2) = env -> KindCoercion -> a go_co env env KindCoercion c1 a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env KindCoercion c2 go_co env env (CoVarCo TyVar cv) = env -> TyVar -> a covar env env TyVar cv go_co env env (AxiomInstCo CoAxiom Branched _ Int _ [KindCoercion] args) = env -> [KindCoercion] -> a go_cos env env [KindCoercion] args go_co env env (HoleCo CoercionHole hole) = env -> CoercionHole -> a cohole env env CoercionHole hole go_co env env (UnivCo UnivCoProvenance p Role _ Kind t1 Kind t2) = env -> UnivCoProvenance -> a go_prov env env UnivCoProvenance p a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> Kind -> a go_ty env env Kind t1 a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> Kind -> a go_ty env env Kind t2 go_co env env (SymCo KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_co env env (TransCo KindCoercion c1 KindCoercion c2) = env -> KindCoercion -> a go_co env env KindCoercion c1 a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env KindCoercion c2 go_co env env (AxiomRuleCo CoAxiomRule _ [KindCoercion] cos) = env -> [KindCoercion] -> a go_cos env env [KindCoercion] cos go_co env env (SelCo CoSel _ KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_co env env (LRCo LeftOrRight _ KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_co env env (InstCo KindCoercion co KindCoercion arg) = env -> KindCoercion -> a go_co env env KindCoercion co a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env KindCoercion arg go_co env env (KindCo KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_co env env (SubCo KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_co env env (FunCo { fco_mult :: KindCoercion -> KindCoercion fco_mult = KindCoercion cw, fco_arg :: KindCoercion -> KindCoercion fco_arg = KindCoercion c1, fco_res :: KindCoercion -> KindCoercion fco_res = KindCoercion c2 }) = env -> KindCoercion -> a go_co env env KindCoercion cw a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env KindCoercion c1 a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env KindCoercion c2 go_co env env (ForAllCo TyVar tv KindCoercion kind_co KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion kind_co a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> Kind -> a go_ty env env (TyVar -> Kind varType TyVar tv) a -> a -> a forall a. Monoid a => a -> a -> a `mappend` env -> KindCoercion -> a go_co env env' KindCoercion co where env' :: env env' = env -> TyVar -> ForAllTyFlag -> env tycobinder env env TyVar tv ForAllTyFlag Inferred go_prov :: env -> UnivCoProvenance -> a go_prov env env (PhantomProv KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_prov env env (ProofIrrelProv KindCoercion co) = env -> KindCoercion -> a go_co env env KindCoercion co go_prov env _ (PluginProv String _) = a forall a. Monoid a => a mempty go_prov env _ (CorePrepProv Bool _) = a forall a. Monoid a => a mempty -- | A view function that looks through nothing. noView :: Type -> Maybe Type noView :: Kind -> Maybe Kind noView Kind _ = Maybe Kind forall a. Maybe a Nothing {- ********************************************************************* * * typeSize, coercionSize * * ********************************************************************* -} -- NB: We put typeSize/coercionSize here because they are mutually -- recursive, and have the CPR property. If we have mutual -- recursion across a hi-boot file, we don't get the CPR property -- and these functions allocate a tremendous amount of rubbish. -- It's not critical (because typeSize is really only used in -- debug mode, but I tripped over an example (T5642) in which -- typeSize was one of the biggest single allocators in all of GHC. -- And it's easy to fix, so I did. -- NB: typeSize does not respect `eqType`, in that two types that -- are `eqType` may return different sizes. This is OK, because this -- function is used only in reporting, not decision-making. typeSize :: Type -> Int typeSize :: Kind -> Int typeSize (LitTy {}) = Int 1 typeSize (TyVarTy {}) = Int 1 typeSize (AppTy Kind t1 Kind t2) = Kind -> Int typeSize Kind t1 Int -> Int -> Int forall a. Num a => a -> a -> a + Kind -> Int typeSize Kind t2 typeSize (FunTy FunTyFlag _ Kind _ Kind t1 Kind t2) = Kind -> Int typeSize Kind t1 Int -> Int -> Int forall a. Num a => a -> a -> a + Kind -> Int typeSize Kind t2 typeSize (ForAllTy (Bndr TyVar tv ForAllTyFlag _) Kind t) = Kind -> Int typeSize (TyVar -> Kind varType TyVar tv) Int -> Int -> Int forall a. Num a => a -> a -> a + Kind -> Int typeSize Kind t typeSize (TyConApp TyCon _ [Kind] ts) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + [Int] -> Int forall a. Num a => [a] -> a forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum ((Kind -> Int) -> [Kind] -> [Int] forall a b. (a -> b) -> [a] -> [b] map Kind -> Int typeSize [Kind] ts) typeSize (CastTy Kind ty KindCoercion co) = Kind -> Int typeSize Kind ty Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co typeSize (CoercionTy KindCoercion co) = KindCoercion -> Int coercionSize KindCoercion co coercionSize :: Coercion -> Int coercionSize :: KindCoercion -> Int coercionSize (Refl Kind ty) = Kind -> Int typeSize Kind ty coercionSize (GRefl Role _ Kind ty MCoercionN MRefl) = Kind -> Int typeSize Kind ty coercionSize (GRefl Role _ Kind ty (MCo KindCoercion co)) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + Kind -> Int typeSize Kind ty Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co coercionSize (TyConAppCo Role _ TyCon _ [KindCoercion] args) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + [Int] -> Int forall a. Num a => [a] -> a forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum ((KindCoercion -> Int) -> [KindCoercion] -> [Int] forall a b. (a -> b) -> [a] -> [b] map KindCoercion -> Int coercionSize [KindCoercion] args) coercionSize (AppCo KindCoercion co KindCoercion arg) = KindCoercion -> Int coercionSize KindCoercion co Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion arg coercionSize (ForAllCo TyVar _ KindCoercion h KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion h coercionSize (FunCo Role _ FunTyFlag _ FunTyFlag _ KindCoercion w KindCoercion c1 KindCoercion c2) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion c1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion c2 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion w coercionSize (CoVarCo TyVar _) = Int 1 coercionSize (HoleCo CoercionHole _) = Int 1 coercionSize (AxiomInstCo CoAxiom Branched _ Int _ [KindCoercion] args) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + [Int] -> Int forall a. Num a => [a] -> a forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum ((KindCoercion -> Int) -> [KindCoercion] -> [Int] forall a b. (a -> b) -> [a] -> [b] map KindCoercion -> Int coercionSize [KindCoercion] args) coercionSize (UnivCo UnivCoProvenance p Role _ Kind t1 Kind t2) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + UnivCoProvenance -> Int provSize UnivCoProvenance p Int -> Int -> Int forall a. Num a => a -> a -> a + Kind -> Int typeSize Kind t1 Int -> Int -> Int forall a. Num a => a -> a -> a + Kind -> Int typeSize Kind t2 coercionSize (SymCo KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co coercionSize (TransCo KindCoercion co1 KindCoercion co2) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co2 coercionSize (SelCo CoSel _ KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co coercionSize (LRCo LeftOrRight _ KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co coercionSize (InstCo KindCoercion co KindCoercion arg) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion arg coercionSize (KindCo KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co coercionSize (SubCo KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co coercionSize (AxiomRuleCo CoAxiomRule _ [KindCoercion] cs) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + [Int] -> Int forall a. Num a => [a] -> a forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum ((KindCoercion -> Int) -> [KindCoercion] -> [Int] forall a b. (a -> b) -> [a] -> [b] map KindCoercion -> Int coercionSize [KindCoercion] cs) provSize :: UnivCoProvenance -> Int provSize :: UnivCoProvenance -> Int provSize (PhantomProv KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co provSize (ProofIrrelProv KindCoercion co) = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + KindCoercion -> Int coercionSize KindCoercion co provSize (PluginProv String _) = Int 1 provSize (CorePrepProv Bool _) = Int 1 {- ************************************************************************ * * Multiplicities * * ************************************************************************ These definitions are here to avoid module loops, and to keep GHC.Core.Multiplicity above this module. -} -- | A shorthand for data with an attached 'Mult' element (the multiplicity). data Scaled a = Scaled !Mult a deriving (Typeable (Scaled a) Typeable (Scaled a) => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a)) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a)) -> (Scaled a -> Constr) -> (Scaled a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a))) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a))) -> ((forall b. Data b => b -> b) -> Scaled a -> Scaled a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r) -> (forall u. (forall d. Data d => d -> u) -> Scaled a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> Scaled a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a)) -> Data (Scaled a) Scaled a -> Constr Scaled a -> DataType (forall b. Data b => b -> b) -> Scaled a -> Scaled a forall a. Data a => Typeable (Scaled a) forall a. Data a => Scaled a -> Constr forall a. Data a => Scaled a -> DataType forall a. Data a => (forall b. Data b => b -> b) -> Scaled a -> Scaled a forall a u. Data a => Int -> (forall d. Data d => d -> u) -> Scaled a -> u forall a u. Data a => (forall d. Data d => d -> u) -> Scaled a -> [u] forall a r r'. Data a => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r forall a r r'. Data a => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r forall a (m :: * -> *). (Data a, Monad m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) forall a (m :: * -> *). (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) forall a (c :: * -> *). Data a => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) forall a (c :: * -> *). Data a => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) forall a (t :: * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) forall a (t :: * -> * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) forall a. Typeable a => (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> Scaled a -> u forall u. (forall d. Data d => d -> u) -> Scaled a -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) $cgfoldl :: forall a (c :: * -> *). Data a => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) $cgunfold :: forall a (c :: * -> *). Data a => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) $ctoConstr :: forall a. Data a => Scaled a -> Constr toConstr :: Scaled a -> Constr $cdataTypeOf :: forall a. Data a => Scaled a -> DataType dataTypeOf :: Scaled a -> DataType $cdataCast1 :: forall a (t :: * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) $cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) $cgmapT :: forall a. Data a => (forall b. Data b => b -> b) -> Scaled a -> Scaled a gmapT :: (forall b. Data b => b -> b) -> Scaled a -> Scaled a $cgmapQl :: forall a r r'. Data a => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r $cgmapQr :: forall a r r'. Data a => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r $cgmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> Scaled a -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> Scaled a -> [u] $cgmapQi :: forall a u. Data a => Int -> (forall d. Data d => d -> u) -> Scaled a -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Scaled a -> u $cgmapM :: forall a (m :: * -> *). (Data a, Monad m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) $cgmapMp :: forall a (m :: * -> *). (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) $cgmapMo :: forall a (m :: * -> *). (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) Data.Data) -- You might think that this would be a natural candidate for -- Functor, Traversable but Krzysztof says (!3674) "it was too easy -- to accidentally lift functions (substitutions, zonking etc.) from -- Type -> Type to Scaled Type -> Scaled Type, ignoring -- multiplicities and causing bugs". So we don't. -- -- Being strict in a is worse for performance, so we are only strict on the -- Mult part of scaled. instance (Outputable a) => Outputable (Scaled a) where ppr :: Scaled a -> SDoc ppr (Scaled Kind _cnt a t) = a -> SDoc forall a. Outputable a => a -> SDoc ppr a t -- Do not print the multiplicity here because it tends to be too verbose scaledMult :: Scaled a -> Mult scaledMult :: forall a. Scaled a -> Kind scaledMult (Scaled Kind m a _) = Kind m scaledThing :: Scaled a -> a scaledThing :: forall a. Scaled a -> a scaledThing (Scaled Kind _ a t) = a t -- | Apply a function to both the Mult and the Type in a 'Scaled Type' mapScaledType :: (Type -> Type) -> Scaled Type -> Scaled Type mapScaledType :: (Kind -> Kind) -> Scaled Kind -> Scaled Kind mapScaledType Kind -> Kind f (Scaled Kind m Kind t) = Kind -> Kind -> Scaled Kind forall a. Kind -> a -> Scaled a Scaled (Kind -> Kind f Kind m) (Kind -> Kind f Kind t) {- | Mult is a type alias for Type. Mult must contain Type because multiplicity variables are mere type variables (of kind Multiplicity) in Haskell. So the simplest implementation is to make Mult be Type. Multiplicities can be formed with: - One: GHC.Types.One (= oneDataCon) - Many: GHC.Types.Many (= manyDataCon) - Multiplication: GHC.Types.MultMul (= multMulTyCon) So that Mult feels a bit more structured, we provide pattern synonyms and smart constructors for these. -} type Mult = Type