-- (c) The University of Glasgow 2006 -- (c) The GRASP/AQUA Project, Glasgow University, 1998 -- -- Type - public interface {-# LANGUAGE CPP, FlexibleContexts #-} {-# OPTIONS_GHC -fno-warn-orphans #-} -- | Main functions for manipulating types and type-related things module Type ( -- Note some of this is just re-exports from TyCon.. -- * Main data types representing Types -- $type_classification -- $representation_types TyThing(..), Type, ArgFlag(..), AnonArgFlag(..), ForallVisFlag(..), KindOrType, PredType, ThetaType, Var, TyVar, isTyVar, TyCoVar, TyCoBinder, TyCoVarBinder, TyVarBinder, KnotTied, -- ** Constructing and deconstructing types mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, repGetTyVar_maybe, getCastedTyVar_maybe, tyVarKind, varType, mkAppTy, mkAppTys, splitAppTy, splitAppTys, repSplitAppTys, splitAppTy_maybe, repSplitAppTy_maybe, tcRepSplitAppTy_maybe, mkVisFunTy, mkInvisFunTy, mkVisFunTys, mkInvisFunTys, splitFunTy, splitFunTy_maybe, splitFunTys, funResultTy, funArgTy, mkTyConApp, mkTyConTy, tyConAppTyCon_maybe, tyConAppTyConPicky_maybe, tyConAppArgs_maybe, tyConAppTyCon, tyConAppArgs, splitTyConApp_maybe, splitTyConApp, tyConAppArgN, nextRole, tcSplitTyConApp_maybe, splitListTyConApp_maybe, repSplitTyConApp_maybe, mkForAllTy, mkForAllTys, mkTyCoInvForAllTys, mkSpecForAllTy, mkSpecForAllTys, mkVisForAllTys, mkTyCoInvForAllTy, mkInvForAllTy, mkInvForAllTys, splitForAllTys, splitForAllTysSameVis, splitForAllVarBndrs, splitForAllTy_maybe, splitForAllTy, splitForAllTy_ty_maybe, splitForAllTy_co_maybe, splitPiTy_maybe, splitPiTy, splitPiTys, mkTyConBindersPreferAnon, mkPiTy, mkPiTys, mkLamType, mkLamTypes, piResultTy, piResultTys, applyTysX, dropForAlls, mkFamilyTyConApp, mkNumLitTy, isNumLitTy, mkStrLitTy, isStrLitTy, isLitTy, isPredTy, getRuntimeRep_maybe, kindRep_maybe, kindRep, mkCastTy, mkCoercionTy, splitCastTy_maybe, discardCast, userTypeError_maybe, pprUserTypeErrorTy, coAxNthLHS, stripCoercionTy, splitPiTysInvisible, splitPiTysInvisibleN, invisibleTyBndrCount, filterOutInvisibleTypes, filterOutInferredTypes, partitionInvisibleTypes, partitionInvisibles, tyConArgFlags, appTyArgFlags, synTyConResKind, modifyJoinResTy, setJoinResTy, -- ** Analyzing types TyCoMapper(..), mapType, mapCoercion, -- (Newtypes) newTyConInstRhs, -- ** Binders sameVis, mkTyCoVarBinder, mkTyCoVarBinders, mkTyVarBinders, mkAnonBinder, isAnonTyCoBinder, binderVar, binderVars, binderType, binderArgFlag, tyCoBinderType, tyCoBinderVar_maybe, tyBinderType, binderRelevantType_maybe, isVisibleArgFlag, isInvisibleArgFlag, isVisibleBinder, isInvisibleBinder, isNamedBinder, tyConBindersTyCoBinders, -- ** Common type constructors funTyCon, -- ** Predicates on types isTyVarTy, isFunTy, isCoercionTy, isCoercionTy_maybe, isForAllTy, isForAllTy_ty, isForAllTy_co, isPiTy, isTauTy, isFamFreeTy, isCoVarType, isValidJoinPointType, tyConAppNeedsKindSig, -- *** Levity and boxity isLiftedType_maybe, isLiftedTypeKind, isUnliftedTypeKind, isLiftedRuntimeRep, isUnliftedRuntimeRep, isUnliftedType, mightBeUnliftedType, isUnboxedTupleType, isUnboxedSumType, isAlgType, isDataFamilyAppType, isPrimitiveType, isStrictType, isRuntimeRepTy, isRuntimeRepVar, isRuntimeRepKindedTy, dropRuntimeRepArgs, getRuntimeRep, -- * Main data types representing Kinds Kind, -- ** Finding the kind of a type typeKind, tcTypeKind, isTypeLevPoly, resultIsLevPoly, tcIsLiftedTypeKind, tcIsConstraintKind, tcReturnsConstraintKind, tcIsRuntimeTypeKind, -- ** Common Kind liftedTypeKind, -- * Type free variables tyCoFVsOfType, tyCoFVsBndr, tyCoFVsVarBndr, tyCoFVsVarBndrs, tyCoVarsOfType, tyCoVarsOfTypes, tyCoVarsOfTypeDSet, coVarsOfType, coVarsOfTypes, closeOverKindsDSet, closeOverKindsFV, closeOverKindsList, closeOverKinds, noFreeVarsOfType, splitVisVarsOfType, splitVisVarsOfTypes, expandTypeSynonyms, typeSize, occCheckExpand, -- * Well-scoped lists of variables scopedSort, tyCoVarsOfTypeWellScoped, tyCoVarsOfTypesWellScoped, -- * Type comparison eqType, eqTypeX, eqTypes, nonDetCmpType, nonDetCmpTypes, nonDetCmpTypeX, nonDetCmpTypesX, nonDetCmpTc, eqVarBndrs, -- * Forcing evaluation of types seqType, seqTypes, -- * Other views onto Types coreView, tcView, tyConsOfType, -- * Main type substitution data types TvSubstEnv, -- Representation widely visible TCvSubst(..), -- Representation visible to a few friends -- ** Manipulating type substitutions emptyTvSubstEnv, emptyTCvSubst, mkEmptyTCvSubst, mkTCvSubst, zipTvSubst, mkTvSubstPrs, zipTCvSubst, notElemTCvSubst, getTvSubstEnv, setTvSubstEnv, zapTCvSubst, getTCvInScope, getTCvSubstRangeFVs, extendTCvInScope, extendTCvInScopeList, extendTCvInScopeSet, extendTCvSubst, extendCvSubst, extendTvSubst, extendTvSubstBinderAndInScope, extendTvSubstList, extendTvSubstAndInScope, extendTCvSubstList, extendTvSubstWithClone, extendTCvSubstWithClone, isInScope, composeTCvSubstEnv, composeTCvSubst, zipTyEnv, zipCoEnv, isEmptyTCvSubst, unionTCvSubst, -- ** Performing substitution on types and kinds substTy, substTys, substTyWith, substTysWith, substTheta, substTyAddInScope, substTyUnchecked, substTysUnchecked, substThetaUnchecked, substTyWithUnchecked, substCoUnchecked, substCoWithUnchecked, substTyVarBndr, substTyVarBndrs, substTyVar, substTyVars, substVarBndr, substVarBndrs, cloneTyVarBndr, cloneTyVarBndrs, lookupTyVar, -- * Tidying type related things up for printing tidyType, tidyTypes, tidyOpenType, tidyOpenTypes, tidyOpenKind, tidyVarBndr, tidyVarBndrs, tidyFreeTyCoVars, tidyOpenTyCoVar, tidyOpenTyCoVars, tidyTyCoVarOcc, tidyTopType, tidyKind, tidyTyCoVarBinder, tidyTyCoVarBinders, -- * Kinds isConstraintKindCon, classifiesTypeWithValues, isKindLevPoly ) where #include "HsVersions.h" import GhcPrelude import BasicTypes -- We import the representation and primitive functions from TyCoRep. -- Many things are reexported, but not the representation! import TyCoRep import TyCoSubst import TyCoTidy import TyCoFVs -- friends: import Var import VarEnv import VarSet import UniqSet import TyCon import TysPrim import {-# SOURCE #-} TysWiredIn ( listTyCon, typeNatKind , typeSymbolKind, liftedTypeKind , constraintKind ) import PrelNames import CoAxiom import {-# SOURCE #-} Coercion( mkNomReflCo, mkGReflCo, mkReflCo , mkTyConAppCo, mkAppCo, mkCoVarCo, mkAxiomRuleCo , mkForAllCo, mkFunCo, mkAxiomInstCo, mkUnivCo , mkSymCo, mkTransCo, mkNthCo, mkLRCo, mkInstCo , mkKindCo, mkSubCo, mkFunCo, mkAxiomInstCo , decomposePiCos, coercionKind, coercionType , isReflexiveCo, seqCo ) -- others import Util import FV import Outputable import FastString import Pair import ListSetOps import Unique ( nonDetCmpUnique ) import Maybes ( orElse ) import Data.Maybe ( isJust ) import Control.Monad ( guard ) -- $type_classification -- #type_classification# -- -- Types are one of: -- -- [Unboxed] Iff its representation is other than a pointer -- Unboxed types are also unlifted. -- -- [Lifted] Iff it has bottom as an element. -- Closures always have lifted types: i.e. any -- let-bound identifier in Core must have a lifted -- type. Operationally, a lifted object is one that -- can be entered. -- Only lifted types may be unified with a type variable. -- -- [Algebraic] Iff it is a type with one or more constructors, whether -- declared with @data@ or @newtype@. -- An algebraic type is one that can be deconstructed -- with a case expression. This is /not/ the same as -- lifted types, because we also include unboxed -- tuples in this classification. -- -- [Data] Iff it is a type declared with @data@, or a boxed tuple. -- -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell. -- -- Currently, all primitive types are unlifted, but that's not necessarily -- the case: for example, @Int@ could be primitive. -- -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed -- but unlifted (such as @ByteArray#@). The only primitive types that we -- classify as algebraic are the unboxed tuples. -- -- Some examples of type classifications that may make this a bit clearer are: -- -- @ -- Type primitive boxed lifted algebraic -- ----------------------------------------------------------------------------- -- Int# Yes No No No -- ByteArray# Yes Yes No No -- (\# a, b \#) Yes No No Yes -- (\# a | b \#) Yes No No Yes -- ( a, b ) No Yes Yes Yes -- [a] No Yes Yes Yes -- @ -- $representation_types -- A /source type/ is a type that is a separate type as far as the type checker is -- concerned, but which has a more low-level representation as far as Core-to-Core -- passes and the rest of the back end is concerned. -- -- You don't normally have to worry about this, as the utility functions in -- this module will automatically convert a source into a representation type -- if they are spotted, to the best of its abilities. If you don't want this -- to happen, use the equivalent functions from the "TcType" module. {- ************************************************************************ * * Type representation * * ************************************************************************ Note [coreView vs tcView] ~~~~~~~~~~~~~~~~~~~~~~~~~ So far as the typechecker is concerned, 'Constraint' and 'TYPE LiftedRep' are distinct kinds. But in Core these two are treated as identical. We implement this by making 'coreView' convert 'Constraint' to 'TYPE LiftedRep' on the fly. The function tcView (used in the type checker) does not do this. See also #11715, which tracks removing this inconsistency. -} -- | Gives the typechecker view of a type. This unwraps synonyms but -- leaves 'Constraint' alone. c.f. coreView, which turns Constraint into -- TYPE LiftedRep. Returns Nothing if no unwrapping happens. -- See also Note [coreView vs tcView] {-# INLINE tcView #-} tcView :: Type -> Maybe Type tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys') -- The free vars of 'rhs' should all be bound by 'tenv', so it's -- ok to use 'substTy' here. -- See also Note [The substitution invariant] in TyCoSubst. -- Its important to use mkAppTys, rather than (foldl AppTy), -- because the function part might well return a -- partially-applied type constructor; indeed, usually will! tcView _ = Nothing {-# INLINE coreView #-} coreView :: Type -> Maybe Type -- ^ This function Strips off the /top layer only/ of a type synonym -- application (if any) its underlying representation type. -- Returns Nothing if there is nothing to look through. -- This function considers 'Constraint' to be a synonym of @TYPE LiftedRep@. -- -- By being non-recursive and inlined, this case analysis gets efficiently -- joined onto the case analysis that the caller is already doing coreView ty@(TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys') -- This equation is exactly like tcView -- At the Core level, Constraint = Type -- See Note [coreView vs tcView] | isConstraintKindCon tc = ASSERT2( null tys, ppr ty ) Just liftedTypeKind coreView _ = Nothing ----------------------------------------------- expandTypeSynonyms :: Type -> Type -- ^ Expand out all type synonyms. Actually, it'd suffice to expand out -- just the ones that discard type variables (e.g. type Funny a = Int) -- But we don't know which those are currently, so we just expand all. -- -- 'expandTypeSynonyms' only expands out type synonyms mentioned in the type, -- not in the kinds of any TyCon or TyVar mentioned in the type. -- -- Keep this synchronized with 'synonymTyConsOfType' expandTypeSynonyms ty = go (mkEmptyTCvSubst in_scope) ty where in_scope = mkInScopeSet (tyCoVarsOfType ty) go subst (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc expanded_tys = let subst' = mkTvSubst in_scope (mkVarEnv tenv) -- Make a fresh substitution; rhs has nothing to -- do with anything that has happened so far -- NB: if you make changes here, be sure to build an -- /idempotent/ substitution, even in the nested case -- type T a b = a -> b -- type S x y = T y x -- (#11665) in mkAppTys (go subst' rhs) tys' | otherwise = TyConApp tc expanded_tys where expanded_tys = (map (go subst) tys) go _ (LitTy l) = LitTy l go subst (TyVarTy tv) = substTyVar subst tv go subst (AppTy t1 t2) = mkAppTy (go subst t1) (go subst t2) go subst ty@(FunTy _ arg res) = ty { ft_arg = go subst arg, ft_res = go subst res } go subst (ForAllTy (Bndr tv vis) t) = let (subst', tv') = substVarBndrUsing go subst tv in ForAllTy (Bndr tv' vis) (go subst' t) go subst (CastTy ty co) = mkCastTy (go subst ty) (go_co subst co) go subst (CoercionTy co) = mkCoercionTy (go_co subst co) go_mco _ MRefl = MRefl go_mco subst (MCo co) = MCo (go_co subst co) go_co subst (Refl ty) = mkNomReflCo (go subst ty) go_co subst (GRefl r ty mco) = mkGReflCo r (go subst ty) (go_mco subst mco) -- NB: coercions are always expanded upon creation go_co subst (TyConAppCo r tc args) = mkTyConAppCo r tc (map (go_co subst) args) go_co subst (AppCo co arg) = mkAppCo (go_co subst co) (go_co subst arg) go_co subst (ForAllCo tv kind_co co) = let (subst', tv', kind_co') = go_cobndr subst tv kind_co in mkForAllCo tv' kind_co' (go_co subst' co) go_co subst (FunCo r co1 co2) = mkFunCo r (go_co subst co1) (go_co subst co2) go_co subst (CoVarCo cv) = substCoVar subst cv go_co subst (AxiomInstCo ax ind args) = mkAxiomInstCo ax ind (map (go_co subst) args) go_co subst (UnivCo p r t1 t2) = mkUnivCo (go_prov subst p) r (go subst t1) (go subst t2) go_co subst (SymCo co) = mkSymCo (go_co subst co) go_co subst (TransCo co1 co2) = mkTransCo (go_co subst co1) (go_co subst co2) go_co subst (NthCo r n co) = mkNthCo r n (go_co subst co) go_co subst (LRCo lr co) = mkLRCo lr (go_co subst co) go_co subst (InstCo co arg) = mkInstCo (go_co subst co) (go_co subst arg) go_co subst (KindCo co) = mkKindCo (go_co subst co) go_co subst (SubCo co) = mkSubCo (go_co subst co) go_co subst (AxiomRuleCo ax cs) = AxiomRuleCo ax (map (go_co subst) cs) go_co _ (HoleCo h) = pprPanic "expandTypeSynonyms hit a hole" (ppr h) go_prov _ UnsafeCoerceProv = UnsafeCoerceProv go_prov subst (PhantomProv co) = PhantomProv (go_co subst co) go_prov subst (ProofIrrelProv co) = ProofIrrelProv (go_co subst co) go_prov _ p@(PluginProv _) = p -- the "False" and "const" are to accommodate the type of -- substForAllCoBndrUsing, which is general enough to -- handle coercion optimization (which sometimes swaps the -- order of a coercion) go_cobndr subst = substForAllCoBndrUsing False (go_co subst) subst -- | Extract the RuntimeRep classifier of a type from its kind. For example, -- @kindRep * = LiftedRep@; Panics if this is not possible. -- Treats * and Constraint as the same kindRep :: HasDebugCallStack => Kind -> Type kindRep k = case kindRep_maybe k of Just r -> r Nothing -> pprPanic "kindRep" (ppr k) -- | Given a kind (TYPE rr), extract its RuntimeRep classifier rr. -- For example, @kindRep_maybe * = Just LiftedRep@ -- Returns 'Nothing' if the kind is not of form (TYPE rr) -- Treats * and Constraint as the same kindRep_maybe :: HasDebugCallStack => Kind -> Maybe Type kindRep_maybe kind | Just kind' <- coreView kind = kindRep_maybe kind' | TyConApp tc [arg] <- kind , tc `hasKey` tYPETyConKey = Just arg | otherwise = Nothing -- | This version considers Constraint to be the same as *. Returns True -- if the argument is equivalent to Type/Constraint and False otherwise. -- See Note [Kind Constraint and kind Type] isLiftedTypeKind :: Kind -> Bool isLiftedTypeKind kind = case kindRep_maybe kind of Just rep -> isLiftedRuntimeRep rep Nothing -> False isLiftedRuntimeRep :: Type -> Bool -- isLiftedRuntimeRep is true of LiftedRep :: RuntimeRep -- False of type variables (a :: RuntimeRep) -- and of other reps e.g. (IntRep :: RuntimeRep) isLiftedRuntimeRep rep | Just rep' <- coreView rep = isLiftedRuntimeRep rep' | TyConApp rr_tc args <- rep , rr_tc `hasKey` liftedRepDataConKey = ASSERT( null args ) True | otherwise = False -- | Returns True if the kind classifies unlifted types and False otherwise. -- Note that this returns False for levity-polymorphic kinds, which may -- be specialized to a kind that classifies unlifted types. isUnliftedTypeKind :: Kind -> Bool isUnliftedTypeKind kind = case kindRep_maybe kind of Just rep -> isUnliftedRuntimeRep rep Nothing -> False isUnliftedRuntimeRep :: Type -> Bool -- True of definitely-unlifted RuntimeReps -- False of (LiftedRep :: RuntimeRep) -- and of variables (a :: RuntimeRep) isUnliftedRuntimeRep rep | Just rep' <- coreView rep = isUnliftedRuntimeRep rep' | TyConApp rr_tc _ <- rep -- NB: args might be non-empty -- e.g. TupleRep [r1, .., rn] = isPromotedDataCon rr_tc && not (rr_tc `hasKey` liftedRepDataConKey) -- Avoid searching all the unlifted RuntimeRep type cons -- In the RuntimeRep data type, only LiftedRep is lifted -- But be careful of type families (F tys) :: RuntimeRep | otherwise {- Variables, applications -} = False -- | Is this the type 'RuntimeRep'? isRuntimeRepTy :: Type -> Bool isRuntimeRepTy ty | Just ty' <- coreView ty = isRuntimeRepTy ty' isRuntimeRepTy (TyConApp tc args) | tc `hasKey` runtimeRepTyConKey = ASSERT( null args ) True isRuntimeRepTy _ = False -- | Is a tyvar of type 'RuntimeRep'? isRuntimeRepVar :: TyVar -> Bool isRuntimeRepVar = isRuntimeRepTy . tyVarKind {- ************************************************************************ * * Analyzing types * * ************************************************************************ These functions do a map-like operation over types, performing some operation on all variables and binding sites. Primarily used for zonking. Note [Efficiency for mapCoercion ForAllCo case] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ As noted in Note [Forall coercions] in TyCoRep, a ForAllCo is a bit redundant. It stores a TyCoVar and a Coercion, where the kind of the TyCoVar always matches the left-hand kind of the coercion. This is convenient lots of the time, but not when mapping a function over a coercion. The problem is that tcm_tybinder will affect the TyCoVar's kind and mapCoercion will affect the Coercion, and we hope that the results will be the same. Even if they are the same (which should generally happen with correct algorithms), then there is an efficiency issue. In particular, this problem seems to make what should be a linear algorithm into a potentially exponential one. But it's only going to be bad in the case where there's lots of foralls in the kinds of other foralls. Like this: forall a : (forall b : (forall c : ...). ...). ... This construction seems unlikely. So we'll do the inefficient, easy way for now. Note [Specialising mappers] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ These INLINABLE pragmas are indispensable. mapType/mapCoercion are used to implement zonking, and it's vital that they get specialised to the TcM monad. This specialisation happens automatically (that is, without a SPECIALISE pragma) as long as the definitions are INLINABLE. For example, this one change made a 20% allocation difference in perf/compiler/T5030. -} -- | This describes how a "map" operation over a type/coercion should behave data TyCoMapper env m = TyCoMapper { tcm_tyvar :: env -> TyVar -> m Type , tcm_covar :: env -> CoVar -> m Coercion , tcm_hole :: env -> CoercionHole -> m Coercion -- ^ What to do with coercion holes. -- See Note [Coercion holes] in TyCoRep. , tcm_tycobinder :: env -> TyCoVar -> ArgFlag -> m (env, TyCoVar) -- ^ The returned env is used in the extended scope , tcm_tycon :: TyCon -> m TyCon -- ^ This is used only for TcTyCons -- a) To zonk TcTyCons -- b) To turn TcTyCons into TyCons. -- See Note [Type checking recursive type and class declarations] -- in TcTyClsDecls } {-# INLINABLE mapType #-} -- See Note [Specialising mappers] mapType :: Monad m => TyCoMapper env m -> env -> Type -> m Type mapType mapper@(TyCoMapper { tcm_tyvar = tyvar , tcm_tycobinder = tycobinder , tcm_tycon = tycon }) env ty = go ty where go (TyVarTy tv) = tyvar env tv go (AppTy t1 t2) = mkAppTy <$> go t1 <*> go t2 go ty@(LitTy {}) = return ty go (CastTy ty co) = mkCastTy <$> go ty <*> mapCoercion mapper env co go (CoercionTy co) = CoercionTy <$> mapCoercion mapper env co go ty@(FunTy _ arg res) = do { arg' <- go arg; res' <- go res ; return (ty { ft_arg = arg', ft_res = res' }) } go ty@(TyConApp tc tys) | isTcTyCon tc = do { tc' <- tycon tc ; mkTyConApp tc' <$> mapM go tys } -- Not a TcTyCon | null tys -- Avoid allocation in this very = return ty -- common case (E.g. Int, LiftedRep etc) | otherwise = mkTyConApp tc <$> mapM go tys go (ForAllTy (Bndr tv vis) inner) = do { (env', tv') <- tycobinder env tv vis ; inner' <- mapType mapper env' inner ; return $ ForAllTy (Bndr tv' vis) inner' } {-# INLINABLE mapCoercion #-} -- See Note [Specialising mappers] mapCoercion :: Monad m => TyCoMapper env m -> env -> Coercion -> m Coercion mapCoercion mapper@(TyCoMapper { tcm_covar = covar , tcm_hole = cohole , tcm_tycobinder = tycobinder , tcm_tycon = tycon }) env co = go co where go_mco MRefl = return MRefl go_mco (MCo co) = MCo <$> (go co) go (Refl ty) = Refl <$> mapType mapper env ty go (GRefl r ty mco) = mkGReflCo r <$> mapType mapper env ty <*> (go_mco mco) go (TyConAppCo r tc args) = do { tc' <- if isTcTyCon tc then tycon tc else return tc ; mkTyConAppCo r tc' <$> mapM go args } go (AppCo c1 c2) = mkAppCo <$> go c1 <*> go c2 go (ForAllCo tv kind_co co) = do { kind_co' <- go kind_co ; (env', tv') <- tycobinder env tv Inferred ; co' <- mapCoercion mapper env' co ; return $ mkForAllCo tv' kind_co' co' } -- See Note [Efficiency for mapCoercion ForAllCo case] go (FunCo r c1 c2) = mkFunCo r <$> go c1 <*> go c2 go (CoVarCo cv) = covar env cv go (AxiomInstCo ax i args) = mkAxiomInstCo ax i <$> mapM go args go (HoleCo hole) = cohole env hole go (UnivCo p r t1 t2) = mkUnivCo <$> go_prov p <*> pure r <*> mapType mapper env t1 <*> mapType mapper env t2 go (SymCo co) = mkSymCo <$> go co go (TransCo c1 c2) = mkTransCo <$> go c1 <*> go c2 go (AxiomRuleCo r cos) = AxiomRuleCo r <$> mapM go cos go (NthCo r i co) = mkNthCo r i <$> go co go (LRCo lr co) = mkLRCo lr <$> go co go (InstCo co arg) = mkInstCo <$> go co <*> go arg go (KindCo co) = mkKindCo <$> go co go (SubCo co) = mkSubCo <$> go co go_prov UnsafeCoerceProv = return UnsafeCoerceProv go_prov (PhantomProv co) = PhantomProv <$> go co go_prov (ProofIrrelProv co) = ProofIrrelProv <$> go co go_prov p@(PluginProv _) = return p {- ************************************************************************ * * \subsection{Constructor-specific functions} * * ************************************************************************ --------------------------------------------------------------------- TyVarTy ~~~~~~~ -} -- | Attempts to obtain the type variable underlying a 'Type', and panics with the -- given message if this is not a type variable type. See also 'getTyVar_maybe' getTyVar :: String -> Type -> TyVar getTyVar msg ty = case getTyVar_maybe ty of Just tv -> tv Nothing -> panic ("getTyVar: " ++ msg) isTyVarTy :: Type -> Bool isTyVarTy ty = isJust (getTyVar_maybe ty) -- | Attempts to obtain the type variable underlying a 'Type' getTyVar_maybe :: Type -> Maybe TyVar getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty' | otherwise = repGetTyVar_maybe ty -- | If the type is a tyvar, possibly under a cast, returns it, along -- with the coercion. Thus, the co is :: kind tv ~N kind ty getCastedTyVar_maybe :: Type -> Maybe (TyVar, CoercionN) getCastedTyVar_maybe ty | Just ty' <- coreView ty = getCastedTyVar_maybe ty' getCastedTyVar_maybe (CastTy (TyVarTy tv) co) = Just (tv, co) getCastedTyVar_maybe (TyVarTy tv) = Just (tv, mkReflCo Nominal (tyVarKind tv)) getCastedTyVar_maybe _ = Nothing -- | Attempts to obtain the type variable underlying a 'Type', without -- any expansion repGetTyVar_maybe :: Type -> Maybe TyVar repGetTyVar_maybe (TyVarTy tv) = Just tv repGetTyVar_maybe _ = Nothing {- --------------------------------------------------------------------- AppTy ~~~~~ We need to be pretty careful with AppTy to make sure we obey the invariant that a TyConApp is always visibly so. mkAppTy maintains the invariant: use it. Note [Decomposing fat arrow c=>t] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Can we unify (a b) with (Eq a => ty)? If we do so, we end up with a partial application like ((=>) Eq a) which doesn't make sense in source Haskell. In contrast, we *can* unify (a b) with (t1 -> t2). Here's an example (#9858) of how you might do it: i :: (Typeable a, Typeable b) => Proxy (a b) -> TypeRep i p = typeRep p j = i (Proxy :: Proxy (Eq Int => Int)) The type (Proxy (Eq Int => Int)) is only accepted with -XImpredicativeTypes, but suppose we want that. But then in the call to 'i', we end up decomposing (Eq Int => Int), and we definitely don't want that. This really only applies to the type checker; in Core, '=>' and '->' are the same, as are 'Constraint' and '*'. But for now I've put the test in repSplitAppTy_maybe, which applies throughout, because the other calls to splitAppTy are in Unify, which is also used by the type checker (e.g. when matching type-function equations). -} -- | Applies a type to another, as in e.g. @k a@ mkAppTy :: Type -> Type -> Type -- See Note [Respecting definitional equality], invariant (EQ1). mkAppTy (CastTy fun_ty co) arg_ty | ([arg_co], res_co) <- decomposePiCos co (coercionKind co) [arg_ty] = (fun_ty `mkAppTy` (arg_ty `mkCastTy` arg_co)) `mkCastTy` res_co mkAppTy (TyConApp tc tys) ty2 = mkTyConApp tc (tys ++ [ty2]) mkAppTy ty1 ty2 = AppTy ty1 ty2 -- Note that the TyConApp could be an -- under-saturated type synonym. GHC allows that; e.g. -- type Foo k = k a -> k a -- type Id x = x -- foo :: Foo Id -> Foo Id -- -- Here Id is partially applied in the type sig for Foo, -- but once the type synonyms are expanded all is well -- -- Moreover in TcHsTypes.tcInferApps we build up a type -- (T t1 t2 t3) one argument at a type, thus forming -- (T t1), (T t1 t2), etc mkAppTys :: Type -> [Type] -> Type mkAppTys ty1 [] = ty1 mkAppTys (CastTy fun_ty co) arg_tys -- much more efficient then nested mkAppTy -- Why do this? See (EQ1) of -- Note [Respecting definitional equality] -- in TyCoRep = foldl' AppTy ((mkAppTys fun_ty casted_arg_tys) `mkCastTy` res_co) leftovers where (arg_cos, res_co) = decomposePiCos co (coercionKind co) arg_tys (args_to_cast, leftovers) = splitAtList arg_cos arg_tys casted_arg_tys = zipWith mkCastTy args_to_cast arg_cos mkAppTys (TyConApp tc tys1) tys2 = mkTyConApp tc (tys1 ++ tys2) mkAppTys ty1 tys2 = foldl' AppTy ty1 tys2 ------------- splitAppTy_maybe :: Type -> Maybe (Type, Type) -- ^ Attempt to take a type application apart, whether it is a -- function, type constructor, or plain type application. Note -- that type family applications are NEVER unsaturated by this! splitAppTy_maybe ty | Just ty' <- coreView ty = splitAppTy_maybe ty' splitAppTy_maybe ty = repSplitAppTy_maybe ty ------------- repSplitAppTy_maybe :: HasDebugCallStack => Type -> Maybe (Type,Type) -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that -- any Core view stuff is already done repSplitAppTy_maybe (FunTy _ ty1 ty2) = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2) where rep1 = getRuntimeRep ty1 rep2 = getRuntimeRep ty2 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2) repSplitAppTy_maybe (TyConApp tc tys) | not (mustBeSaturated tc) || tys `lengthExceeds` tyConArity tc , Just (tys', ty') <- snocView tys = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps! repSplitAppTy_maybe _other = Nothing -- This one doesn't break apart (c => t). -- See Note [Decomposing fat arrow c=>t] -- Defined here to avoid module loops between Unify and TcType. tcRepSplitAppTy_maybe :: Type -> Maybe (Type,Type) -- ^ Does the AppTy split as in 'tcSplitAppTy_maybe', but assumes that -- any coreView stuff is already done. Refuses to look through (c => t) tcRepSplitAppTy_maybe (FunTy { ft_af = af, ft_arg = ty1, ft_res = ty2 }) | InvisArg <- af = Nothing -- See Note [Decomposing fat arrow c=>t] | otherwise = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2) where rep1 = getRuntimeRep ty1 rep2 = getRuntimeRep ty2 tcRepSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2) tcRepSplitAppTy_maybe (TyConApp tc tys) | not (mustBeSaturated tc) || tys `lengthExceeds` tyConArity tc , Just (tys', ty') <- snocView tys = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps! tcRepSplitAppTy_maybe _other = Nothing ------------- splitAppTy :: Type -> (Type, Type) -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe', -- and panics if this is not possible splitAppTy ty = case splitAppTy_maybe ty of Just pr -> pr Nothing -> panic "splitAppTy" ------------- splitAppTys :: Type -> (Type, [Type]) -- ^ Recursively splits a type as far as is possible, leaving a residual -- type being applied to and the type arguments applied to it. Never fails, -- even if that means returning an empty list of type applications. splitAppTys ty = split ty ty [] where split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args split _ (AppTy ty arg) args = split ty ty (arg:args) split _ (TyConApp tc tc_args) args = let -- keep type families saturated n | mustBeSaturated tc = tyConArity tc | otherwise = 0 (tc_args1, tc_args2) = splitAt n tc_args in (TyConApp tc tc_args1, tc_args2 ++ args) split _ (FunTy _ ty1 ty2) args = ASSERT( null args ) (TyConApp funTyCon [], [rep1, rep2, ty1, ty2]) where rep1 = getRuntimeRep ty1 rep2 = getRuntimeRep ty2 split orig_ty _ args = (orig_ty, args) -- | Like 'splitAppTys', but doesn't look through type synonyms repSplitAppTys :: HasDebugCallStack => Type -> (Type, [Type]) repSplitAppTys ty = split ty [] where split (AppTy ty arg) args = split ty (arg:args) split (TyConApp tc tc_args) args = let n | mustBeSaturated tc = tyConArity tc | otherwise = 0 (tc_args1, tc_args2) = splitAt n tc_args in (TyConApp tc tc_args1, tc_args2 ++ args) split (FunTy _ ty1 ty2) args = ASSERT( null args ) (TyConApp funTyCon [], [rep1, rep2, ty1, ty2]) where rep1 = getRuntimeRep ty1 rep2 = getRuntimeRep ty2 split ty args = (ty, args) {- LitTy ~~~~~ -} mkNumLitTy :: Integer -> Type mkNumLitTy n = LitTy (NumTyLit n) -- | Is this a numeric literal. We also look through type synonyms. isNumLitTy :: Type -> Maybe Integer isNumLitTy ty | Just ty1 <- coreView ty = isNumLitTy ty1 isNumLitTy (LitTy (NumTyLit n)) = Just n isNumLitTy _ = Nothing mkStrLitTy :: FastString -> Type mkStrLitTy s = LitTy (StrTyLit s) -- | Is this a symbol literal. We also look through type synonyms. isStrLitTy :: Type -> Maybe FastString isStrLitTy ty | Just ty1 <- coreView ty = isStrLitTy ty1 isStrLitTy (LitTy (StrTyLit s)) = Just s isStrLitTy _ = Nothing -- | Is this a type literal (symbol or numeric). isLitTy :: Type -> Maybe TyLit isLitTy ty | Just ty1 <- coreView ty = isLitTy ty1 isLitTy (LitTy l) = Just l isLitTy _ = Nothing -- | Is this type a custom user error? -- If so, give us the kind and the error message. userTypeError_maybe :: Type -> Maybe Type userTypeError_maybe t = do { (tc, _kind : msg : _) <- splitTyConApp_maybe t -- There may be more than 2 arguments, if the type error is -- used as a type constructor (e.g. at kind `Type -> Type`). ; guard (tyConName tc == errorMessageTypeErrorFamName) ; return msg } -- | Render a type corresponding to a user type error into a SDoc. pprUserTypeErrorTy :: Type -> SDoc pprUserTypeErrorTy ty = case splitTyConApp_maybe ty of -- Text "Something" Just (tc,[txt]) | tyConName tc == typeErrorTextDataConName , Just str <- isStrLitTy txt -> ftext str -- ShowType t Just (tc,[_k,t]) | tyConName tc == typeErrorShowTypeDataConName -> ppr t -- t1 :<>: t2 Just (tc,[t1,t2]) | tyConName tc == typeErrorAppendDataConName -> pprUserTypeErrorTy t1 <> pprUserTypeErrorTy t2 -- t1 :$$: t2 Just (tc,[t1,t2]) | tyConName tc == typeErrorVAppendDataConName -> pprUserTypeErrorTy t1 $$ pprUserTypeErrorTy t2 -- An unevaluated type function _ -> ppr ty {- --------------------------------------------------------------------- FunTy ~~~~~ Note [Representation of function types] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Functions (e.g. Int -> Char) can be thought of as being applications of funTyCon (known in Haskell surface syntax as (->)), (->) :: forall (r1 :: RuntimeRep) (r2 :: RuntimeRep) (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type However, for efficiency's sake we represent saturated applications of (->) with FunTy. For instance, the type, (->) r1 r2 a b is equivalent to, FunTy (Anon a) b Note how the RuntimeReps are implied in the FunTy representation. For this reason we must be careful when recontructing the TyConApp representation (see, for instance, splitTyConApp_maybe). In the compiler we maintain the invariant that all saturated applications of (->) are represented with FunTy. See #11714. -} splitFunTy :: Type -> (Type, Type) -- ^ Attempts to extract the argument and result types from a type, and -- panics if that is not possible. See also 'splitFunTy_maybe' splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty' splitFunTy (FunTy _ arg res) = (arg, res) splitFunTy other = pprPanic "splitFunTy" (ppr other) splitFunTy_maybe :: Type -> Maybe (Type, Type) -- ^ Attempts to extract the argument and result types from a type splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty' splitFunTy_maybe (FunTy _ arg res) = Just (arg, res) splitFunTy_maybe _ = Nothing splitFunTys :: Type -> ([Type], Type) splitFunTys ty = split [] ty ty where split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty' split args _ (FunTy _ arg res) = split (arg:args) res res split args orig_ty _ = (reverse args, orig_ty) funResultTy :: Type -> Type -- ^ Extract the function result type and panic if that is not possible funResultTy ty | Just ty' <- coreView ty = funResultTy ty' funResultTy (FunTy { ft_res = res }) = res funResultTy ty = pprPanic "funResultTy" (ppr ty) funArgTy :: Type -> Type -- ^ Extract the function argument type and panic if that is not possible funArgTy ty | Just ty' <- coreView ty = funArgTy ty' funArgTy (FunTy { ft_arg = arg }) = arg funArgTy ty = pprPanic "funArgTy" (ppr ty) -- ^ Just like 'piResultTys' but for a single argument -- Try not to iterate 'piResultTy', because it's inefficient to substitute -- one variable at a time; instead use 'piResultTys" piResultTy :: HasDebugCallStack => Type -> Type -> Type piResultTy ty arg = case piResultTy_maybe ty arg of Just res -> res Nothing -> pprPanic "piResultTy" (ppr ty $$ ppr arg) piResultTy_maybe :: Type -> Type -> Maybe Type -- We don't need a 'tc' version, because -- this function behaves the same for Type and Constraint piResultTy_maybe ty arg | Just ty' <- coreView ty = piResultTy_maybe ty' arg | FunTy { ft_res = res } <- ty = Just res | ForAllTy (Bndr tv _) res <- ty = let empty_subst = mkEmptyTCvSubst $ mkInScopeSet $ tyCoVarsOfTypes [arg,res] in Just (substTy (extendTCvSubst empty_subst tv arg) res) | otherwise = Nothing -- | (piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn) -- where f :: f_ty -- 'piResultTys' is interesting because: -- 1. 'f_ty' may have more for-alls than there are args -- 2. Less obviously, it may have fewer for-alls -- For case 2. think of: -- piResultTys (forall a.a) [forall b.b, Int] -- This really can happen, but only (I think) in situations involving -- undefined. For example: -- undefined :: forall a. a -- Term: undefined @(forall b. b->b) @Int -- This term should have type (Int -> Int), but notice that -- there are more type args than foralls in 'undefined's type. -- If you edit this function, you may need to update the GHC formalism -- See Note [GHC Formalism] in coreSyn/CoreLint.hs -- This is a heavily used function (e.g. from typeKind), -- so we pay attention to efficiency, especially in the special case -- where there are no for-alls so we are just dropping arrows from -- a function type/kind. piResultTys :: HasDebugCallStack => Type -> [Type] -> Type piResultTys ty [] = ty piResultTys ty orig_args@(arg:args) | Just ty' <- coreView ty = piResultTys ty' orig_args | FunTy { ft_res = res } <- ty = piResultTys res args | ForAllTy (Bndr tv _) res <- ty = go (extendTCvSubst init_subst tv arg) res args | otherwise = pprPanic "piResultTys1" (ppr ty $$ ppr orig_args) where init_subst = mkEmptyTCvSubst $ mkInScopeSet (tyCoVarsOfTypes (ty:orig_args)) go :: TCvSubst -> Type -> [Type] -> Type go subst ty [] = substTyUnchecked subst ty go subst ty all_args@(arg:args) | Just ty' <- coreView ty = go subst ty' all_args | FunTy { ft_res = res } <- ty = go subst res args | ForAllTy (Bndr tv _) res <- ty = go (extendTCvSubst subst tv arg) res args | not (isEmptyTCvSubst subst) -- See Note [Care with kind instantiation] = go init_subst (substTy subst ty) all_args | otherwise = -- We have not run out of arguments, but the function doesn't -- have the right kind to apply to them; so panic. -- Without the explicit isEmptyVarEnv test, an ill-kinded type -- would give an infniite loop, which is very unhelpful -- c.f. #15473 pprPanic "piResultTys2" (ppr ty $$ ppr orig_args $$ ppr all_args) applyTysX :: [TyVar] -> Type -> [Type] -> Type -- applyTyxX beta-reduces (/\tvs. body_ty) arg_tys -- Assumes that (/\tvs. body_ty) is closed applyTysX tvs body_ty arg_tys = ASSERT2( arg_tys `lengthAtLeast` n_tvs, pp_stuff ) ASSERT2( tyCoVarsOfType body_ty `subVarSet` mkVarSet tvs, pp_stuff ) mkAppTys (substTyWith tvs (take n_tvs arg_tys) body_ty) (drop n_tvs arg_tys) where pp_stuff = vcat [ppr tvs, ppr body_ty, ppr arg_tys] n_tvs = length tvs {- Note [Care with kind instantiation] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have T :: forall k. k and we are finding the kind of T (forall b. b -> b) * Int Then T (forall b. b->b) :: k[ k :-> forall b. b->b] :: forall b. b -> b So T (forall b. b->b) * :: (b -> b)[ b :-> *] :: * -> * In other words we must intantiate the forall! Similarly (#15428) S :: forall k f. k -> f k and we are finding the kind of S * (* ->) Int Bool We have S * (* ->) :: (k -> f k)[ k :-> *, f :-> (* ->)] :: * -> * -> * So again we must instantiate. The same thing happens in ToIface.toIfaceAppArgsX. --------------------------------------------------------------------- TyConApp ~~~~~~~~ -} -- | A key function: builds a 'TyConApp' or 'FunTy' as appropriate to -- its arguments. Applies its arguments to the constructor from left to right. mkTyConApp :: TyCon -> [Type] -> Type mkTyConApp tycon tys | isFunTyCon tycon , [_rep1,_rep2,ty1,ty2] <- tys = FunTy { ft_af = VisArg, ft_arg = ty1, ft_res = ty2 } -- The FunTyCon (->) is always a visible one | otherwise = TyConApp tycon tys -- splitTyConApp "looks through" synonyms, because they don't -- mean a distinct type, but all other type-constructor applications -- including functions are returned as Just .. -- | Retrieve the tycon heading this type, if there is one. Does /not/ -- look through synonyms. tyConAppTyConPicky_maybe :: Type -> Maybe TyCon tyConAppTyConPicky_maybe (TyConApp tc _) = Just tc tyConAppTyConPicky_maybe (FunTy {}) = Just funTyCon tyConAppTyConPicky_maybe _ = Nothing -- | The same as @fst . splitTyConApp@ tyConAppTyCon_maybe :: Type -> Maybe TyCon tyConAppTyCon_maybe ty | Just ty' <- coreView ty = tyConAppTyCon_maybe ty' tyConAppTyCon_maybe (TyConApp tc _) = Just tc tyConAppTyCon_maybe (FunTy {}) = Just funTyCon tyConAppTyCon_maybe _ = Nothing tyConAppTyCon :: Type -> TyCon tyConAppTyCon ty = tyConAppTyCon_maybe ty `orElse` pprPanic "tyConAppTyCon" (ppr ty) -- | The same as @snd . splitTyConApp@ tyConAppArgs_maybe :: Type -> Maybe [Type] tyConAppArgs_maybe ty | Just ty' <- coreView ty = tyConAppArgs_maybe ty' tyConAppArgs_maybe (TyConApp _ tys) = Just tys tyConAppArgs_maybe (FunTy _ arg res) | Just rep1 <- getRuntimeRep_maybe arg , Just rep2 <- getRuntimeRep_maybe res = Just [rep1, rep2, arg, res] tyConAppArgs_maybe _ = Nothing tyConAppArgs :: Type -> [Type] tyConAppArgs ty = tyConAppArgs_maybe ty `orElse` pprPanic "tyConAppArgs" (ppr ty) tyConAppArgN :: Int -> Type -> Type -- Executing Nth tyConAppArgN n ty = case tyConAppArgs_maybe ty of Just tys -> ASSERT2( tys `lengthExceeds` n, ppr n <+> ppr tys ) tys `getNth` n Nothing -> pprPanic "tyConAppArgN" (ppr n <+> ppr ty) -- | Attempts to tease a type apart into a type constructor and the application -- of a number of arguments to that constructor. Panics if that is not possible. -- See also 'splitTyConApp_maybe' splitTyConApp :: Type -> (TyCon, [Type]) splitTyConApp ty = case splitTyConApp_maybe ty of Just stuff -> stuff Nothing -> pprPanic "splitTyConApp" (ppr ty) -- | Attempts to tease a type apart into a type constructor and the application -- of a number of arguments to that constructor splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type]) splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty' splitTyConApp_maybe ty = repSplitTyConApp_maybe ty -- | Split a type constructor application into its type constructor and -- applied types. Note that this may fail in the case of a 'FunTy' with an -- argument of unknown kind 'FunTy' (e.g. @FunTy (a :: k) Int@. since the kind -- of @a@ isn't of the form @TYPE rep@). Consequently, you may need to zonk your -- type before using this function. -- -- If you only need the 'TyCon', consider using 'tcTyConAppTyCon_maybe'. tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type]) -- Defined here to avoid module loops between Unify and TcType. tcSplitTyConApp_maybe ty | Just ty' <- tcView ty = tcSplitTyConApp_maybe ty' tcSplitTyConApp_maybe ty = repSplitTyConApp_maybe ty ------------------- repSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type]) -- ^ Like 'splitTyConApp_maybe', but doesn't look through synonyms. This -- assumes the synonyms have already been dealt with. -- -- Moreover, for a FunTy, it only succeeds if the argument types -- have enough info to extract the runtime-rep arguments that -- the funTyCon requires. This will usually be true; -- but may be temporarily false during canonicalization: -- see Note [FunTy and decomposing tycon applications] in TcCanonical -- repSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys) repSplitTyConApp_maybe (FunTy _ arg res) | Just arg_rep <- getRuntimeRep_maybe arg , Just res_rep <- getRuntimeRep_maybe res = Just (funTyCon, [arg_rep, res_rep, arg, res]) repSplitTyConApp_maybe _ = Nothing ------------------- -- | Attempts to tease a list type apart and gives the type of the elements if -- successful (looks through type synonyms) splitListTyConApp_maybe :: Type -> Maybe Type splitListTyConApp_maybe ty = case splitTyConApp_maybe ty of Just (tc,[e]) | tc == listTyCon -> Just e _other -> Nothing nextRole :: Type -> Role nextRole ty | Just (tc, tys) <- splitTyConApp_maybe ty , let num_tys = length tys , num_tys < tyConArity tc = tyConRoles tc `getNth` num_tys | otherwise = Nominal newTyConInstRhs :: TyCon -> [Type] -> Type -- ^ Unwrap one 'layer' of newtype on a type constructor and its -- arguments, using an eta-reduced version of the @newtype@ if possible. -- This requires tys to have at least @newTyConInstArity tycon@ elements. newTyConInstRhs tycon tys = ASSERT2( tvs `leLength` tys, ppr tycon $$ ppr tys $$ ppr tvs ) applyTysX tvs rhs tys where (tvs, rhs) = newTyConEtadRhs tycon {- --------------------------------------------------------------------- CastTy ~~~~~~ A casted type has its *kind* casted into something new. -} splitCastTy_maybe :: Type -> Maybe (Type, Coercion) splitCastTy_maybe ty | Just ty' <- coreView ty = splitCastTy_maybe ty' splitCastTy_maybe (CastTy ty co) = Just (ty, co) splitCastTy_maybe _ = Nothing -- | Make a 'CastTy'. The Coercion must be nominal. Checks the -- Coercion for reflexivity, dropping it if it's reflexive. -- See Note [Respecting definitional equality] in TyCoRep mkCastTy :: Type -> Coercion -> Type mkCastTy ty co | isReflexiveCo co = ty -- (EQ2) from the Note -- NB: Do the slow check here. This is important to keep the splitXXX -- functions working properly. Otherwise, we may end up with something -- like (((->) |> something_reflexive_but_not_obviously_so) biz baz) -- fails under splitFunTy_maybe. This happened with the cheaper check -- in test dependent/should_compile/dynamic-paper. mkCastTy (CastTy ty co1) co2 -- (EQ3) from the Note = mkCastTy ty (co1 `mkTransCo` co2) -- call mkCastTy again for the reflexivity check mkCastTy (ForAllTy (Bndr tv vis) inner_ty) co -- (EQ4) from the Note | isTyVar tv , let fvs = tyCoVarsOfCo co = -- have to make sure that pushing the co in doesn't capture the bound var! if tv `elemVarSet` fvs then let empty_subst = mkEmptyTCvSubst (mkInScopeSet fvs) (subst, tv') = substVarBndr empty_subst tv in ForAllTy (Bndr tv' vis) (substTy subst inner_ty `mkCastTy` co) else ForAllTy (Bndr tv vis) (inner_ty `mkCastTy` co) mkCastTy ty co = CastTy ty co tyConBindersTyCoBinders :: [TyConBinder] -> [TyCoBinder] -- Return the tyConBinders in TyCoBinder form tyConBindersTyCoBinders = map to_tyb where to_tyb (Bndr tv (NamedTCB vis)) = Named (Bndr tv vis) to_tyb (Bndr tv (AnonTCB af)) = Anon af (varType tv) -- | Drop the cast on a type, if any. If there is no -- cast, just return the original type. This is rarely what -- you want. The CastTy data constructor (in TyCoRep) has the -- invariant that another CastTy is not inside. See the -- data constructor for a full description of this invariant. -- Since CastTy cannot be nested, the result of discardCast -- cannot be a CastTy. discardCast :: Type -> Type discardCast (CastTy ty _) = ASSERT(not (isCastTy ty)) ty where isCastTy CastTy{} = True isCastTy _ = False discardCast ty = ty {- -------------------------------------------------------------------- CoercionTy ~~~~~~~~~~ CoercionTy allows us to inject coercions into types. A CoercionTy should appear only in the right-hand side of an application. -} mkCoercionTy :: Coercion -> Type mkCoercionTy = CoercionTy isCoercionTy :: Type -> Bool isCoercionTy (CoercionTy _) = True isCoercionTy _ = False isCoercionTy_maybe :: Type -> Maybe Coercion isCoercionTy_maybe (CoercionTy co) = Just co isCoercionTy_maybe _ = Nothing stripCoercionTy :: Type -> Coercion stripCoercionTy (CoercionTy co) = co stripCoercionTy ty = pprPanic "stripCoercionTy" (ppr ty) {- --------------------------------------------------------------------- SynTy ~~~~~ Notes on type synonyms ~~~~~~~~~~~~~~~~~~~~~~ The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try to return type synonyms wherever possible. Thus type Foo a = a -> a we want splitFunTys (a -> Foo a) = ([a], Foo a) not ([a], a -> a) The reason is that we then get better (shorter) type signatures in interfaces. Notably this plays a role in tcTySigs in TcBinds.hs. --------------------------------------------------------------------- ForAllTy ~~~~~~~~ -} -- | Make a dependent forall over an 'Inferred' variable mkTyCoInvForAllTy :: TyCoVar -> Type -> Type mkTyCoInvForAllTy tv ty | isCoVar tv , not (tv `elemVarSet` tyCoVarsOfType ty) = mkVisFunTy (varType tv) ty | otherwise = ForAllTy (Bndr tv Inferred) ty -- | Like 'mkTyCoInvForAllTy', but tv should be a tyvar mkInvForAllTy :: TyVar -> Type -> Type mkInvForAllTy tv ty = ASSERT( isTyVar tv ) ForAllTy (Bndr tv Inferred) ty -- | Like 'mkForAllTys', but assumes all variables are dependent and -- 'Inferred', a common case mkTyCoInvForAllTys :: [TyCoVar] -> Type -> Type mkTyCoInvForAllTys tvs ty = foldr mkTyCoInvForAllTy ty tvs -- | Like 'mkTyCoInvForAllTys', but tvs should be a list of tyvar mkInvForAllTys :: [TyVar] -> Type -> Type mkInvForAllTys tvs ty = foldr mkInvForAllTy ty tvs -- | Like 'mkForAllTy', but assumes the variable is dependent and 'Specified', -- a common case mkSpecForAllTy :: TyVar -> Type -> Type mkSpecForAllTy tv ty = ASSERT( isTyVar tv ) -- covar is always Inferred, so input should be tyvar ForAllTy (Bndr tv Specified) ty -- | Like 'mkForAllTys', but assumes all variables are dependent and -- 'Specified', a common case mkSpecForAllTys :: [TyVar] -> Type -> Type mkSpecForAllTys tvs ty = foldr mkSpecForAllTy ty tvs -- | Like mkForAllTys, but assumes all variables are dependent and visible mkVisForAllTys :: [TyVar] -> Type -> Type mkVisForAllTys tvs = ASSERT( all isTyVar tvs ) -- covar is always Inferred, so all inputs should be tyvar mkForAllTys [ Bndr tv Required | tv <- tvs ] mkLamType :: Var -> Type -> Type -- ^ Makes a @(->)@ type or an implicit forall type, depending -- on whether it is given a type variable or a term variable. -- This is used, for example, when producing the type of a lambda. -- Always uses Inferred binders. mkLamTypes :: [Var] -> Type -> Type -- ^ 'mkLamType' for multiple type or value arguments mkLamType v body_ty | isTyVar v = ForAllTy (Bndr v Inferred) body_ty | isCoVar v , v `elemVarSet` tyCoVarsOfType body_ty = ForAllTy (Bndr v Required) body_ty | isPredTy arg_ty -- See Note [mkLamType: dictionary arguments] = mkInvisFunTy arg_ty body_ty | otherwise = mkVisFunTy arg_ty body_ty where arg_ty = varType v mkLamTypes vs ty = foldr mkLamType ty vs {- Note [mkLamType: dictionary arguments] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If we have (\ (d :: Ord a). blah), we want to give it type (Ord a => blah_ty) with a fat arrow; that is, using mkInvisFunTy, not mkVisFunTy. Why? After all, we are in Core, where (=>) and (->) behave the same. Yes, but the /specialiser/ does treat dictionary arguments specially. Suppose we do w/w on 'foo' in module A, thus (#11272, #6056) foo :: Ord a => Int -> blah foo a d x = case x of I# x' -> $wfoo @a d x' $wfoo :: Ord a => Int# -> blah Now in module B we see (foo @Int dOrdInt). The specialiser will specialise this to $sfoo, where $sfoo :: Int -> blah $sfoo x = case x of I# x' -> $wfoo @Int dOrdInt x' Now we /must/ also specialise $wfoo! But it wasn't user-written, and has a type built with mkLamTypes. Conclusion: the easiest thing is to make mkLamType build (c => ty) when the argument is a predicate type. See TyCoRep Note [Types for coercions, predicates, and evidence] -} -- | Given a list of type-level vars and the free vars of a result kind, -- makes TyCoBinders, preferring anonymous binders -- if the variable is, in fact, not dependent. -- e.g. mkTyConBindersPreferAnon [(k:*),(b:k),(c:k)] (k->k) -- We want (k:*) Named, (b:k) Anon, (c:k) Anon -- -- All non-coercion binders are /visible/. mkTyConBindersPreferAnon :: [TyVar] -- ^ binders -> TyCoVarSet -- ^ free variables of result -> [TyConBinder] mkTyConBindersPreferAnon vars inner_tkvs = ASSERT( all isTyVar vars) fst (go vars) where go :: [TyVar] -> ([TyConBinder], VarSet) -- also returns the free vars go [] = ([], inner_tkvs) go (v:vs) | v `elemVarSet` fvs = ( Bndr v (NamedTCB Required) : binders , fvs `delVarSet` v `unionVarSet` kind_vars ) | otherwise = ( Bndr v (AnonTCB VisArg) : binders , fvs `unionVarSet` kind_vars ) where (binders, fvs) = go vs kind_vars = tyCoVarsOfType $ tyVarKind v -- | Take a ForAllTy apart, returning the list of tycovars and the result type. -- This always succeeds, even if it returns only an empty list. Note that the -- result type returned may have free variables that were bound by a forall. splitForAllTys :: Type -> ([TyCoVar], Type) splitForAllTys ty = split ty ty [] where split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs split _ (ForAllTy (Bndr tv _) ty) tvs = split ty ty (tv:tvs) split orig_ty _ tvs = (reverse tvs, orig_ty) -- | Like 'splitForAllTys', but only splits a 'ForAllTy' if -- @'sameVis' argf supplied_argf@ is 'True', where @argf@ is the visibility -- of the @ForAllTy@'s binder and @supplied_argf@ is the visibility provided -- as an argument to this function. splitForAllTysSameVis :: ArgFlag -> Type -> ([TyCoVar], Type) splitForAllTysSameVis supplied_argf ty = split ty ty [] where split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs split _ (ForAllTy (Bndr tv argf) ty) tvs | argf `sameVis` supplied_argf = split ty ty (tv:tvs) split orig_ty _ tvs = (reverse tvs, orig_ty) -- | Like splitForAllTys, but split only for tyvars. -- This always succeeds, even if it returns only an empty list. Note that the -- result type returned may have free variables that were bound by a forall. splitTyVarForAllTys :: Type -> ([TyVar], Type) splitTyVarForAllTys ty = split ty ty [] where split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs split _ (ForAllTy (Bndr tv _) ty) tvs | isTyVar tv = split ty ty (tv:tvs) split orig_ty _ tvs = (reverse tvs, orig_ty) -- | Checks whether this is a proper forall (with a named binder) isForAllTy :: Type -> Bool isForAllTy ty | Just ty' <- coreView ty = isForAllTy ty' isForAllTy (ForAllTy {}) = True isForAllTy _ = False -- | Like `isForAllTy`, but returns True only if it is a tyvar binder isForAllTy_ty :: Type -> Bool isForAllTy_ty ty | Just ty' <- coreView ty = isForAllTy_ty ty' isForAllTy_ty (ForAllTy (Bndr tv _) _) | isTyVar tv = True isForAllTy_ty _ = False -- | Like `isForAllTy`, but returns True only if it is a covar binder isForAllTy_co :: Type -> Bool isForAllTy_co ty | Just ty' <- coreView ty = isForAllTy_co ty' isForAllTy_co (ForAllTy (Bndr tv _) _) | isCoVar tv = True isForAllTy_co _ = False -- | Is this a function or forall? isPiTy :: Type -> Bool isPiTy ty | Just ty' <- coreView ty = isPiTy ty' isPiTy (ForAllTy {}) = True isPiTy (FunTy {}) = True isPiTy _ = False -- | Is this a function? isFunTy :: Type -> Bool isFunTy ty | Just ty' <- coreView ty = isFunTy ty' isFunTy (FunTy {}) = True isFunTy _ = False -- | Take a forall type apart, or panics if that is not possible. splitForAllTy :: Type -> (TyCoVar, Type) splitForAllTy ty | Just answer <- splitForAllTy_maybe ty = answer | otherwise = pprPanic "splitForAllTy" (ppr ty) -- | Drops all ForAllTys dropForAlls :: Type -> Type dropForAlls ty = go ty where go ty | Just ty' <- coreView ty = go ty' go (ForAllTy _ res) = go res go res = res -- | Attempts to take a forall type apart, but only if it's a proper forall, -- with a named binder splitForAllTy_maybe :: Type -> Maybe (TyCoVar, Type) splitForAllTy_maybe ty = go ty where go ty | Just ty' <- coreView ty = go ty' go (ForAllTy (Bndr tv _) ty) = Just (tv, ty) go _ = Nothing -- | Like splitForAllTy_maybe, but only returns Just if it is a tyvar binder. splitForAllTy_ty_maybe :: Type -> Maybe (TyCoVar, Type) splitForAllTy_ty_maybe ty = go ty where go ty | Just ty' <- coreView ty = go ty' go (ForAllTy (Bndr tv _) ty) | isTyVar tv = Just (tv, ty) go _ = Nothing -- | Like splitForAllTy_maybe, but only returns Just if it is a covar binder. splitForAllTy_co_maybe :: Type -> Maybe (TyCoVar, Type) splitForAllTy_co_maybe ty = go ty where go ty | Just ty' <- coreView ty = go ty' go (ForAllTy (Bndr tv _) ty) | isCoVar tv = Just (tv, ty) go _ = Nothing -- | Attempts to take a forall type apart; works with proper foralls and -- functions splitPiTy_maybe :: Type -> Maybe (TyCoBinder, Type) splitPiTy_maybe ty = go ty where go ty | Just ty' <- coreView ty = go ty' go (ForAllTy bndr ty) = Just (Named bndr, ty) go (FunTy { ft_af = af, ft_arg = arg, ft_res = res}) = Just (Anon af arg, res) go _ = Nothing -- | Takes a forall type apart, or panics splitPiTy :: Type -> (TyCoBinder, Type) splitPiTy ty | Just answer <- splitPiTy_maybe ty = answer | otherwise = pprPanic "splitPiTy" (ppr ty) -- | Split off all TyCoBinders to a type, splitting both proper foralls -- and functions splitPiTys :: Type -> ([TyCoBinder], Type) splitPiTys ty = split ty ty [] where split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs split _ (ForAllTy b res) bs = split res res (Named b : bs) split _ (FunTy { ft_af = af, ft_arg = arg, ft_res = res }) bs = split res res (Anon af arg : bs) split orig_ty _ bs = (reverse bs, orig_ty) -- | Like 'splitPiTys' but split off only /named/ binders -- and returns TyCoVarBinders rather than TyCoBinders splitForAllVarBndrs :: Type -> ([TyCoVarBinder], Type) splitForAllVarBndrs ty = split ty ty [] where split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs split _ (ForAllTy b res) bs = split res res (b:bs) split orig_ty _ bs = (reverse bs, orig_ty) {-# INLINE splitForAllVarBndrs #-} invisibleTyBndrCount :: Type -> Int -- Returns the number of leading invisible forall'd binders in the type -- Includes invisible predicate arguments; e.g. for -- e.g. forall {k}. (k ~ *) => k -> k -- returns 2 not 1 invisibleTyBndrCount ty = length (fst (splitPiTysInvisible ty)) -- Like splitPiTys, but returns only *invisible* binders, including constraints -- Stops at the first visible binder splitPiTysInvisible :: Type -> ([TyCoBinder], Type) splitPiTysInvisible ty = split ty ty [] where split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs split _ (ForAllTy b res) bs | Bndr _ vis <- b , isInvisibleArgFlag vis = split res res (Named b : bs) split _ (FunTy { ft_af = InvisArg, ft_arg = arg, ft_res = res }) bs = split res res (Anon InvisArg arg : bs) split orig_ty _ bs = (reverse bs, orig_ty) splitPiTysInvisibleN :: Int -> Type -> ([TyCoBinder], Type) -- Same as splitPiTysInvisible, but stop when -- - you have found 'n' TyCoBinders, -- - or you run out of invisible binders splitPiTysInvisibleN n ty = split n ty ty [] where split n orig_ty ty bs | n == 0 = (reverse bs, orig_ty) | Just ty' <- coreView ty = split n orig_ty ty' bs | ForAllTy b res <- ty , Bndr _ vis <- b , isInvisibleArgFlag vis = split (n-1) res res (Named b : bs) | FunTy { ft_af = InvisArg, ft_arg = arg, ft_res = res } <- ty = split (n-1) res res (Anon InvisArg arg : bs) | otherwise = (reverse bs, orig_ty) -- | Given a 'TyCon' and a list of argument types, filter out any invisible -- (i.e., 'Inferred' or 'Specified') arguments. filterOutInvisibleTypes :: TyCon -> [Type] -> [Type] filterOutInvisibleTypes tc tys = snd $ partitionInvisibleTypes tc tys -- | Given a 'TyCon' and a list of argument types, filter out any 'Inferred' -- arguments. filterOutInferredTypes :: TyCon -> [Type] -> [Type] filterOutInferredTypes tc tys = filterByList (map (/= Inferred) $ tyConArgFlags tc tys) tys -- | Given a 'TyCon' and a list of argument types, partition the arguments -- into: -- -- 1. 'Inferred' or 'Specified' (i.e., invisible) arguments and -- -- 2. 'Required' (i.e., visible) arguments partitionInvisibleTypes :: TyCon -> [Type] -> ([Type], [Type]) partitionInvisibleTypes tc tys = partitionByList (map isInvisibleArgFlag $ tyConArgFlags tc tys) tys -- | Given a list of things paired with their visibilities, partition the -- things into (invisible things, visible things). partitionInvisibles :: [(a, ArgFlag)] -> ([a], [a]) partitionInvisibles = partitionWith pick_invis where pick_invis :: (a, ArgFlag) -> Either a a pick_invis (thing, vis) | isInvisibleArgFlag vis = Left thing | otherwise = Right thing -- | Given a 'TyCon' and a list of argument types to which the 'TyCon' is -- applied, determine each argument's visibility -- ('Inferred', 'Specified', or 'Required'). -- -- Wrinkle: consider the following scenario: -- -- > T :: forall k. k -> k -- > tyConArgFlags T [forall m. m -> m -> m, S, R, Q] -- -- After substituting, we get -- -- > T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n -- -- Thus, the first argument is invisible, @S@ is visible, @R@ is invisible again, -- and @Q@ is visible. tyConArgFlags :: TyCon -> [Type] -> [ArgFlag] tyConArgFlags tc = fun_kind_arg_flags (tyConKind tc) -- | Given a 'Type' and a list of argument types to which the 'Type' is -- applied, determine each argument's visibility -- ('Inferred', 'Specified', or 'Required'). -- -- Most of the time, the arguments will be 'Required', but not always. Consider -- @f :: forall a. a -> Type@. In @f Type Bool@, the first argument (@Type@) is -- 'Specified' and the second argument (@Bool@) is 'Required'. It is precisely -- this sort of higher-rank situation in which 'appTyArgFlags' comes in handy, -- since @f Type Bool@ would be represented in Core using 'AppTy's. -- (See also #15792). appTyArgFlags :: Type -> [Type] -> [ArgFlag] appTyArgFlags ty = fun_kind_arg_flags (typeKind ty) -- | Given a function kind and a list of argument types (where each argument's -- kind aligns with the corresponding position in the argument kind), determine -- each argument's visibility ('Inferred', 'Specified', or 'Required'). fun_kind_arg_flags :: Kind -> [Type] -> [ArgFlag] fun_kind_arg_flags = go emptyTCvSubst where go subst ki arg_tys | Just ki' <- coreView ki = go subst ki' arg_tys go _ _ [] = [] go subst (ForAllTy (Bndr tv argf) res_ki) (arg_ty:arg_tys) = argf : go subst' res_ki arg_tys where subst' = extendTvSubst subst tv arg_ty go subst (TyVarTy tv) arg_tys | Just ki <- lookupTyVar subst tv = go subst ki arg_tys -- This FunTy case is important to handle kinds with nested foralls, such -- as this kind (inspired by #16518): -- -- forall {k1} k2. k1 -> k2 -> forall k3. k3 -> Type -- -- Here, we want to get the following ArgFlags: -- -- [Inferred, Specified, Required, Required, Specified, Required] -- forall {k1}. forall k2. k1 -> k2 -> forall k3. k3 -> Type go subst (FunTy{ft_af = af, ft_res = res_ki}) (_:arg_tys) = argf : go subst res_ki arg_tys where argf = case af of VisArg -> Required InvisArg -> Inferred go _ _ arg_tys = map (const Required) arg_tys -- something is ill-kinded. But this can happen -- when printing errors. Assume everything is Required. -- @isTauTy@ tests if a type has no foralls isTauTy :: Type -> Bool isTauTy ty | Just ty' <- coreView ty = isTauTy ty' isTauTy (TyVarTy _) = True isTauTy (LitTy {}) = True isTauTy (TyConApp tc tys) = all isTauTy tys && isTauTyCon tc isTauTy (AppTy a b) = isTauTy a && isTauTy b isTauTy (FunTy _ a b) = isTauTy a && isTauTy b isTauTy (ForAllTy {}) = False isTauTy (CastTy ty _) = isTauTy ty isTauTy (CoercionTy _) = False -- Not sure about this {- %************************************************************************ %* * TyCoBinders %* * %************************************************************************ -} -- | Make an anonymous binder mkAnonBinder :: AnonArgFlag -> Type -> TyCoBinder mkAnonBinder = Anon -- | Does this binder bind a variable that is /not/ erased? Returns -- 'True' for anonymous binders. isAnonTyCoBinder :: TyCoBinder -> Bool isAnonTyCoBinder (Named {}) = False isAnonTyCoBinder (Anon {}) = True tyCoBinderVar_maybe :: TyCoBinder -> Maybe TyCoVar tyCoBinderVar_maybe (Named tv) = Just $ binderVar tv tyCoBinderVar_maybe _ = Nothing tyCoBinderType :: TyCoBinder -> Type tyCoBinderType (Named tvb) = binderType tvb tyCoBinderType (Anon _ ty) = ty tyBinderType :: TyBinder -> Type tyBinderType (Named (Bndr tv _)) = ASSERT( isTyVar tv ) tyVarKind tv tyBinderType (Anon _ ty) = ty -- | Extract a relevant type, if there is one. binderRelevantType_maybe :: TyCoBinder -> Maybe Type binderRelevantType_maybe (Named {}) = Nothing binderRelevantType_maybe (Anon _ ty) = Just ty ------------- Closing over kinds ----------------- -- | Add the kind variables free in the kinds of the tyvars in the given set. -- Returns a non-deterministic set. closeOverKinds :: TyVarSet -> TyVarSet closeOverKinds = fvVarSet . closeOverKindsFV . nonDetEltsUniqSet -- It's OK to use nonDetEltsUniqSet here because we immediately forget -- about the ordering by returning a set. -- | Given a list of tyvars returns a deterministic FV computation that -- returns the given tyvars with the kind variables free in the kinds of the -- given tyvars. closeOverKindsFV :: [TyVar] -> FV closeOverKindsFV tvs = mapUnionFV (tyCoFVsOfType . tyVarKind) tvs `unionFV` mkFVs tvs -- | Add the kind variables free in the kinds of the tyvars in the given set. -- Returns a deterministically ordered list. closeOverKindsList :: [TyVar] -> [TyVar] closeOverKindsList tvs = fvVarList $ closeOverKindsFV tvs -- | Add the kind variables free in the kinds of the tyvars in the given set. -- Returns a deterministic set. closeOverKindsDSet :: DTyVarSet -> DTyVarSet closeOverKindsDSet = fvDVarSet . closeOverKindsFV . dVarSetElems {- ************************************************************************ * * \subsection{Type families} * * ************************************************************************ -} mkFamilyTyConApp :: TyCon -> [Type] -> Type -- ^ Given a family instance TyCon and its arg types, return the -- corresponding family type. E.g: -- -- > data family T a -- > data instance T (Maybe b) = MkT b -- -- Where the instance tycon is :RTL, so: -- -- > mkFamilyTyConApp :RTL Int = T (Maybe Int) mkFamilyTyConApp tc tys | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc , let tvs = tyConTyVars tc fam_subst = ASSERT2( tvs `equalLength` tys, ppr tc <+> ppr tys ) zipTvSubst tvs tys = mkTyConApp fam_tc (substTys fam_subst fam_tys) | otherwise = mkTyConApp tc tys -- | Get the type on the LHS of a coercion induced by a type/data -- family instance. coAxNthLHS :: CoAxiom br -> Int -> Type coAxNthLHS ax ind = mkTyConApp (coAxiomTyCon ax) (coAxBranchLHS (coAxiomNthBranch ax ind)) isFamFreeTy :: Type -> Bool isFamFreeTy ty | Just ty' <- coreView ty = isFamFreeTy ty' isFamFreeTy (TyVarTy _) = True isFamFreeTy (LitTy {}) = True isFamFreeTy (TyConApp tc tys) = all isFamFreeTy tys && isFamFreeTyCon tc isFamFreeTy (AppTy a b) = isFamFreeTy a && isFamFreeTy b isFamFreeTy (FunTy _ a b) = isFamFreeTy a && isFamFreeTy b isFamFreeTy (ForAllTy _ ty) = isFamFreeTy ty isFamFreeTy (CastTy ty _) = isFamFreeTy ty isFamFreeTy (CoercionTy _) = False -- Not sure about this -- | Does this type classify a core (unlifted) Coercion? -- At either role nominal or representational -- (t1 ~# t2) or (t1 ~R# t2) -- See Note [Types for coercions, predicates, and evidence] in TyCoRep isCoVarType :: Type -> Bool -- ToDo: should we check saturation? isCoVarType ty | Just tc <- tyConAppTyCon_maybe ty = tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey | otherwise = False {- ************************************************************************ * * \subsection{Liftedness} * * ************************************************************************ -} -- | Returns Just True if this type is surely lifted, Just False -- if it is surely unlifted, Nothing if we can't be sure (i.e., it is -- levity polymorphic), and panics if the kind does not have the shape -- TYPE r. isLiftedType_maybe :: HasDebugCallStack => Type -> Maybe Bool isLiftedType_maybe ty = go (getRuntimeRep ty) where go rr | Just rr' <- coreView rr = go rr' | isLiftedRuntimeRep rr = Just True | TyConApp {} <- rr = Just False -- Everything else is unlifted | otherwise = Nothing -- levity polymorphic -- | See "Type#type_classification" for what an unlifted type is. -- Panics on levity polymorphic types; See 'mightBeUnliftedType' for -- a more approximate predicate that behaves better in the presence of -- levity polymorphism. isUnliftedType :: HasDebugCallStack => Type -> Bool -- isUnliftedType returns True for forall'd unlifted types: -- x :: forall a. Int# -- I found bindings like these were getting floated to the top level. -- They are pretty bogus types, mind you. It would be better never to -- construct them isUnliftedType ty = not (isLiftedType_maybe ty `orElse` pprPanic "isUnliftedType" (ppr ty <+> dcolon <+> ppr (typeKind ty))) -- | Returns: -- -- * 'False' if the type is /guaranteed/ lifted or -- * 'True' if it is unlifted, OR we aren't sure (e.g. in a levity-polymorphic case) mightBeUnliftedType :: Type -> Bool mightBeUnliftedType ty = case isLiftedType_maybe ty of Just is_lifted -> not is_lifted Nothing -> True -- | Is this a type of kind RuntimeRep? (e.g. LiftedRep) isRuntimeRepKindedTy :: Type -> Bool isRuntimeRepKindedTy = isRuntimeRepTy . typeKind -- | Drops prefix of RuntimeRep constructors in 'TyConApp's. Useful for e.g. -- dropping 'LiftedRep arguments of unboxed tuple TyCon applications: -- -- dropRuntimeRepArgs [ 'LiftedRep, 'IntRep -- , String, Int# ] == [String, Int#] -- dropRuntimeRepArgs :: [Type] -> [Type] dropRuntimeRepArgs = dropWhile isRuntimeRepKindedTy -- | Extract the RuntimeRep classifier of a type. For instance, -- @getRuntimeRep_maybe Int = LiftedRep@. Returns 'Nothing' if this is not -- possible. getRuntimeRep_maybe :: HasDebugCallStack => Type -> Maybe Type getRuntimeRep_maybe = kindRep_maybe . typeKind -- | Extract the RuntimeRep classifier of a type. For instance, -- @getRuntimeRep_maybe Int = LiftedRep@. Panics if this is not possible. getRuntimeRep :: HasDebugCallStack => Type -> Type getRuntimeRep ty = case getRuntimeRep_maybe ty of Just r -> r Nothing -> pprPanic "getRuntimeRep" (ppr ty <+> dcolon <+> ppr (typeKind ty)) isUnboxedTupleType :: Type -> Bool isUnboxedTupleType ty = tyConAppTyCon (getRuntimeRep ty) `hasKey` tupleRepDataConKey -- NB: Do not use typePrimRep, as that can't tell the difference between -- unboxed tuples and unboxed sums isUnboxedSumType :: Type -> Bool isUnboxedSumType ty = tyConAppTyCon (getRuntimeRep ty) `hasKey` sumRepDataConKey -- | See "Type#type_classification" for what an algebraic type is. -- Should only be applied to /types/, as opposed to e.g. partially -- saturated type constructors isAlgType :: Type -> Bool isAlgType ty = case splitTyConApp_maybe ty of Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc ) isAlgTyCon tc _other -> False -- | Check whether a type is a data family type isDataFamilyAppType :: Type -> Bool isDataFamilyAppType ty = case tyConAppTyCon_maybe ty of Just tc -> isDataFamilyTyCon tc _ -> False -- | Computes whether an argument (or let right hand side) should -- be computed strictly or lazily, based only on its type. -- Currently, it's just 'isUnliftedType'. Panics on levity-polymorphic types. isStrictType :: HasDebugCallStack => Type -> Bool isStrictType = isUnliftedType isPrimitiveType :: Type -> Bool -- ^ Returns true of types that are opaque to Haskell. isPrimitiveType ty = case splitTyConApp_maybe ty of Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc ) isPrimTyCon tc _ -> False {- ************************************************************************ * * \subsection{Join points} * * ************************************************************************ -} -- | Determine whether a type could be the type of a join point of given total -- arity, according to the polymorphism rule. A join point cannot be polymorphic -- in its return type, since given -- join j @a @b x y z = e1 in e2, -- the types of e1 and e2 must be the same, and a and b are not in scope for e2. -- (See Note [The polymorphism rule of join points] in CoreSyn.) Returns False -- also if the type simply doesn't have enough arguments. -- -- Note that we need to know how many arguments (type *and* value) the putative -- join point takes; for instance, if -- j :: forall a. a -> Int -- then j could be a binary join point returning an Int, but it could *not* be a -- unary join point returning a -> Int. -- -- TODO: See Note [Excess polymorphism and join points] isValidJoinPointType :: JoinArity -> Type -> Bool isValidJoinPointType arity ty = valid_under emptyVarSet arity ty where valid_under tvs arity ty | arity == 0 = isEmptyVarSet (tvs `intersectVarSet` tyCoVarsOfType ty) | Just (t, ty') <- splitForAllTy_maybe ty = valid_under (tvs `extendVarSet` t) (arity-1) ty' | Just (_, res_ty) <- splitFunTy_maybe ty = valid_under tvs (arity-1) res_ty | otherwise = False {- Note [Excess polymorphism and join points] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In principle, if a function would be a join point except that it fails the polymorphism rule (see Note [The polymorphism rule of join points] in CoreSyn), it can still be made a join point with some effort. This is because all tail calls must return the same type (they return to the same context!), and thus if the return type depends on an argument, that argument must always be the same. For instance, consider: let f :: forall a. a -> Char -> [a] f @a x c = ... f @a y 'a' ... in ... f @Int 1 'b' ... f @Int 2 'c' ... (where the calls are tail calls). `f` fails the polymorphism rule because its return type is [a], where [a] is bound. But since the type argument is always 'Int', we can rewrite it as: let f' :: Int -> Char -> [Int] f' x c = ... f' y 'a' ... in ... f' 1 'b' ... f 2 'c' ... and now we can make f' a join point: join f' :: Int -> Char -> [Int] f' x c = ... jump f' y 'a' ... in ... jump f' 1 'b' ... jump f' 2 'c' ... It's not clear that this comes up often, however. TODO: Measure how often and add this analysis if necessary. See #14620. ************************************************************************ * * \subsection{Sequencing on types} * * ************************************************************************ -} seqType :: Type -> () seqType (LitTy n) = n `seq` () seqType (TyVarTy tv) = tv `seq` () seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2 seqType (FunTy _ t1 t2) = seqType t1 `seq` seqType t2 seqType (TyConApp tc tys) = tc `seq` seqTypes tys seqType (ForAllTy (Bndr tv _) ty) = seqType (varType tv) `seq` seqType ty seqType (CastTy ty co) = seqType ty `seq` seqCo co seqType (CoercionTy co) = seqCo co seqTypes :: [Type] -> () seqTypes [] = () seqTypes (ty:tys) = seqType ty `seq` seqTypes tys {- ************************************************************************ * * Comparison for types (We don't use instances so that we know where it happens) * * ************************************************************************ Note [Equality on AppTys] ~~~~~~~~~~~~~~~~~~~~~~~~~ In our cast-ignoring equality, we want to say that the following two are equal: (Maybe |> co) (Int |> co') ~? Maybe Int But the left is an AppTy while the right is a TyConApp. The solution is to use repSplitAppTy_maybe to break up the TyConApp into its pieces and then continue. Easy to do, but also easy to forget to do. -} eqType :: Type -> Type -> Bool -- ^ Type equality on source types. Does not look through @newtypes@ or -- 'PredType's, but it does look through type synonyms. -- This first checks that the kinds of the types are equal and then -- checks whether the types are equal, ignoring casts and coercions. -- (The kind check is a recursive call, but since all kinds have type -- @Type@, there is no need to check the types of kinds.) -- See also Note [Non-trivial definitional equality] in TyCoRep. eqType t1 t2 = isEqual $ nonDetCmpType t1 t2 -- It's OK to use nonDetCmpType here and eqType is deterministic, -- nonDetCmpType does equality deterministically -- | Compare types with respect to a (presumably) non-empty 'RnEnv2'. eqTypeX :: RnEnv2 -> Type -> Type -> Bool eqTypeX env t1 t2 = isEqual $ nonDetCmpTypeX env t1 t2 -- It's OK to use nonDetCmpType here and eqTypeX is deterministic, -- nonDetCmpTypeX does equality deterministically -- | Type equality on lists of types, looking through type synonyms -- but not newtypes. eqTypes :: [Type] -> [Type] -> Bool eqTypes tys1 tys2 = isEqual $ nonDetCmpTypes tys1 tys2 -- It's OK to use nonDetCmpType here and eqTypes is deterministic, -- nonDetCmpTypes does equality deterministically eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2 -- Check that the var lists are the same length -- and have matching kinds; if so, extend the RnEnv2 -- Returns Nothing if they don't match eqVarBndrs env [] [] = Just env eqVarBndrs env (tv1:tvs1) (tv2:tvs2) | eqTypeX env (varType tv1) (varType tv2) = eqVarBndrs (rnBndr2 env tv1 tv2) tvs1 tvs2 eqVarBndrs _ _ _= Nothing -- Now here comes the real worker {- Note [nonDetCmpType nondeterminism] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ nonDetCmpType is implemented in terms of nonDetCmpTypeX. nonDetCmpTypeX uses nonDetCmpTc which compares TyCons by their Unique value. Using Uniques for ordering leads to nondeterminism. We hit the same problem in the TyVarTy case, comparing type variables is nondeterministic, note the call to nonDetCmpVar in nonDetCmpTypeX. See Note [Unique Determinism] for more details. -} nonDetCmpType :: Type -> Type -> Ordering nonDetCmpType t1 t2 -- we know k1 and k2 have the same kind, because they both have kind *. = nonDetCmpTypeX rn_env t1 t2 where rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes [t1, t2])) nonDetCmpTypes :: [Type] -> [Type] -> Ordering nonDetCmpTypes ts1 ts2 = nonDetCmpTypesX rn_env ts1 ts2 where rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes (ts1 ++ ts2))) -- | An ordering relation between two 'Type's (known below as @t1 :: k1@ -- and @t2 :: k2@) data TypeOrdering = TLT -- ^ @t1 < t2@ | TEQ -- ^ @t1 ~ t2@ and there are no casts in either, -- therefore we can conclude @k1 ~ k2@ | TEQX -- ^ @t1 ~ t2@ yet one of the types contains a cast so -- they may differ in kind. | TGT -- ^ @t1 > t2@ deriving (Eq, Ord, Enum, Bounded) nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse -- See Note [Non-trivial definitional equality] in TyCoRep nonDetCmpTypeX env orig_t1 orig_t2 = case go env orig_t1 orig_t2 of -- If there are casts then we also need to do a comparison of the kinds of -- the types being compared TEQX -> toOrdering $ go env k1 k2 ty_ordering -> toOrdering ty_ordering where k1 = typeKind orig_t1 k2 = typeKind orig_t2 toOrdering :: TypeOrdering -> Ordering toOrdering TLT = LT toOrdering TEQ = EQ toOrdering TEQX = EQ toOrdering TGT = GT liftOrdering :: Ordering -> TypeOrdering liftOrdering LT = TLT liftOrdering EQ = TEQ liftOrdering GT = TGT thenCmpTy :: TypeOrdering -> TypeOrdering -> TypeOrdering thenCmpTy TEQ rel = rel thenCmpTy TEQX rel = hasCast rel thenCmpTy rel _ = rel hasCast :: TypeOrdering -> TypeOrdering hasCast TEQ = TEQX hasCast rel = rel -- Returns both the resulting ordering relation between the two types -- and whether either contains a cast. go :: RnEnv2 -> Type -> Type -> TypeOrdering go env t1 t2 | Just t1' <- coreView t1 = go env t1' t2 | Just t2' <- coreView t2 = go env t1 t2' go env (TyVarTy tv1) (TyVarTy tv2) = liftOrdering $ rnOccL env tv1 `nonDetCmpVar` rnOccR env tv2 go env (ForAllTy (Bndr tv1 _) t1) (ForAllTy (Bndr tv2 _) t2) = go env (varType tv1) (varType tv2) `thenCmpTy` go (rnBndr2 env tv1 tv2) t1 t2 -- See Note [Equality on AppTys] go env (AppTy s1 t1) ty2 | Just (s2, t2) <- repSplitAppTy_maybe ty2 = go env s1 s2 `thenCmpTy` go env t1 t2 go env ty1 (AppTy s2 t2) | Just (s1, t1) <- repSplitAppTy_maybe ty1 = go env s1 s2 `thenCmpTy` go env t1 t2 go env (FunTy _ s1 t1) (FunTy _ s2 t2) = go env s1 s2 `thenCmpTy` go env t1 t2 go env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = liftOrdering (tc1 `nonDetCmpTc` tc2) `thenCmpTy` gos env tys1 tys2 go _ (LitTy l1) (LitTy l2) = liftOrdering (compare l1 l2) go env (CastTy t1 _) t2 = hasCast $ go env t1 t2 go env t1 (CastTy t2 _) = hasCast $ go env t1 t2 go _ (CoercionTy {}) (CoercionTy {}) = TEQ -- Deal with the rest: TyVarTy < CoercionTy < AppTy < LitTy < TyConApp < ForAllTy go _ ty1 ty2 = liftOrdering $ (get_rank ty1) `compare` (get_rank ty2) where get_rank :: Type -> Int get_rank (CastTy {}) = pprPanic "nonDetCmpTypeX.get_rank" (ppr [ty1,ty2]) get_rank (TyVarTy {}) = 0 get_rank (CoercionTy {}) = 1 get_rank (AppTy {}) = 3 get_rank (LitTy {}) = 4 get_rank (TyConApp {}) = 5 get_rank (FunTy {}) = 6 get_rank (ForAllTy {}) = 7 gos :: RnEnv2 -> [Type] -> [Type] -> TypeOrdering gos _ [] [] = TEQ gos _ [] _ = TLT gos _ _ [] = TGT gos env (ty1:tys1) (ty2:tys2) = go env ty1 ty2 `thenCmpTy` gos env tys1 tys2 ------------- nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering nonDetCmpTypesX _ [] [] = EQ nonDetCmpTypesX env (t1:tys1) (t2:tys2) = nonDetCmpTypeX env t1 t2 `thenCmp` nonDetCmpTypesX env tys1 tys2 nonDetCmpTypesX _ [] _ = LT nonDetCmpTypesX _ _ [] = GT ------------- -- | Compare two 'TyCon's. NB: This should /never/ see 'Constraint' (as -- recognized by Kind.isConstraintKindCon) which is considered a synonym for -- 'Type' in Core. -- See Note [Kind Constraint and kind Type] in Kind. -- See Note [nonDetCmpType nondeterminism] nonDetCmpTc :: TyCon -> TyCon -> Ordering nonDetCmpTc tc1 tc2 = ASSERT( not (isConstraintKindCon tc1) && not (isConstraintKindCon tc2) ) u1 `nonDetCmpUnique` u2 where u1 = tyConUnique tc1 u2 = tyConUnique tc2 {- ************************************************************************ * * The kind of a type * * ************************************************************************ Note [typeKind vs tcTypeKind] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We have two functions to get the kind of a type * typeKind ignores the distinction between Constraint and * * tcTypeKind respects the distinction between Constraint and * tcTypeKind is used by the type inference engine, for which Constraint and * are different; after that we use typeKind. See also Note [coreView vs tcView] Note [Kinding rules for types] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In typeKind we consider Constraint and (TYPE LiftedRep) to be identical. We then have t1 : TYPE rep1 t2 : TYPE rep2 (FUN) ---------------- t1 -> t2 : Type ty : TYPE rep `a` is not free in rep (FORALL) ----------------------- forall a. ty : TYPE rep In tcTypeKind we consider Constraint and (TYPE LiftedRep) to be distinct: t1 : TYPE rep1 t2 : TYPE rep2 (FUN) ---------------- t1 -> t2 : Type t1 : Constraint t2 : TYPE rep (PRED1) ---------------- t1 => t2 : Type t1 : Constraint t2 : Constraint (PRED2) --------------------- t1 => t2 : Constraint ty : TYPE rep `a` is not free in rep (FORALL1) ----------------------- forall a. ty : TYPE rep ty : Constraint (FORALL2) ------------------------- forall a. ty : Constraint Note that: * The only way we distinguish '->' from '=>' is by the fact that the argument is a PredTy. Both are FunTys Note [Phantom type variables in kinds] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider type K (r :: RuntimeRep) = Type -- Note 'r' is unused data T r :: K r -- T :: forall r -> K r foo :: forall r. T r The body of the forall in foo's type has kind (K r), and normally it would make no sense to have forall r. (ty :: K r) because the kind of the forall would escape the binding of 'r'. But in this case it's fine because (K r) exapands to Type, so we expliclity /permit/ the type forall r. T r To accommodate such a type, in typeKind (forall a.ty) we use occCheckExpand to expand any type synonyms in the kind of 'ty' to eliminate 'a'. See kinding rule (FORALL) in Note [Kinding rules for types] And in TcValidity.checkEscapingKind, we use also use occCheckExpand, for the same reason. -} ----------------------------- typeKind :: HasDebugCallStack => Type -> Kind -- No need to expand synonyms typeKind (TyConApp tc tys) = piResultTys (tyConKind tc) tys typeKind (LitTy l) = typeLiteralKind l typeKind (FunTy {}) = liftedTypeKind typeKind (TyVarTy tyvar) = tyVarKind tyvar typeKind (CastTy _ty co) = pSnd $ coercionKind co typeKind (CoercionTy co) = coercionType co typeKind (AppTy fun arg) = go fun [arg] where -- Accumulate the type arugments, so we can call piResultTys, -- rather than a succession of calls to piResultTy (which is -- asymptotically costly as the number of arguments increases) go (AppTy fun arg) args = go fun (arg:args) go fun args = piResultTys (typeKind fun) args typeKind ty@(ForAllTy {}) = case occCheckExpand tvs body_kind of -- We must make sure tv does not occur in kind -- As it is already out of scope! -- See Note [Phantom type variables in kinds] Just k' -> k' Nothing -> pprPanic "typeKind" (ppr ty $$ ppr tvs $$ ppr body <+> dcolon <+> ppr body_kind) where (tvs, body) = splitTyVarForAllTys ty body_kind = typeKind body --------------------------------------------- -- Utilities to be used in Unify, which uses "tc" functions --------------------------------------------- tcTypeKind :: HasDebugCallStack => Type -> Kind -- No need to expand synonyms tcTypeKind (TyConApp tc tys) = piResultTys (tyConKind tc) tys tcTypeKind (LitTy l) = typeLiteralKind l tcTypeKind (TyVarTy tyvar) = tyVarKind tyvar tcTypeKind (CastTy _ty co) = pSnd $ coercionKind co tcTypeKind (CoercionTy co) = coercionType co tcTypeKind (FunTy { ft_af = af, ft_res = res }) | InvisArg <- af , tcIsConstraintKind (tcTypeKind res) = constraintKind -- Eq a => Ord a :: Constraint | otherwise -- Eq a => a -> a :: TYPE LiftedRep = liftedTypeKind -- Eq a => Array# Int :: Type LiftedRep (not TYPE PtrRep) tcTypeKind (AppTy fun arg) = go fun [arg] where -- Accumulate the type arugments, so we can call piResultTys, -- rather than a succession of calls to piResultTy (which is -- asymptotically costly as the number of arguments increases) go (AppTy fun arg) args = go fun (arg:args) go fun args = piResultTys (tcTypeKind fun) args tcTypeKind ty@(ForAllTy {}) | tcIsConstraintKind body_kind = constraintKind | otherwise = case occCheckExpand tvs body_kind of -- We must make sure tv does not occur in kind -- As it is already out of scope! -- See Note [Phantom type variables in kinds] Just k' -> k' Nothing -> pprPanic "tcTypeKind" (ppr ty $$ ppr tvs $$ ppr body <+> dcolon <+> ppr body_kind) where (tvs, body) = splitTyVarForAllTys ty body_kind = tcTypeKind body isPredTy :: HasDebugCallStack => Type -> Bool -- See Note [Types for coercions, predicates, and evidence] in TyCoRep isPredTy ty = tcIsConstraintKind (tcTypeKind ty) -- tcIsConstraintKind stuff only makes sense in the typechecker -- After that Constraint = Type -- See Note [coreView vs tcView] -- Defined here because it is used in isPredTy and tcRepSplitAppTy_maybe (sigh) tcIsConstraintKind :: Kind -> Bool tcIsConstraintKind ty | Just (tc, args) <- tcSplitTyConApp_maybe ty -- Note: tcSplit here , isConstraintKindCon tc = ASSERT2( null args, ppr ty ) True | otherwise = False -- | Is this kind equivalent to @*@? -- -- This considers 'Constraint' to be distinct from @*@. For a version that -- treats them as the same type, see 'isLiftedTypeKind'. tcIsLiftedTypeKind :: Kind -> Bool tcIsLiftedTypeKind ty | Just (tc, [arg]) <- tcSplitTyConApp_maybe ty -- Note: tcSplit here , tc `hasKey` tYPETyConKey = isLiftedRuntimeRep arg | otherwise = False -- | Is this kind equivalent to @TYPE r@ (for some unknown r)? -- -- This considers 'Constraint' to be distinct from @*@. tcIsRuntimeTypeKind :: Kind -> Bool tcIsRuntimeTypeKind ty | Just (tc, _) <- tcSplitTyConApp_maybe ty -- Note: tcSplit here , tc `hasKey` tYPETyConKey = True | otherwise = False tcReturnsConstraintKind :: Kind -> Bool -- True <=> the Kind ultimately returns a Constraint -- E.g. * -> Constraint -- forall k. k -> Constraint tcReturnsConstraintKind kind | Just kind' <- tcView kind = tcReturnsConstraintKind kind' tcReturnsConstraintKind (ForAllTy _ ty) = tcReturnsConstraintKind ty tcReturnsConstraintKind (FunTy { ft_res = ty }) = tcReturnsConstraintKind ty tcReturnsConstraintKind (TyConApp tc _) = isConstraintKindCon tc tcReturnsConstraintKind _ = False -------------------------- typeLiteralKind :: TyLit -> Kind typeLiteralKind (NumTyLit {}) = typeNatKind typeLiteralKind (StrTyLit {}) = typeSymbolKind -- | Returns True if a type is levity polymorphic. Should be the same -- as (isKindLevPoly . typeKind) but much faster. -- Precondition: The type has kind (TYPE blah) isTypeLevPoly :: Type -> Bool isTypeLevPoly = go where go ty@(TyVarTy {}) = check_kind ty go ty@(AppTy {}) = check_kind ty go ty@(TyConApp tc _) | not (isTcLevPoly tc) = False | otherwise = check_kind ty go (ForAllTy _ ty) = go ty go (FunTy {}) = False go (LitTy {}) = False go ty@(CastTy {}) = check_kind ty go ty@(CoercionTy {}) = pprPanic "isTypeLevPoly co" (ppr ty) check_kind = isKindLevPoly . typeKind -- | Looking past all pi-types, is the end result potentially levity polymorphic? -- Example: True for (forall r (a :: TYPE r). String -> a) -- Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type) resultIsLevPoly :: Type -> Bool resultIsLevPoly = isTypeLevPoly . snd . splitPiTys {- ********************************************************************** * * Occurs check expansion %* * %********************************************************************* -} {- Note [Occurs check expansion] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (occurCheckExpand tv xi) expands synonyms in xi just enough to get rid of occurrences of tv outside type function arguments, if that is possible; otherwise, it returns Nothing. For example, suppose we have type F a b = [a] Then occCheckExpand b (F Int b) = Just [Int] but occCheckExpand a (F a Int) = Nothing We don't promise to do the absolute minimum amount of expanding necessary, but we try not to do expansions we don't need to. We prefer doing inner expansions first. For example, type F a b = (a, Int, a, [a]) type G b = Char We have occCheckExpand b (F (G b)) = Just (F Char) even though we could also expand F to get rid of b. -} occCheckExpand :: [Var] -> Type -> Maybe Type -- See Note [Occurs check expansion] -- We may have needed to do some type synonym unfolding in order to -- get rid of the variable (or forall), so we also return the unfolded -- version of the type, which is guaranteed to be syntactically free -- of the given type variable. If the type is already syntactically -- free of the variable, then the same type is returned. occCheckExpand vs_to_avoid ty | null vs_to_avoid -- Efficient shortcut = Just ty -- Can happen, eg. CoreUtils.mkSingleAltCase | otherwise = go (mkVarSet vs_to_avoid, emptyVarEnv) ty where go :: (VarSet, VarEnv TyCoVar) -> Type -> Maybe Type -- The VarSet is the set of variables we are trying to avoid -- The VarEnv carries mappings necessary -- because of kind expansion go cxt@(as, env) (TyVarTy tv') | tv' `elemVarSet` as = Nothing | Just tv'' <- lookupVarEnv env tv' = return (mkTyVarTy tv'') | otherwise = do { tv'' <- go_var cxt tv' ; return (mkTyVarTy tv'') } go _ ty@(LitTy {}) = return ty go cxt (AppTy ty1 ty2) = do { ty1' <- go cxt ty1 ; ty2' <- go cxt ty2 ; return (mkAppTy ty1' ty2') } go cxt ty@(FunTy _ ty1 ty2) = do { ty1' <- go cxt ty1 ; ty2' <- go cxt ty2 ; return (ty { ft_arg = ty1', ft_res = ty2' }) } go cxt@(as, env) (ForAllTy (Bndr tv vis) body_ty) = do { ki' <- go cxt (varType tv) ; let tv' = setVarType tv ki' env' = extendVarEnv env tv tv' as' = as `delVarSet` tv ; body' <- go (as', env') body_ty ; return (ForAllTy (Bndr tv' vis) body') } -- For a type constructor application, first try expanding away the -- offending variable from the arguments. If that doesn't work, next -- see if the type constructor is a type synonym, and if so, expand -- it and try again. go cxt ty@(TyConApp tc tys) = case mapM (go cxt) tys of Just tys' -> return (mkTyConApp tc tys') Nothing | Just ty' <- tcView ty -> go cxt ty' | otherwise -> Nothing -- Failing that, try to expand a synonym go cxt (CastTy ty co) = do { ty' <- go cxt ty ; co' <- go_co cxt co ; return (mkCastTy ty' co') } go cxt (CoercionTy co) = do { co' <- go_co cxt co ; return (mkCoercionTy co') } ------------------ go_var cxt v = do { k' <- go cxt (varType v) ; return (setVarType v k') } -- Works for TyVar and CoVar -- See Note [Occurrence checking: look inside kinds] ------------------ go_mco _ MRefl = return MRefl go_mco ctx (MCo co) = MCo <$> go_co ctx co ------------------ go_co cxt (Refl ty) = do { ty' <- go cxt ty ; return (mkNomReflCo ty') } go_co cxt (GRefl r ty mco) = do { mco' <- go_mco cxt mco ; ty' <- go cxt ty ; return (mkGReflCo r ty' mco') } -- Note: Coercions do not contain type synonyms go_co cxt (TyConAppCo r tc args) = do { args' <- mapM (go_co cxt) args ; return (mkTyConAppCo r tc args') } go_co cxt (AppCo co arg) = do { co' <- go_co cxt co ; arg' <- go_co cxt arg ; return (mkAppCo co' arg') } go_co cxt@(as, env) (ForAllCo tv kind_co body_co) = do { kind_co' <- go_co cxt kind_co ; let tv' = setVarType tv $ pFst (coercionKind kind_co') env' = extendVarEnv env tv tv' as' = as `delVarSet` tv ; body' <- go_co (as', env') body_co ; return (ForAllCo tv' kind_co' body') } go_co cxt (FunCo r co1 co2) = do { co1' <- go_co cxt co1 ; co2' <- go_co cxt co2 ; return (mkFunCo r co1' co2') } go_co cxt@(as,env) (CoVarCo c) | c `elemVarSet` as = Nothing | Just c' <- lookupVarEnv env c = return (mkCoVarCo c') | otherwise = do { c' <- go_var cxt c ; return (mkCoVarCo c') } go_co cxt (HoleCo h) = do { c' <- go_var cxt (ch_co_var h) ; return (HoleCo (h { ch_co_var = c' })) } go_co cxt (AxiomInstCo ax ind args) = do { args' <- mapM (go_co cxt) args ; return (mkAxiomInstCo ax ind args') } go_co cxt (UnivCo p r ty1 ty2) = do { p' <- go_prov cxt p ; ty1' <- go cxt ty1 ; ty2' <- go cxt ty2 ; return (mkUnivCo p' r ty1' ty2') } go_co cxt (SymCo co) = do { co' <- go_co cxt co ; return (mkSymCo co') } go_co cxt (TransCo co1 co2) = do { co1' <- go_co cxt co1 ; co2' <- go_co cxt co2 ; return (mkTransCo co1' co2') } go_co cxt (NthCo r n co) = do { co' <- go_co cxt co ; return (mkNthCo r n co') } go_co cxt (LRCo lr co) = do { co' <- go_co cxt co ; return (mkLRCo lr co') } go_co cxt (InstCo co arg) = do { co' <- go_co cxt co ; arg' <- go_co cxt arg ; return (mkInstCo co' arg') } go_co cxt (KindCo co) = do { co' <- go_co cxt co ; return (mkKindCo co') } go_co cxt (SubCo co) = do { co' <- go_co cxt co ; return (mkSubCo co') } go_co cxt (AxiomRuleCo ax cs) = do { cs' <- mapM (go_co cxt) cs ; return (mkAxiomRuleCo ax cs') } ------------------ go_prov _ UnsafeCoerceProv = return UnsafeCoerceProv go_prov cxt (PhantomProv co) = PhantomProv <$> go_co cxt co go_prov cxt (ProofIrrelProv co) = ProofIrrelProv <$> go_co cxt co go_prov _ p@(PluginProv _) = return p {- %************************************************************************ %* * Miscellaneous functions %* * %************************************************************************ -} -- | All type constructors occurring in the type; looking through type -- synonyms, but not newtypes. -- When it finds a Class, it returns the class TyCon. tyConsOfType :: Type -> UniqSet TyCon tyConsOfType ty = go ty where go :: Type -> UniqSet TyCon -- The UniqSet does duplicate elim go ty | Just ty' <- coreView ty = go ty' go (TyVarTy {}) = emptyUniqSet go (LitTy {}) = emptyUniqSet go (TyConApp tc tys) = go_tc tc `unionUniqSets` go_s tys go (AppTy a b) = go a `unionUniqSets` go b go (FunTy _ a b) = go a `unionUniqSets` go b `unionUniqSets` go_tc funTyCon go (ForAllTy (Bndr tv _) ty) = go ty `unionUniqSets` go (varType tv) go (CastTy ty co) = go ty `unionUniqSets` go_co co go (CoercionTy co) = go_co co go_co (Refl ty) = go ty go_co (GRefl _ ty mco) = go ty `unionUniqSets` go_mco mco go_co (TyConAppCo _ tc args) = go_tc tc `unionUniqSets` go_cos args go_co (AppCo co arg) = go_co co `unionUniqSets` go_co arg go_co (ForAllCo _ kind_co co) = go_co kind_co `unionUniqSets` go_co co go_co (FunCo _ co1 co2) = go_co co1 `unionUniqSets` go_co co2 go_co (AxiomInstCo ax _ args) = go_ax ax `unionUniqSets` go_cos args go_co (UnivCo p _ t1 t2) = go_prov p `unionUniqSets` go t1 `unionUniqSets` go t2 go_co (CoVarCo {}) = emptyUniqSet go_co (HoleCo {}) = emptyUniqSet go_co (SymCo co) = go_co co go_co (TransCo co1 co2) = go_co co1 `unionUniqSets` go_co co2 go_co (NthCo _ _ co) = go_co co go_co (LRCo _ co) = go_co co go_co (InstCo co arg) = go_co co `unionUniqSets` go_co arg go_co (KindCo co) = go_co co go_co (SubCo co) = go_co co go_co (AxiomRuleCo _ cs) = go_cos cs go_mco MRefl = emptyUniqSet go_mco (MCo co) = go_co co go_prov UnsafeCoerceProv = emptyUniqSet go_prov (PhantomProv co) = go_co co go_prov (ProofIrrelProv co) = go_co co go_prov (PluginProv _) = emptyUniqSet -- this last case can happen from the tyConsOfType used from -- checkTauTvUpdate go_s tys = foldr (unionUniqSets . go) emptyUniqSet tys go_cos cos = foldr (unionUniqSets . go_co) emptyUniqSet cos go_tc tc = unitUniqSet tc go_ax ax = go_tc $ coAxiomTyCon ax -- | Find the result 'Kind' of a type synonym, -- after applying it to its 'arity' number of type variables -- Actually this function works fine on data types too, -- but they'd always return '*', so we never need to ask synTyConResKind :: TyCon -> Kind synTyConResKind tycon = piResultTys (tyConKind tycon) (mkTyVarTys (tyConTyVars tycon)) -- | Retrieve the free variables in this type, splitting them based -- on whether they are used visibly or invisibly. Invisible ones come -- first. splitVisVarsOfType :: Type -> Pair TyCoVarSet splitVisVarsOfType orig_ty = Pair invis_vars vis_vars where Pair invis_vars1 vis_vars = go orig_ty invis_vars = invis_vars1 `minusVarSet` vis_vars go (TyVarTy tv) = Pair (tyCoVarsOfType $ tyVarKind tv) (unitVarSet tv) go (AppTy t1 t2) = go t1 `mappend` go t2 go (TyConApp tc tys) = go_tc tc tys go (FunTy _ t1 t2) = go t1 `mappend` go t2 go (ForAllTy (Bndr tv _) ty) = ((`delVarSet` tv) <$> go ty) `mappend` (invisible (tyCoVarsOfType $ varType tv)) go (LitTy {}) = mempty go (CastTy ty co) = go ty `mappend` invisible (tyCoVarsOfCo co) go (CoercionTy co) = invisible $ tyCoVarsOfCo co invisible vs = Pair vs emptyVarSet go_tc tc tys = let (invis, vis) = partitionInvisibleTypes tc tys in invisible (tyCoVarsOfTypes invis) `mappend` foldMap go vis splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet splitVisVarsOfTypes = foldMap splitVisVarsOfType modifyJoinResTy :: Int -- Number of binders to skip -> (Type -> Type) -- Function to apply to result type -> Type -- Type of join point -> Type -- New type -- INVARIANT: If any of the first n binders are foralls, those tyvars cannot -- appear in the original result type. See isValidJoinPointType. modifyJoinResTy orig_ar f orig_ty = go orig_ar orig_ty where go 0 ty = f ty go n ty | Just (arg_bndr, res_ty) <- splitPiTy_maybe ty = mkPiTy arg_bndr (go (n-1) res_ty) | otherwise = pprPanic "modifyJoinResTy" (ppr orig_ar <+> ppr orig_ty) setJoinResTy :: Int -- Number of binders to skip -> Type -- New result type -> Type -- Type of join point -> Type -- New type -- INVARIANT: Same as for modifyJoinResTy setJoinResTy ar new_res_ty ty = modifyJoinResTy ar (const new_res_ty) ty {- ************************************************************************ * * Functions over Kinds * * ************************************************************************ Note [Kind Constraint and kind Type] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The kind Constraint is the kind of classes and other type constraints. The special thing about types of kind Constraint is that * They are displayed with double arrow: f :: Ord a => a -> a * They are implicitly instantiated at call sites; so the type inference engine inserts an extra argument of type (Ord a) at every call site to f. However, once type inference is over, there is *no* distinction between Constraint and Type. Indeed we can have coercions between the two. Consider class C a where op :: a -> a For this single-method class we may generate a newtype, which in turn generates an axiom witnessing C a ~ (a -> a) so on the left we have Constraint, and on the right we have Type. See #7451. Bottom line: although 'Type' and 'Constraint' are distinct TyCons, with distinct uniques, they are treated as equal at all times except during type inference. -} isConstraintKindCon :: TyCon -> Bool isConstraintKindCon tc = tyConUnique tc == constraintKindTyConKey -- | Tests whether the given kind (which should look like @TYPE x@) -- is something other than a constructor tree (that is, constructors at every node). -- E.g. True of TYPE k, TYPE (F Int) -- False of TYPE 'LiftedRep isKindLevPoly :: Kind -> Bool isKindLevPoly k = ASSERT2( isLiftedTypeKind k || _is_type, ppr k ) -- the isLiftedTypeKind check is necessary b/c of Constraint go k where go ty | Just ty' <- coreView ty = go ty' go TyVarTy{} = True go AppTy{} = True -- it can't be a TyConApp go (TyConApp tc tys) = isFamilyTyCon tc || any go tys go ForAllTy{} = True go (FunTy _ t1 t2) = go t1 || go t2 go LitTy{} = False go CastTy{} = True go CoercionTy{} = True _is_type = classifiesTypeWithValues k ----------------------------------------- -- Subkinding -- The tc variants are used during type-checking, where ConstraintKind -- is distinct from all other kinds -- After type-checking (in core), Constraint and liftedTypeKind are -- indistinguishable -- | Does this classify a type allowed to have values? Responds True to things -- like *, #, TYPE Lifted, TYPE v, Constraint. classifiesTypeWithValues :: Kind -> Bool -- ^ True of any sub-kind of OpenTypeKind classifiesTypeWithValues k = isJust (kindRep_maybe k) {- %************************************************************************ %* * Pretty-printing %* * %************************************************************************ Most pretty-printing is either in TyCoRep or IfaceType. -} -- | Does a 'TyCon' (that is applied to some number of arguments) need to be -- ascribed with an explicit kind signature to resolve ambiguity if rendered as -- a source-syntax type? -- (See @Note [When does a tycon application need an explicit kind signature?]@ -- for a full explanation of what this function checks for.) tyConAppNeedsKindSig :: Bool -- ^ Should specified binders count towards injective positions in -- the kind of the TyCon? (If you're using visible kind -- applications, then you want True here. -> TyCon -> Int -- ^ The number of args the 'TyCon' is applied to. -> Bool -- ^ Does @T t_1 ... t_n@ need a kind signature? (Where @n@ is the -- number of arguments) tyConAppNeedsKindSig spec_inj_pos tc n_args | LT <- listLengthCmp tc_binders n_args = False | otherwise = let (dropped_binders, remaining_binders) = splitAt n_args tc_binders result_kind = mkTyConKind remaining_binders tc_res_kind result_vars = tyCoVarsOfType result_kind dropped_vars = fvVarSet $ mapUnionFV injective_vars_of_binder dropped_binders in not (subVarSet result_vars dropped_vars) where tc_binders = tyConBinders tc tc_res_kind = tyConResKind tc -- Returns the variables that would be fixed by knowing a TyConBinder. See -- Note [When does a tycon application need an explicit kind signature?] -- for a more detailed explanation of what this function does. injective_vars_of_binder :: TyConBinder -> FV injective_vars_of_binder (Bndr tv vis) = case vis of AnonTCB VisArg -> injectiveVarsOfType False -- conservative choice (varType tv) NamedTCB argf | source_of_injectivity argf -> unitFV tv `unionFV` injectiveVarsOfType False (varType tv) _ -> emptyFV source_of_injectivity Required = True source_of_injectivity Specified = spec_inj_pos source_of_injectivity Inferred = False {- Note [When does a tycon application need an explicit kind signature?] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ There are a couple of places in GHC where we convert Core Types into forms that more closely resemble user-written syntax. These include: 1. Template Haskell Type reification (see, for instance, TcSplice.reify_tc_app) 2. Converting Types to LHsTypes (in GHC.Hs.Utils.typeToLHsType, or in Haddock) This conversion presents a challenge: how do we ensure that the resulting type has enough kind information so as not to be ambiguous? To better motivate this question, consider the following Core type: -- Foo :: Type -> Type type Foo = Proxy Type There is nothing ambiguous about the RHS of Foo in Core. But if we were to, say, reify it into a TH Type, then it's tempting to just drop the invisible Type argument and simply return `Proxy`. But now we've lost crucial kind information: we don't know if we're dealing with `Proxy Type` or `Proxy Bool` or `Proxy Int` or something else! We've inadvertently introduced ambiguity. Unlike in other situations in GHC, we can't just turn on -fprint-explicit-kinds, as we need to produce something which has the same structure as a source-syntax type. Moreover, we can't rely on visible kind application, since the first kind argument to Proxy is inferred, not specified. Our solution is to annotate certain tycons with their kinds whenever they appear in applied form in order to resolve the ambiguity. For instance, we would reify the RHS of Foo like so: type Foo = (Proxy :: Type -> Type) We need to devise an algorithm that determines precisely which tycons need these explicit kind signatures. We certainly don't want to annotate _every_ tycon with a kind signature, or else we might end up with horribly bloated types like the following: (Either :: Type -> Type -> Type) (Int :: Type) (Char :: Type) We only want to annotate tycons that absolutely require kind signatures in order to resolve some sort of ambiguity, and nothing more. Suppose we have a tycon application (T ty_1 ... ty_n). Why might this type require a kind signature? It might require it when we need to fill in any of T's omitted arguments. By "omitted argument", we mean one that is dropped when reifying ty_1 ... ty_n. Sometimes, the omitted arguments are inferred and specified arguments (e.g., TH reification in TcSplice), and sometimes the omitted arguments are only the inferred ones (e.g., in GHC.Hs.Utils.typeToLHsType, which reifies specified arguments through visible kind application). Regardless, the key idea is that _some_ arguments are going to be omitted after reification, and the only mechanism we have at our disposal for filling them in is through explicit kind signatures. What do we mean by "fill in"? Let's consider this small example: T :: forall {k}. Type -> (k -> Type) -> k Moreover, we have this application of T: T @{j} Int aty When we reify this type, we omit the inferred argument @{j}. Is it fixed by the other (non-inferred) arguments? Yes! If we know the kind of (aty :: blah), then we'll generate an equality constraint (kappa -> Type) and, assuming we can solve it, that will fix `kappa`. (Here, `kappa` is the unification variable that we instantiate `k` with.) Therefore, for any application of a tycon T to some arguments, the Question We Must Answer is: * Given the first n arguments of T, do the kinds of the non-omitted arguments fill in the omitted arguments? (This is still a bit hand-wavey, but we'll refine this question incrementally as we explain more of the machinery underlying this process.) Answering this question is precisely the role that the `injectiveVarsOfType` and `injective_vars_of_binder` functions exist to serve. If an omitted argument `a` appears in the set returned by `injectiveVarsOfType ty`, then knowing `ty` determines (i.e., fills in) `a`. (More on `injective_vars_of_binder` in a bit.) More formally, if `a` is in `injectiveVarsOfType ty` and S1(ty) ~ S2(ty), then S1(a) ~ S2(a), where S1 and S2 are arbitrary substitutions. For example, is `F` is a non-injective type family, then injectiveVarsOfType(Either c (Maybe (a, F b c))) = {a, c} Now that we know what this function does, here is a second attempt at the Question We Must Answer: * Given the first n arguments of T (ty_1 ... ty_n), consider the binders of T that are instantiated by non-omitted arguments. Do the injective variables of these binders fill in the remainder of T's kind? Alright, we're getting closer. Next, we need to clarify what the injective variables of a tycon binder are. This the role that the `injective_vars_of_binder` function serves. Here is what this function does for each form of tycon binder: * Anonymous binders are injective positions. For example, in the promoted data constructor '(:): '(:) :: forall a. a -> [a] -> [a] The second and third tyvar binders (of kinds `a` and `[a]`) are both anonymous, so if we had '(:) 'True '[], then the kinds of 'True and '[] would contribute to the kind of '(:) 'True '[]. Therefore, injective_vars_of_binder(_ :: a) = injectiveVarsOfType(a) = {a}. (Similarly, injective_vars_of_binder(_ :: [a]) = {a}.) * Named binders: - Inferred binders are never injective positions. For example, in this data type: data Proxy a Proxy :: forall {k}. k -> Type If we had Proxy 'True, then the kind of 'True would not contribute to the kind of Proxy 'True. Therefore, injective_vars_of_binder(forall {k}. ...) = {}. - Required binders are injective positions. For example, in this data type: data Wurble k (a :: k) :: k Wurble :: forall k -> k -> k The first tyvar binder (of kind `forall k`) has required visibility, so if we had Wurble (Maybe a) Nothing, then the kind of Maybe a would contribute to the kind of Wurble (Maybe a) Nothing. Hence, injective_vars_of_binder(forall a -> ...) = {a}. - Specified binders /might/ be injective positions, depending on how you approach things. Continuing the '(:) example: '(:) :: forall a. a -> [a] -> [a] Normally, the (forall a. ...) tyvar binder wouldn't contribute to the kind of '(:) 'True '[], since it's not explicitly instantiated by the user. But if visible kind application is enabled, then this is possible, since the user can write '(:) @Bool 'True '[]. (In that case, injective_vars_of_binder(forall a. ...) = {a}.) There are some situations where using visible kind application is appropriate (e.g., GHC.Hs.Utils.typeToLHsType) and others where it is not (e.g., TH reification), so the `injective_vars_of_binder` function is parametrized by a Bool which decides if specified binders should be counted towards injective positions or not. Now that we've defined injective_vars_of_binder, we can refine the Question We Must Answer once more: * Given the first n arguments of T (ty_1 ... ty_n), consider the binders of T that are instantiated by non-omitted arguments. For each such binder b_i, take the union of all injective_vars_of_binder(b_i). Is this set a superset of the free variables of the remainder of T's kind? If the answer to this question is "no", then (T ty_1 ... ty_n) needs an explicit kind signature, since T's kind has kind variables leftover that aren't fixed by the non-omitted arguments. One last sticking point: what does "the remainder of T's kind" mean? You might be tempted to think that it corresponds to all of the arguments in the kind of T that would normally be instantiated by omitted arguments. But this isn't quite right, strictly speaking. Consider the following (silly) example: S :: forall {k}. Type -> Type And suppose we have this application of S: S Int Bool The Int argument would be omitted, and injective_vars_of_binder(_ :: Type) = {}. This is not a superset of {k}, which might suggest that (S Bool) needs an explicit kind signature. But (S Bool :: Type) doesn't actually fix `k`! This is because the kind signature only affects the /result/ of the application, not all of the individual arguments. So adding a kind signature here won't make a difference. Therefore, the fourth (and final) iteration of the Question We Must Answer is: * Given the first n arguments of T (ty_1 ... ty_n), consider the binders of T that are instantiated by non-omitted arguments. For each such binder b_i, take the union of all injective_vars_of_binder(b_i). Is this set a superset of the free variables of the kind of (T ty_1 ... ty_n)? Phew, that was a lot of work! How can be sure that this is correct? That is, how can we be sure that in the event that we leave off a kind annotation, that one could infer the kind of the tycon application from its arguments? It's essentially a proof by induction: if we can infer the kinds of every subtree of a type, then the whole tycon application will have an inferrable kind--unless, of course, the remainder of the tycon application's kind has uninstantiated kind variables. What happens if T is oversaturated? That is, if T's kind has fewer than n arguments, in the case that the concrete application instantiates a result kind variable with an arrow kind? If we run out of arguments, we do not attach a kind annotation. This should be a rare case, indeed. Here is an example: data T1 :: k1 -> k2 -> * data T2 :: k1 -> k2 -> * type family G (a :: k) :: k type instance G T1 = T2 type instance F Char = (G T1 Bool :: (* -> *) -> *) -- F from above Here G's kind is (forall k. k -> k), and the desugared RHS of that last instance of F is (G (* -> (* -> *) -> *) (T1 * (* -> *)) Bool). According to the algorithm above, there are 3 arguments to G so we should peel off 3 arguments in G's kind. But G's kind has only two arguments. This is the rare special case, and we choose not to annotate the application of G with a kind signature. After all, we needn't do this, since that instance would be reified as: type instance F Char = G (T1 :: * -> (* -> *) -> *) Bool So the kind of G isn't ambiguous anymore due to the explicit kind annotation on its argument. See #8953 and test th/T8953. -}