-- as used in System FC. See 'CoreSyn.Expr' for
-- more on System FC and how coercions fit into it.
--
--- Coercions are represented as types, and their kinds tell what types the
--- coercion works on. The coercion kind constructor is a special TyCon that
--- must always be saturated, like so:
---
--- > typeKind (symCoercion type) :: TyConApp CoTyCon{...} [type, type]
module Coercion (
-- * Main data type
- Coercion, Kind,
- typeKind,
+ Coercion(..), Var, CoVar,
-- ** Deconstructing Kinds
kindFunResult, kindAppResult, synTyConResKind,
-- ** Predicates on Kinds
isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
- isCoSuperKind, isSuperKind, isCoercionKind,
+ isSuperKind, isCoercionKind,
mkArrowKind, mkArrowKinds,
isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
isSubKindCon,
- mkCoKind, mkCoPredTy, coVarKind, coVarKind_maybe,
- coercionKind, coercionKinds, isIdentityCoercion,
-
- -- ** Equality predicates
- isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
-
- -- ** Coercion transformations
- mkCoercion,
- mkSymCoercion, mkTransCoercion,
- mkLeftCoercion, mkRightCoercion,
- mkInstCoercion, mkAppCoercion, mkTyConCoercion, mkFunCoercion,
- mkForAllCoercion, mkInstsCoercion, mkUnsafeCoercion,
- mkNewTypeCoercion, mkFamInstCoercion, mkAppsCoercion,
- mkCsel1Coercion, mkCsel2Coercion, mkCselRCoercion,
-
- mkCoVarCoercion,
-
+ mkCoType, coVarKind, coVarKind_maybe,
+ coercionType, coercionKind, coercionKinds, isReflCo,
- unsafeCoercionTyCon, symCoercionTyCon,
- transCoercionTyCon, leftCoercionTyCon,
- rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn
- csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon,
+ -- ** Constructing coercions
+ mkReflCo, mkCoVarCo,
+ mkAxInstCo, mkPiCo, mkPiCos,
+ mkSymCo, mkTransCo, mkNthCo,
+ mkInstCo, mkAppCo, mkTyConAppCo, mkFunCo,
+ mkForAllCo, mkUnsafeCo,
+ mkNewTypeCo, mkFamInstCo,
+ mkPredCo,
-- ** Decomposition
- decompLR_maybe, decompCsel_maybe, decompInst_maybe,
splitCoPredTy_maybe,
splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo,
-
+ getCoVar_maybe,
+
+ splitTyConAppCo_maybe,
+ splitAppCo_maybe,
+ splitForAllCo_maybe,
+
+ -- ** Coercion variables
+ mkCoVar, isCoVar, isCoVarType, coVarName, setCoVarName, setCoVarUnique,
+
+ -- ** Free variables
+ tyCoVarsOfCo, tyCoVarsOfCos, coVarsOfCo, coercionSize,
+
+ -- ** Substitution
+ CvSubstEnv, emptyCvSubstEnv,
+ CvSubst(..), emptyCvSubst, Coercion.lookupTyVar, lookupCoVar,
+ isEmptyCvSubst, zapCvSubstEnv, getCvInScope,
+ substCo, substCos, substCoVar, substCoVars,
+ substCoWithTy, substCoWithTys,
+ cvTvSubst, tvCvSubst, zipOpenCvSubst,
+ substTy, extendTvSubst,
+ substTyVarBndr, substCoVarBndr,
+
+ -- ** Lifting
+ liftCoMatch, liftCoSubst, liftCoSubstTyVar, liftCoSubstWith,
+
-- ** Comparison
coreEqCoercion, coreEqCoercion2,
- -- * CoercionI
- CoercionI(..),
- isIdentityCoI,
- mkSymCoI, mkTransCoI,
- mkTyConAppCoI, mkAppTyCoI, mkFunTyCoI,
- mkForAllTyCoI,
- fromCoI,
- mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI
+ -- ** Forcing evaluation of coercions
+ seqCo,
+
+ -- * Pretty-printing
+ pprCo, pprParendCo,
+ -- * Other
+ applyCo, coVarPred
+
) where
#include "HsVersions.h"
+import Unify ( MatchEnv(..), ruleMatchTyX, matchList )
import TypeRep
-import Type
+import qualified Type
+import Type hiding( substTy, substTyVarBndr, extendTvSubst )
+import Kind
import TyCon
-import Class
import Var
import VarEnv
import VarSet
-import Name
-import PrelNames
+import UniqFM ( minusUFM )
+import Maybes ( orElse )
+import Name ( Name, NamedThing(..), nameUnique )
+import OccName ( isSymOcc )
import Util
import BasicTypes
import Outputable
+import Unique
+import Pair
+import PrelNames( funTyConKey )
+import Control.Applicative
+import Data.Traversable (traverse, sequenceA)
+import Control.Arrow (second)
import FastString
+
+import qualified Data.Data as Data hiding ( TyCon )
\end{code}
%************************************************************************
%* *
- Functions over Kinds
+ Coercions
%* *
%************************************************************************
\begin{code}
--- | Essentially 'funResultTy' on kinds
-kindFunResult :: Kind -> Kind
-kindFunResult k = funResultTy k
-
-kindAppResult :: Kind -> [arg] -> Kind
-kindAppResult k [] = k
-kindAppResult k (_:as) = kindAppResult (kindFunResult k) as
-
--- | Essentially 'splitFunTys' on kinds
-splitKindFunTys :: Kind -> ([Kind],Kind)
-splitKindFunTys k = splitFunTys k
-
-splitKindFunTy_maybe :: Kind -> Maybe (Kind,Kind)
-splitKindFunTy_maybe = splitFunTy_maybe
-
--- | Essentially 'splitFunTysN' on kinds
-splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
-splitKindFunTysN k = splitFunTysN k
-
--- | 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 = kindAppResult (tyConKind tycon) (tyConTyVars tycon)
-
--- | See "Type#kind_subtyping" for details of the distinction between these 'Kind's
-isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
-isOpenTypeKindCon, isUbxTupleKindCon, isArgTypeKindCon,
- isUnliftedTypeKindCon, isSubArgTypeKindCon :: TyCon -> Bool
-
-isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
-
-isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
-isOpenTypeKind _ = False
-
-isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
-
-isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
-isUbxTupleKind _ = False
-
-isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
-
-isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
-isArgTypeKind _ = False
-
-isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
-
-isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
-isUnliftedTypeKind _ = False
-
-isSubOpenTypeKind :: Kind -> Bool
--- ^ True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
-isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
- ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
- False
-isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
-isSubOpenTypeKind other = ASSERT( isKind other ) False
- -- This is a conservative answer
- -- It matters in the call to isSubKind in
- -- checkExpectedKind.
-
-isSubArgTypeKindCon kc
- | isUnliftedTypeKindCon kc = True
- | isLiftedTypeKindCon kc = True
- | isArgTypeKindCon kc = True
- | otherwise = False
-
-isSubArgTypeKind :: Kind -> Bool
--- ^ True of any sub-kind of ArgTypeKind
-isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
-isSubArgTypeKind _ = False
-
--- | Is this a super-kind (i.e. a type-of-kinds)?
-isSuperKind :: Type -> Bool
-isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
-isSuperKind _ = False
-
--- | Is this a kind (i.e. a type-of-types)?
-isKind :: Kind -> Bool
-isKind k = isSuperKind (typeKind k)
-
-isSubKind :: Kind -> Kind -> Bool
--- ^ @k1 \`isSubKind\` k2@ checks that @k1@ <: @k2@
-isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
-isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
-isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
- = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
-isSubKind _ _ = False
-
-eqKind :: Kind -> Kind -> Bool
-eqKind = tcEqType
-
-isSubKindCon :: TyCon -> TyCon -> Bool
--- ^ @kc1 \`isSubKindCon\` kc2@ checks that @kc1@ <: @kc2@
-isSubKindCon kc1 kc2
- | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
- | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
- | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
- | isOpenTypeKindCon kc2 = True
- -- we already know kc1 is not a fun, its a TyCon
- | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
- | otherwise = False
-
-defaultKind :: Kind -> Kind
--- ^ Used when generalising: default kind ? and ?? to *. See "Type#kind_subtyping" for more
--- information on what that means
-
--- When we generalise, we make generic type variables whose kind is
--- simple (* or *->* etc). So generic type variables (other than
--- built-in constants like 'error') always have simple kinds. This is important;
--- consider
--- f x = True
--- We want f to get type
--- f :: forall (a::*). a -> Bool
--- Not
--- f :: forall (a::??). a -> Bool
--- because that would allow a call like (f 3#) as well as (f True),
---and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
-defaultKind k
- | isSubOpenTypeKind k = liftedTypeKind
- | isSubArgTypeKind k = liftedTypeKind
- | otherwise = k
+-- | A 'Coercion' is concrete evidence of the equality/convertibility
+-- of two types.
+data Coercion
+ -- These ones mirror the shape of types
+ = Refl Type -- See Note [Refl invariant]
+ -- Invariant: applications of (Refl T) to a bunch of identity coercions
+ -- always show up as Refl.
+ -- For example (Refl T) (Refl a) (Refl b) shows up as (Refl (T a b)).
+
+ -- Applications of (Refl T) to some coercions, at least one of
+ -- which is NOT the identity, show up as TyConAppCo.
+ -- (They may not be fully saturated however.)
+ -- ConAppCo coercions (like all coercions other than Refl)
+ -- are NEVER the identity.
+
+ -- These ones simply lift the correspondingly-named
+ -- Type constructors into Coercions
+ | TyConAppCo TyCon [Coercion] -- lift TyConApp
+ -- The TyCon is never a synonym;
+ -- we expand synonyms eagerly
+
+ | AppCo Coercion Coercion -- lift AppTy
+
+ -- See Note [Forall coercions]
+ | ForAllCo TyVar Coercion -- forall a. g
+ | PredCo (Pred Coercion) -- (g1~g2) etc
+
+ -- These are special
+ | CoVarCo CoVar
+ | AxiomInstCo CoAxiom [Coercion] -- The coercion arguments always *precisely*
+ -- saturate arity of CoAxiom.
+ -- See [Coercion axioms applied to coercions]
+ | UnsafeCo Type Type
+ | SymCo Coercion
+ | TransCo Coercion Coercion
+
+ -- These are destructors
+ | NthCo Int Coercion -- Zero-indexed
+ | InstCo Coercion Type
+ deriving (Data.Data, Data.Typeable)
\end{code}
+Note [Refl invariant]
+~~~~~~~~~~~~~~~~~~~~~
+Coercions have the following invariant
+ Refl is always lifted as far as possible.
+
+You might think that a consequencs is:
+ Every identity coercions has Refl at the root
+
+But that's not quite true because of coercion variables. Consider
+ g where g :: Int~Int
+ Left h where h :: Maybe Int ~ Maybe Int
+etc. So the consequence is only true of coercions that
+have no coercion variables.
+
+Note [Coercion axioms applied to coercions]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+The reason coercion axioms can be applied to coercions and not just
+types is to allow for better optimization. There are some cases where
+we need to be able to "push transitivity inside" an axiom in order to
+expose further opportunities for optimization.
+
+For example, suppose we have
+
+ C a : t[a] ~ F a
+ g : b ~ c
+
+and we want to optimize
+
+ sym (C b) ; t[g] ; C c
+
+which has the kind
+
+ F b ~ F c
+
+(stopping through t[b] and t[c] along the way).
+
+We'd like to optimize this to just F g -- but how? The key is
+that we need to allow axioms to be instantiated by *coercions*,
+not just by types. Then we can (in certain cases) push
+transitivity inside the axiom instantiations, and then react
+opposite-polarity instantiations of the same axiom. In this
+case, e.g., we match t[g] against the LHS of (C c)'s kind, to
+obtain the substitution a |-> g (note this operation is sort
+of the dual of lifting!) and hence end up with
+
+ C g : t[b] ~ F c
+
+which indeed has the same kind as t[g] ; C c.
+
+Now we have
+
+ sym (C b) ; C g
+
+which can be optimized to F g.
+
+
+Note [Forall coercions]
+~~~~~~~~~~~~~~~~~~~~~~~
+Constructing coercions between forall-types can be a bit tricky.
+Currently, the situation is as follows:
+
+ ForAllCo TyVar Coercion
+
+represents a coercion between polymorphic types, with the rule
+
+ v : k g : t1 ~ t2
+ ----------------------------------------------
+ ForAllCo v g : (all v:k . t1) ~ (all v:k . t2)
+
+Note that it's only necessary to coerce between polymorphic types
+where the type variables have identical kinds, because equality on
+kinds is trivial.
+
+ ForAllCoCo Coercion Coercion Coercion
+
+represents a coercion between types abstracted over equality proofs,
+which we might more suggestively write as
+
+ ForAllCoCo (_:Coercion~Coercion) Coercion
+
+The rule is
+
+ g1 : t1 ~ t1' g2 : t2 ~ t2' g3 : t3 ~ t3'
+ ------------------------------------------------------------------
+ ForAllCoCo g1 g2 g3 : ( (t1 ~ t2) => t3 ) ~ ( (t1' ~ t2') => t3' )
+
+There are several things to note. First, we don't need to bind a
+variable, since coercion variables do not appear in types. Second,
+note that here we DO need to convert between "kinds" (the types of the
+required coercions).
+
+In the future, if we collapse the type and kind levels and add a bit
+more dependency, we will need something like
+
+ | ForAllCo TyVar Coercion Coercion
+ | ForAllCoCo CoVar Coercion Coercion Coercion
+
+The addition of the extra coercion in the first case handles
+converting between possibly different kinds; the addition of a CoVar
+in the second case is needed since now types may mention coercion
+variables (in casts).
+
+
%************************************************************************
%* *
- Coercions
+\subsection{Coercion variables}
%* *
%************************************************************************
+\begin{code}
+coVarName :: CoVar -> Name
+coVarName = varName
+
+setCoVarUnique :: CoVar -> Unique -> CoVar
+setCoVarUnique = setVarUnique
+
+setCoVarName :: CoVar -> Name -> CoVar
+setCoVarName = setVarName
+
+isCoVar :: Var -> Bool
+isCoVar v = isCoVarType (varType v)
+
+isCoVarType :: Type -> Bool
+isCoVarType = isEqPredTy
+\end{code}
+
\begin{code}
--- | A 'Coercion' represents a 'Type' something should be coerced to.
-type Coercion = Type
+tyCoVarsOfCo :: Coercion -> VarSet
+-- Extracts type and coercion variables from a coercion
+tyCoVarsOfCo (Refl ty) = tyVarsOfType ty
+tyCoVarsOfCo (TyConAppCo _ cos) = tyCoVarsOfCos cos
+tyCoVarsOfCo (AppCo co1 co2) = tyCoVarsOfCo co1 `unionVarSet` tyCoVarsOfCo co2
+tyCoVarsOfCo (ForAllCo tv co) = tyCoVarsOfCo co `delVarSet` tv
+tyCoVarsOfCo (PredCo pred) = varsOfPred tyCoVarsOfCo pred
+tyCoVarsOfCo (CoVarCo v) = unitVarSet v
+tyCoVarsOfCo (AxiomInstCo _ cos) = tyCoVarsOfCos cos
+tyCoVarsOfCo (UnsafeCo ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
+tyCoVarsOfCo (SymCo co) = tyCoVarsOfCo co
+tyCoVarsOfCo (TransCo co1 co2) = tyCoVarsOfCo co1 `unionVarSet` tyCoVarsOfCo co2
+tyCoVarsOfCo (NthCo _ co) = tyCoVarsOfCo co
+tyCoVarsOfCo (InstCo co ty) = tyCoVarsOfCo co `unionVarSet` tyVarsOfType ty
+
+tyCoVarsOfCos :: [Coercion] -> VarSet
+tyCoVarsOfCos cos = foldr (unionVarSet . tyCoVarsOfCo) emptyVarSet cos
+
+coVarsOfCo :: Coercion -> VarSet
+-- Extract *coerction* variables only. Tiresome to repeat the code, but easy.
+coVarsOfCo (Refl _) = emptyVarSet
+coVarsOfCo (TyConAppCo _ cos) = coVarsOfCos cos
+coVarsOfCo (AppCo co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
+coVarsOfCo (ForAllCo _ co) = coVarsOfCo co
+coVarsOfCo (PredCo pred) = varsOfPred coVarsOfCo pred
+coVarsOfCo (CoVarCo v) = unitVarSet v
+coVarsOfCo (AxiomInstCo _ cos) = coVarsOfCos cos
+coVarsOfCo (UnsafeCo _ _) = emptyVarSet
+coVarsOfCo (SymCo co) = coVarsOfCo co
+coVarsOfCo (TransCo co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
+coVarsOfCo (NthCo _ co) = coVarsOfCo co
+coVarsOfCo (InstCo co _) = coVarsOfCo co
+
+coVarsOfCos :: [Coercion] -> VarSet
+coVarsOfCos cos = foldr (unionVarSet . coVarsOfCo) emptyVarSet cos
+
+coercionSize :: Coercion -> Int
+coercionSize (Refl ty) = typeSize ty
+coercionSize (TyConAppCo _ cos) = 1 + sum (map coercionSize cos)
+coercionSize (AppCo co1 co2) = coercionSize co1 + coercionSize co2
+coercionSize (ForAllCo _ co) = 1 + coercionSize co
+coercionSize (PredCo pred) = predSize coercionSize pred
+coercionSize (CoVarCo _) = 1
+coercionSize (AxiomInstCo _ cos) = 1 + sum (map coercionSize cos)
+coercionSize (UnsafeCo ty1 ty2) = typeSize ty1 + typeSize ty2
+coercionSize (SymCo co) = 1 + coercionSize co
+coercionSize (TransCo co1 co2) = 1 + coercionSize co1 + coercionSize co2
+coercionSize (NthCo _ co) = 1 + coercionSize co
+coercionSize (InstCo co ty) = 1 + coercionSize co + typeSize ty
+\end{code}
+
+%************************************************************************
+%* *
+ Pretty-printing coercions
+%* *
+%************************************************************************
+
+@pprCo@ is the standard @Coercion@ printer; the overloaded @ppr@
+function is defined to use this. @pprParendCo@ is the same, except it
+puts parens around the type, except for the atomic cases.
+@pprParendCo@ works just by setting the initial context precedence
+very high.
+
+\begin{code}
+instance Outputable Coercion where
+ ppr = pprCo
+
+pprCo, pprParendCo :: Coercion -> SDoc
+pprCo co = ppr_co TopPrec co
+pprParendCo co = ppr_co TyConPrec co
+
+ppr_co :: Prec -> Coercion -> SDoc
+ppr_co _ (Refl ty) = angles (ppr ty)
+
+ppr_co p co@(TyConAppCo tc cos)
+ | tc `hasKey` funTyConKey = ppr_fun_co p co
+ | otherwise = maybeParen p TyConPrec $
+ pprTcApp p ppr_co tc cos
+
+ppr_co p (AppCo co1 co2) = maybeParen p TyConPrec $
+ pprCo co1 <+> ppr_co TyConPrec co2
+
+ppr_co p co@(ForAllCo {}) = ppr_forall_co p co
+ppr_co _ (PredCo pred) = pprPred ppr_co pred
+
+ppr_co _ (CoVarCo cv)
+ | isSymOcc (getOccName cv) = parens (ppr cv)
+ | otherwise = ppr cv
+
+ppr_co p (AxiomInstCo con cos) = pprTypeNameApp p ppr_co (getName con) cos
+
+
+ppr_co p (TransCo co1 co2) = maybeParen p FunPrec $
+ ppr_co FunPrec co1
+ <+> ptext (sLit ";")
+ <+> ppr_co FunPrec co2
+ppr_co p (InstCo co ty) = maybeParen p TyConPrec $
+ pprParendCo co <> ptext (sLit "@") <> pprType ty
+
+ppr_co p (UnsafeCo ty1 ty2) = pprPrefixApp p (ptext (sLit "UnsafeCo")) [pprParendType ty1, pprParendType ty2]
+ppr_co p (SymCo co) = pprPrefixApp p (ptext (sLit "Sym")) [pprParendCo co]
+ppr_co p (NthCo n co) = pprPrefixApp p (ptext (sLit "Nth:") <+> int n) [pprParendCo co]
+
+
+angles :: SDoc -> SDoc
+angles p = char '<' <> p <> char '>'
+
+ppr_fun_co :: Prec -> Coercion -> SDoc
+ppr_fun_co p co = pprArrowChain p (split co)
+ where
+ split (TyConAppCo f [arg,res])
+ | f `hasKey` funTyConKey
+ = ppr_co FunPrec arg : split res
+ split co = [ppr_co TopPrec co]
+
+ppr_forall_co :: Prec -> Coercion -> SDoc
+ppr_forall_co p ty
+ = maybeParen p FunPrec $
+ sep [pprForAll tvs, pprThetaArrow ppr_co ctxt, ppr_co TopPrec tau]
+ where
+ (tvs, rho) = split1 [] ty
+ (ctxt, tau) = split2 [] rho
+
+ -- We need to be extra careful here as equality constraints will occur as
+ -- type variables with an equality kind. So, while collecting quantified
+ -- variables, we separate the coercion variables out and turn them into
+ -- equality predicates.
+ split1 tvs (ForAllCo tv ty) = split1 (tv:tvs) ty
+ split1 tvs ty = (reverse tvs, ty)
+
+ split2 ps (TyConAppCo tc [PredCo p, co])
+ | tc `hasKey` funTyConKey = split2 (p:ps) co
+ split2 ps co = (reverse ps, co)
+\end{code}
--- | A 'CoercionKind' is always of form @ty1 ~ ty2@ and indicates the
--- types that a 'Coercion' will work on.
-type CoercionKind = Kind
-------------------------------
+%************************************************************************
+%* *
+ Functions over Kinds
+%* *
+%************************************************************************
--- | This breaks a 'Coercion' with 'CoercionKind' @T A B C ~ T D E F@ into
+\begin{code}
+-- | This breaks a 'Coercion' with type @T A B C ~ T D E F@ into
-- a list of 'Coercion's of kinds @A ~ D@, @B ~ E@ and @E ~ F@. Hence:
--
--- > decomposeCo 3 c = [right (left (left c)), right (left c), right c]
+-- > decomposeCo 3 c = [nth 0 c, nth 1 c, nth 2 c]
decomposeCo :: Arity -> Coercion -> [Coercion]
-decomposeCo n co
- = go n co []
- where
- go 0 _ cos = cos
- go n co cos = go (n-1) (mkLeftCoercion co)
- (mkRightCoercion co : cos)
-
+decomposeCo arity co = [mkNthCo n co | n <- [0..(arity-1)] ]
+
+-- | Attempts to obtain the type variable underlying a 'Coercion'
+getCoVar_maybe :: Coercion -> Maybe CoVar
+getCoVar_maybe (CoVarCo cv) = Just cv
+getCoVar_maybe _ = Nothing
+
+-- | Attempts to tease a coercion apart into a type constructor and the application
+-- of a number of coercion arguments to that constructor
+splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion])
+splitTyConAppCo_maybe (Refl ty) = (fmap . second . map) Refl (splitTyConApp_maybe ty)
+splitTyConAppCo_maybe (TyConAppCo tc cos) = Just (tc, cos)
+splitTyConAppCo_maybe _ = Nothing
+
+splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion)
+-- ^ Attempt to take a coercion application apart.
+splitAppCo_maybe (AppCo co1 co2) = Just (co1, co2)
+splitAppCo_maybe (TyConAppCo tc cos)
+ | not (null cos) = Just (mkTyConAppCo tc (init cos), last cos)
+ -- Use mkTyConAppCo to preserve the invariant
+ -- that identity coercions are always represented by Refl
+splitAppCo_maybe (Refl ty)
+ | Just (ty1, ty2) <- splitAppTy_maybe ty = Just (Refl ty1, Refl ty2)
+ | otherwise = Nothing
+splitAppCo_maybe _ = Nothing
+
+splitForAllCo_maybe :: Coercion -> Maybe (TyVar, Coercion)
+splitForAllCo_maybe (ForAllCo tv co) = Just (tv, co)
+splitForAllCo_maybe _ = Nothing
-------------------------------------------------------
-- and some coercion kind stuff
+coVarPred :: CoVar -> PredType
+coVarPred cv
+ = ASSERT( isCoVar cv )
+ case splitPredTy_maybe (varType cv) of
+ Just pred -> pred
+ other -> pprPanic "coVarPred" (ppr cv $$ ppr other)
+
coVarKind :: CoVar -> (Type,Type)
-- c :: t1 ~ t2
coVarKind cv = case coVarKind_maybe cv of
Nothing -> pprPanic "coVarKind" (ppr cv $$ ppr (tyVarKind cv))
coVarKind_maybe :: CoVar -> Maybe (Type,Type)
-coVarKind_maybe cv = splitCoKind_maybe (tyVarKind cv)
+coVarKind_maybe cv = splitEqPredTy_maybe (varType cv)
--- | Take a 'CoercionKind' apart into the two types it relates: see also 'mkCoKind'.
--- Panics if the argument is not a valid 'CoercionKind'
-splitCoKind_maybe :: Kind -> Maybe (Type, Type)
-splitCoKind_maybe co | Just co' <- kindView co = splitCoKind_maybe co'
-splitCoKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)
-splitCoKind_maybe _ = Nothing
-
--- | Makes a 'CoercionKind' from two types: the types whose equality
+-- | Makes a coercion type from two types: the types whose equality
-- is proven by the relevant 'Coercion'
-mkCoKind :: Type -> Type -> CoercionKind
-mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)
-
--- | (mkCoPredTy s t r) produces the type: (s~t) => r
-mkCoPredTy :: Type -> Type -> Type -> Type
-mkCoPredTy s t r = ASSERT( not (co_var `elemVarSet` tyVarsOfType r) )
- ForAllTy co_var r
- where
- co_var = mkWildCoVar (mkCoKind s t)
+mkCoType :: Type -> Type -> Type
+mkCoType ty1 ty2 = PredTy (EqPred ty1 ty2)
splitCoPredTy_maybe :: Type -> Maybe (Type, Type, Type)
splitCoPredTy_maybe ty
| otherwise
= Nothing
--- | Tests whether a type is just a type equality predicate
-isEqPredTy :: Type -> Bool
-isEqPredTy (PredTy pred) = isEqPred pred
-isEqPredTy _ = False
-
--- | Creates a type equality predicate
-mkEqPred :: (Type, Type) -> PredType
-mkEqPred (ty1, ty2) = EqPred ty1 ty2
-
--- | Splits apart a type equality predicate, if the supplied 'PredType' is one.
--- Panics otherwise
-getEqPredTys :: PredType -> (Type,Type)
-getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)
-getEqPredTys other = pprPanic "getEqPredTys" (ppr other)
-
-isIdentityCoercion :: Coercion -> Bool
-isIdentityCoercion co
- = case coercionKind co of
- (t1,t2) -> t1 `coreEqType` t2
+isReflCo :: Coercion -> Bool
+isReflCo (Refl {}) = True
+isReflCo _ = False
+
+isReflCo_maybe :: Coercion -> Maybe Type
+isReflCo_maybe (Refl ty) = Just ty
+isReflCo_maybe _ = Nothing
\end{code}
%************************************************************************
%* *
%************************************************************************
-Coercion kind and type mk's (make saturated TyConApp CoercionTyCon{...} args)
-
\begin{code}
--- | Make a coercion from the specified coercion 'TyCon' and the 'Type' arguments to
--- that coercion. Try to use the @mk*Coercion@ family of functions instead of using this function
--- if possible
-mkCoercion :: TyCon -> [Type] -> Coercion
-mkCoercion coCon args = ASSERT( tyConArity coCon == length args )
- TyConApp coCon args
+mkCoVarCo :: CoVar -> Coercion
+mkCoVarCo cv
+ | ty1 `eqType` ty2 = Refl ty1
+ | otherwise = CoVarCo cv
+ where
+ (ty1, ty2) = ASSERT( isCoVar cv ) coVarKind cv
-mkCoVarCoercion :: CoVar -> Coercion
-mkCoVarCoercion cv = mkTyVarTy cv
+mkReflCo :: Type -> Coercion
+mkReflCo = Refl
--- | Apply a 'Coercion' to another 'Coercion', which is presumably a
--- 'Coercion' constructor of some kind
-mkAppCoercion :: Coercion -> Coercion -> Coercion
-mkAppCoercion co1 co2 = mkAppTy co1 co2
+mkAxInstCo :: CoAxiom -> [Type] -> Coercion
+mkAxInstCo ax tys
+ | arity == n_tys = AxiomInstCo ax rtys
+ | otherwise = ASSERT( arity < n_tys )
+ foldl AppCo (AxiomInstCo ax (take arity rtys))
+ (drop arity rtys)
+ where
+ n_tys = length tys
+ arity = coAxiomArity ax
+ rtys = map Refl tys
+
+-- | Apply a 'Coercion' to another 'Coercion'.
+mkAppCo :: Coercion -> Coercion -> Coercion
+mkAppCo (Refl ty1) (Refl ty2) = Refl (mkAppTy ty1 ty2)
+mkAppCo (Refl (TyConApp tc tys)) co = TyConAppCo tc (map Refl tys ++ [co])
+mkAppCo (TyConAppCo tc cos) co = TyConAppCo tc (cos ++ [co])
+mkAppCo co1 co2 = AppCo co1 co2
+-- Note, mkAppCo is careful to maintain invariants regarding
+-- where Refl constructors appear; see the comments in the definition
+-- of Coercion and the Note [Refl invariant] in types/TypeRep.lhs.
-- | Applies multiple 'Coercion's to another 'Coercion', from left to right.
--- See also 'mkAppCoercion'
-mkAppsCoercion :: Coercion -> [Coercion] -> Coercion
-mkAppsCoercion co1 tys = foldl mkAppTy co1 tys
+-- See also 'mkAppCo'
+mkAppCos :: Coercion -> [Coercion] -> Coercion
+mkAppCos co1 tys = foldl mkAppCo co1 tys
-- | Apply a type constructor to a list of coercions.
-mkTyConCoercion :: TyCon -> [Coercion] -> Coercion
-mkTyConCoercion con cos = mkTyConApp con cos
+mkTyConAppCo :: TyCon -> [Coercion] -> Coercion
+mkTyConAppCo tc cos
+ -- Expand type synonyms
+ | Just (tv_co_prs, rhs_ty, leftover_cos) <- tcExpandTyCon_maybe tc cos
+ = mkAppCos (liftCoSubst (mkTopCvSubst tv_co_prs) rhs_ty) leftover_cos
+
+ | Just tys <- traverse isReflCo_maybe cos
+ = Refl (mkTyConApp tc tys) -- See Note [Refl invariant]
+
+ | otherwise = TyConAppCo tc cos
-- | Make a function 'Coercion' between two other 'Coercion's
-mkFunCoercion :: Coercion -> Coercion -> Coercion
-mkFunCoercion co1 co2 = mkFunTy co1 co2
+mkFunCo :: Coercion -> Coercion -> Coercion
+mkFunCo co1 co2 = mkTyConAppCo funTyCon [co1, co2]
-- | Make a 'Coercion' which binds a variable within an inner 'Coercion'
-mkForAllCoercion :: Var -> Coercion -> Coercion
+mkForAllCo :: Var -> Coercion -> Coercion
-- note that a TyVar should be used here, not a CoVar (nor a TcTyVar)
-mkForAllCoercion tv co = ASSERT ( isTyCoVar tv ) mkForAllTy tv co
+mkForAllCo tv (Refl ty) = ASSERT( isTyVar tv ) Refl (mkForAllTy tv ty)
+mkForAllCo tv co = ASSERT ( isTyVar tv ) ForAllCo tv co
+mkPredCo :: Pred Coercion -> Coercion
+mkPredCo pred_co
+ = case traverse isReflCo_maybe pred_co of
+ Just pred_ty -> Refl (PredTy pred_ty)
+ Nothing -> PredCo pred_co
-------------------------------
-mkSymCoercion :: Coercion -> Coercion
--- ^ Create a symmetric version of the given 'Coercion' that asserts equality
--- between the same types but in the other "direction", so a kind of @t1 ~ t2@
--- becomes the kind @t2 ~ t1@.
-mkSymCoercion g = mkCoercion symCoercionTyCon [g]
-
-mkTransCoercion :: Coercion -> Coercion -> Coercion
--- ^ Create a new 'Coercion' by exploiting transitivity on the two given 'Coercion's.
-mkTransCoercion g1 g2 = mkCoercion transCoercionTyCon [g1, g2]
-
-mkLeftCoercion :: Coercion -> Coercion
--- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
--- the "functions" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
---
--- > mkLeftCoercion c :: f ~ g
-mkLeftCoercion co = mkCoercion leftCoercionTyCon [co]
-
-mkRightCoercion :: Coercion -> Coercion
--- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
--- the "arguments" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
---
--- > mkLeftCoercion c :: x ~ y
-mkRightCoercion co = mkCoercion rightCoercionTyCon [co]
-
-mkCsel1Coercion, mkCsel2Coercion, mkCselRCoercion :: Coercion -> Coercion
-mkCsel1Coercion co = mkCoercion csel1CoercionTyCon [co]
-mkCsel2Coercion co = mkCoercion csel2CoercionTyCon [co]
-mkCselRCoercion co = mkCoercion cselRCoercionTyCon [co]
-
--------------------------------
-mkInstCoercion :: Coercion -> Type -> Coercion
--- ^ Instantiates a 'Coercion' with a 'Type' argument. If possible, it immediately performs
--- the resulting beta-reduction, otherwise it creates a suspended instantiation.
-mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]
-
-mkInstsCoercion :: Coercion -> [Type] -> Coercion
--- ^ As 'mkInstCoercion', but instantiates the coercion with a number of type arguments, left-to-right
-mkInstsCoercion co tys = foldl mkInstCoercion co tys
-
--- | Manufacture a coercion from this air. Needless to say, this is not usually safe,
--- but it is used when we know we are dealing with bottom, which is one case in which
--- it is safe. This is also used implement the @unsafeCoerce#@ primitive.
--- Optimise by pushing down through type constructors
-mkUnsafeCoercion :: Type -> Type -> Coercion
-mkUnsafeCoercion (TyConApp tc1 tys1) (TyConApp tc2 tys2)
+-- | Create a symmetric version of the given 'Coercion' that asserts
+-- equality between the same types but in the other "direction", so
+-- a kind of @t1 ~ t2@ becomes the kind @t2 ~ t1@.
+mkSymCo :: Coercion -> Coercion
+
+-- Do a few simple optimizations, but don't bother pushing occurrences
+-- of symmetry to the leaves; the optimizer will take care of that.
+mkSymCo co@(Refl {}) = co
+mkSymCo (UnsafeCo ty1 ty2) = UnsafeCo ty2 ty1
+mkSymCo (SymCo co) = co
+mkSymCo co = SymCo co
+
+-- | Create a new 'Coercion' by composing the two given 'Coercion's transitively.
+mkTransCo :: Coercion -> Coercion -> Coercion
+mkTransCo (Refl _) co = co
+mkTransCo co (Refl _) = co
+mkTransCo co1 co2 = TransCo co1 co2
+
+mkNthCo :: Int -> Coercion -> Coercion
+mkNthCo n (Refl ty) = Refl (getNth n ty)
+mkNthCo n co = NthCo n co
+
+-- | Instantiates a 'Coercion' with a 'Type' argument. If possible, it immediately performs
+-- the resulting beta-reduction, otherwise it creates a suspended instantiation.
+mkInstCo :: Coercion -> Type -> Coercion
+mkInstCo (ForAllCo tv co) ty = substCoWithTy tv ty co
+mkInstCo co ty = InstCo co ty
+
+-- | Manufacture a coercion from thin air. Needless to say, this is
+-- not usually safe, but it is used when we know we are dealing with
+-- bottom, which is one case in which it is safe. This is also used
+-- to implement the @unsafeCoerce#@ primitive. Optimise by pushing
+-- down through type constructors.
+mkUnsafeCo :: Type -> Type -> Coercion
+mkUnsafeCo ty1 ty2 | ty1 `eqType` ty2 = Refl ty1
+mkUnsafeCo (TyConApp tc1 tys1) (TyConApp tc2 tys2)
| tc1 == tc2
- = TyConApp tc1 (zipWith mkUnsafeCoercion tys1 tys2)
+ = mkTyConAppCo tc1 (zipWith mkUnsafeCo tys1 tys2)
-mkUnsafeCoercion (FunTy a1 r1) (FunTy a2 r2)
- = FunTy (mkUnsafeCoercion a1 a2) (mkUnsafeCoercion r1 r2)
+mkUnsafeCo (FunTy a1 r1) (FunTy a2 r2)
+ = mkFunCo (mkUnsafeCo a1 a2) (mkUnsafeCo r1 r2)
-mkUnsafeCoercion ty1 ty2
- | ty1 `coreEqType` ty2 = ty1
- | otherwise = mkCoercion unsafeCoercionTyCon [ty1, ty2]
+mkUnsafeCo ty1 ty2 = UnsafeCo ty1 ty2
-- See note [Newtype coercions] in TyCon
--- | Create a coercion suitable for the given 'TyCon'. The 'Name' should be that of a
--- new coercion 'TyCon', the 'TyVar's the arguments expected by the @newtype@ and the
--- type the appropriate right hand side of the @newtype@, with the free variables
--- a subset of those 'TyVar's.
-mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
-mkNewTypeCoercion name tycon tvs rhs_ty
- = mkCoercionTyCon name arity desc
- where
- arity = length tvs
- desc = CoAxiom { co_ax_tvs = tvs
- , co_ax_lhs = mkTyConApp tycon (mkTyVarTys tvs)
- , co_ax_rhs = rhs_ty }
+-- | Create a coercion constructor (axiom) suitable for the given
+-- newtype 'TyCon'. The 'Name' should be that of a new coercion
+-- 'CoAxiom', the 'TyVar's the arguments expected by the @newtype@ and
+-- the type the appropriate right hand side of the @newtype@, with
+-- the free variables a subset of those 'TyVar's.
+mkNewTypeCo :: Name -> TyCon -> [TyVar] -> Type -> CoAxiom
+mkNewTypeCo name tycon tvs rhs_ty
+ = CoAxiom { co_ax_unique = nameUnique name
+ , co_ax_name = name
+ , co_ax_tvs = tvs
+ , co_ax_lhs = mkTyConApp tycon (mkTyVarTys tvs)
+ , co_ax_rhs = rhs_ty }
-- | Create a coercion identifying a @data@, @newtype@ or @type@ representation type
-- and its family instance. It has the form @Co tvs :: F ts ~ R tvs@, where @Co@ is
--- the coercion tycon built here, @F@ the family tycon and @R@ the (derived)
+-- the coercion constructor built here, @F@ the family tycon and @R@ the (derived)
-- representation tycon.
-mkFamInstCoercion :: Name -- ^ Unique name for the coercion tycon
+mkFamInstCo :: Name -- ^ Unique name for the coercion tycon
-> [TyVar] -- ^ Type parameters of the coercion (@tvs@)
-> TyCon -- ^ Family tycon (@F@)
-> [Type] -- ^ Type instance (@ts@)
-> TyCon -- ^ Representation tycon (@R@)
- -> TyCon -- ^ Coercion tycon (@Co@)
-mkFamInstCoercion name tvs family inst_tys rep_tycon
- = mkCoercionTyCon name arity desc
- where
- arity = length tvs
- desc = CoAxiom { co_ax_tvs = tvs
- , co_ax_lhs = mkTyConApp family inst_tys
- , co_ax_rhs = mkTyConApp rep_tycon (mkTyVarTys tvs) }
+ -> CoAxiom -- ^ Coercion constructor (@Co@)
+mkFamInstCo name tvs family inst_tys rep_tycon
+ = CoAxiom { co_ax_unique = nameUnique name
+ , co_ax_name = name
+ , co_ax_tvs = tvs
+ , co_ax_lhs = mkTyConApp family inst_tys
+ , co_ax_rhs = mkTyConApp rep_tycon (mkTyVarTys tvs) }
+
+mkPiCos :: [Var] -> Coercion -> Coercion
+mkPiCos vs co = foldr mkPiCo co vs
+
+mkPiCo :: Var -> Coercion -> Coercion
+mkPiCo v co | isTyVar v = mkForAllCo v co
+ | otherwise = mkFunCo (mkReflCo (varType v)) co
\end{code}
-
-%************************************************************************
-%* *
- Coercion Type Constructors
-%* *
-%************************************************************************
-
-Example. The coercion ((sym c) (sym d) (sym e))
-will be represented by (TyConApp sym [c, sym d, sym e])
-If sym c :: p1=q1
- sym d :: p2=q2
- sym e :: p3=q3
-then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)
-
-\begin{code}
--- | Coercion type constructors: avoid using these directly and instead use
--- the @mk*Coercion@ and @split*Coercion@ family of functions if possible.
---
--- Each coercion TyCon is built with the special CoercionTyCon record and
--- carries its own kinding rule. Such CoercionTyCons must be fully applied
--- by any TyConApp in which they are applied, however they may also be over
--- applied (see example above) and the kinding function must deal with this.
-symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon,
- rightCoercionTyCon, instCoercionTyCon, unsafeCoercionTyCon,
- csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon :: TyCon
-
-symCoercionTyCon = mkCoercionTyCon symCoercionTyConName 1 CoSym
-transCoercionTyCon = mkCoercionTyCon transCoercionTyConName 2 CoTrans
-leftCoercionTyCon = mkCoercionTyCon leftCoercionTyConName 1 CoLeft
-rightCoercionTyCon = mkCoercionTyCon rightCoercionTyConName 1 CoRight
-instCoercionTyCon = mkCoercionTyCon instCoercionTyConName 2 CoInst
-csel1CoercionTyCon = mkCoercionTyCon csel1CoercionTyConName 1 CoCsel1
-csel2CoercionTyCon = mkCoercionTyCon csel2CoercionTyConName 1 CoCsel2
-cselRCoercionTyCon = mkCoercionTyCon cselRCoercionTyConName 1 CoCselR
-unsafeCoercionTyCon = mkCoercionTyCon unsafeCoercionTyConName 2 CoUnsafe
-
-transCoercionTyConName, symCoercionTyConName, leftCoercionTyConName,
- rightCoercionTyConName, instCoercionTyConName, unsafeCoercionTyConName,
- csel1CoercionTyConName, csel2CoercionTyConName, cselRCoercionTyConName :: Name
-
-transCoercionTyConName = mkCoConName (fsLit "trans") transCoercionTyConKey transCoercionTyCon
-symCoercionTyConName = mkCoConName (fsLit "sym") symCoercionTyConKey symCoercionTyCon
-leftCoercionTyConName = mkCoConName (fsLit "left") leftCoercionTyConKey leftCoercionTyCon
-rightCoercionTyConName = mkCoConName (fsLit "right") rightCoercionTyConKey rightCoercionTyCon
-instCoercionTyConName = mkCoConName (fsLit "inst") instCoercionTyConKey instCoercionTyCon
-csel1CoercionTyConName = mkCoConName (fsLit "csel1") csel1CoercionTyConKey csel1CoercionTyCon
-csel2CoercionTyConName = mkCoConName (fsLit "csel2") csel2CoercionTyConKey csel2CoercionTyCon
-cselRCoercionTyConName = mkCoConName (fsLit "cselR") cselRCoercionTyConKey cselRCoercionTyCon
-unsafeCoercionTyConName = mkCoConName (fsLit "CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon
-
-mkCoConName :: FastString -> Unique -> TyCon -> Name
-mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkTcOccFS occ)
- key (ATyCon coCon) BuiltInSyntax
-\end{code}
-
-\begin{code}
-------------
-decompLR_maybe :: (Type,Type) -> Maybe ((Type,Type), (Type,Type))
--- Helper for left and right. Finds coercion kind of its input and
--- returns the left and right projections of the coercion...
---
--- if c :: t1 s1 ~ t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))
-decompLR_maybe (ty1,ty2)
- | Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
- , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
- = Just ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
-decompLR_maybe _ = Nothing
-
-------------
-decompInst_maybe :: (Type, Type) -> Maybe ((TyVar,TyVar), (Type,Type))
-decompInst_maybe (ty1, ty2)
- | Just (tv1,r1) <- splitForAllTy_maybe ty1
- , Just (tv2,r2) <- splitForAllTy_maybe ty2
- = Just ((tv1,tv2), (r1,r2))
-decompInst_maybe _ = Nothing
-
-------------
-decompCsel_maybe :: (Type, Type) -> Maybe ((Type,Type), (Type,Type), (Type,Type))
--- If co :: (s1~t1 => r1) ~ (s2~t2 => r2)
--- Then csel1 co :: s1 ~ s2
--- csel2 co :: t1 ~ t2
--- cselR co :: r1 ~ r2
-decompCsel_maybe (ty1, ty2)
- | Just (s1, t1, r1) <- splitCoPredTy_maybe ty1
- , Just (s2, t2, r2) <- splitCoPredTy_maybe ty2
- = Just ((s1,s2), (t1,t2), (r1,r2))
-decompCsel_maybe _ = Nothing
-\end{code}
-
-
%************************************************************************
%* *
Newtypes
%************************************************************************
\begin{code}
-instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, CoercionI)
+instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion)
-- ^ If @co :: T ts ~ rep_ty@ then:
--
-- > instNewTyCon_maybe T ts = Just (rep_ty, co)
instNewTyCon_maybe tc tys
- | Just (tvs, ty, mb_co_tc) <- unwrapNewTyCon_maybe tc
+ | Just (tvs, ty, co_tc) <- unwrapNewTyCon_maybe tc
= ASSERT( tys `lengthIs` tyConArity tc )
- Just (substTyWith tvs tys ty,
- case mb_co_tc of
- Nothing -> IdCo (mkTyConApp tc tys)
- Just co_tc -> ACo (mkTyConApp co_tc tys))
+ Just (substTyWith tvs tys ty, mkAxInstCo co_tc tys)
| otherwise
= Nothing
splitNewTypeRepCo_maybe ty
| Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
splitNewTypeRepCo_maybe (TyConApp tc tys)
- | Just (ty', coi) <- instNewTyCon_maybe tc tys
- = case coi of
- ACo co -> Just (ty', co)
- IdCo _ -> panic "splitNewTypeRepCo_maybe"
+ | Just (ty', co) <- instNewTyCon_maybe tc tys
+ = case co of
+ Refl _ -> panic "splitNewTypeRepCo_maybe"
-- This case handled by coreView
+ _ -> Just (ty', co)
splitNewTypeRepCo_maybe _
= Nothing
-- | Determines syntactic equality of coercions
coreEqCoercion :: Coercion -> Coercion -> Bool
-coreEqCoercion = coreEqType
+coreEqCoercion co1 co2 = coreEqCoercion2 rn_env co1 co2
+ where rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfCo co1 `unionVarSet` tyCoVarsOfCo co2))
coreEqCoercion2 :: RnEnv2 -> Coercion -> Coercion -> Bool
-coreEqCoercion2 = coreEqType2
-\end{code}
+coreEqCoercion2 env (Refl ty1) (Refl ty2) = eqTypeX env ty1 ty2
+coreEqCoercion2 env (TyConAppCo tc1 cos1) (TyConAppCo tc2 cos2)
+ = tc1 == tc2 && all2 (coreEqCoercion2 env) cos1 cos2
+
+coreEqCoercion2 env (AppCo co11 co12) (AppCo co21 co22)
+ = coreEqCoercion2 env co11 co21 && coreEqCoercion2 env co12 co22
+
+coreEqCoercion2 env (ForAllCo v1 co1) (ForAllCo v2 co2)
+ = coreEqCoercion2 (rnBndr2 env v1 v2) co1 co2
+
+coreEqCoercion2 env (CoVarCo cv1) (CoVarCo cv2)
+ = rnOccL env cv1 == rnOccR env cv2
+
+coreEqCoercion2 env (AxiomInstCo con1 cos1) (AxiomInstCo con2 cos2)
+ = con1 == con2
+ && all2 (coreEqCoercion2 env) cos1 cos2
+coreEqCoercion2 env (UnsafeCo ty11 ty12) (UnsafeCo ty21 ty22)
+ = eqTypeX env ty11 ty21 && eqTypeX env ty12 ty22
+
+coreEqCoercion2 env (SymCo co1) (SymCo co2)
+ = coreEqCoercion2 env co1 co2
+
+coreEqCoercion2 env (TransCo co11 co12) (TransCo co21 co22)
+ = coreEqCoercion2 env co11 co21 && coreEqCoercion2 env co12 co22
+
+coreEqCoercion2 env (NthCo d1 co1) (NthCo d2 co2)
+ = d1 == d2 && coreEqCoercion2 env co1 co2
+
+coreEqCoercion2 env (InstCo co1 ty1) (InstCo co2 ty2)
+ = coreEqCoercion2 env co1 co2 && eqTypeX env ty1 ty2
+
+coreEqCoercion2 _ _ _ = False
+\end{code}
%************************************************************************
%* *
- CoercionI and its constructors
-%* *
+ Substitution of coercions
+%* *
%************************************************************************
---------------------------------------
--- CoercionI smart constructors
--- lifted smart constructors of ordinary coercions
+\begin{code}
+-- | A substitution of 'Coercion's for 'CoVar's (OR 'TyVar's, when
+-- doing a \"lifting\" substitution)
+type CvSubstEnv = VarEnv Coercion
+
+emptyCvSubstEnv :: CvSubstEnv
+emptyCvSubstEnv = emptyVarEnv
+
+data CvSubst
+ = CvSubst InScopeSet -- The in-scope type variables
+ TvSubstEnv -- Substitution of types
+ CvSubstEnv -- Substitution of coercions
+
+instance Outputable CvSubst where
+ ppr (CvSubst ins tenv cenv)
+ = brackets $ sep[ ptext (sLit "CvSubst"),
+ nest 2 (ptext (sLit "In scope:") <+> ppr ins),
+ nest 2 (ptext (sLit "Type env:") <+> ppr tenv),
+ nest 2 (ptext (sLit "Coercion env:") <+> ppr cenv) ]
+
+emptyCvSubst :: CvSubst
+emptyCvSubst = CvSubst emptyInScopeSet emptyVarEnv emptyVarEnv
+
+isEmptyCvSubst :: CvSubst -> Bool
+isEmptyCvSubst (CvSubst _ tenv cenv) = isEmptyVarEnv tenv && isEmptyVarEnv cenv
+
+getCvInScope :: CvSubst -> InScopeSet
+getCvInScope (CvSubst in_scope _ _) = in_scope
+
+zapCvSubstEnv :: CvSubst -> CvSubst
+zapCvSubstEnv (CvSubst in_scope _ _) = CvSubst in_scope emptyVarEnv emptyVarEnv
+
+cvTvSubst :: CvSubst -> TvSubst
+cvTvSubst (CvSubst in_scope tvs _) = TvSubst in_scope tvs
+
+tvCvSubst :: TvSubst -> CvSubst
+tvCvSubst (TvSubst in_scope tenv) = CvSubst in_scope tenv emptyCvSubstEnv
+
+extendTvSubst :: CvSubst -> TyVar -> Type -> CvSubst
+extendTvSubst (CvSubst in_scope tenv cenv) tv ty
+ = CvSubst in_scope (extendVarEnv tenv tv ty) cenv
+
+substCoVarBndr :: CvSubst -> CoVar -> (CvSubst, CoVar)
+substCoVarBndr subst@(CvSubst in_scope tenv cenv) old_var
+ = ASSERT( isCoVar old_var )
+ (CvSubst (in_scope `extendInScopeSet` new_var) tenv new_cenv, new_var)
+ where
+ -- When we substitute (co :: t1 ~ t2) we may get the identity (co :: t ~ t)
+ -- In that case, mkCoVarCo will return a ReflCoercion, and
+ -- we want to substitute that (not new_var) for old_var
+ new_co = mkCoVarCo new_var
+ no_change = new_var == old_var && not (isReflCo new_co)
+
+ new_cenv | no_change = delVarEnv cenv old_var
+ | otherwise = extendVarEnv cenv old_var new_co
+
+ new_var = uniqAway in_scope subst_old_var
+ subst_old_var = mkCoVar (varName old_var) (substTy subst (varType old_var))
+ -- It's important to do the substitution for coercions,
+ -- because only they can have free type variables
+
+substTyVarBndr :: CvSubst -> TyVar -> (CvSubst, TyVar)
+substTyVarBndr (CvSubst in_scope tenv cenv) old_var
+ = case Type.substTyVarBndr (TvSubst in_scope tenv) old_var of
+ (TvSubst in_scope' tenv', new_var) -> (CvSubst in_scope' tenv' cenv, new_var)
+
+zipOpenCvSubst :: [Var] -> [Coercion] -> CvSubst
+zipOpenCvSubst vs cos
+ | debugIsOn && (length vs /= length cos)
+ = pprTrace "zipOpenCvSubst" (ppr vs $$ ppr cos) emptyCvSubst
+ | otherwise
+ = CvSubst (mkInScopeSet (tyCoVarsOfCos cos)) emptyTvSubstEnv (zipVarEnv vs cos)
+
+mkTopCvSubst :: [(Var,Coercion)] -> CvSubst
+mkTopCvSubst prs = CvSubst emptyInScopeSet emptyTvSubstEnv (mkVarEnv prs)
+
+substCoWithTy :: TyVar -> Type -> Coercion -> Coercion
+substCoWithTy tv ty = substCoWithTys [tv] [ty]
+
+substCoWithTys :: [TyVar] -> [Type] -> Coercion -> Coercion
+substCoWithTys tvs tys co
+ | debugIsOn && (length tvs /= length tys)
+ = pprTrace "substCoWithTys" (ppr tvs $$ ppr tys) co
+ | otherwise
+ = ASSERT( length tvs == length tys )
+ substCo (CvSubst in_scope (zipVarEnv tvs tys) emptyVarEnv) co
+ where
+ in_scope = mkInScopeSet (tyVarsOfTypes tys)
+
+-- | Substitute within a 'Coercion'
+substCo :: CvSubst -> Coercion -> Coercion
+substCo subst co | isEmptyCvSubst subst = co
+ | otherwise = subst_co subst co
+
+-- | Substitute within several 'Coercion's
+substCos :: CvSubst -> [Coercion] -> [Coercion]
+substCos subst cos | isEmptyCvSubst subst = cos
+ | otherwise = map (substCo subst) cos
+
+substTy :: CvSubst -> Type -> Type
+substTy subst = Type.substTy (cvTvSubst subst)
+
+subst_co :: CvSubst -> Coercion -> Coercion
+subst_co subst co
+ = go co
+ where
+ go_ty :: Type -> Type
+ go_ty = Coercion.substTy subst
+
+ go :: Coercion -> Coercion
+ go (Refl ty) = Refl $! go_ty ty
+ go (TyConAppCo tc cos) = let args = map go cos
+ in args `seqList` TyConAppCo tc args
+
+ go (AppCo co1 co2) = mkAppCo (go co1) $! go co2
+ go (ForAllCo tv co) = case substTyVarBndr subst tv of
+ (subst', tv') ->
+ ForAllCo tv' $! subst_co subst' co
+
+ go (PredCo p) = mkPredCo (go <$> p)
+ go (CoVarCo cv) = substCoVar subst cv
+ go (AxiomInstCo con cos) = AxiomInstCo con $! map go cos
+ go (UnsafeCo ty1 ty2) = (UnsafeCo $! go_ty ty1) $! go_ty ty2
+ go (SymCo co) = mkSymCo (go co)
+ go (TransCo co1 co2) = mkTransCo (go co1) (go co2)
+ go (NthCo d co) = mkNthCo d (go co)
+ go (InstCo co ty) = mkInstCo (go co) $! go_ty ty
+
+substCoVar :: CvSubst -> CoVar -> Coercion
+substCoVar (CvSubst in_scope _ cenv) cv
+ | Just co <- lookupVarEnv cenv cv = co
+ | Just cv1 <- lookupInScope in_scope cv = ASSERT( isCoVar cv1 ) CoVarCo cv1
+ | otherwise = WARN( True, ptext (sLit "substCoVar not in scope") <+> ppr cv )
+ ASSERT( isCoVar cv ) CoVarCo cv
+
+substCoVars :: CvSubst -> [CoVar] -> [Coercion]
+substCoVars subst cvs = map (substCoVar subst) cvs
+
+lookupTyVar :: CvSubst -> TyVar -> Maybe Type
+lookupTyVar (CvSubst _ tenv _) tv = lookupVarEnv tenv tv
+
+lookupCoVar :: CvSubst -> Var -> Maybe Coercion
+lookupCoVar (CvSubst _ _ cenv) v = lookupVarEnv cenv v
+\end{code}
+
+%************************************************************************
+%* *
+ "Lifting" substitution
+ [(TyVar,Coercion)] -> Type -> Coercion
+%* *
+%************************************************************************
\begin{code}
--- | 'CoercionI' represents a /lifted/ ordinary 'Coercion', in that it
--- can represent either one of:
---
--- 1. A proper 'Coercion'
+liftCoSubstWith :: [TyVar] -> [Coercion] -> Type -> Coercion
+liftCoSubstWith tvs cos = liftCoSubst (zipOpenCvSubst tvs cos)
+
+-- | The \"lifting\" operation which substitutes coercions for type
+-- variables in a type to produce a coercion.
--
--- 2. The identity coercion
-data CoercionI = IdCo Type | ACo Coercion
+-- For the inverse operation, see 'liftCoMatch'
+liftCoSubst :: CvSubst -> Type -> Coercion
+-- The CvSubst maps TyVar -> Type (mainly for cloning foralls)
+-- TyVar -> Coercion (this is the payload)
+-- The unusual thing is that the *coercion* substitution maps
+-- some *type* variables. That's the whole point of this function!
+liftCoSubst subst ty | isEmptyCvSubst subst = Refl ty
+ | otherwise = ty_co_subst subst ty
+
+ty_co_subst :: CvSubst -> Type -> Coercion
+ty_co_subst subst ty
+ = go ty
+ where
+ go (TyVarTy tv) = liftCoSubstTyVar subst tv `orElse` Refl (TyVarTy tv)
+ go (AppTy ty1 ty2) = mkAppCo (go ty1) (go ty2)
+ go (TyConApp tc tys) = mkTyConAppCo tc (map go tys)
+ go (FunTy ty1 ty2) = mkFunCo (go ty1) (go ty2)
+ go (ForAllTy v ty) = mkForAllCo v' $! (ty_co_subst subst' ty)
+ where
+ (subst', v') = liftCoSubstTyVarBndr subst v
+ go (PredTy p) = mkPredCo (go <$> p)
+
+liftCoSubstTyVar :: CvSubst -> TyVar -> Maybe Coercion
+liftCoSubstTyVar subst@(CvSubst _ tenv cenv) tv
+ = case (lookupVarEnv tenv tv, lookupVarEnv cenv tv) of
+ (Nothing, Nothing) -> Nothing
+ (Just ty, Nothing) -> Just (Refl ty)
+ (Nothing, Just co) -> Just co
+ (Just {}, Just {}) -> pprPanic "ty_co_subst" (ppr tv $$ ppr subst)
+
+liftCoSubstTyVarBndr :: CvSubst -> TyVar -> (CvSubst, TyVar)
+liftCoSubstTyVarBndr (CvSubst in_scope tenv cenv) old_var
+ = (CvSubst (in_scope `extendInScopeSet` new_var)
+ new_tenv
+ (delVarEnv cenv old_var) -- See Note [Lifting substitutions]
+ , new_var)
+ where
+ new_tenv | no_change = delVarEnv tenv old_var
+ | otherwise = extendVarEnv tenv old_var (TyVarTy new_var)
+
+ no_change = new_var == old_var
+ new_var = uniqAway in_scope old_var
+\end{code}
-liftCoI :: (Type -> Type) -> CoercionI -> CoercionI
-liftCoI f (IdCo ty) = IdCo (f ty)
-liftCoI f (ACo ty) = ACo (f ty)
+Note [Lifting substitutions]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Consider liftCoSubstWith [a] [co] (a, forall a. a)
+Then we want to substitute for the free 'a', but obviously not for
+the bound 'a'. hence the (delVarEnv cent old_var) in liftCoSubstTyVarBndr.
-liftCoI2 :: (Type -> Type -> Type) -> CoercionI -> CoercionI -> CoercionI
-liftCoI2 f (IdCo ty1) (IdCo ty2) = IdCo (f ty1 ty2)
-liftCoI2 f coi1 coi2 = ACo (f (fromCoI coi1) (fromCoI coi2))
+This also why we need a full CvSubst when doing lifting substitutions.
-liftCoIs :: ([Type] -> Type) -> [CoercionI] -> CoercionI
-liftCoIs f cois = go_id [] cois
+\begin{code}
+-- | 'liftCoMatch' is sort of inverse to 'liftCoSubst'. In particular, if
+-- @liftCoMatch vars ty co == Just s@, then @tyCoSubst s ty == co@.
+-- That is, it matches a type against a coercion of the same
+-- "shape", and returns a lifting substitution which could have been
+-- used to produce the given coercion from the given type.
+liftCoMatch :: TyVarSet -> Type -> Coercion -> Maybe CvSubst
+liftCoMatch tmpls ty co
+ = case ty_co_match menv (emptyVarEnv, emptyVarEnv) ty co of
+ Just (tv_env, cv_env) -> Just (CvSubst in_scope tv_env cv_env)
+ Nothing -> Nothing
where
- go_id rev_tys [] = IdCo (f (reverse rev_tys))
- go_id rev_tys (IdCo ty : cois) = go_id (ty:rev_tys) cois
- go_id rev_tys (ACo co : cois) = go_aco (co:rev_tys) cois
-
- go_aco rev_tys [] = ACo (f (reverse rev_tys))
- go_aco rev_tys (IdCo ty : cois) = go_aco (ty:rev_tys) cois
- go_aco rev_tys (ACo co : cois) = go_aco (co:rev_tys) cois
-
-instance Outputable CoercionI where
- ppr (IdCo _) = ptext (sLit "IdCo")
- ppr (ACo co) = ppr co
-
-isIdentityCoI :: CoercionI -> Bool
-isIdentityCoI (IdCo _) = True
-isIdentityCoI (ACo _) = False
-
--- | Return either the 'Coercion' contained within the 'CoercionI' or the given
--- 'Type' if the 'CoercionI' is the identity 'Coercion'
-fromCoI :: CoercionI -> Type
-fromCoI (IdCo ty) = ty -- Identity coercion represented
-fromCoI (ACo co) = co -- by the type itself
-
--- | Smart constructor for @sym@ on 'CoercionI', see also 'mkSymCoercion'
-mkSymCoI :: CoercionI -> CoercionI
-mkSymCoI (IdCo ty) = IdCo ty
-mkSymCoI (ACo co) = ACo $ mkCoercion symCoercionTyCon [co]
- -- the smart constructor
- -- is too smart with tyvars
-
--- | Smart constructor for @trans@ on 'CoercionI', see also 'mkTransCoercion'
-mkTransCoI :: CoercionI -> CoercionI -> CoercionI
-mkTransCoI (IdCo _) aco = aco
-mkTransCoI aco (IdCo _) = aco
-mkTransCoI (ACo co1) (ACo co2) = ACo $ mkTransCoercion co1 co2
-
--- | Smart constructor for type constructor application on 'CoercionI', see also 'mkAppCoercion'
-mkTyConAppCoI :: TyCon -> [CoercionI] -> CoercionI
-mkTyConAppCoI tyCon cois = liftCoIs (mkTyConApp tyCon) cois
-
--- | Smart constructor for honest-to-god 'Coercion' application on 'CoercionI', see also 'mkAppCoercion'
-mkAppTyCoI :: CoercionI -> CoercionI -> CoercionI
-mkAppTyCoI = liftCoI2 mkAppTy
-
-mkFunTyCoI :: CoercionI -> CoercionI -> CoercionI
-mkFunTyCoI = liftCoI2 mkFunTy
-
--- | Smart constructor for quantified 'Coercion's on 'CoercionI', see also 'mkForAllCoercion'
-mkForAllTyCoI :: TyVar -> CoercionI -> CoercionI
-mkForAllTyCoI tv = liftCoI (ForAllTy tv)
-
--- | Smart constructor for class 'Coercion's on 'CoercionI'. Satisfies:
---
--- > mkClassPPredCoI cls tys cois :: PredTy (cls tys) ~ PredTy (cls (tys `cast` cois))
-mkClassPPredCoI :: Class -> [CoercionI] -> CoercionI
-mkClassPPredCoI cls = liftCoIs (PredTy . ClassP cls)
+ menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope }
+ in_scope = mkInScopeSet (tmpls `unionVarSet` tyCoVarsOfCo co)
+ -- Like tcMatchTy, assume all the interesting variables
+ -- in ty are in tmpls
+
+type TyCoSubstEnv = (TvSubstEnv, CvSubstEnv)
+ -- Used locally inside ty_co_match only
+
+-- | 'ty_co_match' does all the actual work for 'liftCoMatch'.
+ty_co_match :: MatchEnv -> TyCoSubstEnv -> Type -> Coercion -> Maybe TyCoSubstEnv
+ty_co_match menv subst ty co | Just ty' <- coreView ty = ty_co_match menv subst ty' co
+
+ -- Deal with the Refl case by delegating to type matching
+ty_co_match menv (tenv, cenv) ty co
+ | Just ty' <- isReflCo_maybe co
+ = case ruleMatchTyX ty_menv tenv ty ty' of
+ Just tenv' -> Just (tenv', cenv)
+ Nothing -> Nothing
+ where
+ ty_menv = menv { me_tmpls = me_tmpls menv `minusUFM` cenv }
+ -- Remove from the template set any variables already bound to non-refl coercions
+
+ -- Match a type variable against a non-refl coercion
+ty_co_match menv subst@(tenv, cenv) (TyVarTy tv1) co
+ | Just {} <- lookupVarEnv tenv tv1' -- tv1' is already bound to (Refl ty)
+ = Nothing -- The coercion 'co' is not Refl
+
+ | Just co1' <- lookupVarEnv cenv tv1' -- tv1' is already bound to co1
+ = if coreEqCoercion2 (nukeRnEnvL rn_env) co1' co
+ then Just subst
+ else Nothing -- no match since tv1 matches two different coercions
+
+ | tv1' `elemVarSet` me_tmpls menv -- tv1' is a template var
+ = if any (inRnEnvR rn_env) (varSetElems (tyCoVarsOfCo co))
+ then Nothing -- occurs check failed
+ else return (tenv, extendVarEnv cenv tv1' co)
+ -- BAY: I don't think we need to do any kind matching here yet
+ -- (compare 'match'), but we probably will when moving to SHE.
+
+ | otherwise -- tv1 is not a template ty var, so the only thing it
+ -- can match is a reflexivity coercion for itself.
+ -- But that case is dealt with already
+ = Nothing
+
+ where
+ rn_env = me_env menv
+ tv1' = rnOccL rn_env tv1
+
+ty_co_match menv subst (AppTy ty1 ty2) (AppCo co1 co2) -- BAY: do we need to work harder to decompose the AppCo?
+ = do { subst' <- ty_co_match menv subst ty1 co1
+ ; ty_co_match menv subst' ty2 co2 }
+
+ty_co_match menv subst (TyConApp tc1 tys) (TyConAppCo tc2 cos)
+ | tc1 == tc2 = ty_co_matches menv subst tys cos
+
+ty_co_match menv subst (FunTy ty1 ty2) (TyConAppCo tc cos)
+ | tc == funTyCon = ty_co_matches menv subst [ty1,ty2] cos
+
+ty_co_match menv subst (ForAllTy tv1 ty) (ForAllCo tv2 co)
+ = ty_co_match menv' subst ty co
+ where
+ menv' = menv { me_env = rnBndr2 (me_env menv) tv1 tv2 }
--- | Smart constructor for implicit parameter 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI'
-mkIParamPredCoI :: (IPName Name) -> CoercionI -> CoercionI
-mkIParamPredCoI ipn = liftCoI (PredTy . IParam ipn)
+ty_co_match _ _ _ _ = Nothing
--- | Smart constructor for type equality 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI'
-mkEqPredCoI :: CoercionI -> CoercionI -> CoercionI
-mkEqPredCoI = liftCoI2 (\t1 t2 -> PredTy (EqPred t1 t2))
+ty_co_matches :: MatchEnv -> TyCoSubstEnv -> [Type] -> [Coercion] -> Maybe TyCoSubstEnv
+ty_co_matches menv = matchList (ty_co_match menv)
\end{code}
%************************************************************************
%* *
- The kind of a type, and of a coercion
+ Sequencing on coercions
%* *
%************************************************************************
\begin{code}
-typeKind :: Type -> Kind
-typeKind ty@(TyConApp tc tys)
- | isCoercionTyCon tc = typeKind (fst (coercionKind ty))
- | otherwise = kindAppResult (tyConKind tc) tys
- -- During coercion optimisation we *do* match a type
- -- against a coercion (see OptCoercion.matchesAxiomLhs)
- -- So the use of typeKind in Unify.match_kind must work on coercions too
- -- Hence the isCoercionTyCon case above
-
-typeKind (PredTy pred) = predKind pred
-typeKind (AppTy fun _) = kindFunResult (typeKind fun)
-typeKind (ForAllTy _ ty) = typeKind ty
-typeKind (TyVarTy tyvar) = tyVarKind tyvar
-typeKind (FunTy _arg res)
- -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
- -- not unliftedTypKind (#)
- -- The only things that can be after a function arrow are
- -- (a) types (of kind openTypeKind or its sub-kinds)
- -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
- | isTySuperKind k = k
- | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
- where
- k = typeKind res
+seqCo :: Coercion -> ()
+seqCo (Refl ty) = seqType ty
+seqCo (TyConAppCo tc cos) = tc `seq` seqCos cos
+seqCo (AppCo co1 co2) = seqCo co1 `seq` seqCo co2
+seqCo (ForAllCo tv co) = tv `seq` seqCo co
+seqCo (PredCo p) = seqPred seqCo p
+seqCo (CoVarCo cv) = cv `seq` ()
+seqCo (AxiomInstCo con cos) = con `seq` seqCos cos
+seqCo (UnsafeCo ty1 ty2) = seqType ty1 `seq` seqType ty2
+seqCo (SymCo co) = seqCo co
+seqCo (TransCo co1 co2) = seqCo co1 `seq` seqCo co2
+seqCo (NthCo _ co) = seqCo co
+seqCo (InstCo co ty) = seqCo co `seq` seqType ty
+
+seqCos :: [Coercion] -> ()
+seqCos [] = ()
+seqCos (co:cos) = seqCo co `seq` seqCos cos
+\end{code}
-------------------
-predKind :: PredType -> Kind
-predKind (EqPred {}) = coSuperKind -- A coercion kind!
-predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
-predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
+
+%************************************************************************
+%* *
+ The kind of a type, and of a coercion
+%* *
+%************************************************************************
+
+\begin{code}
+coercionType :: Coercion -> Type
+coercionType co = case coercionKind co of
+ Pair ty1 ty2 -> mkCoType ty1 ty2
------------------
-- | If it is the case that
--
-- > c :: (t1 ~ t2)
--
--- i.e. the kind of @c@ is a 'CoercionKind' relating @t1@ and @t2@,
--- then @coercionKind c = (t1, t2)@.
-coercionKind :: Coercion -> (Type, Type)
-coercionKind ty@(TyVarTy a) | isCoVar a = coVarKind a
- | otherwise = (ty, ty)
-coercionKind (AppTy ty1 ty2)
- = let (s1, t1) = coercionKind ty1
- (s2, t2) = coercionKind ty2 in
- (mkAppTy s1 s2, mkAppTy t1 t2)
-coercionKind co@(TyConApp tc args)
- | Just (ar, desc) <- isCoercionTyCon_maybe tc
- -- CoercionTyCons carry their kinding rule, so we use it here
- = WARN( not (length args >= ar), ppr co ) -- Always saturated
- (let (ty1, ty2) = coTyConAppKind desc (take ar args)
- (tys1, tys2) = coercionKinds (drop ar args)
- in (mkAppTys ty1 tys1, mkAppTys ty2 tys2))
-
- | otherwise
- = let (lArgs, rArgs) = coercionKinds args in
- (TyConApp tc lArgs, TyConApp tc rArgs)
-
-coercionKind (FunTy ty1 ty2)
- = let (t1, t2) = coercionKind ty1
- (s1, s2) = coercionKind ty2 in
- (mkFunTy t1 s1, mkFunTy t2 s2)
-
-coercionKind (ForAllTy tv ty)
- | isCoVar tv
+-- i.e. the kind of @c@ relates @t1@ and @t2@, then @coercionKind c = Pair t1 t2@.
+coercionKind :: Coercion -> Pair Type
+coercionKind (Refl ty) = Pair ty ty
+coercionKind (TyConAppCo tc cos) = mkTyConApp tc <$> (sequenceA $ map coercionKind cos)
+coercionKind (AppCo co1 co2) = mkAppTy <$> coercionKind co1 <*> coercionKind co2
+coercionKind (ForAllCo tv co) = mkForAllTy tv <$> coercionKind co
+ -- BAY*: is the above still correct for equality
+ -- abstractions? the System FC paper seems to imply we can
+ -- only ever construct coercions between foralls whose
+ -- variables have *equal* kinds. But there was this comment
+ -- below suggesting otherwise:
+
-- c1 :: s1~s2 c2 :: t1~t2 c3 :: r1~r2
-- ----------------------------------------------
-- c1~c2 => c3 :: (s1~t1) => r1 ~ (s2~t2) => r2
-- or
-- forall (_:c1~c2)
- = let (c1,c2) = coVarKind tv
- (s1,s2) = coercionKind c1
- (t1,t2) = coercionKind c2
- (r1,r2) = coercionKind ty
- in
- (mkCoPredTy s1 t1 r1, mkCoPredTy s2 t2 r2)
-
- | otherwise
--- c1 :: s1~s2 c2 :: t1~t2 c3 :: r1~r2
--- ----------------------------------------------
--- forall a:k. c :: forall a:k. t1 ~ forall a:k. t2
- = let (ty1, ty2) = coercionKind ty in
- (ForAllTy tv ty1, ForAllTy tv ty2)
-
-coercionKind (PredTy (ClassP cl args))
- = let (lArgs, rArgs) = coercionKinds args in
- (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
-coercionKind (PredTy (IParam name ty))
- = let (ty1, ty2) = coercionKind ty in
- (PredTy (IParam name ty1), PredTy (IParam name ty2))
-coercionKind (PredTy (EqPred c1 c2))
- = pprTrace "coercionKind" (pprEqPred (c1,c2)) $
- -- These should not show up in coercions at all
- -- becuase they are in the form of for-alls
- let k1 = coercionKindPredTy c1
- k2 = coercionKindPredTy c2 in
- (k1,k2)
- where
- coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2
+coercionKind (CoVarCo cv) = ASSERT( isCoVar cv ) toPair $ coVarKind cv
+coercionKind (AxiomInstCo ax cos) = let Pair tys1 tys2 = coercionKinds cos
+ in Pair (substTyWith (co_ax_tvs ax) tys1 (co_ax_lhs ax))
+ (substTyWith (co_ax_tvs ax) tys2 (co_ax_rhs ax))
+coercionKind (UnsafeCo ty1 ty2) = Pair ty1 ty2
+coercionKind (SymCo co) = swap $ coercionKind co
+coercionKind (TransCo co1 co2) = Pair (pFst $ coercionKind co1) (pSnd $ coercionKind co2)
+coercionKind (NthCo d co) = getNth d <$> coercionKind co
+coercionKind (InstCo co ty) | Just ks <- splitForAllTy_maybe `traverse` coercionKind co
+ = (\(tv, body) -> substTyWith [tv] [ty] body) <$> ks
+ -- fall-through error case.
+coercionKind co = pprPanic "coercionKind" (ppr co)
-------------------
-- | Apply 'coercionKind' to multiple 'Coercion's
-coercionKinds :: [Coercion] -> ([Type], [Type])
-coercionKinds tys = unzip $ map coercionKind tys
+coercionKinds :: [Coercion] -> Pair [Type]
+coercionKinds tys = sequenceA $ map coercionKind tys
-------------------
--- | 'coTyConAppKind' is given a list of the type arguments to the 'CoTyCon',
--- and constructs the types that the resulting coercion relates.
--- Fails (in the monad) if ill-kinded.
--- Typically the monad is
--- either the Lint monad (with the consistency-check flag = True),
--- or the ID monad with a panic on failure (and the consistency-check flag = False)
-coTyConAppKind
- :: CoTyConDesc
- -> [Type] -- Exactly right number of args
- -> (Type, Type) -- Kind of this application
-coTyConAppKind CoUnsafe (ty1:ty2:_)
- = (ty1,ty2)
-coTyConAppKind CoSym (co:_)
- | (ty1,ty2) <- coercionKind co = (ty2,ty1)
-coTyConAppKind CoTrans (co1:co2:_)
- = (fst (coercionKind co1), snd (coercionKind co2))
-coTyConAppKind CoLeft (co:_)
- | Just (res,_) <- decompLR_maybe (coercionKind co) = res
-coTyConAppKind CoRight (co:_)
- | Just (_,res) <- decompLR_maybe (coercionKind co) = res
-coTyConAppKind CoCsel1 (co:_)
- | Just (res,_,_) <- decompCsel_maybe (coercionKind co) = res
-coTyConAppKind CoCsel2 (co:_)
- | Just (_,res,_) <- decompCsel_maybe (coercionKind co) = res
-coTyConAppKind CoCselR (co:_)
- | Just (_,_,res) <- decompCsel_maybe (coercionKind co) = res
-coTyConAppKind CoInst (co:ty:_)
- | Just ((tv1,tv2), (ty1,ty2)) <- decompInst_maybe (coercionKind co)
- = (substTyWith [tv1] [ty] ty1, substTyWith [tv2] [ty] ty2)
-coTyConAppKind (CoAxiom { co_ax_tvs = tvs
- , co_ax_lhs = lhs_ty, co_ax_rhs = rhs_ty }) cos
- = (substTyWith tvs tys1 lhs_ty, substTyWith tvs tys2 rhs_ty)
- where
- (tys1, tys2) = coercionKinds cos
-coTyConAppKind desc cos = pprTrace "coTyConAppKind" (ppr desc $$ braces (vcat
- [ ppr co <+> dcolon <+> pprEqPred (coercionKind co)
- | co <- cos ])) $
- coercionKind (head cos)
+getNth :: Int -> Type -> Type
+getNth n ty | Just (_, tys) <- splitTyConApp_maybe ty
+ = ASSERT2( n < length tys, ppr n <+> ppr tys ) tys !! n
+getNth n ty = pprPanic "getNth" (ppr n <+> ppr ty)
\end{code}
+
+\begin{code}
+applyCo :: Type -> Coercion -> Type
+-- Gives the type of (e co) where e :: (a~b) => ty
+applyCo ty co | Just ty' <- coreView ty = applyCo ty' co
+applyCo (FunTy _ ty) _ = ty
+applyCo _ _ = panic "applyCo"
+\end{code}
\ No newline at end of file