ghc-9.12.1: GHC/Core/Coercion.hs
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-
(c) The University of Glasgow 2006
-}
-- | Module for (a) type kinds and (b) type coercions,
-- as used in System FC. See 'GHC.Core.Expr' for
-- more on System FC and how coercions fit into it.
--
module GHC.Core.Coercion (
-- * Main data type
Coercion, CoercionN, CoercionR, CoercionP,
MCoercion(..), MCoercionN, MCoercionR,
CoSel(..), FunSel(..),
UnivCoProvenance, CoercionHole(..),
coHoleCoVar, setCoHoleCoVar,
LeftOrRight(..),
Var, CoVar, TyCoVar,
Role(..), ltRole,
-- ** Functions over coercions
coVarRType, coVarLType, coVarTypes,
coVarKind, coVarTypesRole, coVarRole,
coercionType, mkCoercionType,
coercionKind, coercionLKind, coercionRKind,coercionKinds,
coercionRole, coercionKindRole,
-- ** Constructing coercions
mkGReflCo, mkGReflMCo, mkReflCo, mkRepReflCo, mkNomReflCo,
mkCoVarCo, mkCoVarCos,
mkAxInstCo, mkUnbranchedAxInstCo,
mkAxInstRHS, mkUnbranchedAxInstRHS,
mkAxInstLHS, mkUnbranchedAxInstLHS,
mkPiCo, mkPiCos, mkCoCast,
mkSymCo, mkTransCo,
mkSelCo, mkSelCoResRole, getNthFun, selectFromType, mkLRCo,
mkInstCo, mkAppCo, mkAppCos, mkTyConAppCo,
mkFunCo, mkFunCo2, mkFunCoNoFTF, mkFunResCo,
mkNakedFunCo,
mkNakedForAllCo, mkForAllCo, mkHomoForAllCos,
mkPhantomCo,
mkHoleCo, mkUnivCo, mkSubCo,
mkProofIrrelCo,
downgradeRole, mkAxiomCo,
mkGReflRightCo, mkGReflLeftCo, mkCoherenceLeftCo, mkCoherenceRightCo,
mkKindCo,
castCoercionKind, castCoercionKind1, castCoercionKind2,
mkPrimEqPred, mkReprPrimEqPred, mkPrimEqPredRole,
mkNomPrimEqPred,
-- ** Decomposition
instNewTyCon_maybe,
NormaliseStepper, NormaliseStepResult(..), composeSteppers, unwrapNewTypeStepper,
topNormaliseNewType_maybe, topNormaliseTypeX,
decomposeCo, decomposeFunCo, decomposePiCos, getCoVar_maybe,
splitAppCo_maybe,
splitFunCo_maybe,
splitForAllCo_maybe,
splitForAllCo_ty_maybe, splitForAllCo_co_maybe,
tyConRole, tyConRolesX, tyConRolesRepresentational, setNominalRole_maybe,
tyConRoleListX, tyConRoleListRepresentational, funRole,
pickLR,
isGReflCo, isReflCo, isReflCo_maybe, isGReflCo_maybe, isReflexiveCo, isReflexiveCo_maybe,
isReflCoVar_maybe, isGReflMCo, mkGReflLeftMCo, mkGReflRightMCo,
mkCoherenceRightMCo,
coToMCo, mkTransMCo, mkTransMCoL, mkTransMCoR, mkCastTyMCo, mkSymMCo,
mkFunResMCo, mkPiMCos,
isReflMCo, checkReflexiveMCo,
-- ** Coercion variables
mkCoVar, isCoVar, coVarName, setCoVarName, setCoVarUnique,
-- ** Free variables
tyCoVarsOfCo, tyCoVarsOfCos, coVarsOfCo,
tyCoFVsOfCo, tyCoFVsOfCos, tyCoVarsOfCoDSet,
coercionSize, anyFreeVarsOfCo,
-- ** Substitution
CvSubstEnv, emptyCvSubstEnv,
lookupCoVar,
substCo, substCos, substCoVar, substCoVars, substCoWith,
substCoVarBndr,
extendTvSubstAndInScope, getCvSubstEnv,
-- ** Lifting
liftCoSubst, liftCoSubstTyVar, liftCoSubstWith, liftCoSubstWithEx,
emptyLiftingContext, extendLiftingContext, extendLiftingContextAndInScope,
liftCoSubstVarBndrUsing, isMappedByLC, extendLiftingContextCvSubst,
mkSubstLiftingContext, liftingContextSubst, zapLiftingContext,
substForAllCoBndrUsingLC, lcLookupCoVar, lcInScopeSet,
LiftCoEnv, LiftingContext(..), liftEnvSubstLeft, liftEnvSubstRight,
substRightCo, substLeftCo, swapLiftCoEnv, lcSubstLeft, lcSubstRight,
-- ** Comparison
eqCoercion, eqCoercionX,
-- ** Forcing evaluation of coercions
seqCo,
-- * Pretty-printing
pprCo, pprParendCo,
pprCoAxiom, pprCoAxBranch, pprCoAxBranchLHS,
pprCoAxBranchUser, tidyCoAxBndrsForUser,
etaExpandCoAxBranch,
-- * Tidying
tidyCo, tidyCos,
-- * Other
promoteCoercion, buildCoercion,
multToCo, mkRuntimeRepCo,
hasCoercionHoleTy, hasCoercionHoleCo, hasThisCoercionHoleTy,
setCoHoleType
) where
import {-# SOURCE #-} GHC.CoreToIface (toIfaceTyCon, tidyToIfaceTcArgs)
import GHC.Prelude
import GHC.Iface.Type
import GHC.Core.TyCo.Rep
import GHC.Core.TyCo.FVs
import GHC.Core.TyCo.Ppr
import GHC.Core.TyCo.Subst
import GHC.Core.TyCo.Tidy
import GHC.Core.TyCo.Compare
import GHC.Core.Type
import GHC.Core.TyCon
import GHC.Core.TyCon.RecWalk
import GHC.Core.Coercion.Axiom
import GHC.Types.Var
import GHC.Types.Var.Env
import GHC.Types.Var.Set
import GHC.Types.Name hiding ( varName )
import GHC.Types.Basic
import GHC.Types.Unique
import GHC.Data.FastString
import GHC.Data.Pair
import GHC.Types.SrcLoc
import GHC.Builtin.Names
import GHC.Builtin.Types.Prim
import GHC.Data.List.SetOps
import GHC.Data.Maybe
import GHC.Types.Unique.FM
import GHC.Data.List.Infinite (Infinite (..))
import qualified GHC.Data.List.Infinite as Inf
import GHC.Utils.Misc
import GHC.Utils.Outputable
import GHC.Utils.Panic
import Control.Monad (foldM, zipWithM)
import Data.Function ( on )
import Data.Char( isDigit )
import qualified Data.Monoid as Monoid
import Control.DeepSeq
{-
%************************************************************************
%* *
-- The coercion arguments always *precisely* saturate
-- arity of (that branch of) the CoAxiom. If there are
-- any left over, we use AppCo. See
-- See [Coercion axioms applied to coercions] in GHC.Core.TyCo.Rep
\subsection{Coercion variables}
%* *
%************************************************************************
-}
coVarName :: CoVar -> Name
coVarName = varName
setCoVarUnique :: CoVar -> Unique -> CoVar
setCoVarUnique = setVarUnique
setCoVarName :: CoVar -> Name -> CoVar
setCoVarName = setVarName
{-
%************************************************************************
%* *
Pretty-printing CoAxioms
%* *
%************************************************************************
Defined here to avoid module loops. CoAxiom is loaded very early on.
-}
etaExpandCoAxBranch :: CoAxBranch -> ([TyVar], [Type], Type)
-- Return the (tvs,lhs,rhs) after eta-expanding,
-- to the way in which the axiom was originally written
-- See Note [Eta reduction for data families] in GHC.Core.Coercion.Axiom
etaExpandCoAxBranch (CoAxBranch { cab_tvs = tvs
, cab_eta_tvs = eta_tvs
, cab_lhs = lhs
, cab_rhs = rhs })
-- ToDo: what about eta_cvs?
= (tvs ++ eta_tvs, lhs ++ eta_tys, mkAppTys rhs eta_tys)
where
eta_tys = mkTyVarTys eta_tvs
pprCoAxiom :: CoAxiom br -> SDoc
-- Used in debug-printing only
pprCoAxiom ax@(CoAxiom { co_ax_tc = tc, co_ax_branches = branches })
= hang (text "axiom" <+> ppr ax)
2 (braces $ vcat (map (pprCoAxBranchUser tc) (fromBranches branches)))
pprCoAxBranchUser :: TyCon -> CoAxBranch -> SDoc
-- Used when printing injectivity errors (FamInst.reportInjectivityErrors)
-- and inaccessible branches (GHC.Tc.Validity.inaccessibleCoAxBranch)
-- This happens in error messages: don't print the RHS of a data
-- family axiom, which is meaningless to a user
pprCoAxBranchUser tc br
| isDataFamilyTyCon tc = pprCoAxBranchLHS tc br
| otherwise = pprCoAxBranch tc br
pprCoAxBranchLHS :: TyCon -> CoAxBranch -> SDoc
-- Print the family-instance equation when reporting
-- a conflict between equations (FamInst.conflictInstErr)
-- For type families the RHS is important; for data families not so.
-- Indeed for data families the RHS is a mysterious internal
-- type constructor, so we suppress it (#14179)
-- See FamInstEnv Note [Family instance overlap conflicts]
pprCoAxBranchLHS = ppr_co_ax_branch pp_rhs
where
pp_rhs _ _ = empty
pprCoAxBranch :: TyCon -> CoAxBranch -> SDoc
pprCoAxBranch = ppr_co_ax_branch ppr_rhs
where
ppr_rhs env rhs = equals <+> pprPrecTypeX env topPrec rhs
ppr_co_ax_branch :: (TidyEnv -> Type -> SDoc)
-> TyCon -> CoAxBranch -> SDoc
ppr_co_ax_branch ppr_rhs fam_tc branch
= foldr1 (flip hangNotEmpty 2)
[ pprUserForAll (mkForAllTyBinders Inferred bndrs')
-- See Note [Printing foralls in type family instances] in GHC.Iface.Type
, pp_lhs <+> ppr_rhs tidy_env ee_rhs
, vcat [ text "-- Defined" <+> pp_loc
, ppUnless (null incomps) $ whenPprDebug $
text "-- Incomps:" <+> vcat (map (pprCoAxBranch fam_tc) incomps) ]
]
where
incomps = coAxBranchIncomps branch
loc = coAxBranchSpan branch
pp_loc | isGoodSrcSpan loc = text "at" <+> ppr (srcSpanStart loc)
| otherwise = text "in" <+> ppr loc
-- Eta-expand LHS and RHS types, because sometimes data family
-- instances are eta-reduced.
-- See Note [Eta reduction for data families] in GHC.Core.Coercion.Axiom.
(ee_tvs, ee_lhs, ee_rhs) = etaExpandCoAxBranch branch
pp_lhs = pprIfaceTypeApp topPrec (toIfaceTyCon fam_tc)
(tidyToIfaceTcArgs tidy_env fam_tc ee_lhs)
(tidy_env, bndrs') = tidyCoAxBndrsForUser emptyTidyEnv ee_tvs
tidyCoAxBndrsForUser :: TidyEnv -> [Var] -> (TidyEnv, [Var])
-- Tidy wildcards "_1", "_2" to "_", and do not return them
-- in the list of binders to be printed
-- This is so that in error messages we see
-- forall a. F _ [a] _ = ...
-- rather than
-- forall a _1 _2. F _1 [a] _2 = ...
--
-- This is a rather disgusting function
-- See Note [Wildcard names] in GHC.Tc.Gen.HsType
tidyCoAxBndrsForUser init_env tcvs
= (tidy_env, reverse tidy_bndrs)
where
(tidy_env, tidy_bndrs) = foldl tidy_one (init_env, []) tcvs
tidy_one (env@(occ_env, subst), rev_bndrs') bndr
| is_wildcard bndr = (env_wild, rev_bndrs')
| otherwise = (env', bndr' : rev_bndrs')
where
(env', bndr') = tidyVarBndr env bndr
env_wild = (occ_env, extendVarEnv subst bndr wild_bndr)
wild_bndr = setVarName bndr $
tidyNameOcc (varName bndr) (mkTyVarOccFS (fsLit "_"))
-- Tidy the binder to "_"
is_wildcard :: Var -> Bool
is_wildcard tv = case occNameString (getOccName tv) of
('_' : rest) -> all isDigit rest
_ -> False
{- *********************************************************************
* *
MCoercion
* *
********************************************************************* -}
coToMCo :: Coercion -> MCoercion
-- Convert a coercion to a MCoercion,
-- It's not clear whether or not isReflexiveCo would be better here
-- See #19815 for a bit of data and discussion on this point
coToMCo co | isReflCo co = MRefl
| otherwise = MCo co
checkReflexiveMCo :: MCoercion -> MCoercion
checkReflexiveMCo MRefl = MRefl
checkReflexiveMCo (MCo co) | isReflexiveCo co = MRefl
| otherwise = MCo co
-- | Tests if this MCoercion is obviously generalized reflexive
-- Guaranteed to work very quickly.
isGReflMCo :: MCoercion -> Bool
isGReflMCo MRefl = True
isGReflMCo (MCo co) | isGReflCo co = True
isGReflMCo _ = False
-- | Make a generalized reflexive coercion
mkGReflCo :: Role -> Type -> MCoercionN -> Coercion
mkGReflCo r ty mco
| isGReflMCo mco = if r == Nominal then Refl ty
else GRefl r ty MRefl
| otherwise
= -- I'd like to have this assert, but sadly it's not true during type
-- inference because the types are not fully zonked
-- assertPpr (case mco of
-- MCo co -> typeKind ty `eqType` coercionLKind co
-- MRefl -> True)
-- (vcat [ text "ty" <+> ppr ty <+> dcolon <+> ppr (typeKind ty)
-- , case mco of
-- MCo co -> text "co" <+> ppr co
-- <+> dcolon <+> ppr (coercionKind co)
-- MRefl -> text "MRefl"
-- , callStackDoc ]) $
GRefl r ty mco
mkGReflMCo :: HasDebugCallStack => Role -> Type -> CoercionN -> Coercion
mkGReflMCo r ty co = mkGReflCo r ty (MCo co)
-- | Compose two MCoercions via transitivity
mkTransMCo :: MCoercion -> MCoercion -> MCoercion
mkTransMCo MRefl co2 = co2
mkTransMCo co1 MRefl = co1
mkTransMCo (MCo co1) (MCo co2) = MCo (mkTransCo co1 co2)
mkTransMCoL :: MCoercion -> Coercion -> MCoercion
mkTransMCoL MRefl co2 = coToMCo co2
mkTransMCoL (MCo co1) co2 = MCo (mkTransCo co1 co2)
mkTransMCoR :: Coercion -> MCoercion -> MCoercion
mkTransMCoR co1 MRefl = coToMCo co1
mkTransMCoR co1 (MCo co2) = MCo (mkTransCo co1 co2)
-- | Get the reverse of an 'MCoercion'
mkSymMCo :: MCoercion -> MCoercion
mkSymMCo MRefl = MRefl
mkSymMCo (MCo co) = MCo (mkSymCo co)
-- | Cast a type by an 'MCoercion'
mkCastTyMCo :: Type -> MCoercion -> Type
mkCastTyMCo ty MRefl = ty
mkCastTyMCo ty (MCo co) = ty `mkCastTy` co
mkPiMCos :: [Var] -> MCoercion -> MCoercion
mkPiMCos _ MRefl = MRefl
mkPiMCos vs (MCo co) = MCo (mkPiCos Representational vs co)
mkFunResMCo :: Id -> MCoercionR -> MCoercionR
mkFunResMCo _ MRefl = MRefl
mkFunResMCo arg_id (MCo co) = MCo (mkFunResCo Representational arg_id co)
mkGReflLeftMCo :: Role -> Type -> MCoercionN -> Coercion
mkGReflLeftMCo r ty MRefl = mkReflCo r ty
mkGReflLeftMCo r ty (MCo co) = mkGReflLeftCo r ty co
mkGReflRightMCo :: Role -> Type -> MCoercionN -> Coercion
mkGReflRightMCo r ty MRefl = mkReflCo r ty
mkGReflRightMCo r ty (MCo co) = mkGReflRightCo r ty co
-- | Like 'mkCoherenceRightCo', but with an 'MCoercion'
mkCoherenceRightMCo :: Role -> Type -> MCoercionN -> Coercion -> Coercion
mkCoherenceRightMCo _ _ MRefl co2 = co2
mkCoherenceRightMCo r ty (MCo co) co2 = mkCoherenceRightCo r ty co co2
isReflMCo :: MCoercion -> Bool
isReflMCo MRefl = True
isReflMCo _ = False
{-
%************************************************************************
%* *
Destructing coercions
%* *
%************************************************************************
-}
-- | 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 [r1, r2, r3] = [nth r1 0 c, nth r2 1 c, nth r3 2 c]
decomposeCo :: Arity -> Coercion
-> Infinite Role -- the roles of the output coercions
-> [Coercion]
decomposeCo arity co rs
= [mkSelCo (SelTyCon n r) co | (n,r) <- [0..(arity-1)] `zip` Inf.toList rs ]
-- Remember, SelTyCon is zero-indexed
decomposeFunCo :: HasDebugCallStack
=> Coercion -- Input coercion
-> (CoercionN, Coercion, Coercion)
-- Expects co :: (s1 %m1-> t1) ~ (s2 %m2-> t2)
-- Returns (cow :: m1 ~N m2, co1 :: s1~s2, co2 :: t1~t2)
-- actually cow will be a Phantom coercion if the input is a Phantom coercion
decomposeFunCo (FunCo { fco_mult = w, fco_arg = co1, fco_res = co2 })
= (w, co1, co2)
-- Short-circuits the calls to mkSelCo
decomposeFunCo co
= assertPpr all_ok (ppr co) $
( mkSelCo (SelFun SelMult) co
, mkSelCo (SelFun SelArg) co
, mkSelCo (SelFun SelRes) co )
where
Pair s1t1 s2t2 = coercionKind co
all_ok = isFunTy s1t1 && isFunTy s2t2
{- Note [Pushing a coercion into a pi-type]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have this:
(f |> co) t1 .. tn
Then we want to push the coercion into the arguments, so as to make
progress. For example of why you might want to do so, see Note
[Respecting definitional equality] in GHC.Core.TyCo.Rep.
This is done by decomposePiCos. Specifically, if
decomposePiCos co [t1,..,tn] = ([co1,...,cok], cor)
then
(f |> co) t1 .. tn = (f (t1 |> co1) ... (tk |> cok)) |> cor) t(k+1) ... tn
Notes:
* k can be smaller than n! That is decomposePiCos can return *fewer*
coercions than there are arguments (ie k < n), if the kind provided
doesn't have enough binders.
* If there is a type error, we might see
(f |> co) t1
where co :: (forall a. ty) ~ (ty1 -> ty2)
Here 'co' is insoluble, but we don't want to crash in decoposePiCos.
So decomposePiCos carefully tests both sides of the coercion to check
they are both foralls or both arrows. Not doing this caused #15343.
-}
decomposePiCos :: HasDebugCallStack
=> CoercionN -> Pair Type -- Coercion and its kind
-> [Type]
-> ([CoercionN], CoercionN)
-- See Note [Pushing a coercion into a pi-type]
decomposePiCos orig_co (Pair orig_k1 orig_k2) orig_args
= go [] (orig_subst,orig_k1) orig_co (orig_subst,orig_k2) orig_args
where
orig_subst = mkEmptySubst $ mkInScopeSet $
tyCoVarsOfTypes orig_args `unionVarSet` tyCoVarsOfCo orig_co
go :: [CoercionN] -- accumulator for argument coercions, reversed
-> (Subst,Kind) -- Lhs kind of coercion
-> CoercionN -- coercion originally applied to the function
-> (Subst,Kind) -- Rhs kind of coercion
-> [Type] -- Arguments to that function
-> ([CoercionN], Coercion)
-- Invariant: co :: subst1(k1) ~ subst2(k2)
go acc_arg_cos (subst1,k1) co (subst2,k2) (ty:tys)
| Just (a, t1) <- splitForAllTyCoVar_maybe k1
, Just (b, t2) <- splitForAllTyCoVar_maybe k2
-- know co :: (forall a:s1.t1) ~ (forall b:s2.t2)
-- function :: forall a:s1.t1 (the function is not passed to decomposePiCos)
-- a :: s1
-- b :: s2
-- ty :: s2
-- need arg_co :: s2 ~ s1
-- res_co :: t1[ty |> arg_co / a] ~ t2[ty / b]
= let arg_co = mkSelCo SelForAll (mkSymCo co)
res_co = mkInstCo co (mkGReflLeftCo Nominal ty arg_co)
subst1' = extendTCvSubst subst1 a (ty `CastTy` arg_co)
subst2' = extendTCvSubst subst2 b ty
in
go (arg_co : acc_arg_cos) (subst1', t1) res_co (subst2', t2) tys
| Just (af1, _w1, _s1, t1) <- splitFunTy_maybe k1
, Just (af2, _w1, _s2, t2) <- splitFunTy_maybe k2
, af1 == af2 -- Same sort of arrow
-- know co :: (s1 -> t1) ~ (s2 -> t2)
-- function :: s1 -> t1
-- ty :: s2
-- need arg_co :: s2 ~ s1
-- res_co :: t1 ~ t2
= let (_, sym_arg_co, res_co) = decomposeFunCo co
-- It should be fine to ignore the multiplicity bit
-- of the coercion for a Nominal coercion.
arg_co = mkSymCo sym_arg_co
in
go (arg_co : acc_arg_cos) (subst1,t1) res_co (subst2,t2) tys
| not (isEmptyTCvSubst subst1) || not (isEmptyTCvSubst subst2)
= go acc_arg_cos (zapSubst subst1, substTy subst1 k1)
co
(zapSubst subst2, substTy subst1 k2)
(ty:tys)
-- tys might not be empty, if the left-hand type of the original coercion
-- didn't have enough binders
go acc_arg_cos _ki1 co _ki2 _tys = (reverse acc_arg_cos, co)
-- | Extract a covar, if possible. This check is dirty. Be ashamed
-- of yourself. (It's dirty because it cares about the structure of
-- a coercion, which is morally reprehensible.)
getCoVar_maybe :: Coercion -> Maybe CoVar
getCoVar_maybe (CoVarCo cv) = Just cv
getCoVar_maybe _ = Nothing
multToCo :: Mult -> Coercion
multToCo r = mkNomReflCo r
-- first result has role equal to input; third result is Nominal
splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion)
-- ^ Attempt to take a coercion application apart.
splitAppCo_maybe (AppCo co arg) = Just (co, arg)
splitAppCo_maybe (TyConAppCo r tc args)
| args `lengthExceeds` tyConArity tc
, Just (args', arg') <- snocView args
= Just ( mkTyConAppCo r tc args', arg' )
| not (tyConMustBeSaturated tc)
-- Never create unsaturated type family apps!
, Just (args', arg') <- snocView args
, Just arg'' <- setNominalRole_maybe (tyConRole r tc (length args')) arg'
= Just ( mkTyConAppCo r tc args', arg'' )
-- Use mkTyConAppCo to preserve the invariant
-- that identity coercions are always represented by Refl
splitAppCo_maybe co
| Just (ty, r) <- isReflCo_maybe co
, Just (ty1, ty2) <- splitAppTy_maybe ty
= Just (mkReflCo r ty1, mkNomReflCo ty2)
splitAppCo_maybe _ = Nothing
-- Only used in specialise/Rules
splitFunCo_maybe :: Coercion -> Maybe (Coercion, Coercion)
splitFunCo_maybe (FunCo { fco_arg = arg, fco_res = res }) = Just (arg, res)
splitFunCo_maybe _ = Nothing
splitForAllCo_maybe :: Coercion -> Maybe (TyCoVar, ForAllTyFlag, ForAllTyFlag, Coercion, Coercion)
splitForAllCo_maybe (ForAllCo { fco_tcv = tv, fco_visL = vL, fco_visR = vR
, fco_kind = k_co, fco_body = co })
= Just (tv, vL, vR, k_co, co)
splitForAllCo_maybe co
| Just (ty, r) <- isReflCo_maybe co
, Just (Bndr tcv vis, body_ty) <- splitForAllForAllTyBinder_maybe ty
= Just (tcv, vis, vis, mkNomReflCo (varType tcv), mkReflCo r body_ty)
splitForAllCo_maybe _ = Nothing
-- | Like 'splitForAllCo_maybe', but only returns Just for tyvar binder
splitForAllCo_ty_maybe :: Coercion -> Maybe (TyVar, ForAllTyFlag, ForAllTyFlag, Coercion, Coercion)
splitForAllCo_ty_maybe co
| Just stuff@(tv, _, _, _, _) <- splitForAllCo_maybe co
, isTyVar tv
= Just stuff
splitForAllCo_ty_maybe _ = Nothing
-- | Like 'splitForAllCo_maybe', but only returns Just for covar binder
splitForAllCo_co_maybe :: Coercion -> Maybe (CoVar, ForAllTyFlag, ForAllTyFlag, Coercion, Coercion)
splitForAllCo_co_maybe co
| Just stuff@(cv, _, _, _, _) <- splitForAllCo_maybe co
, isCoVar cv
= Just stuff
splitForAllCo_co_maybe _ = Nothing
-------------------------------------------------------
-- and some coercion kind stuff
coVarLType, coVarRType :: HasDebugCallStack => CoVar -> Type
coVarLType cv | (ty1, _, _) <- coVarTypesRole cv = ty1
coVarRType cv | (_, ty2, _) <- coVarTypesRole cv = ty2
coVarTypes :: HasDebugCallStack => CoVar -> Pair Type
coVarTypes cv | (ty1, ty2, _) <- coVarTypesRole cv = Pair ty1 ty2
coVarTypesRole :: HasDebugCallStack => CoVar -> (Type,Type,Role)
coVarTypesRole cv
| Just (tc, [_,_,ty1,ty2]) <- splitTyConApp_maybe (varType cv)
= (ty1, ty2, eqTyConRole tc)
| otherwise
= pprPanic "coVarTypesRole, non coercion variable"
(ppr cv $$ ppr (varType cv))
coVarKind :: CoVar -> Type
coVarKind cv
= assert (isCoVar cv )
varType cv
coVarRole :: CoVar -> Role
coVarRole cv
= eqTyConRole (case tyConAppTyCon_maybe (varType cv) of
Just tc0 -> tc0
Nothing -> pprPanic "coVarRole: not tyconapp" (ppr cv))
eqTyConRole :: TyCon -> Role
-- Given (~#) or (~R#) return the Nominal or Representational respectively
eqTyConRole tc
| tc `hasKey` eqPrimTyConKey
= Nominal
| tc `hasKey` eqReprPrimTyConKey
= Representational
| otherwise
= pprPanic "eqTyConRole: unknown tycon" (ppr tc)
-- | Given a coercion `co :: (t1 :: TYPE r1) ~ (t2 :: TYPE r2)`
-- produce a coercion `rep_co :: r1 ~ r2`
-- But actually it is possible that
-- co :: (t1 :: CONSTRAINT r1) ~ (t2 :: CONSTRAINT r2)
-- or co :: (t1 :: TYPE r1) ~ (t2 :: CONSTRAINT r2)
-- or co :: (t1 :: CONSTRAINT r1) ~ (t2 :: TYPE r2)
-- See Note [mkRuntimeRepCo]
mkRuntimeRepCo :: HasDebugCallStack => Coercion -> Coercion
mkRuntimeRepCo co
= assert (isTYPEorCONSTRAINT k1 && isTYPEorCONSTRAINT k2) $
mkSelCo (SelTyCon 0 Nominal) kind_co
where
kind_co = mkKindCo co -- kind_co :: TYPE r1 ~ TYPE r2
Pair k1 k2 = coercionKind kind_co
{- Note [mkRuntimeRepCo]
~~~~~~~~~~~~~~~~~~~~~~~~
Given
class C a where { op :: Maybe a }
we will get an axiom
axC a :: (C a :: CONSTRAINT r1) ~ (Maybe a :: TYPE r2)
(See Note [Type and Constraint are not apart] in GHC.Builtin.Types.Prim.)
Then we may call mkRuntimeRepCo on (axC ty), and that will return
mkSelCo (SelTyCon 0 Nominal) (Kind (axC ty)) :: r1 ~ r2
So mkSelCo needs to be happy with decomposing a coercion of kind
CONSTRAINT r1 ~ TYPE r2
Hence the use of `tyConIsTYPEorCONSTRAINT` in the assertion `good_call`
in `mkSelCo`. See #23018 for a concrete example. (In this context it's
important that TYPE and CONSTRAINT have the same arity and kind, not
merely that they are not-apart; otherwise SelCo would not make sense.)
-}
isReflCoVar_maybe :: Var -> Maybe Coercion
-- If cv :: t~t then isReflCoVar_maybe cv = Just (Refl t)
-- Works on all kinds of Vars, not just CoVars
isReflCoVar_maybe cv
| isCoVar cv
, Pair ty1 ty2 <- coVarTypes cv
, ty1 `eqType` ty2
= Just (mkReflCo (coVarRole cv) ty1)
| otherwise
= Nothing
-- | Tests if this coercion is obviously a generalized reflexive coercion.
-- Guaranteed to work very quickly.
isGReflCo :: Coercion -> Bool
isGReflCo (GRefl{}) = True
isGReflCo (Refl{}) = True -- Refl ty == GRefl N ty MRefl
isGReflCo _ = False
-- | Tests if this coercion is obviously reflexive. Guaranteed to work
-- very quickly. Sometimes a coercion can be reflexive, but not obviously
-- so. c.f. 'isReflexiveCo'
isReflCo :: Coercion -> Bool
isReflCo (Refl{}) = True
isReflCo (GRefl _ _ mco) | isGReflMCo mco = True
isReflCo _ = False
-- | Returns the type coerced if this coercion is a generalized reflexive
-- coercion. Guaranteed to work very quickly.
isGReflCo_maybe :: Coercion -> Maybe (Type, Role)
isGReflCo_maybe (GRefl r ty _) = Just (ty, r)
isGReflCo_maybe (Refl ty) = Just (ty, Nominal)
isGReflCo_maybe _ = Nothing
-- | Returns the type coerced if this coercion is reflexive. Guaranteed
-- to work very quickly. Sometimes a coercion can be reflexive, but not
-- obviously so. c.f. 'isReflexiveCo_maybe'
isReflCo_maybe :: Coercion -> Maybe (Type, Role)
isReflCo_maybe (Refl ty) = Just (ty, Nominal)
isReflCo_maybe (GRefl r ty mco) | isGReflMCo mco = Just (ty, r)
isReflCo_maybe _ = Nothing
-- | Slowly checks if the coercion is reflexive. Don't call this in a loop,
-- as it walks over the entire coercion.
isReflexiveCo :: Coercion -> Bool
isReflexiveCo = isJust . isReflexiveCo_maybe
-- | Extracts the coerced type from a reflexive coercion. This potentially
-- walks over the entire coercion, so avoid doing this in a loop.
isReflexiveCo_maybe :: Coercion -> Maybe (Type, Role)
isReflexiveCo_maybe (Refl ty) = Just (ty, Nominal)
isReflexiveCo_maybe (GRefl r ty mco) | isGReflMCo mco = Just (ty, r)
isReflexiveCo_maybe co
| ty1 `eqType` ty2
= Just (ty1, r)
| otherwise
= Nothing
where (Pair ty1 ty2, r) = coercionKindRole co
{-
%************************************************************************
%* *
Building coercions
%* *
%************************************************************************
These "smart constructors" maintain the invariants listed in the definition
of Coercion, and they perform very basic optimizations.
Note [Role twiddling functions]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
There are a plethora of functions for twiddling roles:
mkSubCo: Requires a nominal input coercion and always produces a
representational output. This is used when you (the programmer) are sure you
know exactly that role you have and what you want.
downgradeRole_maybe: This function takes both the input role and the output role
as parameters. (The *output* role comes first!) It can only *downgrade* a
role -- that is, change it from N to R or P, or from R to P. This one-way
behavior is why there is the "_maybe". If an upgrade is requested, this
function produces Nothing. This is used when you need to change the role of a
coercion, but you're not sure (as you're writing the code) of which roles are
involved.
This function could have been written using coercionRole to ascertain the role
of the input. But, that function is recursive, and the caller of downgradeRole_maybe
often knows the input role. So, this is more efficient.
downgradeRole: This is just like downgradeRole_maybe, but it panics if the
conversion isn't a downgrade.
setNominalRole_maybe: This is the only function that can *upgrade* a coercion.
The result (if it exists) is always Nominal. The input can be at any role. It
works on a "best effort" basis, as it should never be strictly necessary to
upgrade a coercion during compilation. It is currently only used within GHC in
splitAppCo_maybe. In order to be a proper inverse of mkAppCo, the second
coercion that splitAppCo_maybe returns must be nominal. But, it's conceivable
that splitAppCo_maybe is operating over a TyConAppCo that uses a
representational coercion. Hence the need for setNominalRole_maybe.
splitAppCo_maybe, in turn, is used only within coercion optimization -- thus,
it is not absolutely critical that setNominalRole_maybe be complete.
Note that setNominalRole_maybe will never upgrade a phantom UnivCo. Phantom
UnivCos are perfectly type-safe, whereas representational and nominal ones are
not. (Nominal ones are no worse than representational ones, so this function *will*
change a UnivCo Representational to a UnivCo Nominal.)
Conal Elliott also came across a need for this function while working with the
GHC API, as he was decomposing Core casts. The Core casts use representational
coercions, as they must, but his use case required nominal coercions (he was
building a GADT). So, that's why this function is exported from this module.
One might ask: shouldn't downgradeRole_maybe just use setNominalRole_maybe as
appropriate? I (Richard E.) have decided not to do this, because upgrading a
role is bizarre and a caller should have to ask for this behavior explicitly.
-}
-- | Make a reflexive coercion
mkReflCo :: Role -> Type -> Coercion
mkReflCo Nominal ty = Refl ty
mkReflCo r ty = GRefl r ty MRefl
-- | Make a representational reflexive coercion
mkRepReflCo :: Type -> Coercion
mkRepReflCo ty = GRefl Representational ty MRefl
-- | Make a nominal reflexive coercion
mkNomReflCo :: Type -> Coercion
mkNomReflCo = Refl
-- | Apply a type constructor to a list of coercions. It is the
-- caller's responsibility to get the roles correct on argument coercions.
mkTyConAppCo :: HasDebugCallStack => Role -> TyCon -> [Coercion] -> Coercion
mkTyConAppCo r tc cos
| Just co <- tyConAppFunCo_maybe r tc cos
= co
-- Expand type synonyms
| ExpandsSyn tv_co_prs rhs_ty leftover_cos <- expandSynTyCon_maybe tc cos
= mkAppCos (liftCoSubst r (mkLiftingContext tv_co_prs) rhs_ty) leftover_cos
| Just tys_roles <- traverse isReflCo_maybe cos
= mkReflCo r (mkTyConApp tc (map fst tys_roles))
-- See Note [Refl invariant]
| otherwise = TyConAppCo r tc cos
mkFunCoNoFTF :: HasDebugCallStack => Role -> CoercionN -> Coercion -> Coercion -> Coercion
-- This version of mkFunCo takes no FunTyFlags; it works them out
mkFunCoNoFTF r w arg_co res_co
= mkFunCo2 r afl afr w arg_co res_co
where
afl = chooseFunTyFlag argl_ty resl_ty
afr = chooseFunTyFlag argr_ty resr_ty
Pair argl_ty argr_ty = coercionKind arg_co
Pair resl_ty resr_ty = coercionKind res_co
-- | Build a function 'Coercion' from two other 'Coercion's. That is,
-- given @co1 :: a ~ b@ and @co2 :: x ~ y@ produce @co :: (a -> x) ~ (b -> y)@
-- or @(a => x) ~ (b => y)@, depending on the kind of @a@/@b@.
-- This (most common) version takes a single FunTyFlag, which is used
-- for both fco_afl and ftf_afr of the FunCo
mkFunCo :: Role -> FunTyFlag -> CoercionN -> Coercion -> Coercion -> Coercion
mkFunCo r af w arg_co res_co
= mkFunCo2 r af af w arg_co res_co
mkNakedFunCo :: Role -> FunTyFlag -> CoercionN -> Coercion -> Coercion -> Coercion
-- This version of mkFunCo does not check FunCo invariants (checkFunCo)
-- It's a historical vestige; See Note [No assertion check on mkFunCo]
mkNakedFunCo = mkFunCo
mkFunCo2 :: Role -> FunTyFlag -> FunTyFlag
-> CoercionN -> Coercion -> Coercion -> Coercion
-- This is the smart constructor for FunCo; it checks invariants
mkFunCo2 r afl afr w arg_co res_co
-- See Note [No assertion check on mkFunCo]
| Just (ty1, _) <- isReflCo_maybe arg_co
, Just (ty2, _) <- isReflCo_maybe res_co
, Just (w, _) <- isReflCo_maybe w
= mkReflCo r (mkFunTy afl w ty1 ty2) -- See Note [Refl invariant]
| otherwise
= FunCo { fco_role = r, fco_afl = afl, fco_afr = afr
, fco_mult = w, fco_arg = arg_co, fco_res = res_co }
{- Note [No assertion check on mkFunCo]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We used to have a checkFunCo assertion on mkFunCo, but during typechecking
we can (legitimately) have not-full-zonked types or coercion variables, so
the assertion spuriously fails (test T11480b is a case in point). Lint
checks all these things anyway.
We used to get around the problem by calling mkNakedFunCo from within the
typechecker, which dodged the assertion check. But then mkAppCo calls
mkTyConAppCo, which calls tyConAppFunCo_maybe, which calls mkFunCo.
Duplicating this stack of calls with "naked" versions of each seems too much.
-- Commented out: see Note [No assertion check on mkFunCo]
checkFunCo :: Role -> FunTyFlag -> FunTyFlag
-> CoercionN -> Coercion -> Coercion
-> Maybe SDoc
-- Checks well-formed-ness for FunCo
-- Used only in assertions and Lint
{-# NOINLINE checkFunCo #-}
checkFunCo _r afl afr _w arg_co res_co
| not (ok argl_ty && ok argr_ty && ok resl_ty && ok resr_ty)
= Just (hang (text "Bad arg or res types") 2 pp_inputs)
| afl == computed_afl
, afr == computed_afr
= Nothing
| otherwise
= Just (vcat [ text "afl (provided,computed):" <+> ppr afl <+> ppr computed_afl
, text "afr (provided,computed):" <+> ppr afr <+> ppr computed_afr
, pp_inputs ])
where
computed_afl = chooseFunTyFlag argl_ty resl_ty
computed_afr = chooseFunTyFlag argr_ty resr_ty
Pair argl_ty argr_ty = coercionKind arg_co
Pair resl_ty resr_ty = coercionKind res_co
pp_inputs = vcat [ pp_ty "argl" argl_ty, pp_ty "argr" argr_ty
, pp_ty "resl" resl_ty, pp_ty "resr" resr_ty
, text "arg_co:" <+> ppr arg_co
, text "res_co:" <+> ppr res_co ]
ok ty = isTYPEorCONSTRAINT (typeKind ty)
pp_ty str ty = text str <> colon <+> hang (ppr ty)
2 (dcolon <+> ppr (typeKind ty))
-}
-- | Apply a 'Coercion' to another 'Coercion'.
-- The second coercion must be Nominal, unless the first is Phantom.
-- If the first is Phantom, then the second can be either Phantom or Nominal.
mkAppCo :: Coercion -- ^ :: t1 ~r t2
-> Coercion -- ^ :: s1 ~N s2, where s1 :: k1, s2 :: k2
-> Coercion -- ^ :: t1 s1 ~r t2 s2
mkAppCo co arg
| Just (ty1, r) <- isReflCo_maybe co
, Just (ty2, _) <- isReflCo_maybe arg
= mkReflCo r (mkAppTy ty1 ty2)
| Just (ty1, r) <- isReflCo_maybe co
, Just (tc, tys) <- splitTyConApp_maybe ty1
-- Expand type synonyms; a TyConAppCo can't have a type synonym (#9102)
= mkTyConAppCo r tc (zip_roles (tyConRolesX r tc) tys)
where
zip_roles (Inf r1 _) [] = [downgradeRole r1 Nominal arg]
zip_roles (Inf r1 rs) (ty1:tys) = mkReflCo r1 ty1 : zip_roles rs tys
mkAppCo (TyConAppCo r tc args) arg
= case r of
Nominal -> mkTyConAppCo Nominal tc (args ++ [arg])
Representational -> mkTyConAppCo Representational tc (args ++ [arg'])
where new_role = tyConRolesRepresentational tc Inf.!! length args
arg' = downgradeRole new_role Nominal arg
Phantom -> mkTyConAppCo Phantom tc (args ++ [toPhantomCo arg])
mkAppCo co arg = AppCo co arg
-- 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 GHC.Core.TyCo.Rep.
-- | Applies multiple 'Coercion's to another 'Coercion', from left to right.
-- See also 'mkAppCo'.
mkAppCos :: Coercion
-> [Coercion]
-> Coercion
mkAppCos co1 cos = foldl' mkAppCo co1 cos
-- | Make a Coercion from a tycovar, a kind coercion, and a body coercion.
mkForAllCo :: HasDebugCallStack => TyCoVar -> ForAllTyFlag -> ForAllTyFlag -> CoercionN -> Coercion -> Coercion
mkForAllCo v visL visR kind_co co
| Just (ty, r) <- isReflCo_maybe co
, isReflCo kind_co
, visL `eqForAllVis` visR
= mkReflCo r (mkTyCoForAllTy v visL ty)
| otherwise
= mkForAllCo_NoRefl v visL visR kind_co co
-- | Make a Coercion quantified over a type/coercion variable;
-- the variable has the same kind and visibility in both sides of the coercion
mkHomoForAllCos :: [ForAllTyBinder] -> Coercion -> Coercion
mkHomoForAllCos vs orig_co
| Just (ty, r) <- isReflCo_maybe orig_co
= mkReflCo r (mkTyCoForAllTys vs ty)
| otherwise
= foldr go orig_co vs
where
go (Bndr var vis) co
= mkForAllCo_NoRefl var vis vis (mkNomReflCo (varType var)) co
-- | Like 'mkForAllCo', but there is no need to check that the inner coercion isn't Refl;
-- the caller has done that. (For example, it is guaranteed in 'mkHomoForAllCos'.)
-- The kind of the tycovar should be the left-hand kind of the kind coercion.
mkForAllCo_NoRefl :: TyCoVar -> ForAllTyFlag -> ForAllTyFlag -> CoercionN -> Coercion -> Coercion
mkForAllCo_NoRefl tcv visL visR kind_co co
= assertGoodForAllCo tcv visL visR kind_co co $
assertPpr (not (isReflCo co && isReflCo kind_co && visL == visR)) (ppr co) $
ForAllCo { fco_tcv = tcv, fco_visL = visL, fco_visR = visR
, fco_kind = kind_co, fco_body = co }
assertGoodForAllCo :: HasDebugCallStack
=> TyCoVar -> ForAllTyFlag -> ForAllTyFlag
-> CoercionN -> Coercion -> a -> a
-- Check ForAllCo invariants; see Note [ForAllCo] in GHC.Core.TyCo.Rep
assertGoodForAllCo tcv visL visR kind_co co
| isTyVar tcv
= assertPpr (tcv_type `eqType` kind_co_lkind) doc
| otherwise
= assertPpr (tcv_type `eqType` kind_co_lkind) doc
-- The kind of the tycovar should be the left-hand kind of the kind coercion.
. assertPpr (almostDevoidCoVarOfCo tcv co) doc
-- See (FC6) in Note [ForAllCo] in GHC.Core.TyCo.Rep
. assertPpr (visL == coreTyLamForAllTyFlag
&& visR == coreTyLamForAllTyFlag) doc
-- See (FC7) in Note [ForAllCo] in GHC.Core.TyCo.Rep
where
tcv_type = varType tcv
kind_co_lkind = coercionLKind kind_co
doc = vcat [ text "Var:" <+> ppr tcv <+> dcolon <+> ppr tcv_type
, text "Vis:" <+> ppr visL <+> ppr visR
, text "kind_co:" <+> ppr kind_co
, text "kind_co_lkind" <+> ppr kind_co_lkind
, text "body_co" <+> ppr co ]
mkNakedForAllCo :: TyVar -- Never a CoVar
-> ForAllTyFlag -> ForAllTyFlag
-> CoercionN -> Coercion -> Coercion
-- This version lacks the assertion checks.
-- Used during type checking when the arguments may (legitimately) not be zonked
-- and so the assertions might (bogusly) fail
-- NB: since the coercions are un-zonked, we can't really deal with
-- (FC6) and (FC7) in Note [ForAllCo] in GHC.Core.TyCo.Rep.
-- Fortunately we don't have to: this function is needed only for /type/ variables.
mkNakedForAllCo tv visL visR kind_co co
| assertPpr (isTyVar tv) (ppr tv) True
, Just (ty, r) <- isReflCo_maybe co
, isReflCo kind_co
, visL `eqForAllVis` visR
= mkReflCo r (mkForAllTy (Bndr tv visL) ty)
| otherwise
= ForAllCo { fco_tcv = tv, fco_visL = visL, fco_visR = visR
, fco_kind = kind_co, fco_body = co }
mkCoVarCo :: CoVar -> Coercion
-- cv :: s ~# t
-- See Note [mkCoVarCo]
mkCoVarCo cv = CoVarCo cv
mkCoVarCos :: [CoVar] -> [Coercion]
mkCoVarCos = map mkCoVarCo
{- Note [mkCoVarCo]
~~~~~~~~~~~~~~~~~~~
In the past, mkCoVarCo optimised (c :: t~t) to (Refl t). That is
valid (although see Note [Unbound RULE binders] in GHC.Core.Rules), but
it's a relatively expensive test and perhaps better done in
optCoercion. Not a big deal either way.
-}
mkAxInstCo :: Role
-> CoAxiomRule -- Always BranchedAxiom or UnbranchedAxiom
-> [Type] -> [Coercion]
-> Coercion
-- mkAxInstCo can legitimately be called over-saturated;
-- i.e. with more type arguments than the coercion requires
-- Only called with BranchedAxiom or UnbranchedAxiom
mkAxInstCo role axr tys cos
| arity == n_tys = downgradeRole role ax_role $
AxiomCo axr (rtys `chkAppend` cos)
| otherwise = assert (arity < n_tys) $
downgradeRole role ax_role $
mkAppCos (AxiomCo axr (ax_args `chkAppend` cos))
leftover_args
where
(ax_role, branch) = case coAxiomRuleBranch_maybe axr of
Just (_tc, ax_role, branch) -> (ax_role, branch)
Nothing -> pprPanic "mkAxInstCo" (ppr axr)
n_tys = length tys
arity = length (coAxBranchTyVars branch)
arg_roles = coAxBranchRoles branch
rtys = zipWith mkReflCo (arg_roles ++ repeat Nominal) tys
(ax_args, leftover_args) = splitAt arity rtys
-- worker function
mkAxiomCo :: CoAxiomRule -> [Coercion] -> Coercion
mkAxiomCo = AxiomCo
-- to be used only with unbranched axioms
mkUnbranchedAxInstCo :: Role -> CoAxiom Unbranched
-> [Type] -> [Coercion] -> Coercion
mkUnbranchedAxInstCo role ax tys cos
= mkAxInstCo role (UnbranchedAxiom ax) tys cos
mkAxInstRHS :: CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Type
-- Instantiate the axiom with specified types,
-- returning the instantiated RHS
-- A companion to mkAxInstCo:
-- mkAxInstRhs ax index tys = snd (coercionKind (mkAxInstCo ax index tys))
mkAxInstRHS ax index tys cos
= assert (tvs `equalLength` tys1) $
mkAppTys rhs' tys2
where
branch = coAxiomNthBranch ax index
tvs = coAxBranchTyVars branch
cvs = coAxBranchCoVars branch
(tys1, tys2) = splitAtList tvs tys
rhs' = substTyWith tvs tys1 $
substTyWithCoVars cvs cos $
coAxBranchRHS branch
mkUnbranchedAxInstRHS :: CoAxiom Unbranched -> [Type] -> [Coercion] -> Type
mkUnbranchedAxInstRHS ax = mkAxInstRHS ax 0
-- | Return the left-hand type of the axiom, when the axiom is instantiated
-- at the types given.
mkAxInstLHS :: CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Type
mkAxInstLHS ax index tys cos
= assert (tvs `equalLength` tys1) $
mkTyConApp fam_tc (lhs_tys `chkAppend` tys2)
where
branch = coAxiomNthBranch ax index
tvs = coAxBranchTyVars branch
cvs = coAxBranchCoVars branch
(tys1, tys2) = splitAtList tvs tys
lhs_tys = substTysWith tvs tys1 $
substTysWithCoVars cvs cos $
coAxBranchLHS branch
fam_tc = coAxiomTyCon ax
-- | Instantiate the left-hand side of an unbranched axiom
mkUnbranchedAxInstLHS :: CoAxiom Unbranched -> [Type] -> [Coercion] -> Type
mkUnbranchedAxInstLHS ax = mkAxInstLHS ax 0
-- | Make a coercion from a coercion hole
mkHoleCo :: CoercionHole -> Coercion
mkHoleCo h = HoleCo h
-- | Make a universal coercion between two arbitrary types.
mkUnivCo :: UnivCoProvenance
-> [Coercion] -- ^ Coercions on which this depends
-> Role -- ^ role of the built coercion, "r"
-> Type -- ^ t1 :: k1
-> Type -- ^ t2 :: k2
-> Coercion -- ^ :: t1 ~r t2
mkUnivCo prov deps role ty1 ty2
| ty1 `eqType` ty2 = mkReflCo role ty1
| otherwise = UnivCo { uco_prov = prov, uco_role = role
, uco_lty = ty1, uco_rty = ty2
, uco_deps = deps }
-- | 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, mainly to expose the underlying
-- constructors to other 'mk' functions. E.g.
-- mkInstCo (mkSymCo (ForAllCo ...)) ty
-- We want to push the SymCo inside the ForallCo, so that we can instantiate
-- This can make a big difference. E.g without coercion optimisation, GHC.Read
-- totally explodes; but when we push Sym inside ForAll, it's fine.
mkSymCo co | isReflCo co = co
mkSymCo (SymCo co) = co
mkSymCo (SubCo (SymCo co)) = SubCo co
mkSymCo co@(ForAllCo { fco_kind = kco, fco_body = body_co })
| isReflCo kco = co { fco_body = mkSymCo body_co }
mkSymCo co = SymCo co
-- | mkTransCo creates a new 'Coercion' by composing the two
-- given 'Coercion's transitively: (co1 ; co2)
mkTransCo :: HasDebugCallStack => Coercion -> Coercion -> Coercion
mkTransCo co1 co2
| isReflCo co1 = co2
| isReflCo co2 = co1
| GRefl r t1 (MCo kco1) <- co1
, GRefl _ _ (MCo kco2) <- co2
= GRefl r t1 (MCo $ mkTransCo kco1 kco2)
| otherwise
= TransCo co1 co2
--------------------
{- Note [mkSelCo precondition]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To satisfy the Purely Kinded Type Invariant (PKTI), we require that
in any call (mkSelCo cs co)
* selectFromType cs (coercionLKind co) works
* selectFromType cs (coercionRKind co) works
* and hence coercionKind (SelCo cs co) works (PKTI)
-}
mkSelCo :: HasDebugCallStack
=> CoSel
-> Coercion
-> Coercion
-- See Note [mkSelCo precondition]
mkSelCo n co = mkSelCo_maybe n co `orElse` SelCo n co
mkSelCo_maybe :: HasDebugCallStack
=> CoSel
-> Coercion
-> Maybe Coercion
-- Note [mkSelCo precondition]
mkSelCo_maybe cs co
= assertPpr (good_call cs) bad_call_msg $
go cs co
where
go SelForAll (ForAllCo { fco_kind = kind_co })
= Just kind_co
-- If co :: (forall a1:k1. t1) ~ (forall a2:k2. t2)
-- then (nth SelForAll co :: k1 ~N k2)
-- If co :: (forall a1:t1 ~ t2. t1) ~ (forall a2:t3 ~ t4. t2)
-- then (nth SelForAll co :: (t1 ~ t2) ~N (t3 ~ t4))
go (SelFun fs) (FunCo _ _ _ w arg res)
= Just (getNthFun fs w arg res)
go (SelTyCon i r) (TyConAppCo r0 tc arg_cos)
= assertPpr (r == tyConRole r0 tc i)
(vcat [ ppr tc, ppr arg_cos, ppr r0, ppr i, ppr r ]) $
Just (arg_cos `getNth` i)
go cs (SymCo co) -- Recurse, hoping to get to a TyConAppCo or FunCo
= do { co' <- go cs co; return (mkSymCo co') }
go cs co
| Just (ty, co_role) <- isReflCo_maybe co
= Just (mkReflCo (mkSelCoResRole cs co_role) (selectFromType cs ty))
-- mkSelCoreResRole: The role of the result may not be
-- be equal to co_role, the role of co, per Note [SelCo].
-- This was revealed by #23938.
| Pair ty1 ty2 <- coercionKind co
, let sty1 = selectFromType cs ty1
sty2 = selectFromType cs ty2
co_role = coercionRole co
, sty1 `eqType` sty2
= Just (mkReflCo (mkSelCoResRole cs co_role) sty1)
-- Checking for fully reflexive-ness (by seeing if sty1=sty2)
-- is worthwhile, because a non-Refl coercion `co` may well have a
-- reflexive (SelCo cs co).
-- E.g. co :: Either a b ~ Either a c
-- Then (SubCo (SelTyCon 0) co) is reflexive
| otherwise = Nothing
----------- Assertion checking --------------
-- NB: using coercionKind requires Note [mkSelCo precondition]
Pair ty1 ty2 = coercionKind co
bad_call_msg = vcat [ text "Coercion =" <+> ppr co
, text "LHS ty =" <+> ppr ty1
, text "RHS ty =" <+> ppr ty2
, text "cs =" <+> ppr cs
, text "coercion role =" <+> ppr (coercionRole co) ]
-- good_call checks the typing rules given in Note [SelCo]
good_call SelForAll
| Just (_tv1, _) <- splitForAllTyCoVar_maybe ty1
, Just (_tv2, _) <- splitForAllTyCoVar_maybe ty2
= True
good_call (SelFun {})
= isFunTy ty1 && isFunTy ty2
good_call (SelTyCon n r)
| Just (tc1, tys1) <- splitTyConApp_maybe ty1
, Just (tc2, tys2) <- splitTyConApp_maybe ty2
, let { len1 = length tys1
; len2 = length tys2 }
= (tc1 == tc2 || (tyConIsTYPEorCONSTRAINT tc1 && tyConIsTYPEorCONSTRAINT tc2))
-- tyConIsTYPEorCONSTRAINT: see Note [mkRuntimeRepCo]
&& len1 == len2
&& n < len1
&& r == tyConRole (coercionRole co) tc1 n
good_call _ = False
mkSelCoResRole :: CoSel -> Role -> Role
-- What is the role of (SelCo cs co), if co has role 'r'?
-- It is not just 'r'!
-- c.f. the SelCo case of coercionRole
mkSelCoResRole SelForAll _ = Nominal
mkSelCoResRole (SelTyCon _ r') _ = r'
mkSelCoResRole (SelFun fs) r = funRole r fs
-- | Extract the nth field of a FunCo
getNthFun :: FunSel
-> a -- ^ multiplicity
-> a -- ^ argument
-> a -- ^ result
-> a -- ^ One of the above three
getNthFun SelMult mult _ _ = mult
getNthFun SelArg _ arg _ = arg
getNthFun SelRes _ _ res = res
selectFromType :: HasDebugCallStack => CoSel -> Type -> Type
selectFromType (SelFun fs) ty
| Just (_af, mult, arg, res) <- splitFunTy_maybe ty
= getNthFun fs mult arg res
selectFromType (SelTyCon n _) ty
| Just args <- tyConAppArgs_maybe ty
= assertPpr (args `lengthExceeds` n) (ppr n $$ ppr ty) $
args `getNth` n
selectFromType SelForAll ty -- Works for both tyvar and covar
| Just (tv,_) <- splitForAllTyCoVar_maybe ty
= tyVarKind tv
selectFromType cs ty
= pprPanic "selectFromType" (ppr cs $$ ppr ty)
--------------------
mkLRCo :: LeftOrRight -> Coercion -> Coercion
mkLRCo lr co
| Just (ty, eq) <- isReflCo_maybe co
= mkReflCo eq (pickLR lr (splitAppTy ty))
| otherwise
= LRCo lr co
-- | Instantiates a 'Coercion'.
-- Works for both tyvar and covar
mkInstCo :: Coercion -> CoercionN -> Coercion
mkInstCo co_fun co_arg
| Just (tcv, _, _, kind_co, body_co) <- splitForAllCo_maybe co_fun
, Just (arg, _) <- isReflCo_maybe co_arg
= assertPpr (isReflexiveCo kind_co) (ppr co_fun $$ ppr co_arg) $
-- If the arg is Refl, then kind_co must be reflexive too
substCoUnchecked (zipTCvSubst [tcv] [arg]) body_co
mkInstCo co arg = InstCo co arg
-- | Given @ty :: k1@, @co :: k1 ~ k2@,
-- produces @co' :: ty ~r (ty |> co)@
mkGReflRightCo :: Role -> Type -> CoercionN -> Coercion
mkGReflRightCo r ty co
| isGReflCo co = mkReflCo r ty
-- the kinds of @k1@ and @k2@ are the same, thus @isGReflCo@
-- instead of @isReflCo@
| otherwise = mkGReflMCo r ty co
-- | Given @r@, @ty :: k1@, and @co :: k1 ~N k2@,
-- produces @co' :: (ty |> co) ~r ty@
mkGReflLeftCo :: Role -> Type -> CoercionN -> Coercion
mkGReflLeftCo r ty co
| isGReflCo co = mkReflCo r ty
-- the kinds of @k1@ and @k2@ are the same, thus @isGReflCo@
-- instead of @isReflCo@
| otherwise = mkSymCo $ mkGReflMCo r ty co
-- | Given @ty :: k1@, @co :: k1 ~ k2@, @co2:: ty ~r ty'@,
-- produces @co' :: (ty |> co) ~r ty'
-- It is not only a utility function, but it saves allocation when co
-- is a GRefl coercion.
mkCoherenceLeftCo :: Role -> Type -> CoercionN -> Coercion -> Coercion
mkCoherenceLeftCo r ty co co2
| isGReflCo co = co2
| otherwise = (mkSymCo $ mkGReflMCo r ty co) `mkTransCo` co2
-- | Given @ty :: k1@, @co :: k1 ~ k2@, @co2:: ty' ~r ty@,
-- produces @co' :: ty' ~r (ty |> co)
-- It is not only a utility function, but it saves allocation when co
-- is a GRefl coercion.
mkCoherenceRightCo :: HasDebugCallStack => Role -> Type -> CoercionN -> Coercion -> Coercion
mkCoherenceRightCo r ty co co2
| isGReflCo co = co2
| otherwise = co2 `mkTransCo` mkGReflMCo r ty co
-- | Given @co :: (a :: k) ~ (b :: k')@ produce @co' :: k ~ k'@.
mkKindCo :: Coercion -> Coercion
mkKindCo co | Just (ty, _) <- isReflCo_maybe co = Refl (typeKind ty)
mkKindCo (GRefl _ _ (MCo co)) = co
mkKindCo co
| Pair ty1 ty2 <- coercionKind co
-- Generally, calling coercionKind during coercion creation is a bad idea,
-- as it can lead to exponential behavior. But, we don't have nested mkKindCos,
-- so it's OK here.
, let tk1 = typeKind ty1
tk2 = typeKind ty2
, tk1 `eqType` tk2
= Refl tk1
| otherwise
= KindCo co
mkSubCo :: HasDebugCallStack => Coercion -> Coercion
-- Input coercion is Nominal, result is Representational
-- see also Note [Role twiddling functions]
mkSubCo (Refl ty) = GRefl Representational ty MRefl
mkSubCo (GRefl Nominal ty co) = GRefl Representational ty co
mkSubCo (TyConAppCo Nominal tc cos)
= TyConAppCo Representational tc (applyRoles tc cos)
mkSubCo co@(FunCo { fco_role = Nominal, fco_arg = arg, fco_res = res })
= co { fco_role = Representational
, fco_arg = downgradeRole Representational Nominal arg
, fco_res = downgradeRole Representational Nominal res }
mkSubCo co = assertPpr (coercionRole co == Nominal) (ppr co <+> ppr (coercionRole co)) $
SubCo co
-- | Changes a role, but only a downgrade. See Note [Role twiddling functions]
downgradeRole_maybe :: Role -- ^ desired role
-> Role -- ^ current role
-> Coercion -> Maybe Coercion
-- In (downgradeRole_maybe dr cr co) it's a precondition that
-- cr = coercionRole co
downgradeRole_maybe Nominal Nominal co = Just co
downgradeRole_maybe Nominal _ _ = Nothing
downgradeRole_maybe Representational Nominal co = Just (mkSubCo co)
downgradeRole_maybe Representational Representational co = Just co
downgradeRole_maybe Representational Phantom _ = Nothing
downgradeRole_maybe Phantom Phantom co = Just co
downgradeRole_maybe Phantom _ co = Just (toPhantomCo co)
-- | Like 'downgradeRole_maybe', but panics if the change isn't a downgrade.
-- See Note [Role twiddling functions]
downgradeRole :: Role -- desired role
-> Role -- current role
-> Coercion -> Coercion
downgradeRole r1 r2 co
= case downgradeRole_maybe r1 r2 co of
Just co' -> co'
Nothing -> pprPanic "downgradeRole" (ppr co)
-- | Make a "coercion between coercions".
mkProofIrrelCo :: Role -- ^ role of the created coercion, "r"
-> CoercionN -- ^ :: phi1 ~N phi2
-> Coercion -- ^ g1 :: phi1
-> Coercion -- ^ g2 :: phi2
-> Coercion -- ^ :: g1 ~r g2
-- if the two coercion prove the same fact, I just don't care what
-- the individual coercions are.
mkProofIrrelCo r co g _ | isGReflCo co = mkReflCo r (mkCoercionTy g)
-- kco is a kind coercion, thus @isGReflCo@ rather than @isReflCo@
mkProofIrrelCo r kco g1 g2 = mkUnivCo ProofIrrelProv [kco] r
(mkCoercionTy g1) (mkCoercionTy g2)
{-
%************************************************************************
%* *
Roles
%* *
%************************************************************************
-}
-- | Converts a coercion to be nominal, if possible.
-- See Note [Role twiddling functions]
setNominalRole_maybe :: Role -- of input coercion
-> Coercion -> Maybe CoercionN
setNominalRole_maybe r co
| r == Nominal = Just co
| otherwise = setNominalRole_maybe_helper co
where
setNominalRole_maybe_helper (SubCo co) = Just co
setNominalRole_maybe_helper co@(Refl _) = Just co
setNominalRole_maybe_helper (GRefl _ ty co) = Just $ GRefl Nominal ty co
setNominalRole_maybe_helper (TyConAppCo Representational tc cos)
= do { cos' <- zipWithM setNominalRole_maybe (tyConRoleListX Representational tc) cos
; return $ TyConAppCo Nominal tc cos' }
setNominalRole_maybe_helper co@(FunCo { fco_role = Representational
, fco_arg = co1, fco_res = co2 })
= do { co1' <- setNominalRole_maybe Representational co1
; co2' <- setNominalRole_maybe Representational co2
; return $ co { fco_role = Nominal, fco_arg = co1', fco_res = co2' }
}
setNominalRole_maybe_helper (SymCo co)
= SymCo <$> setNominalRole_maybe_helper co
setNominalRole_maybe_helper (TransCo co1 co2)
= TransCo <$> setNominalRole_maybe_helper co1 <*> setNominalRole_maybe_helper co2
setNominalRole_maybe_helper (AppCo co1 co2)
= AppCo <$> setNominalRole_maybe_helper co1 <*> pure co2
setNominalRole_maybe_helper co@(ForAllCo { fco_visL = visL, fco_visR = visR, fco_body = body_co })
| visL `eqForAllVis` visR -- See (FC3) in Note [ForAllCo] in GHC.Core.TyCo.Rep
= do { body_co' <- setNominalRole_maybe_helper body_co
; return (co { fco_body = body_co' }) }
setNominalRole_maybe_helper (SelCo cs co) =
-- NB, this case recurses via setNominalRole_maybe, not
-- setNominalRole_maybe_helper!
case cs of
SelTyCon n _r ->
-- Remember to update the role in SelTyCon to nominal;
-- not doing this caused #23362.
-- See the typing rule in Note [SelCo] in GHC.Core.TyCo.Rep.
SelCo (SelTyCon n Nominal) <$> setNominalRole_maybe (coercionRole co) co
SelFun fs ->
SelCo (SelFun fs) <$> setNominalRole_maybe (coercionRole co) co
SelForAll ->
pprPanic "setNominalRole_maybe: the coercion should already be nominal" (ppr co)
setNominalRole_maybe_helper (InstCo co arg)
= InstCo <$> setNominalRole_maybe_helper co <*> pure arg
setNominalRole_maybe_helper co@(UnivCo { uco_prov = prov })
| case prov of PhantomProv {} -> False -- should always be phantom
ProofIrrelProv {} -> True -- it's always safe
PluginProv {} -> False -- who knows? This choice is conservative.
= Just $ co { uco_role = Nominal }
setNominalRole_maybe_helper _ = Nothing
-- | Make a phantom coercion between two types. The coercion passed
-- in must be a nominal coercion between the kinds of the
-- types.
mkPhantomCo :: Coercion -> Type -> Type -> Coercion
mkPhantomCo h t1 t2
= mkUnivCo PhantomProv [h] Phantom t1 t2
-- takes any coercion and turns it into a Phantom coercion
toPhantomCo :: Coercion -> Coercion
toPhantomCo co
= mkPhantomCo (mkKindCo co) ty1 ty2
where Pair ty1 ty2 = coercionKind co
-- Convert args to a TyConAppCo Nominal to the same TyConAppCo Representational
applyRoles :: TyCon -> [Coercion] -> [Coercion]
applyRoles = zipWith (`downgradeRole` Nominal) . tyConRoleListRepresentational
-- The Role parameter is the Role of the TyConAppCo
-- defined here because this is intimately concerned with the implementation
-- of TyConAppCo
-- Always returns an infinite list (with a infinite tail of Nominal)
tyConRolesX :: Role -> TyCon -> Infinite Role
tyConRolesX Representational tc = tyConRolesRepresentational tc
tyConRolesX role _ = Inf.repeat role
tyConRoleListX :: Role -> TyCon -> [Role]
tyConRoleListX role = Inf.toList . tyConRolesX role
-- Returns the roles of the parameters of a tycon, with an infinite tail
-- of Nominal
tyConRolesRepresentational :: TyCon -> Infinite Role
tyConRolesRepresentational tc = tyConRoles tc Inf.++ Inf.repeat Nominal
-- Returns the roles of the parameters of a tycon, with an infinite tail
-- of Nominal
tyConRoleListRepresentational :: TyCon -> [Role]
tyConRoleListRepresentational = Inf.toList . tyConRolesRepresentational
tyConRole :: Role -> TyCon -> Int -> Role
tyConRole Nominal _ _ = Nominal
tyConRole Phantom _ _ = Phantom
tyConRole Representational tc n = tyConRolesRepresentational tc Inf.!! n
funRole :: Role -> FunSel -> Role
funRole Nominal _ = Nominal
funRole Phantom _ = Phantom
funRole Representational fs = funRoleRepresentational fs
funRoleRepresentational :: FunSel -> Role
funRoleRepresentational SelMult = Nominal
funRoleRepresentational SelArg = Representational
funRoleRepresentational SelRes = Representational
ltRole :: Role -> Role -> Bool
-- Is one role "less" than another?
-- Nominal < Representational < Phantom
ltRole Phantom _ = False
ltRole Representational Phantom = True
ltRole Representational _ = False
ltRole Nominal Nominal = False
ltRole Nominal _ = True
-------------------------------
-- | like mkKindCo, but aggressively & recursively optimizes to avoid using
-- a KindCo constructor. The output role is nominal.
promoteCoercion :: HasDebugCallStack => Coercion -> CoercionN
-- First cases handles anything that should yield refl.
promoteCoercion co = case co of
Refl _ -> mkNomReflCo ki1
GRefl _ _ MRefl -> mkNomReflCo ki1
GRefl _ _ (MCo co) -> co
_ | ki1 `eqType` ki2
-> mkNomReflCo (typeKind ty1)
-- No later branch should return refl
-- The assert (False )s throughout
-- are these cases explicitly, but they should never fire.
TyConAppCo _ tc args
| Just co' <- instCoercions (mkNomReflCo (tyConKind tc)) args
-> co'
| otherwise
-> mkKindCo co
AppCo co1 arg
| Just co' <- instCoercion (coercionKind (mkKindCo co1))
(promoteCoercion co1) arg
-> co'
| otherwise
-> mkKindCo co
ForAllCo { fco_tcv = tv, fco_body = g }
| isTyVar tv
-> promoteCoercion g
ForAllCo {}
-> assert False $
-- (ForAllCo {} :: (forall cv.t1) ~ (forall cv.t2)
-- The tyvar case is handled above, so the bound var is a
-- a coercion variable. So both sides have kind Type
-- (Note [Weird typing rule for ForAllTy] in GHC.Core.TyCo.Rep).
-- So the result is Refl, and that should have been caught by
-- the first equation above. Hence `assert False`
mkNomReflCo liftedTypeKind
FunCo {} -> mkKindCo co
-- We can get Type~Constraint or Constraint~Type
-- from FunCo {} :: (a -> (b::Type)) ~ (a -=> (b'::Constraint))
CoVarCo {} -> mkKindCo co
HoleCo {} -> mkKindCo co
AxiomCo {} -> mkKindCo co
UnivCo {} -> mkKindCo co -- We could instead return the (single) `uco_deps` coercion in
-- the `ProofIrrelProv` and `PhantomProv` cases, but it doesn't
-- quite seem worth doing.
SymCo g
-> mkSymCo (promoteCoercion g)
TransCo co1 co2
-> mkTransCo (promoteCoercion co1) (promoteCoercion co2)
SelCo n co1
| Just co' <- mkSelCo_maybe n co1
-> promoteCoercion co'
| otherwise
-> mkKindCo co
LRCo lr co1
| Just (lco, rco) <- splitAppCo_maybe co1
-> case lr of
CLeft -> promoteCoercion lco
CRight -> promoteCoercion rco
| otherwise
-> mkKindCo co
InstCo g _
| isForAllTy_ty ty1
-> assert (isForAllTy_ty ty2) $
promoteCoercion g
| otherwise
-> assert False $
mkNomReflCo liftedTypeKind
-- See Note [Weird typing rule for ForAllTy] in GHC.Core.TyCo.Rep
KindCo _
-> assert False $ -- See the first equation above
mkNomReflCo liftedTypeKind
SubCo g
-> promoteCoercion g
where
Pair ty1 ty2 = coercionKind co
ki1 = typeKind ty1
ki2 = typeKind ty2
-- | say @g = promoteCoercion h@. Then, @instCoercion g w@ yields @Just g'@,
-- where @g' = promoteCoercion (h w)@.
-- fails if this is not possible, if @g@ coerces between a forall and an ->
-- or if second parameter has a representational role and can't be used
-- with an InstCo.
instCoercion :: Pair Type -- g :: lty ~ rty
-> CoercionN -- ^ must be nominal
-> Coercion
-> Maybe CoercionN
instCoercion (Pair lty rty) g w
| (isForAllTy_ty lty && isForAllTy_ty rty)
|| (isForAllTy_co lty && isForAllTy_co rty)
, Just w' <- setNominalRole_maybe (coercionRole w) w
-- g :: (forall t1. t2) ~ (forall t1. t3)
-- w :: s1 ~ s2
-- returns mkInstCo g w' :: t2 [t1 |-> s1 ] ~ t3 [t1 |-> s2]
= Just $ mkInstCo g w'
| isFunTy lty && isFunTy rty
-- g :: (t1 -> t2) ~ (t3 -> t4)
-- returns t2 ~ t4
= Just $ mkSelCo (SelFun SelRes) g -- extract result type
| otherwise -- one forall, one funty...
= Nothing
-- | Repeated use of 'instCoercion'
instCoercions :: CoercionN -> [Coercion] -> Maybe CoercionN
instCoercions g ws
= let arg_ty_pairs = map coercionKind ws in
snd <$> foldM go (coercionKind g, g) (zip arg_ty_pairs ws)
where
go :: (Pair Type, Coercion) -> (Pair Type, Coercion)
-> Maybe (Pair Type, Coercion)
go (g_tys, g) (w_tys, w)
= do { g' <- instCoercion g_tys g w
; return (piResultTy <$> g_tys <*> w_tys, g') }
-- | Creates a new coercion with both of its types casted by different casts
-- @castCoercionKind2 g r t1 t2 h1 h2@, where @g :: t1 ~r t2@,
-- has type @(t1 |> h1) ~r (t2 |> h2)@.
-- @h1@ and @h2@ must be nominal.
castCoercionKind2 :: Coercion -> Role -> Type -> Type
-> CoercionN -> CoercionN -> Coercion
castCoercionKind2 g r t1 t2 h1 h2
= mkCoherenceRightCo r t2 h2 (mkCoherenceLeftCo r t1 h1 g)
-- | @castCoercionKind1 g r t1 t2 h@ = @coercionKind g r t1 t2 h h@
-- That is, it's a specialised form of castCoercionKind, where the two
-- kind coercions are identical
-- @castCoercionKind1 g r t1 t2 h@, where @g :: t1 ~r t2@,
-- has type @(t1 |> h) ~r (t2 |> h)@.
-- @h@ must be nominal.
-- See Note [castCoercionKind1]
castCoercionKind1 :: Coercion -> Role -> Type -> Type
-> CoercionN -> Coercion
castCoercionKind1 g r t1 t2 h
= case g of
Refl {} -> assert (r == Nominal) $ -- Refl is always Nominal
mkNomReflCo (mkCastTy t2 h)
GRefl _ _ mco -> case mco of
MRefl -> mkReflCo r (mkCastTy t2 h)
MCo kind_co -> mkGReflMCo r (mkCastTy t1 h)
(mkSymCo h `mkTransCo` kind_co `mkTransCo` h)
_ -> castCoercionKind2 g r t1 t2 h h
-- | Creates a new coercion with both of its types casted by different casts
-- @castCoercionKind g h1 h2@, where @g :: t1 ~r t2@,
-- has type @(t1 |> h1) ~r (t2 |> h2)@.
-- @h1@ and @h2@ must be nominal.
-- It calls @coercionKindRole@, so it's quite inefficient (which 'I' stands for)
-- Use @castCoercionKind2@ instead if @t1@, @t2@, and @r@ are known beforehand.
castCoercionKind :: Coercion -> CoercionN -> CoercionN -> Coercion
castCoercionKind g h1 h2
= castCoercionKind2 g r t1 t2 h1 h2
where
(Pair t1 t2, r) = coercionKindRole g
mkPiCos :: Role -> [Var] -> Coercion -> Coercion
mkPiCos r vs co = foldr (mkPiCo r) co vs
-- | Make a forall 'Coercion', where both types related by the coercion
-- are quantified over the same variable.
mkPiCo :: Role -> Var -> Coercion -> Coercion
mkPiCo r v co | isTyVar v = mkHomoForAllCos [Bndr v coreTyLamForAllTyFlag] co
| isCoVar v = assert (not (v `elemVarSet` tyCoVarsOfCo co)) $
-- We didn't call mkForAllCo here because if v does not appear
-- in co, the argument coercion will be nominal. But here we
-- want it to be r. It is only called in 'mkPiCos', which is
-- only used in GHC.Core.Opt.Simplify.Utils, where we are sure for
-- now (Aug 2018) v won't occur in co.
mkFunResCo r v co
| otherwise = mkFunResCo r v co
mkFunResCo :: Role -> Id -> Coercion -> Coercion
-- Given res_co :: res1 ~ res2,
-- mkFunResCo r m arg res_co :: (arg -> res1) ~r (arg -> res2)
-- Reflexive in the multiplicity argument
mkFunResCo role id res_co
= mkFunCoNoFTF role mult arg_co res_co
where
arg_co = mkReflCo role (varType id)
mult = multToCo (varMult id)
-- mkCoCast (c :: s1 ~?r t1) (g :: (s1 ~?r t1) ~#R (s2 ~?r t2)) :: s2 ~?r t2
-- The first coercion might be lifted or unlifted; thus the ~? above
-- Lifted and unlifted equalities take different numbers of arguments,
-- so we have to make sure to supply the right parameter to decomposeCo.
-- Also, note that the role of the first coercion is the same as the role of
-- the equalities related by the second coercion. The second coercion is
-- itself always representational.
mkCoCast :: Coercion -> CoercionR -> Coercion
mkCoCast c g
| (g2:g1:_) <- reverse co_list
= mkSymCo g1 `mkTransCo` c `mkTransCo` g2
| otherwise
= pprPanic "mkCoCast" (ppr g $$ ppr (coercionKind g))
where
-- g :: (s1 ~# t1) ~# (s2 ~# t2)
-- g1 :: s1 ~# s2
-- g2 :: t1 ~# t2
(tc, _) = splitTyConApp (coercionLKind g)
co_list = decomposeCo (tyConArity tc) g (tyConRolesRepresentational tc)
{- Note [castCoercionKind1]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
castCoercionKind1 deals with the very important special case of castCoercionKind2
where the two kind coercions are identical. In that case we can exploit the
situation where the main coercion is reflexive, via the special cases for Refl
and GRefl.
This is important when rewriting (ty |> co). We rewrite ty, yielding
fco :: ty ~ ty'
and now we want a coercion xco between
xco :: (ty |> co) ~ (ty' |> co)
That's exactly what castCoercionKind1 does. And it's very very common for
fco to be Refl. In that case we do NOT want to get some terrible composition
of mkLeftCoherenceCo and mkRightCoherenceCo, which is what castCoercionKind2
has to do in its full generality. See #18413.
-}
{-
%************************************************************************
%* *
Newtypes
%* *
%************************************************************************
-}
-- | If `instNewTyCon_maybe T ts = Just (rep_ty, co)`
-- then `co :: T ts ~R# rep_ty`
--
-- Checks for a newtype, and for being saturated
instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion)
instNewTyCon_maybe tc tys
| Just (tvs, ty, co_tc) <- unwrapNewTyConEtad_maybe tc -- Check for newtype
, tvs `leLength` tys -- Check saturated enough
= Just (applyTysX tvs ty tys, mkUnbranchedAxInstCo Representational co_tc tys [])
| otherwise
= Nothing
{-
************************************************************************
* *
Type normalisation
* *
************************************************************************
-}
-- | A function to check if we can reduce a type by one step. Used
-- with 'topNormaliseTypeX'.
type NormaliseStepper ev = RecTcChecker
-> TyCon -- tc
-> [Type] -- tys
-> NormaliseStepResult ev
-- | The result of stepping in a normalisation function.
-- See 'topNormaliseTypeX'.
data NormaliseStepResult ev
= NS_Done -- ^ Nothing more to do
| NS_Abort -- ^ Utter failure. The outer function should fail too.
| NS_Step RecTcChecker Type ev -- ^ We stepped, yielding new bits;
-- ^ ev is evidence;
-- Usually a co :: old type ~ new type
deriving (Functor)
instance Outputable ev => Outputable (NormaliseStepResult ev) where
ppr NS_Done = text "NS_Done"
ppr NS_Abort = text "NS_Abort"
ppr (NS_Step _ ty ev) = sep [text "NS_Step", ppr ty, ppr ev]
-- | Try one stepper and then try the next, if the first doesn't make
-- progress.
-- So if it returns NS_Done, it means that both steppers are satisfied
composeSteppers :: NormaliseStepper ev -> NormaliseStepper ev
-> NormaliseStepper ev
composeSteppers step1 step2 rec_nts tc tys
= case step1 rec_nts tc tys of
success@(NS_Step {}) -> success
NS_Done -> step2 rec_nts tc tys
NS_Abort -> NS_Abort
-- | A 'NormaliseStepper' that unwraps newtypes, careful not to fall into
-- a loop. If it would fall into a loop, it produces 'NS_Abort'.
unwrapNewTypeStepper :: NormaliseStepper Coercion
unwrapNewTypeStepper rec_nts tc tys
| Just (ty', co) <- instNewTyCon_maybe tc tys
= -- pprTrace "unNS" (ppr tc <+> ppr (getUnique tc) <+> ppr tys $$ ppr ty' $$ ppr rec_nts) $
case checkRecTc rec_nts tc of
Just rec_nts' -> NS_Step rec_nts' ty' co
Nothing -> NS_Abort
| otherwise
= NS_Done
-- | A general function for normalising the top-level of a type. It continues
-- to use the provided 'NormaliseStepper' until that function fails, and then
-- this function returns. The roles of the coercions produced by the
-- 'NormaliseStepper' must all be the same, which is the role returned from
-- the call to 'topNormaliseTypeX'.
--
-- Typically ev is Coercion.
--
-- If topNormaliseTypeX step plus ty = Just (ev, ty')
-- then ty ~ev1~ t1 ~ev2~ t2 ... ~evn~ ty'
-- and ev = ev1 `plus` ev2 `plus` ... `plus` evn
-- If it returns Nothing then no newtype unwrapping could happen
topNormaliseTypeX :: NormaliseStepper ev
-> (ev -> ev -> ev)
-> Type -> Maybe (ev, Type)
topNormaliseTypeX stepper plus ty
| Just (tc, tys) <- splitTyConApp_maybe ty
-- SPJ: The default threshold for initRecTc is 100 which is extremely dangerous
-- for certain type synonyms, we should think about reducing it (see #20990)
, NS_Step rec_nts ty' ev <- stepper initRecTc tc tys
= go rec_nts ev ty'
| otherwise
= Nothing
where
go rec_nts ev ty
| Just (tc, tys) <- splitTyConApp_maybe ty
= case stepper rec_nts tc tys of
NS_Step rec_nts' ty' ev' -> go rec_nts' (ev `plus` ev') ty'
NS_Done -> Just (ev, ty)
NS_Abort -> Nothing
| otherwise
= Just (ev, ty)
topNormaliseNewType_maybe :: Type -> Maybe (Coercion, Type)
-- ^ Sometimes we want to look through a @newtype@ and get its associated coercion.
-- This function strips off @newtype@ layers enough to reveal something that isn't
-- a @newtype@. Specifically, here's the invariant:
--
-- > topNormaliseNewType_maybe rec_nts ty = Just (co, ty')
--
-- then (a) @co : ty ~R ty'@.
-- (b) ty' is not a newtype.
--
-- The function returns @Nothing@ for non-@newtypes@,
-- or unsaturated applications
--
-- This function does *not* look through type families, because it has no access to
-- the type family environment. If you do have that at hand, consider to use
-- topNormaliseType_maybe, which should be a drop-in replacement for
-- topNormaliseNewType_maybe
-- If topNormliseNewType_maybe ty = Just (co, ty'), then co : ty ~R ty'
topNormaliseNewType_maybe ty
= topNormaliseTypeX unwrapNewTypeStepper mkTransCo ty
{-
%************************************************************************
%* *
Comparison of coercions
%* *
%************************************************************************
-}
-- | Syntactic equality of coercions
eqCoercion :: Coercion -> Coercion -> Bool
eqCoercion = eqType `on` coercionType
-- | Compare two 'Coercion's, with respect to an RnEnv2
eqCoercionX :: RnEnv2 -> Coercion -> Coercion -> Bool
eqCoercionX env = eqTypeX env `on` coercionType
{-
%************************************************************************
%* *
"Lifting" substitution
[(TyCoVar,Coercion)] -> Type -> Coercion
%* *
%************************************************************************
Note [Lifting coercions over types: liftCoSubst]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The KPUSH rule deals with this situation
data T a = K (a -> Maybe a)
g :: T t1 ~ T t2
x :: t1 -> Maybe t1
case (K @t1 x) |> g of
K (y:t2 -> Maybe t2) -> rhs
We want to push the coercion inside the constructor application.
So we do this
g' :: t1~t2 = SelCo (SelTyCon 0) g
case K @t2 (x |> g' -> Maybe g') of
K (y:t2 -> Maybe t2) -> rhs
The crucial operation is that we
* take the type of K's argument: a -> Maybe a
* and substitute g' for a
thus giving *coercion*. This is what liftCoSubst does.
In the presence of kind coercions, this is a bit
of a hairy operation. So, we refer you to the paper introducing kind coercions,
available at www.cis.upenn.edu/~sweirich/papers/fckinds-extended.pdf
Note [extendLiftingContextEx]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider we have datatype
K :: /\k. /\a::k. P -> T k -- P be some type
g :: T k1 ~ T k2
case (K @k1 @t1 x) |> g of
K y -> rhs
We want to push the coercion inside the constructor application.
We first get the coercion mapped by the universal type variable k:
lc = k |-> SelCo (SelTyCon 0) g :: k1~k2
Here, the important point is that the kind of a is coerced, and P might be
dependent on the existential type variable a.
Thus we first get the coercion of a's kind
g2 = liftCoSubst lc k :: k1 ~ k2
Then we store a new mapping into the lifting context
lc2 = a |-> (t1 ~ t1 |> g2), lc
So later when we can correctly deal with the argument type P
liftCoSubst lc2 P :: P [k|->k1][a|->t1] ~ P[k|->k2][a |-> (t1|>g2)]
This is exactly what extendLiftingContextEx does.
* For each (tyvar:k, ty) pair, we product the mapping
tyvar |-> (ty ~ ty |> (liftCoSubst lc k))
* For each (covar:s1~s2, ty) pair, we produce the mapping
covar |-> (co ~ co')
co' = Sym (liftCoSubst lc s1) ;; covar ;; liftCoSubst lc s2 :: s1'~s2'
This follows the lifting context extension definition in the
"FC with Explicit Kind Equality" paper.
-}
-- ----------------------------------------------------
-- See Note [Lifting coercions over types: liftCoSubst]
-- ----------------------------------------------------
data LiftingContext = LC Subst LiftCoEnv
-- in optCoercion, we need to lift when optimizing InstCo.
-- See Note [Optimising InstCo] in GHC.Core.Coercion.Opt
-- We thus propagate the substitution from GHC.Core.Coercion.Opt here.
instance Outputable LiftingContext where
ppr (LC _ env) = hang (text "LiftingContext:") 2 (ppr env)
type LiftCoEnv = VarEnv Coercion
-- Maps *type variables* to *coercions*.
-- That's the whole point of this function!
-- Also maps coercion variables to ProofIrrelCos.
-- like liftCoSubstWith, but allows for existentially-bound types as well
liftCoSubstWithEx :: Role -- desired role for output coercion
-> [TyVar] -- universally quantified tyvars
-> [Coercion] -- coercions to substitute for those
-> [TyCoVar] -- existentially quantified tycovars
-> [Type] -- types and coercions to be bound to ex vars
-> (Type -> Coercion, [Type]) -- (lifting function, converted ex args)
liftCoSubstWithEx role univs omegas exs rhos
= let theta = mkLiftingContext (zipEqual "liftCoSubstWithExU" univs omegas)
psi = extendLiftingContextEx theta (zipEqual "liftCoSubstWithExX" exs rhos)
in (ty_co_subst psi role, substTys (lcSubstRight psi) (mkTyCoVarTys exs))
liftCoSubstWith :: Role -> [TyCoVar] -> [Coercion] -> Type -> Coercion
liftCoSubstWith r tvs cos ty
= liftCoSubst r (mkLiftingContext $ zipEqual "liftCoSubstWith" tvs cos) ty
-- | @liftCoSubst role lc ty@ produces a coercion (at role @role@)
-- that coerces between @lc_left(ty)@ and @lc_right(ty)@, where
-- @lc_left@ is a substitution mapping type variables to the left-hand
-- types of the mapped coercions in @lc@, and similar for @lc_right@.
liftCoSubst :: HasDebugCallStack => Role -> LiftingContext -> Type -> Coercion
{-# INLINE liftCoSubst #-}
-- Inlining this function is worth 2% of allocation in T9872d,
liftCoSubst r lc@(LC subst env) ty
| isEmptyVarEnv env = mkReflCo r (substTy subst ty)
| otherwise = ty_co_subst lc r ty
emptyLiftingContext :: InScopeSet -> LiftingContext
emptyLiftingContext in_scope = LC (mkEmptySubst in_scope) emptyVarEnv
mkLiftingContext :: [(TyCoVar,Coercion)] -> LiftingContext
mkLiftingContext pairs
= LC (mkEmptySubst $ mkInScopeSet $ tyCoVarsOfCos (map snd pairs))
(mkVarEnv pairs)
mkSubstLiftingContext :: Subst -> LiftingContext
mkSubstLiftingContext subst = LC subst emptyVarEnv
liftingContextSubst :: LiftingContext -> Subst
liftingContextSubst (LC subst _) = subst
-- | Extend a lifting context with a new mapping.
extendLiftingContext :: LiftingContext -- ^ original LC
-> TyCoVar -- ^ new variable to map...
-> Coercion -- ^ ...to this lifted version
-> LiftingContext
-- mappings to reflexive coercions are just substitutions
extendLiftingContext (LC subst env) tv arg
| Just (ty, _) <- isReflCo_maybe arg
= LC (extendTCvSubst subst tv ty) env
| otherwise
= LC subst (extendVarEnv env tv arg)
-- | Extend the substitution component of a lifting context with
-- a new binding for a coercion variable. Used during coercion optimisation.
extendLiftingContextCvSubst :: LiftingContext
-> CoVar
-> Coercion
-> LiftingContext
extendLiftingContextCvSubst (LC subst env) cv co
= LC (extendCvSubst subst cv co) env
-- | Extend a lifting context with a new mapping, and extend the in-scope set
extendLiftingContextAndInScope :: LiftingContext -- ^ Original LC
-> TyCoVar -- ^ new variable to map...
-> Coercion -- ^ to this coercion
-> LiftingContext
extendLiftingContextAndInScope (LC subst env) tv co
= extendLiftingContext (LC (extendSubstInScopeSet subst (tyCoVarsOfCo co)) env) tv co
-- | Extend a lifting context with existential-variable bindings.
-- See Note [extendLiftingContextEx]
extendLiftingContextEx :: LiftingContext -- ^ original lifting context
-> [(TyCoVar,Type)] -- ^ ex. var / value pairs
-> LiftingContext
-- Note that this is more involved than extendLiftingContext. That function
-- takes a coercion to extend with, so it's assumed that the caller has taken
-- into account any of the kind-changing stuff worried about here.
extendLiftingContextEx lc [] = lc
extendLiftingContextEx lc@(LC subst env) ((v,ty):rest)
-- This function adds bindings for *Nominal* coercions. Why? Because it
-- works with existentially bound variables, which are considered to have
-- nominal roles.
| isTyVar v
= let lc' = LC (subst `extendSubstInScopeSet` tyCoVarsOfType ty)
(extendVarEnv env v $
mkGReflRightCo Nominal
ty
(ty_co_subst lc Nominal (tyVarKind v)))
in extendLiftingContextEx lc' rest
| CoercionTy co <- ty
= -- co :: s1 ~r s2
-- lift_s1 :: s1 ~r s1'
-- lift_s2 :: s2 ~r s2'
-- kco :: (s1 ~r s2) ~N (s1' ~r s2')
assert (isCoVar v) $
let (s1, s2, r) = coVarTypesRole v
lift_s1 = ty_co_subst lc r s1
lift_s2 = ty_co_subst lc r s2
kco = mkTyConAppCo Nominal (equalityTyCon r)
[ mkKindCo lift_s1, mkKindCo lift_s2
, lift_s1 , lift_s2 ]
lc' = LC (subst `extendSubstInScopeSet` tyCoVarsOfCo co)
(extendVarEnv env v
(mkProofIrrelCo Nominal kco co $
(mkSymCo lift_s1) `mkTransCo` co `mkTransCo` lift_s2))
in extendLiftingContextEx lc' rest
| otherwise
= pprPanic "extendLiftingContextEx" (ppr v <+> text "|->" <+> ppr ty)
-- | Erase the environments in a lifting context
zapLiftingContext :: LiftingContext -> LiftingContext
zapLiftingContext (LC subst _) = LC (zapSubst subst) emptyVarEnv
-- | Like 'substForAllCoBndr', but works on a lifting context
substForAllCoBndrUsingLC :: SwapFlag
-> (Coercion -> Coercion)
-> LiftingContext -> TyCoVar -> Coercion
-> (LiftingContext, TyCoVar, Coercion)
substForAllCoBndrUsingLC sym sco (LC subst lc_env) tv co
= (LC subst' lc_env, tv', co')
where
(subst', tv', co') = substForAllCoBndrUsing sym sco subst tv co
-- | The \"lifting\" operation which substitutes coercions for type
-- variables in a type to produce a coercion.
--
-- For the inverse operation, see 'liftCoMatch'
ty_co_subst :: LiftingContext -> Role -> Type -> Coercion
ty_co_subst !lc role ty
-- !lc: making this function strict in lc allows callers to
-- pass its two components separately, rather than boxing them.
-- Unfortunately, Boxity Analysis concludes that we need lc boxed
-- because it's used that way in liftCoSubstTyVarBndrUsing.
= go role ty
where
go :: Role -> Type -> Coercion
go r ty | Just ty' <- coreView ty
= go r ty'
go Phantom ty = lift_phantom ty
go r (TyVarTy tv) = expectJust "ty_co_subst bad roles" $
liftCoSubstTyVar lc r tv
go r (AppTy ty1 ty2) = mkAppCo (go r ty1) (go Nominal ty2)
go r (TyConApp tc tys) = mkTyConAppCo r tc (zipWith go (tyConRoleListX r tc) tys)
go r (FunTy af w t1 t2) = mkFunCo r af (go Nominal w) (go r t1) (go r t2)
go r t@(ForAllTy (Bndr v vis) ty)
= let (lc', v', h) = liftCoSubstVarBndr lc v
body_co = ty_co_subst lc' r ty in
if isTyVar v' || almostDevoidCoVarOfCo v' body_co
-- Lifting a ForAllTy over a coercion variable could fail as ForAllCo
-- imposes an extra restriction on where a covar can appear. See
-- (FC6) of Note [ForAllCo] in GHC.Tc.TyCo.Rep
-- We specifically check for this and panic because we know that
-- there's a hole in the type system here (see (FC6), and we'd rather
-- panic than fall into it.
then mkForAllCo v' vis vis h body_co
else pprPanic "ty_co_subst: covar is not almost devoid" (ppr t)
go r ty@(LitTy {}) = assert (r == Nominal) $
mkNomReflCo ty
go r (CastTy ty co) = castCoercionKind (go r ty) (substLeftCo lc co)
(substRightCo lc co)
go r (CoercionTy co) = mkProofIrrelCo r kco (substLeftCo lc co)
(substRightCo lc co)
where kco = go Nominal (coercionType co)
lift_phantom ty = mkPhantomCo (go Nominal (typeKind ty))
(substTy (lcSubstLeft lc) ty)
(substTy (lcSubstRight lc) ty)
{-
Note [liftCoSubstTyVar]
~~~~~~~~~~~~~~~~~~~~~~~~~
This function can fail if a coercion in the environment is of too low a role.
liftCoSubstTyVar is called from two places: in liftCoSubst (naturally), and
also in matchAxiom in GHC.Core.Coercion.Opt. From liftCoSubst, the so-called lifting
lemma guarantees that the roles work out. If we fail in this
case, we really should panic -- something is deeply wrong. But, in matchAxiom,
failing is fine. matchAxiom is trying to find a set of coercions
that match, but it may fail, and this is healthy behavior.
-}
-- See Note [liftCoSubstTyVar]
liftCoSubstTyVar :: LiftingContext -> Role -> TyVar -> Maybe Coercion
liftCoSubstTyVar (LC subst env) r v
| Just co_arg <- lookupVarEnv env v
= downgradeRole_maybe r (coercionRole co_arg) co_arg
| otherwise
= Just $ mkReflCo r (substTyVar subst v)
{- Note [liftCoSubstVarBndr]
~~~~~~~~~~~~~~~~~~~~~~~~~
callback:
'liftCoSubstVarBndrUsing' needs to be general enough to work in two
situations:
- in this module, which manipulates 'Coercion's, and
- in GHC.Core.FamInstEnv, where we work with 'Reduction's, which contain
a coercion as well as a type.
To achieve this, we require that the return type of the 'callback' function
contain a coercion within it. This is witnessed by the first argument
to 'liftCoSubstVarBndrUsing': a getter, which allows us to retrieve
the coercion inside the return type. Thus:
- in this module, we simply pass 'id' as the getter,
- in GHC.Core.FamInstEnv, we pass 'reductionCoercion' as the getter.
liftCoSubstTyVarBndrUsing:
Given
forall tv:k. t
We want to get
forall (tv:k1) (kind_co :: k1 ~ k2) body_co
We lift the kind k to get the kind_co
kind_co = ty_co_subst k :: k1 ~ k2
Now in the LiftingContext, we add the new mapping
tv |-> (tv :: k1) ~ ((tv |> kind_co) :: k2)
liftCoSubstCoVarBndrUsing:
Given
forall cv:(s1 ~ s2). t
We want to get
forall (cv:s1'~s2') (kind_co :: (s1'~s2') ~ (t1 ~ t2)) body_co
We lift s1 and s2 respectively to get
eta1 :: s1' ~ t1
eta2 :: s2' ~ t2
And
kind_co = TyConAppCo Nominal (~#) eta1 eta2
Now in the liftingContext, we add the new mapping
cv |-> (cv :: s1' ~ s2') ~ ((sym eta1;cv;eta2) :: t1 ~ t2)
-}
-- See Note [liftCoSubstVarBndr]
liftCoSubstVarBndr :: LiftingContext -> TyCoVar
-> (LiftingContext, TyCoVar, Coercion)
liftCoSubstVarBndr lc tv
= liftCoSubstVarBndrUsing id callback lc tv
where
callback lc' ty' = ty_co_subst lc' Nominal ty'
-- the callback must produce a nominal coercion
liftCoSubstVarBndrUsing :: (r -> CoercionN) -- ^ coercion getter
-> (LiftingContext -> Type -> r) -- ^ callback
-> LiftingContext -> TyCoVar
-> (LiftingContext, TyCoVar, r)
liftCoSubstVarBndrUsing view_co fun lc old_var
| isTyVar old_var
= liftCoSubstTyVarBndrUsing view_co fun lc old_var
| otherwise
= liftCoSubstCoVarBndrUsing view_co fun lc old_var
-- Works for tyvar binder
liftCoSubstTyVarBndrUsing :: (r -> CoercionN) -- ^ coercion getter
-> (LiftingContext -> Type -> r) -- ^ callback
-> LiftingContext -> TyVar
-> (LiftingContext, TyVar, r)
liftCoSubstTyVarBndrUsing view_co fun lc@(LC subst cenv) old_var
= assert (isTyVar old_var) $
( LC (subst `extendSubstInScope` new_var) new_cenv
, new_var, stuff )
where
old_kind = tyVarKind old_var
stuff = fun lc old_kind
eta = view_co stuff
k1 = coercionLKind eta
new_var = uniqAway (getSubstInScope subst) (setVarType old_var k1)
lifted = mkGReflRightCo Nominal (TyVarTy new_var) eta
-- :: new_var ~ new_var |> eta
new_cenv = extendVarEnv cenv old_var lifted
-- Works for covar binder
liftCoSubstCoVarBndrUsing :: (r -> CoercionN) -- ^ coercion getter
-> (LiftingContext -> Type -> r) -- ^ callback
-> LiftingContext -> CoVar
-> (LiftingContext, CoVar, r)
liftCoSubstCoVarBndrUsing view_co fun lc@(LC subst cenv) old_var
= assert (isCoVar old_var) $
( LC (subst `extendSubstInScope` new_var) new_cenv
, new_var, stuff )
where
old_kind = coVarKind old_var
stuff = fun lc old_kind
eta = view_co stuff
k1 = coercionLKind eta
new_var = uniqAway (getSubstInScope subst) (setVarType old_var k1)
-- old_var :: s1 ~r s2
-- eta :: (s1' ~r s2') ~N (t1 ~r t2)
-- eta1 :: s1' ~r t1
-- eta2 :: s2' ~r t2
-- co1 :: s1' ~r s2'
-- co2 :: t1 ~r t2
-- lifted :: co1 ~N co2
role = coVarRole old_var
eta' = downgradeRole role Nominal eta
eta1 = mkSelCo (SelTyCon 2 role) eta'
eta2 = mkSelCo (SelTyCon 3 role) eta'
co1 = mkCoVarCo new_var
co2 = mkSymCo eta1 `mkTransCo` co1 `mkTransCo` eta2
lifted = mkProofIrrelCo Nominal eta co1 co2
new_cenv = extendVarEnv cenv old_var lifted
-- | Is a var in the domain of a lifting context?
isMappedByLC :: TyCoVar -> LiftingContext -> Bool
isMappedByLC tv (LC _ env) = tv `elemVarEnv` env
-- If [a |-> g] is in the substitution and g :: t1 ~ t2, substitute a for t1
-- If [a |-> (g1, g2)] is in the substitution, substitute a for g1
substLeftCo :: LiftingContext -> Coercion -> Coercion
substLeftCo lc co
= substCo (lcSubstLeft lc) co
-- Ditto, but for t2 and g2
substRightCo :: LiftingContext -> Coercion -> Coercion
substRightCo lc co
= substCo (lcSubstRight lc) co
-- | Apply "sym" to all coercions in a 'LiftCoEnv'
swapLiftCoEnv :: LiftCoEnv -> LiftCoEnv
swapLiftCoEnv = mapVarEnv mkSymCo
lcSubstLeft :: LiftingContext -> Subst
lcSubstLeft (LC subst lc_env) = liftEnvSubstLeft subst lc_env
lcSubstRight :: LiftingContext -> Subst
lcSubstRight (LC subst lc_env) = liftEnvSubstRight subst lc_env
liftEnvSubstLeft :: Subst -> LiftCoEnv -> Subst
liftEnvSubstLeft = liftEnvSubst pFst
liftEnvSubstRight :: Subst -> LiftCoEnv -> Subst
liftEnvSubstRight = liftEnvSubst pSnd
liftEnvSubst :: (forall a. Pair a -> a) -> Subst -> LiftCoEnv -> Subst
liftEnvSubst selector subst lc_env
= composeTCvSubst (Subst in_scope emptyIdSubstEnv tenv cenv) subst
where
pairs = nonDetUFMToList lc_env
-- It's OK to use nonDetUFMToList here because we
-- immediately forget the ordering by creating
-- a VarEnv
(tpairs, cpairs) = partitionWith ty_or_co pairs
-- Make sure the in-scope set is wide enough to cover the range of the
-- substitution (#22235).
in_scope = mkInScopeSet $
tyCoVarsOfTypes (map snd tpairs) `unionVarSet`
tyCoVarsOfCos (map snd cpairs)
tenv = mkVarEnv_Directly tpairs
cenv = mkVarEnv_Directly cpairs
ty_or_co :: (Unique, Coercion) -> Either (Unique, Type) (Unique, Coercion)
ty_or_co (u, co)
| Just equality_co <- isCoercionTy_maybe equality_ty
= Right (u, equality_co)
| otherwise
= Left (u, equality_ty)
where
equality_ty = selector (coercionKind co)
-- | Lookup a 'CoVar' in the substitution in a 'LiftingContext'
lcLookupCoVar :: LiftingContext -> CoVar -> Maybe Coercion
lcLookupCoVar (LC subst _) cv = lookupCoVar subst cv
-- | Get the 'InScopeSet' from a 'LiftingContext'
lcInScopeSet :: LiftingContext -> InScopeSet
lcInScopeSet (LC subst _) = getSubstInScope subst
{-
%************************************************************************
%* *
Sequencing on coercions
%* *
%************************************************************************
-}
seqMCo :: MCoercion -> ()
seqMCo MRefl = ()
seqMCo (MCo co) = seqCo co
seqCo :: Coercion -> ()
seqCo (Refl ty) = seqType ty
seqCo (GRefl r ty mco) = r `seq` seqType ty `seq` seqMCo mco
seqCo (TyConAppCo r tc cos) = r `seq` tc `seq` seqCos cos
seqCo (AppCo co1 co2) = seqCo co1 `seq` seqCo co2
seqCo (CoVarCo cv) = cv `seq` ()
seqCo (HoleCo h) = coHoleCoVar h `seq` ()
seqCo (SymCo co) = seqCo co
seqCo (TransCo co1 co2) = seqCo co1 `seq` seqCo co2
seqCo (SelCo n co) = n `seq` seqCo co
seqCo (LRCo lr co) = lr `seq` seqCo co
seqCo (InstCo co arg) = seqCo co `seq` seqCo arg
seqCo (KindCo co) = seqCo co
seqCo (SubCo co) = seqCo co
seqCo (AxiomCo _ cs) = seqCos cs
seqCo (ForAllCo tv visL visR k co)
= seqType (varType tv) `seq` rnf visL `seq` rnf visR `seq`
seqCo k `seq` seqCo co
seqCo (FunCo r af1 af2 w co1 co2)
= r `seq` af1 `seq` af2 `seq` seqCo w `seq` seqCo co1 `seq` seqCo co2
seqCo (UnivCo { uco_prov = p, uco_role = r
, uco_lty = t1, uco_rty = t2, uco_deps = deps })
= p `seq` r `seq` seqType t1 `seq` seqType t2 `seq` seqCos deps
seqCos :: [Coercion] -> ()
seqCos [] = ()
seqCos (co:cos) = seqCo co `seq` seqCos cos
{-
%************************************************************************
%* *
The kind of a type, and of a coercion
%* *
%************************************************************************
-}
{- Note [coercionKind performance]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
coercionKind, coercionLKind, and coercionRKind are very "hot" functions; in some
coercion-heavy programs they can have a material effect on compile time/allocation.
Hence
* Rather than making one function which returns a pair (lots of allocation and
de-allocation) we have two functions, coercionLKind and coercionRKind, which
return the left and right kind respectively.
* Both are defined by a single worker function `coercion_lr_kind`, which takes a
flag of type `LeftOrRight`. This worker function is marked INLINE, and inlined
at its precisely-two call-sites in coercionLKind and coercionRKind.
Take care when making changes here... it's easy to accidentally add allocation!
-}
-- | Apply 'coercionKind' to multiple 'Coercion's
coercionKinds :: [Coercion] -> Pair [Type]
coercionKinds tys = sequenceA $ map coercionKind tys
-- | Get a coercion's kind and role.
coercionKindRole :: Coercion -> (Pair Type, Role)
coercionKindRole co = (coercionKind co, coercionRole co)
coercionType :: Coercion -> Type
coercionType co = case coercionKindRole co of
(Pair ty1 ty2, r) -> mkCoercionType r ty1 ty2
------------------
-- | If it is the case that
--
-- > c :: (t1 ~ t2)
--
-- i.e. the kind of @c@ relates @t1@ and @t2@, then @coercionKind c = Pair t1 t2@.
coercionKind :: HasDebugCallStack => Coercion -> Pair Type
-- See Note [coercionKind performance]
coercionKind co = Pair (coercionLKind co) (coercionRKind co)
coercionLKind, coercionRKind :: HasDebugCallStack => Coercion -> Type
-- See Note [coercionKind performance]
coercionLKind co = coercion_lr_kind CLeft co
coercionRKind co = coercion_lr_kind CRight co
coercion_lr_kind :: HasDebugCallStack => LeftOrRight -> Coercion -> Type
{-# INLINE coercion_lr_kind #-}
-- See Note [coercionKind performance]
coercion_lr_kind which orig_co
= go orig_co
where
go (Refl ty) = ty
go (GRefl _ ty MRefl) = ty
go (GRefl _ ty (MCo co1)) = pickLR which (ty, mkCastTy ty co1)
go (TyConAppCo _ tc cos) = mkTyConApp tc (map go cos)
go (AppCo co1 co2) = mkAppTy (go co1) (go co2)
go (CoVarCo cv) = go_covar cv
go (HoleCo h) = go_covar (coHoleCoVar h)
go (SymCo co) = pickLR which (coercionRKind co, coercionLKind co)
go (TransCo co1 co2) = pickLR which (go co1, go co2)
go (LRCo lr co) = pickLR lr (splitAppTy (go co))
go (InstCo aco arg) = go_app aco [go arg]
go (KindCo co) = typeKind (go co)
go (SubCo co) = go co
go (SelCo d co) = selectFromType d (go co)
go (AxiomCo ax cos) = go_ax ax cos
go (UnivCo { uco_lty = lty, uco_rty = rty})
= pickLR which (lty, rty)
go (FunCo { fco_afl = afl, fco_afr = afr, fco_mult = mult
, fco_arg = arg, fco_res = res})
= -- See Note [FunCo]
FunTy { ft_af = pickLR which (afl, afr), ft_mult = go mult
, ft_arg = go arg, ft_res = go res }
go co@(ForAllCo { fco_tcv = tv1, fco_visL = visL, fco_visR = visR
, fco_kind = k_co, fco_body = co1 })
= case which of
CLeft -> mkTyCoForAllTy tv1 visL (go co1)
CRight | isGReflCo k_co -- kind_co always has kind `Type`, thus `isGReflCo`
-> mkTyCoForAllTy tv1 visR (go co1)
| otherwise
-> go_forall_right empty_subst co
where
empty_subst = mkEmptySubst (mkInScopeSet $ tyCoVarsOfCo co)
-------------
go_covar cv = pickLR which (coVarLType cv, coVarRType cv)
-------------
go_app :: Coercion -> [Type] -> Type
-- Collect up all the arguments and apply all at once
-- See Note [Nested InstCos]
go_app (InstCo co arg) args = go_app co (go arg:args)
go_app co args = piResultTys (go co) args
-------------
go_ax axr@(BuiltInFamRew bif) cos = check_bif_res axr (bifrw_proves bif (map coercionKind cos))
go_ax axr@(BuiltInFamInj bif) [co] = check_bif_res axr (bifinj_proves bif (coercionKind co))
go_ax axr@(BuiltInFamInj {}) _ = crash axr
go_ax (UnbranchedAxiom ax) cos = go_branch ax (coAxiomSingleBranch ax) cos
go_ax (BranchedAxiom ax i) cos = go_branch ax (coAxiomNthBranch ax i) cos
-------------
check_bif_res _ (Just (Pair lhs rhs)) = pickLR which (lhs,rhs)
check_bif_res axr Nothing = crash axr
crash :: CoAxiomRule -> Type
crash axr = pprPanic "coercionKind" (ppr axr)
-------------
go_branch :: CoAxiom br -> CoAxBranch -> [Coercion] -> Type
go_branch ax (CoAxBranch { cab_tvs = tvs, cab_cvs = cvs
, cab_lhs = lhs_tys, cab_rhs = rhs_ty }) cos
= assert (cos `equalLength` tcvs) $
-- Invariant of AxiomRuleCo: cos should
-- exactly saturate the axiom branch
let (tys1, cotys1) = splitAtList tvs tys
cos1 = map stripCoercionTy cotys1
in
-- You might think to use
-- substTy (zipTCvSubst tcvs ltys) (pickLR ...)
-- but #25066 makes it much less efficient than the silly calls below
substTyWith tvs tys1 $
substTyWithCoVars cvs cos1 $
pickLR which (mkTyConApp tc lhs_tys, rhs_ty)
where
tc = coAxiomTyCon ax
tcvs | null cvs = tvs -- Very common case (currently always!)
| otherwise = tvs ++ cvs
tys = map go cos
-------------
go_forall_right subst (ForAllCo { fco_tcv = tv1, fco_visR = visR
, fco_kind = k_co, fco_body = co })
-- See Note [Nested ForAllCos]
| isTyVar tv1
= mkForAllTy (Bndr tv2 visR) (go_forall_right subst' co)
where
k2 = coercionRKind k_co
tv2 = setTyVarKind tv1 (substTy subst k2)
subst' | isGReflCo k_co = extendSubstInScope subst tv1
-- kind_co always has kind @Type@, thus @isGReflCo@
| otherwise = extendTvSubst (extendSubstInScope subst tv2) tv1 $
TyVarTy tv2 `mkCastTy` mkSymCo k_co
go_forall_right subst (ForAllCo { fco_tcv = cv1, fco_visR = visR
, fco_kind = k_co, fco_body = co })
| isCoVar cv1
= mkTyCoForAllTy cv2 visR (go_forall_right subst' co)
where
k2 = coercionRKind k_co
r = coVarRole cv1
k_co' = downgradeRole r Nominal k_co
eta1 = mkSelCo (SelTyCon 2 r) k_co'
eta2 = mkSelCo (SelTyCon 3 r) k_co'
-- k_co :: (t1 ~r t2) ~N (s1 ~r s2)
-- k1 = t1 ~r t2
-- k2 = s1 ~r s2
-- cv1 :: t1 ~r t2
-- cv2 :: s1 ~r s2
-- eta1 :: t1 ~r s1
-- eta2 :: t2 ~r s2
-- n_subst = (eta1 ; cv2 ; sym eta2) :: t1 ~r t2
cv2 = setVarType cv1 (substTy subst k2)
n_subst = eta1 `mkTransCo` (mkCoVarCo cv2) `mkTransCo` (mkSymCo eta2)
subst' | isReflCo k_co = extendSubstInScope subst cv1
| otherwise = extendCvSubst (extendSubstInScope subst cv2)
cv1 n_subst
go_forall_right subst other_co
-- when other_co is not a ForAllCo
= substTy subst (go other_co)
{- Note [Nested ForAllCos]
~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we need `coercionKind (ForAllCo a1 (ForAllCo a2 ... (ForAllCo an co)...) )`.
We do not want to perform `n` single-type-variable substitutions over the kind
of `co`; rather we want to do one substitution which substitutes for all of
`a1`, `a2` ... simultaneously. If we do one at a time we get the performance
hole reported in #11735.
Solution: gather up the type variables for nested `ForAllCos`, and
substitute for them all at once. Remarkably, for #11735 this single
change reduces /total/ compile time by a factor of more than ten.
Note [Nested InstCos]
~~~~~~~~~~~~~~~~~~~~~
In #5631 we found that 70% of the entire compilation time was
being spent in coercionKind! The reason was that we had
(g @ ty1 @ ty2 .. @ ty100) -- The "@s" are InstCos
where
g :: forall a1 a2 .. a100. phi
If we deal with the InstCos one at a time, we'll do this:
1. Find the kind of (g @ ty1 .. @ ty99) : forall a100. phi'
2. Substitute phi'[ ty100/a100 ], a single tyvar->type subst
But this is a *quadratic* algorithm, and the blew up #5631.
So it's very important to do the substitution simultaneously;
cf Type.piResultTys (which in fact we call here).
-}
-- | Retrieve the role from a coercion.
coercionRole :: Coercion -> Role
coercionRole = go
where
go (Refl _) = Nominal
go (GRefl r _ _) = r
go (TyConAppCo r _ _) = r
go (AppCo co1 _) = go co1
go (ForAllCo { fco_body = co }) = go co
go (FunCo { fco_role = r }) = r
go (CoVarCo cv) = coVarRole cv
go (HoleCo h) = coVarRole (coHoleCoVar h)
go (UnivCo { uco_role = r }) = r
go (SymCo co) = go co
go (TransCo co1 _co2) = go co1
go (SelCo cs co) = mkSelCoResRole cs (coercionRole co)
go (LRCo {}) = Nominal
go (InstCo co _) = go co
go (KindCo {}) = Nominal
go (SubCo _) = Representational
go (AxiomCo ax _) = coAxiomRuleRole ax
-- | Makes a coercion type from two types: the types whose equality
-- is proven by the relevant 'Coercion'
mkCoercionType :: Role -> Type -> Type -> Type
mkCoercionType Nominal = mkPrimEqPred
mkCoercionType Representational = mkReprPrimEqPred
mkCoercionType Phantom = \ty1 ty2 ->
let ki1 = typeKind ty1
ki2 = typeKind ty2
in
TyConApp eqPhantPrimTyCon [ki1, ki2, ty1, ty2]
-- | Creates a primitive nominal type equality predicate.
-- t1 ~# t2
-- Invariant: the types are not Coercions
mkPrimEqPred :: Type -> Type -> Type
mkPrimEqPred ty1 ty2
= mkTyConApp eqPrimTyCon [k1, k2, ty1, ty2]
where
k1 = typeKind ty1
k2 = typeKind ty2
-- | Creates a primitive representational type equality predicate.
-- t1 ~R# t2
-- Invariant: the types are not Coercions
mkReprPrimEqPred :: Type -> Type -> Type
mkReprPrimEqPred ty1 ty2
= mkTyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
where
k1 = typeKind ty1
k2 = typeKind ty2
-- | Makes a lifted equality predicate at the given role
mkPrimEqPredRole :: Role -> Type -> Type -> PredType
mkPrimEqPredRole Nominal = mkPrimEqPred
mkPrimEqPredRole Representational = mkReprPrimEqPred
mkPrimEqPredRole Phantom = panic "mkPrimEqPredRole phantom"
-- | Creates a primitive nominal type equality predicate with an explicit
-- (but homogeneous) kind: (~#) k k ty1 ty2
mkNomPrimEqPred :: Kind -> Type -> Type -> Type
mkNomPrimEqPred k ty1 ty2 = mkTyConApp eqPrimTyCon [k, k, ty1, ty2]
-- | Assuming that two types are the same, ignoring coercions, find
-- a nominal coercion between the types. This is useful when optimizing
-- transitivity over coercion applications, where splitting two
-- AppCos might yield different kinds. See Note [EtaAppCo] in
-- "GHC.Core.Coercion.Opt".
buildCoercion :: HasDebugCallStack => Type -> Type -> CoercionN
buildCoercion orig_ty1 orig_ty2 = go orig_ty1 orig_ty2
where
go ty1 ty2 | Just ty1' <- coreView ty1 = go ty1' ty2
| Just ty2' <- coreView ty2 = go ty1 ty2'
go (CastTy ty1 co) ty2
= let co' = go ty1 ty2
r = coercionRole co'
in mkCoherenceLeftCo r ty1 co co'
go ty1 (CastTy ty2 co)
= let co' = go ty1 ty2
r = coercionRole co'
in mkCoherenceRightCo r ty2 co co'
go ty1@(TyVarTy tv1) _tyvarty
= assert (case _tyvarty of
{ TyVarTy tv2 -> tv1 == tv2
; _ -> False }) $
mkNomReflCo ty1
go (FunTy { ft_af = af1, ft_mult = w1, ft_arg = arg1, ft_res = res1 })
(FunTy { ft_af = af2, ft_mult = w2, ft_arg = arg2, ft_res = res2 })
= assert (af1 == af2) $
mkFunCo Nominal af1 (go w1 w2) (go arg1 arg2) (go res1 res2)
go (TyConApp tc1 args1) (TyConApp tc2 args2)
= assertPpr (tc1 == tc2) (vcat [ ppr tc1 <+> ppr tc2
, text "orig_ty1:" <+> ppr orig_ty1
, text "orig_ty2:" <+> ppr orig_ty2
]) $
mkTyConAppCo Nominal tc1 (zipWith go args1 args2)
go (AppTy ty1a ty1b) ty2
| Just (ty2a, ty2b) <- splitAppTyNoView_maybe ty2
= mkAppCo (go ty1a ty2a) (go ty1b ty2b)
go ty1 (AppTy ty2a ty2b)
| Just (ty1a, ty1b) <- splitAppTyNoView_maybe ty1
= mkAppCo (go ty1a ty2a) (go ty1b ty2b)
go (ForAllTy (Bndr tv1 flag1) ty1) (ForAllTy (Bndr tv2 flag2) ty2)
| isTyVar tv1
= assert (isTyVar tv2) $
mkForAllCo tv1 flag1 flag2 kind_co (go ty1 ty2')
where kind_co = go (tyVarKind tv1) (tyVarKind tv2)
in_scope = mkInScopeSet $ tyCoVarsOfType ty2 `unionVarSet` tyCoVarsOfCo kind_co
ty2' = substTyWithInScope in_scope [tv2]
[mkTyVarTy tv1 `mkCastTy` kind_co]
ty2
go (ForAllTy (Bndr cv1 flag1) ty1) (ForAllTy (Bndr cv2 flag2) ty2)
= assert (isCoVar cv1 && isCoVar cv2) $
mkForAllCo cv1 flag1 flag2 kind_co (go ty1 ty2')
where s1 = varType cv1
s2 = varType cv2
kind_co = go s1 s2
-- s1 = t1 ~r t2
-- s2 = t3 ~r t4
-- kind_co :: (t1 ~r t2) ~N (t3 ~r t4)
-- eta1 :: t1 ~r t3
-- eta2 :: t2 ~r t4
r = coVarRole cv1
kind_co' = downgradeRole r Nominal kind_co
eta1 = mkSelCo (SelTyCon 2 r) kind_co'
eta2 = mkSelCo (SelTyCon 3 r) kind_co'
subst = mkEmptySubst $ mkInScopeSet $
tyCoVarsOfType ty2 `unionVarSet` tyCoVarsOfCo kind_co
ty2' = substTy (extendCvSubst subst cv2 $ mkSymCo eta1 `mkTransCo`
mkCoVarCo cv1 `mkTransCo`
eta2)
ty2
go ty1@(LitTy lit1) _lit2
= assert (case _lit2 of
{ LitTy lit2 -> lit1 == lit2
; _ -> False }) $
mkNomReflCo ty1
go (CoercionTy co1) (CoercionTy co2)
= mkProofIrrelCo Nominal kind_co co1 co2
where
kind_co = go (coercionType co1) (coercionType co2)
go ty1 ty2
= pprPanic "buildKindCoercion" (vcat [ ppr orig_ty1, ppr orig_ty2
, ppr ty1, ppr ty2 ])
{-
%************************************************************************
%* *
Coercion holes
%* *
%************************************************************************
-}
has_co_hole_ty :: Type -> Monoid.Any
has_co_hole_co :: Coercion -> Monoid.Any
(has_co_hole_ty, _, has_co_hole_co, _)
= foldTyCo folder ()
where
folder = TyCoFolder { tcf_view = noView
, tcf_tyvar = const2 (Monoid.Any False)
, tcf_covar = const2 (Monoid.Any False)
, tcf_hole = \_ hole -> Monoid.Any (isHeteroKindCoHole hole)
, tcf_tycobinder = const2
}
-- | Is there a hetero-kind coercion hole in this type?
-- (That is, a coercion hole with ch_hetero_kind=True.)
-- See wrinkle (EIK2) of Note [Equalities with incompatible kinds] in GHC.Tc.Solver.Equality
hasCoercionHoleTy :: Type -> Bool
hasCoercionHoleTy = Monoid.getAny . has_co_hole_ty
-- | Is there a hetero-kind coercion hole in this coercion?
hasCoercionHoleCo :: Coercion -> Bool
hasCoercionHoleCo = Monoid.getAny . has_co_hole_co
hasThisCoercionHoleTy :: Type -> CoercionHole -> Bool
hasThisCoercionHoleTy ty hole = Monoid.getAny (f ty)
where
(f, _, _, _) = foldTyCo folder ()
folder = TyCoFolder { tcf_view = noView
, tcf_tyvar = const2 (Monoid.Any False)
, tcf_covar = const2 (Monoid.Any False)
, tcf_hole = \ _ h -> Monoid.Any (getUnique h == getUnique hole)
, tcf_tycobinder = const2
}
-- | Set the type of a 'CoercionHole'
setCoHoleType :: CoercionHole -> Type -> CoercionHole
setCoHoleType h t = setCoHoleCoVar h (setVarType (coHoleCoVar h) t)