{- (c) The University of Glasgow 2006 -} {-# LANGUAGE RankNTypes, CPP, MultiWayIf, FlexibleContexts, BangPatterns, ScopedTypeVariables #-} -- | Module for (a) type kinds and (b) type coercions, -- as used in System FC. See 'CoreSyn.Expr' for -- more on System FC and how coercions fit into it. -- module Coercion ( -- * Main data type Coercion, CoercionN, CoercionR, CoercionP, MCoercion(..), MCoercionR, UnivCoProvenance, CoercionHole(..), coHoleCoVar, setCoHoleCoVar, LeftOrRight(..), Var, CoVar, TyCoVar, Role(..), ltRole, -- ** Functions over coercions coVarTypes, coVarKind, coVarKindsTypesRole, coVarRole, coercionType, coercionKind, coercionKinds, mkCoercionType, coercionRole, coercionKindRole, -- ** Constructing coercions mkGReflCo, mkReflCo, mkRepReflCo, mkNomReflCo, mkCoVarCo, mkCoVarCos, mkAxInstCo, mkUnbranchedAxInstCo, mkAxInstRHS, mkUnbranchedAxInstRHS, mkAxInstLHS, mkUnbranchedAxInstLHS, mkPiCo, mkPiCos, mkCoCast, mkSymCo, mkTransCo, mkTransMCo, mkNthCo, nthCoRole, mkLRCo, mkInstCo, mkAppCo, mkAppCos, mkTyConAppCo, mkFunCo, mkForAllCo, mkForAllCos, mkHomoForAllCos, mkPhantomCo, mkUnsafeCo, mkHoleCo, mkUnivCo, mkSubCo, mkAxiomInstCo, mkProofIrrelCo, downgradeRole, maybeSubCo, mkAxiomRuleCo, mkGReflRightCo, mkGReflLeftCo, mkCoherenceLeftCo, mkCoherenceRightCo, mkKindCo, castCoercionKind, castCoercionKindI, mkHeteroCoercionType, -- ** Decomposition instNewTyCon_maybe, NormaliseStepper, NormaliseStepResult(..), composeSteppers, mapStepResult, unwrapNewTypeStepper, topNormaliseNewType_maybe, topNormaliseTypeX, decomposeCo, decomposeFunCo, decomposePiCos, getCoVar_maybe, splitTyConAppCo_maybe, splitAppCo_maybe, splitFunCo_maybe, splitForAllCo_maybe, splitForAllCo_ty_maybe, splitForAllCo_co_maybe, nthRole, tyConRolesX, tyConRolesRepresentational, setNominalRole_maybe, pickLR, isGReflCo, isReflCo, isReflCo_maybe, isGReflCo_maybe, isReflexiveCo, isReflexiveCo_maybe, isReflCoVar_maybe, -- ** Coercion variables mkCoVar, isCoVar, coVarName, setCoVarName, setCoVarUnique, isCoVar_maybe, -- ** Free variables tyCoVarsOfCo, tyCoVarsOfCos, coVarsOfCo, tyCoFVsOfCo, tyCoFVsOfCos, tyCoVarsOfCoDSet, coercionSize, -- ** Substitution CvSubstEnv, emptyCvSubstEnv, lookupCoVar, substCo, substCos, substCoVar, substCoVars, substCoWith, substCoVarBndr, extendTvSubstAndInScope, getCvSubstEnv, -- ** Lifting liftCoSubst, liftCoSubstTyVar, liftCoSubstWith, liftCoSubstWithEx, emptyLiftingContext, extendLiftingContext, extendLiftingContextAndInScope, liftCoSubstVarBndrUsing, isMappedByLC, mkSubstLiftingContext, zapLiftingContext, substForAllCoBndrUsingLC, lcTCvSubst, 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, simplifyArgsWorker ) where #include "HsVersions.h" import {-# SOURCE #-} ToIface (toIfaceTyCon, tidyToIfaceTcArgs) import GhcPrelude import IfaceType import TyCoRep import Type import TyCon import CoAxiom import Var import VarEnv import VarSet import Name hiding ( varName ) import Util import BasicTypes import Outputable import Unique import Pair import SrcLoc import PrelNames import TysPrim ( eqPhantPrimTyCon ) import ListSetOps import Maybes import UniqFM import Control.Monad (foldM, zipWithM) import Data.Function ( on ) import Data.Char( isDigit ) {- %************************************************************************ %* * -- 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 TyCoRep \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 CoAxiom 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 <+> dcolon) 2 (vcat (map (pprCoAxBranchUser tc) (fromBranches branches))) pprCoAxBranchUser :: TyCon -> CoAxBranch -> SDoc -- Used when printing injectivity errors (FamInst.makeInjectivityErrors) -- and inaccessible branches (TcValidity.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 (mkTyCoVarBinders Inferred bndrs') -- See Note [Printing foralls in type family instances] in IfaceType , pp_lhs <+> ppr_rhs tidy_env ee_rhs , text "-- Defined" <+> pp_loc ] where 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 FamInstEnv. (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 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) (mkTyVarOcc "_") -- Tidy the binder to "_" is_wildcard :: Var -> Bool is_wildcard tv = case occNameString (getOccName tv) of ('_' : rest) -> all isDigit rest _ -> False {- %************************************************************************ %* * Destructing coercions %* * %************************************************************************ Note [Function coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~ Remember that (->) :: forall r1 r2. TYPE r1 -> TYPE r2 -> TYPE LiftedRep Hence FunCo r co1 co2 :: (s1->t1) ~r (s2->t2) is short for TyConAppCo (->) co_rep1 co_rep2 co1 co2 where co_rep1, co_rep2 are the coercions on the representations. -} -- | 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 -> [Role] -- the roles of the output coercions -- this must have at least as many -- entries as the Arity provided -> [Coercion] decomposeCo arity co rs = [mkNthCo r n co | (n,r) <- [0..(arity-1)] `zip` rs ] -- Remember, Nth is zero-indexed decomposeFunCo :: HasDebugCallStack => Role -- Role of the input coercion -> Coercion -- Input coercion -> (Coercion, Coercion) -- Expects co :: (s1 -> t1) ~ (s2 -> t2) -- Returns (co1 :: s1~s2, co2 :: t1~t2) -- See Note [Function coercions] for the "2" and "3" decomposeFunCo r co = ASSERT2( all_ok, ppr co ) (mkNthCo r 2 co, mkNthCo r 3 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 TyCoRep. 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 = mkEmptyTCvSubst $ mkInScopeSet $ tyCoVarsOfTypes orig_args `unionVarSet` tyCoVarsOfCo orig_co go :: [CoercionN] -- accumulator for argument coercions, reversed -> (TCvSubst,Kind) -- Lhs kind of coercion -> CoercionN -- coercion originally applied to the function -> (TCvSubst,Kind) -- Rhs kind of coercion -> [Type] -- Arguments to that function -> ([CoercionN], Coercion) -- Invariant: co :: subst1(k2) ~ subst2(k2) go acc_arg_cos (subst1,k1) co (subst2,k2) (ty:tys) | Just (a, t1) <- splitForAllTy_maybe k1 , Just (b, t2) <- splitForAllTy_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 = mkNthCo Nominal 0 (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 (_s1, t1) <- splitFunTy_maybe k1 , Just (_s2, t2) <- splitFunTy_maybe k2 -- 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 Nominal co 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 (zapTCvSubst subst1, substTy subst1 k1) co (zapTCvSubst 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) -- | Attempts to obtain the type variable underlying a 'Coercion' getCoVar_maybe :: Coercion -> Maybe CoVar getCoVar_maybe (CoVarCo cv) = Just cv getCoVar_maybe _ = Nothing -- | Attempts to tease a coercion apart into a type constructor and the application -- of a number of coercion arguments to that constructor splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion]) splitTyConAppCo_maybe co | Just (ty, r) <- isReflCo_maybe co = do { (tc, tys) <- splitTyConApp_maybe ty ; let args = zipWith mkReflCo (tyConRolesX r tc) tys ; return (tc, args) } splitTyConAppCo_maybe (TyConAppCo _ tc cos) = Just (tc, cos) splitTyConAppCo_maybe (FunCo _ arg res) = Just (funTyCon, cos) where cos = [mkRuntimeRepCo arg, mkRuntimeRepCo res, arg, res] splitTyConAppCo_maybe _ = Nothing -- 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 (mustBeSaturated tc) -- Never create unsaturated type family apps! , Just (args', arg') <- snocView args , Just arg'' <- setNominalRole_maybe (nthRole 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 splitFunCo_maybe :: Coercion -> Maybe (Coercion, Coercion) splitFunCo_maybe (FunCo _ arg res) = Just (arg, res) splitFunCo_maybe _ = Nothing splitForAllCo_maybe :: Coercion -> Maybe (TyCoVar, Coercion, Coercion) splitForAllCo_maybe (ForAllCo tv k_co co) = Just (tv, k_co, co) splitForAllCo_maybe _ = Nothing -- | Like 'splitForAllCo_maybe', but only returns Just for tyvar binder splitForAllCo_ty_maybe :: Coercion -> Maybe (TyVar, Coercion, Coercion) splitForAllCo_ty_maybe (ForAllCo tv k_co co) | isTyVar tv = Just (tv, k_co, co) splitForAllCo_ty_maybe _ = Nothing -- | Like 'splitForAllCo_maybe', but only returns Just for covar binder splitForAllCo_co_maybe :: Coercion -> Maybe (CoVar, Coercion, Coercion) splitForAllCo_co_maybe (ForAllCo cv k_co co) | isCoVar cv = Just (cv, k_co, co) splitForAllCo_co_maybe _ = Nothing ------------------------------------------------------- -- and some coercion kind stuff coVarTypes :: HasDebugCallStack => CoVar -> Pair Type coVarTypes cv | (_, _, ty1, ty2, _) <- coVarKindsTypesRole cv = Pair ty1 ty2 coVarKindsTypesRole :: HasDebugCallStack => CoVar -> (Kind,Kind,Type,Type,Role) coVarKindsTypesRole cv | Just (tc, [k1,k2,ty1,ty2]) <- splitTyConApp_maybe (varType cv) = let role | tc `hasKey` eqPrimTyConKey = Nominal | tc `hasKey` eqReprPrimTyConKey = Representational | otherwise = panic "coVarKindsTypesRole" in (k1,k2,ty1,ty2,role) | otherwise = pprPanic "coVarKindsTypesRole, non coercion variable" (ppr cv $$ ppr (varType cv)) coVarKind :: CoVar -> Type coVarKind cv = ASSERT( isCoVar cv ) varType cv coVarRole :: CoVar -> Role coVarRole cv | tc `hasKey` eqPrimTyConKey = Nominal | tc `hasKey` eqReprPrimTyConKey = Representational | otherwise = pprPanic "coVarRole: unknown tycon" (ppr cv <+> dcolon <+> ppr (varType cv)) where tc = case tyConAppTyCon_maybe (varType cv) of Just tc0 -> tc0 Nothing -> pprPanic "coVarRole: not tyconapp" (ppr cv) -- | 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] mkHeteroCoercionType :: Role -> Kind -> Kind -> Type -> Type -> Type mkHeteroCoercionType Nominal = mkHeteroPrimEqPred mkHeteroCoercionType Representational = mkHeteroReprPrimEqPred mkHeteroCoercionType Phantom = panic "mkHeteroCoercionType" -- | Given a coercion @co1 :: (a :: TYPE r1) ~ (b :: TYPE r2)@, -- produce a coercion @rep_co :: r1 ~ r2@. mkRuntimeRepCo :: HasDebugCallStack => Coercion -> Coercion mkRuntimeRepCo co = mkNthCo Nominal 0 kind_co where kind_co = mkKindCo co -- kind_co :: TYPE r1 ~ TYPE r2 -- (up to silliness with Constraint) 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 MCoercion is obviously generalized reflexive -- Guaranteed to work very quickly. isGReflMCo :: MCoercion -> Bool isGReflMCo MRefl = True isGReflMCo (MCo co) | isGReflCo co = True isGReflMCo _ = 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. Indeed, `unsafeCoerce` is implemented via a representational UnivCo. (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 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 = GRefl r ty mco -- | 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 | tc `hasKey` funTyConKey , [_rep1, _rep2, co1, co2] <- cos -- See Note [Function coercions] = -- (a :: TYPE ra) -> (b :: TYPE rb) ~ (c :: TYPE rc) -> (d :: TYPE rd) -- rep1 :: ra ~ rc rep2 :: rb ~ rd -- co1 :: a ~ c co2 :: b ~ d mkFunCo r co1 co2 -- Expand type synonyms | Just (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 -- | 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)@. mkFunCo :: Role -> Coercion -> Coercion -> Coercion mkFunCo r co1 co2 -- See Note [Refl invariant] | Just (ty1, _) <- isReflCo_maybe co1 , Just (ty2, _) <- isReflCo_maybe co2 = mkReflCo r (mkVisFunTy ty1 ty2) | otherwise = FunCo r co1 co2 -- | 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 (r1:_) [] = [downgradeRole r1 Nominal arg] zip_roles (r1:rs) (ty1:tys) = mkReflCo r1 ty1 : zip_roles rs tys zip_roles _ _ = panic "zip_roles" -- but the roles are infinite... 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) !! (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 TyCoRep. -- | 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 {- Note [Unused coercion variable in ForAllCo] See Note [Unused coercion variable in ForAllTy] in TyCoRep for the motivation for checking coercion variable in types. To lift the design choice to (ForAllCo cv kind_co body_co), we have two options: (1) In mkForAllCo, we check whether cv is a coercion variable and whether it is not used in body_co. If so we construct a FunCo. (2) We don't do this check in mkForAllCo. In coercionKind, we use mkTyCoForAllTy to perform the check and construct a FunTy when necessary. We chose (2) for two reasons: * for a coercion, all that matters is its kind, So ForAllCo or FunCo does not make a difference. * even if cv occurs in body_co, it is possible that cv does not occur in the kind of body_co. Therefore the check in coercionKind is inevitable. The last wrinkle is that there are restrictions around the use of the cv in the coercion, as described in Section 5.8.5.2 of Richard's thesis. The idea is that we cannot prove that the type system is consistent with unrestricted use of this cv; the consistency proof uses an untyped rewrite relation that works over types with all coercions and casts removed. So, we can allow the cv to appear only in positions that are erased. As an approximation of this (and keeping close to the published theory), we currently allow the cv only within the type in a Refl node and under a GRefl node (including in the Coercion stored in a GRefl). It's possible other places are OK, too, but this is a safe approximation. Sadly, with heterogeneous equality, this restriction might be able to be violated; Richard's thesis is unable to prove that it isn't. Specifically, the liftCoSubst function might create an invalid coercion. Because a violation of the restriction might lead to a program that "goes wrong", it is checked all the time, even in a production compiler and without -dcore-list. We *have* proved that the problem does not occur with homogeneous equality, so this check can be dropped once ~# is made to be homogeneous. -} -- | Make a Coercion from a tycovar, a kind coercion, and a body coercion. -- The kind of the tycovar should be the left-hand kind of the kind coercion. -- See Note [Unused coercion variable in ForAllCo] mkForAllCo :: TyCoVar -> CoercionN -> Coercion -> Coercion mkForAllCo v kind_co co | ASSERT( varType v `eqType` (pFst $ coercionKind kind_co)) True , ASSERT( isTyVar v || almostDevoidCoVarOfCo v co) True , Just (ty, r) <- isReflCo_maybe co , isGReflCo kind_co = mkReflCo r (mkTyCoInvForAllTy v ty) | otherwise = ForAllCo v kind_co co -- | Like 'mkForAllCo', but the inner coercion shouldn't be an obvious -- reflexive coercion. For example, it is guaranteed in 'mkForAllCos'. -- The kind of the tycovar should be the left-hand kind of the kind coercion. mkForAllCo_NoRefl :: TyCoVar -> CoercionN -> Coercion -> Coercion mkForAllCo_NoRefl v kind_co co | ASSERT( varType v `eqType` (pFst $ coercionKind kind_co)) True , ASSERT( isTyVar v || almostDevoidCoVarOfCo v co) True , ASSERT( not (isReflCo co)) True , isCoVar v , not (v `elemVarSet` tyCoVarsOfCo co) = FunCo (coercionRole co) kind_co co | otherwise = ForAllCo v kind_co co -- | Make nested ForAllCos mkForAllCos :: [(TyCoVar, CoercionN)] -> Coercion -> Coercion mkForAllCos bndrs co | Just (ty, r ) <- isReflCo_maybe co = let (refls_rev'd, non_refls_rev'd) = span (isReflCo . snd) (reverse bndrs) in foldl' (flip $ uncurry mkForAllCo_NoRefl) (mkReflCo r (mkTyCoInvForAllTys (reverse (map fst refls_rev'd)) ty)) non_refls_rev'd | otherwise = foldr (uncurry mkForAllCo_NoRefl) co bndrs -- | Make a Coercion quantified over a type/coercion variable; -- the variable has the same type in both sides of the coercion mkHomoForAllCos :: [TyCoVar] -> Coercion -> Coercion mkHomoForAllCos vs co | Just (ty, r) <- isReflCo_maybe co = mkReflCo r (mkTyCoInvForAllTys vs ty) | otherwise = mkHomoForAllCos_NoRefl vs co -- | Like 'mkHomoForAllCos', but the inner coercion shouldn't be an obvious -- reflexive coercion. For example, it is guaranteed in 'mkHomoForAllCos'. mkHomoForAllCos_NoRefl :: [TyCoVar] -> Coercion -> Coercion mkHomoForAllCos_NoRefl vs orig_co = ASSERT( not (isReflCo orig_co)) foldr go orig_co vs where go v co = mkForAllCo_NoRefl v (mkNomReflCo (varType v)) 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 Rules), but it's a relatively expensive test and perhaps better done in optCoercion. Not a big deal either way. -} -- | 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.) isCoVar_maybe :: Coercion -> Maybe CoVar isCoVar_maybe (CoVarCo cv) = Just cv isCoVar_maybe _ = Nothing mkAxInstCo :: Role -> CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Coercion -- mkAxInstCo can legitimately be called over-staturated; -- i.e. with more type arguments than the coercion requires mkAxInstCo role ax index tys cos | arity == n_tys = downgradeRole role ax_role $ mkAxiomInstCo ax_br index (rtys `chkAppend` cos) | otherwise = ASSERT( arity < n_tys ) downgradeRole role ax_role $ mkAppCos (mkAxiomInstCo ax_br index (ax_args `chkAppend` cos)) leftover_args where n_tys = length tys ax_br = toBranchedAxiom ax branch = coAxiomNthBranch ax_br index tvs = coAxBranchTyVars branch arity = length tvs arg_roles = coAxBranchRoles branch rtys = zipWith mkReflCo (arg_roles ++ repeat Nominal) tys (ax_args, leftover_args) = splitAt arity rtys ax_role = coAxiomRole ax -- worker function mkAxiomInstCo :: CoAxiom Branched -> BranchIndex -> [Coercion] -> Coercion mkAxiomInstCo ax index args = ASSERT( args `lengthIs` coAxiomArity ax index ) AxiomInstCo ax index args -- to be used only with unbranched axioms mkUnbranchedAxInstCo :: Role -> CoAxiom Unbranched -> [Type] -> [Coercion] -> Coercion mkUnbranchedAxInstCo role ax tys cos = mkAxInstCo role ax 0 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 -- | Manufacture an unsafe coercion from thin air. -- Currently (May 14) this is used only to implement the -- @unsafeCoerce#@ primitive. Optimise by pushing -- down through type constructors. mkUnsafeCo :: Role -> Type -> Type -> Coercion mkUnsafeCo role ty1 ty2 = mkUnivCo UnsafeCoerceProv role ty1 ty2 -- | Make a coercion from a coercion hole mkHoleCo :: CoercionHole -> Coercion mkHoleCo h = HoleCo h -- | Make a universal coercion between two arbitrary types. mkUnivCo :: UnivCoProvenance -> Role -- ^ role of the built coercion, "r" -> Type -- ^ t1 :: k1 -> Type -- ^ t2 :: k2 -> Coercion -- ^ :: t1 ~r t2 mkUnivCo prov role ty1 ty2 | ty1 `eqType` ty2 = mkReflCo role ty1 | otherwise = UnivCo prov role ty1 ty2 -- | Create a symmetric version of the given 'Coercion' that asserts -- equality between the same types but in the other "direction", so -- a kind of @t1 ~ t2@ becomes the kind @t2 ~ t1@. mkSymCo :: Coercion -> Coercion -- Do a few simple optimizations, but don't bother pushing occurrences -- of symmetry to the leaves; the optimizer will take care of that. mkSymCo co | isReflCo co = co mkSymCo (SymCo co) = co mkSymCo (SubCo (SymCo co)) = SubCo co mkSymCo co = SymCo co -- | Create a new 'Coercion' by composing the two given 'Coercion's transitively. -- (co1 ; co2) mkTransCo :: Coercion -> Coercion -> Coercion mkTransCo co1 co2 | isReflCo co1 = co2 | isReflCo co2 = co1 mkTransCo (GRefl r t1 (MCo co1)) (GRefl _ _ (MCo co2)) = GRefl r t1 (MCo $ mkTransCo co1 co2) mkTransCo co1 co2 = TransCo co1 co2 -- | 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) mkNthCo :: HasDebugCallStack => Role -- The role of the coercion you're creating -> Int -- Zero-indexed -> Coercion -> Coercion mkNthCo r n co = ASSERT2( good_call, bad_call_msg ) go r n co where Pair ty1 ty2 = coercionKind co go r 0 co | Just (ty, _) <- isReflCo_maybe co , Just (tv, _) <- splitForAllTy_maybe ty = -- works for both tyvar and covar ASSERT( r == Nominal ) mkNomReflCo (varType tv) go r n co | Just (ty, r0) <- isReflCo_maybe co , let tc = tyConAppTyCon ty = ASSERT2( ok_tc_app ty n, ppr n $$ ppr ty ) ASSERT( nthRole r0 tc n == r ) mkReflCo r (tyConAppArgN n ty) where ok_tc_app :: Type -> Int -> Bool ok_tc_app ty n | Just (_, tys) <- splitTyConApp_maybe ty = tys `lengthExceeds` n | isForAllTy ty -- nth:0 pulls out a kind coercion from a hetero forall = n == 0 | otherwise = False go r 0 (ForAllCo _ kind_co _) = ASSERT( r == Nominal ) kind_co -- If co :: (forall a1:k1. t1) ~ (forall a2:k2. t2) -- then (nth 0 co :: k1 ~N k2) -- If co :: (forall a1:t1 ~ t2. t1) ~ (forall a2:t3 ~ t4. t2) -- then (nth 0 co :: (t1 ~ t2) ~N (t3 ~ t4)) go r n co@(FunCo r0 arg res) -- See Note [Function coercions] -- If FunCo _ arg_co res_co :: (s1:TYPE sk1 -> s2:TYPE sk2) -- ~ (t1:TYPE tk1 -> t2:TYPE tk2) -- Then we want to behave as if co was -- TyConAppCo argk_co resk_co arg_co res_co -- where -- argk_co :: sk1 ~ tk1 = mkNthCo 0 (mkKindCo arg_co) -- resk_co :: sk2 ~ tk2 = mkNthCo 0 (mkKindCo res_co) -- i.e. mkRuntimeRepCo = case n of 0 -> ASSERT( r == Nominal ) mkRuntimeRepCo arg 1 -> ASSERT( r == Nominal ) mkRuntimeRepCo res 2 -> ASSERT( r == r0 ) arg 3 -> ASSERT( r == r0 ) res _ -> pprPanic "mkNthCo(FunCo)" (ppr n $$ ppr co) go r n (TyConAppCo r0 tc arg_cos) = ASSERT2( r == nthRole r0 tc n , (vcat [ ppr tc , ppr arg_cos , ppr r0 , ppr n , ppr r ]) ) arg_cos `getNth` n go r n co = NthCo r n co -- Assertion checking bad_call_msg = vcat [ text "Coercion =" <+> ppr co , text "LHS ty =" <+> ppr ty1 , text "RHS ty =" <+> ppr ty2 , text "n =" <+> ppr n, text "r =" <+> ppr r , text "coercion role =" <+> ppr (coercionRole co) ] good_call -- If the Coercion passed in is between forall-types, then the Int must -- be 0 and the role must be Nominal. | Just (_tv1, _) <- splitForAllTy_maybe ty1 , Just (_tv2, _) <- splitForAllTy_maybe ty2 = n == 0 && r == Nominal -- If the Coercion passed in is between T tys and T tys', then the Int -- must be less than the length of tys/tys' (which must be the same -- lengths). -- -- If the role of the Coercion is nominal, then the role passed in must -- be nominal. If the role of the Coercion is representational, then the -- role passed in must be tyConRolesRepresentational T !! n. If the role -- of the Coercion is Phantom, then the role passed in must be Phantom. -- -- See also Note [NthCo Cached Roles] if you're wondering why it's -- blaringly obvious that we should be *computing* this role instead of -- passing it in. | Just (tc1, tys1) <- splitTyConApp_maybe ty1 , Just (tc2, tys2) <- splitTyConApp_maybe ty2 , tc1 == tc2 = let len1 = length tys1 len2 = length tys2 good_role = case coercionRole co of Nominal -> r == Nominal Representational -> r == (tyConRolesRepresentational tc1 !! n) Phantom -> r == Phantom in len1 == len2 && n < len1 && good_role | otherwise = True -- | If you're about to call @mkNthCo r n co@, then @r@ should be -- whatever @nthCoRole n co@ returns. nthCoRole :: Int -> Coercion -> Role nthCoRole n co | Just (tc, _) <- splitTyConApp_maybe lty = nthRole r tc n | Just _ <- splitForAllTy_maybe lty = Nominal | otherwise = pprPanic "nthCoRole" (ppr co) where (Pair lty _, r) = coercionKindRole co 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'. mkInstCo :: Coercion -> Coercion -> Coercion mkInstCo (ForAllCo tcv _kind_co body_co) co | Just (arg, _) <- isReflCo_maybe co -- works for both tyvar and covar = 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 = GRefl r ty (MCo co) -- | Given @ty :: k1@, @co :: k1 ~ 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 $ GRefl r ty (MCo 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 $ GRefl r ty (MCo 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 :: Role -> Type -> CoercionN -> Coercion -> Coercion mkCoherenceRightCo r ty co co2 | isGReflCo co = co2 | otherwise = co2 `mkTransCo` GRefl r ty (MCo 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 (UnivCo (PhantomProv h) _ _ _) = h mkKindCo (UnivCo (ProofIrrelProv h) _ _ _) = h 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 :: 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 (FunCo Nominal arg res) = FunCo Representational (downgradeRole Representational Nominal arg) (downgradeRole Representational Nominal res) mkSubCo co = ASSERT2( 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) -- | If the EqRel is ReprEq, makes a SubCo; otherwise, does nothing. -- Note that the input coercion should always be nominal. maybeSubCo :: EqRel -> Coercion -> Coercion maybeSubCo NomEq = id maybeSubCo ReprEq = mkSubCo mkAxiomRuleCo :: CoAxiomRule -> [Coercion] -> Coercion mkAxiomRuleCo = AxiomRuleCo -- | Make a "coercion between coercions". mkProofIrrelCo :: Role -- ^ role of the created coercion, "r" -> Coercion -- ^ :: 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 Coercion 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 (tyConRolesX Representational tc) cos ; return $ TyConAppCo Nominal tc cos' } setNominalRole_maybe_helper (FunCo Representational co1 co2) = do { co1' <- setNominalRole_maybe Representational co1 ; co2' <- setNominalRole_maybe Representational co2 ; return $ FunCo Nominal co1' 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 (ForAllCo tv kind_co co) = ForAllCo tv kind_co <$> setNominalRole_maybe_helper co setNominalRole_maybe_helper (NthCo _r n co) -- NB, this case recurses via setNominalRole_maybe, not -- setNominalRole_maybe_helper! = NthCo Nominal n <$> setNominalRole_maybe (coercionRole co) co setNominalRole_maybe_helper (InstCo co arg) = InstCo <$> setNominalRole_maybe_helper co <*> pure arg setNominalRole_maybe_helper (UnivCo prov _ co1 co2) | case prov of UnsafeCoerceProv -> True -- it's always unsafe PhantomProv _ -> False -- should always be phantom ProofIrrelProv _ -> True -- it's always safe PluginProv _ -> False -- who knows? This choice is conservative. = Just $ UnivCo prov Nominal co1 co2 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 tc cos = zipWith (\r -> downgradeRole r Nominal) (tyConRolesRepresentational tc) cos -- 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 -> [Role] tyConRolesX Representational tc = tyConRolesRepresentational tc tyConRolesX role _ = repeat role -- Returns the roles of the parameters of a tycon, with an infinite tail -- of Nominal tyConRolesRepresentational :: TyCon -> [Role] tyConRolesRepresentational tc = tyConRoles tc ++ repeat Nominal nthRole :: Role -> TyCon -> Int -> Role nthRole Nominal _ _ = Nominal nthRole Phantom _ _ = Phantom nthRole Representational tc n = (tyConRolesRepresentational tc) `getNth` n 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 :: Coercion -> CoercionN -- First cases handles anything that should yield refl. promoteCoercion co = case co of _ | 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. Refl _ -> ASSERT( False ) mkNomReflCo ki1 GRefl _ _ MRefl -> ASSERT( False ) mkNomReflCo ki1 GRefl _ _ (MCo co) -> co 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 tv _ g | isTyVar tv -> promoteCoercion g ForAllCo _ _ _ -> ASSERT( False ) mkNomReflCo liftedTypeKind -- See Note [Weird typing rule for ForAllTy] in Type FunCo _ _ _ -> ASSERT( False ) mkNomReflCo liftedTypeKind CoVarCo {} -> mkKindCo co HoleCo {} -> mkKindCo co AxiomInstCo {} -> mkKindCo co AxiomRuleCo {} -> mkKindCo co UnivCo UnsafeCoerceProv _ t1 t2 -> mkUnsafeCo Nominal (typeKind t1) (typeKind t2) UnivCo (PhantomProv kco) _ _ _ -> kco UnivCo (ProofIrrelProv kco) _ _ _ -> kco UnivCo (PluginProv _) _ _ _ -> mkKindCo co SymCo g -> mkSymCo (promoteCoercion g) TransCo co1 co2 -> mkTransCo (promoteCoercion co1) (promoteCoercion co2) NthCo _ n co1 | Just (_, args) <- splitTyConAppCo_maybe co1 , args `lengthExceeds` n -> promoteCoercion (args !! n) | Just _ <- splitForAllCo_maybe co , n == 0 -> ASSERT( False ) mkNomReflCo liftedTypeKind | 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 Type KindCo _ -> ASSERT( False ) 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 $ mkNthCo Nominal 3 g -- extract result type, which is the 4th argument to (->) | 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 -- @castCoercionKind g r t1 t2 h1 h2@, where @g :: t1 ~r t2@, -- has type @(t1 |> h1) ~r (t2 |> h2)@. -- @h1@ and @h2@ must be nominal. castCoercionKind :: Coercion -> Role -> Type -> Type -> CoercionN -> CoercionN -> Coercion castCoercionKind g r t1 t2 h1 h2 = mkCoherenceRightCo r t2 h2 (mkCoherenceLeftCo r t1 h1 g) -- | 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 @castCoercionKind@ instead if @t1@, @t2@, and @r@ are known beforehand. castCoercionKindI :: Coercion -> CoercionN -> CoercionN -> Coercion castCoercionKindI g h1 h2 = mkCoherenceRightCo r t2 h2 (mkCoherenceLeftCo r t1 h1 g) where (Pair t1 t2, r) = coercionKindRole g -- See note [Newtype coercions] in TyCon 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 [v] co | isCoVar v = ASSERT( not (v `elemVarSet` tyCoVarsOfCo co) ) -- We didn't call mkForAllCo here because if v does not appear -- in co, the argement coercion will be nominal. But here we -- want it to be r. It is only called in 'mkPiCos', which is -- only used in SimplUtils, where we are sure for -- now (Aug 2018) v won't occur in co. mkFunCo r (mkReflCo r (varType v)) co | otherwise = mkFunCo r (mkReflCo r (varType v)) co -- 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 (pFst $ coercionKind g) co_list = decomposeCo (tyConArity tc) g (tyConRolesRepresentational tc) {- %************************************************************************ %* * Newtypes %* * %************************************************************************ -} -- | If @co :: T ts ~ rep_ty@ then: -- -- > instNewTyCon_maybe T ts = Just (rep_ty, co) -- -- 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 mapStepResult :: (ev1 -> ev2) -> NormaliseStepResult ev1 -> NormaliseStepResult ev2 mapStepResult f (NS_Step rec_nts ty ev) = NS_Step rec_nts ty (f ev) mapStepResult _ NS_Done = NS_Done mapStepResult _ NS_Abort = NS_Abort -- | 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 = 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 , 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 : ty0 ~ ty'@. -- (b) ty' is not a newtype. -- -- The function returns @Nothing@ for non-@newtypes@, -- or unsaturated applications -- -- This function does *not* look through type families, because it has no access to -- the type family environment. If you do have that at hand, consider to use -- topNormaliseType_maybe, which should be a drop-in replacement for -- topNormaliseNewType_maybe -- 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 = Nth 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 |-> Nth 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 TCvSubst LiftCoEnv -- in optCoercion, we need to lift when optimizing InstCo. -- See Note [Optimising InstCo] in OptCoercion -- We thus propagate the substitution from OptCoercion 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 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 (mkEmptyTCvSubst in_scope) emptyVarEnv mkLiftingContext :: [(TyCoVar,Coercion)] -> LiftingContext mkLiftingContext pairs = LC (mkEmptyTCvSubst $ mkInScopeSet $ tyCoVarsOfCos (map snd pairs)) (mkVarEnv pairs) mkSubstLiftingContext :: TCvSubst -> LiftingContext mkSubstLiftingContext subst = LC subst emptyVarEnv -- | 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 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 (extendTCvInScopeSet 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 `extendTCvInScopeSet` 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) = coVarKindsTypesRole 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 `extendTCvInScopeSet` 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 (zapTCvSubst subst) emptyVarEnv -- | Like 'substForAllCoBndr', but works on a lifting context substForAllCoBndrUsingLC :: Bool -> (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 = 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 (tyConRolesX r tc) tys) go r (FunTy _ ty1 ty2) = mkFunCo r (go r ty1) (go r ty2) go r t@(ForAllTy (Bndr v _) 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 last -- wrinkle in Note [Unused coercion variable in ForAllCo]. -- We specifically check for this and panic because we know that -- there's a hole in the type system here, and we'd rather panic than -- fall into it. then mkForAllCo v' 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) = castCoercionKindI (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 OptCoercion. 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: We want 'liftCoSubstVarBndrUsing' to be general enough to be reused in FamInstEnv, therefore the input arg 'fun' returns a pair with polymophic type in snd. However in 'liftCoSubstVarBndr', we don't need the snd, so we use unit and ignore the fourth component of the return value. 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 = let (lc', tv', h, _) = liftCoSubstVarBndrUsing callback lc tv in (lc', tv', h) where callback lc' ty' = (ty_co_subst lc' Nominal ty', ()) -- the callback must produce a nominal coercion liftCoSubstVarBndrUsing :: (LiftingContext -> Type -> (CoercionN, a)) -> LiftingContext -> TyCoVar -> (LiftingContext, TyCoVar, CoercionN, a) liftCoSubstVarBndrUsing fun lc old_var | isTyVar old_var = liftCoSubstTyVarBndrUsing fun lc old_var | otherwise = liftCoSubstCoVarBndrUsing fun lc old_var -- Works for tyvar binder liftCoSubstTyVarBndrUsing :: (LiftingContext -> Type -> (CoercionN, a)) -> LiftingContext -> TyVar -> (LiftingContext, TyVar, CoercionN, a) liftCoSubstTyVarBndrUsing fun lc@(LC subst cenv) old_var = ASSERT( isTyVar old_var ) ( LC (subst `extendTCvInScope` new_var) new_cenv , new_var, eta, stuff ) where old_kind = tyVarKind old_var (eta, stuff) = fun lc old_kind Pair k1 _ = coercionKind eta new_var = uniqAway (getTCvInScope 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 :: (LiftingContext -> Type -> (CoercionN, a)) -> LiftingContext -> CoVar -> (LiftingContext, CoVar, CoercionN, a) liftCoSubstCoVarBndrUsing fun lc@(LC subst cenv) old_var = ASSERT( isCoVar old_var ) ( LC (subst `extendTCvInScope` new_var) new_cenv , new_var, kind_co, stuff ) where old_kind = coVarKind old_var (eta, stuff) = fun lc old_kind Pair k1 _ = coercionKind eta new_var = uniqAway (getTCvInScope 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 -- kind_co :: (s1' ~r s2') ~N (t1 ~r t2) -- lifted :: co1 ~N co2 role = coVarRole old_var eta' = downgradeRole role Nominal eta eta1 = mkNthCo role 2 eta' eta2 = mkNthCo role 3 eta' co1 = mkCoVarCo new_var co2 = mkSymCo eta1 `mkTransCo` co1 `mkTransCo` eta2 kind_co = mkTyConAppCo Nominal (equalityTyCon role) [ mkKindCo co1, mkKindCo co2 , co1 , co2 ] lifted = mkProofIrrelCo Nominal kind_co 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 -> TCvSubst lcSubstLeft (LC subst lc_env) = liftEnvSubstLeft subst lc_env lcSubstRight :: LiftingContext -> TCvSubst lcSubstRight (LC subst lc_env) = liftEnvSubstRight subst lc_env liftEnvSubstLeft :: TCvSubst -> LiftCoEnv -> TCvSubst liftEnvSubstLeft = liftEnvSubst pFst liftEnvSubstRight :: TCvSubst -> LiftCoEnv -> TCvSubst liftEnvSubstRight = liftEnvSubst pSnd liftEnvSubst :: (forall a. Pair a -> a) -> TCvSubst -> LiftCoEnv -> TCvSubst liftEnvSubst selector subst lc_env = composeTCvSubst (TCvSubst emptyInScopeSet 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 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) -- | Extract the underlying substitution from the LiftingContext lcTCvSubst :: LiftingContext -> TCvSubst lcTCvSubst (LC subst _) = subst -- | Get the 'InScopeSet' from a 'LiftingContext' lcInScopeSet :: LiftingContext -> InScopeSet lcInScopeSet (LC subst _) = getTCvInScope 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 (ForAllCo tv k co) = seqType (varType tv) `seq` seqCo k `seq` seqCo co seqCo (FunCo r co1 co2) = r `seq` seqCo co1 `seq` seqCo co2 seqCo (CoVarCo cv) = cv `seq` () seqCo (HoleCo h) = coHoleCoVar h `seq` () seqCo (AxiomInstCo con ind cos) = con `seq` ind `seq` seqCos cos seqCo (UnivCo p r t1 t2) = seqProv p `seq` r `seq` seqType t1 `seq` seqType t2 seqCo (SymCo co) = seqCo co seqCo (TransCo co1 co2) = seqCo co1 `seq` seqCo co2 seqCo (NthCo r n co) = r `seq` 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 (AxiomRuleCo _ cs) = seqCos cs seqProv :: UnivCoProvenance -> () seqProv UnsafeCoerceProv = () seqProv (PhantomProv co) = seqCo co seqProv (ProofIrrelProv co) = seqCo co seqProv (PluginProv _) = () seqCos :: [Coercion] -> () seqCos [] = () seqCos (co:cos) = seqCo co `seq` seqCos cos {- %************************************************************************ %* * The kind of a type, and of a coercion %* * %************************************************************************ -} 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 :: Coercion -> Pair Type coercionKind co = go co where go (Refl ty) = Pair ty ty go (GRefl _ ty MRefl) = Pair ty ty go (GRefl _ ty (MCo co1)) = Pair ty (mkCastTy ty co1) go (TyConAppCo _ tc cos)= mkTyConApp tc <$> (sequenceA $ map go cos) go (AppCo co1 co2) = mkAppTy <$> go co1 <*> go co2 go co@(ForAllCo tv1 k_co co1) -- works for both tyvar and covar | isGReflCo k_co = mkTyCoInvForAllTy tv1 <$> go co1 -- kind_co always has kind @Type@, thus @isGReflCo@ | otherwise = go_forall empty_subst co where empty_subst = mkEmptyTCvSubst (mkInScopeSet $ tyCoVarsOfCo co) go (FunCo _ co1 co2) = mkVisFunTy <$> go co1 <*> go co2 go (CoVarCo cv) = coVarTypes cv go (HoleCo h) = coVarTypes (coHoleCoVar h) go (AxiomInstCo ax ind cos) | CoAxBranch { cab_tvs = tvs, cab_cvs = cvs , cab_lhs = lhs, cab_rhs = rhs } <- coAxiomNthBranch ax ind , let Pair tycos1 tycos2 = sequenceA (map go cos) (tys1, cotys1) = splitAtList tvs tycos1 (tys2, cotys2) = splitAtList tvs tycos2 cos1 = map stripCoercionTy cotys1 cos2 = map stripCoercionTy cotys2 = ASSERT( cos `equalLength` (tvs ++ cvs) ) -- Invariant of AxiomInstCo: cos should -- exactly saturate the axiom branch Pair (substTyWith tvs tys1 $ substTyWithCoVars cvs cos1 $ mkTyConApp (coAxiomTyCon ax) lhs) (substTyWith tvs tys2 $ substTyWithCoVars cvs cos2 rhs) go (UnivCo _ _ ty1 ty2) = Pair ty1 ty2 go (SymCo co) = swap $ go co go (TransCo co1 co2) = Pair (pFst $ go co1) (pSnd $ go co2) go g@(NthCo _ d co) | Just argss <- traverse tyConAppArgs_maybe tys = ASSERT( and $ (`lengthExceeds` d) <$> argss ) (`getNth` d) <$> argss | d == 0 , Just splits <- traverse splitForAllTy_maybe tys = (tyVarKind . fst) <$> splits | otherwise = pprPanic "coercionKind" (ppr g) where tys = go co go (LRCo lr co) = (pickLR lr . splitAppTy) <$> go co go (InstCo aco arg) = go_app aco [arg] go (KindCo co) = typeKind <$> go co go (SubCo co) = go co go (AxiomRuleCo ax cos) = expectJust "coercionKind" $ coaxrProves ax (map go cos) go_app :: Coercion -> [Coercion] -> Pair Type -- Collect up all the arguments and apply all at once -- See Note [Nested InstCos] go_app (InstCo co arg) args = go_app co (arg:args) go_app co args = piResultTys <$> go co <*> (sequenceA $ map go args) go_forall subst (ForAllCo tv1 k_co co) -- See Note [Nested ForAllCos] | isTyVar tv1 = mkInvForAllTy <$> Pair tv1 tv2 <*> go_forall subst' co where Pair _ k2 = go k_co tv2 = setTyVarKind tv1 (substTy subst k2) subst' | isGReflCo k_co = extendTCvInScope subst tv1 -- kind_co always has kind @Type@, thus @isGReflCo@ | otherwise = extendTvSubst (extendTCvInScope subst tv2) tv1 $ TyVarTy tv2 `mkCastTy` mkSymCo k_co go_forall subst (ForAllCo cv1 k_co co) | isCoVar cv1 = mkTyCoInvForAllTy <$> Pair cv1 cv2 <*> go_forall subst' co where Pair _ k2 = go k_co r = coVarRole cv1 eta1 = mkNthCo r 2 (downgradeRole r Nominal k_co) eta2 = mkNthCo r 3 (downgradeRole r Nominal 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 = extendTCvInScope subst cv1 | otherwise = extendCvSubst (extendTCvInScope subst cv2) cv1 n_subst go_forall subst other_co -- when other_co is not a ForAllCo = substTy subst `pLiftSnd` 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. -} -- | 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) -- | 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 _ _ co) = go co go (FunCo r _ _) = r go (CoVarCo cv) = coVarRole cv go (HoleCo h) = coVarRole (coHoleCoVar h) go (AxiomInstCo ax _ _) = coAxiomRole ax go (UnivCo _ r _ _) = r go (SymCo co) = go co go (TransCo co1 _co2) = go co1 go (NthCo r _d _co) = r go (LRCo {}) = Nominal go (InstCo co _) = go co go (KindCo {}) = Nominal go (SubCo _) = Representational go (AxiomRuleCo ax _) = coaxrRole ax {- 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). -} -- | 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 OptCoercion. buildCoercion :: 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_arg = arg1, ft_res = res1 }) (FunTy { ft_arg = arg2, ft_res = res2 }) = mkFunCo Nominal (go arg1 arg2) (go res1 res2) go (TyConApp tc1 args1) (TyConApp tc2 args2) = ASSERT( tc1 == tc2 ) mkTyConAppCo Nominal tc1 (zipWith go args1 args2) go (AppTy ty1a ty1b) ty2 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2 = mkAppCo (go ty1a ty2a) (go ty1b ty2b) go ty1 (AppTy ty2a ty2b) | Just (ty1a, ty1b) <- repSplitAppTy_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 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 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 = mkNthCo r 2 kind_co' eta2 = mkNthCo r 3 kind_co' subst = mkEmptyTCvSubst $ 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 ]) {- %************************************************************************ %* * Simplifying types %* * %************************************************************************ The function below morally belongs in TcFlatten, but it is used also in FamInstEnv, and so lives here. Note [simplifyArgsWorker] ~~~~~~~~~~~~~~~~~~~~~~~~~ Invariant (F2) of Note [Flattening] says that flattening is homogeneous. This causes some trouble when flattening a function applied to a telescope of arguments, perhaps with dependency. For example, suppose type family F :: forall (j :: Type) (k :: Type). Maybe j -> Either j k -> Bool -> [k] and we wish to flatten the args of (with kind applications explicit) F a b (Just a c) (Right a b d) False where all variables are skolems and a :: Type b :: Type c :: a d :: k [G] aco :: a ~ fa [G] bco :: b ~ fb [G] cco :: c ~ fc [G] dco :: d ~ fd The first step is to flatten all the arguments. This is done before calling simplifyArgsWorker. We start from a b Just a c Right a b d False and get (fa, co1 :: fa ~ a) (fb, co2 :: fb ~ b) (Just fa (fc |> aco) |> co6, co3 :: (Just fa (fc |> aco) |> co6) ~ (Just a c)) (Right fa fb (fd |> bco) |> co7, co4 :: (Right fa fb (fd |> bco) |> co7) ~ (Right a b d)) (False, co5 :: False ~ False) where co6 :: Maybe fa ~ Maybe a co7 :: Either fa fb ~ Either a b We now process the flattened args in left-to-right order. The first two args need no further processing. But now consider the third argument. Let f3 = the flattened result, Just fa (fc |> aco) |> co6. This f3 flattened argument has kind (Maybe a), due to (F2). And yet, when we build the application (F fa fb ...), we need this argument to have kind (Maybe fa), not (Maybe a). We must cast this argument. The coercion to use is determined by the kind of F: we see in F's kind that the third argument has kind Maybe j. Critically, we also know that the argument corresponding to j (in our example, a) flattened with a coercion co1. We can thus know the coercion needed for the 3rd argument is (Maybe (sym co1)), thus building (f3 |> Maybe (sym co1)) More generally, we must use the Lifting Lemma, as implemented in Coercion.liftCoSubst. As we work left-to-right, any variable that is a dependent parameter (j and k, in our example) gets mapped in a lifting context to the coercion that is output from flattening the corresponding argument (co1 and co2, in our example). Then, after flattening later arguments, we lift the kind of these arguments in the lifting context that we've be building up. This coercion is then used to keep the result of flattening well-kinded. Working through our example, this is what happens: 1. Extend the (empty) LC with [j |-> co1]. No new casting must be done, because the binder associated with the first argument has a closed type (no variables). 2. Extend the LC with [k |-> co2]. No casting to do. 3. Lifting the kind (Maybe j) with our LC yields co8 :: Maybe fa ~ Maybe a. Use (f3 |> sym co8) as the argument to F. 4. Lifting the kind (Either j k) with our LC yields co9 :: Either fa fb ~ Either a b. Use (f4 |> sym co9) as the 4th argument to F, where f4 is the flattened form of argument 4, written above. 5. We lift Bool with our LC, getting ; casting has no effect. We're now almost done, but the new application (F fa fb (f3 |> sym co8) (f4 > sym co9) False) has the wrong kind. Its kind is [fb], instead of the original [b]. So we must use our LC one last time to lift the result kind [k], getting res_co :: [fb] ~ [b], and we cast our result. Accordingly, the final result is F fa fb (Just fa (fc |> aco) |> Maybe (sym aco) |> sym (Maybe (sym aco))) (Right fa fb (fd |> bco) |> Either (sym aco) (sym bco) |> sym (Either (sym aco) (sym bco))) False |> [sym bco] The res_co (in this case, [sym bco]) is returned as the third return value from simplifyArgsWorker. Note [Last case in simplifyArgsWorker] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In writing simplifyArgsWorker's `go`, we know here that args cannot be empty, because that case is first. We've run out of binders. But perhaps inner_ki is a tyvar that has been instantiated with a Π-type. Here is an example. a :: forall (k :: Type). k -> k type family Star Proxy :: forall j. j -> Type axStar :: Star ~ Type type family NoWay :: Bool axNoWay :: NoWay ~ False bo :: Type [G] bc :: bo ~ Bool (in inert set) co :: (forall j. j -> Type) ~ (forall (j :: Star). (j |> axStar) -> Star) co = forall (j :: sym axStar). ( -> sym axStar) We are flattening: a (forall (j :: Star). (j |> axStar) -> Star) -- 1 (Proxy |> co) -- 2 (bo |> sym axStar) -- 3 (NoWay |> sym bc) -- 4 :: Star First, we flatten all the arguments (before simplifyArgsWorker), like so: (forall j. j -> Type, co1 :: (forall j. j -> Type) ~ (forall (j :: Star). (j |> axStar) -> Star)) -- 1 (Proxy |> co, co2 :: (Proxy |> co) ~ (Proxy |> co)) -- 2 (Bool |> sym axStar, co3 :: (Bool |> sym axStar) ~ (bo |> sym axStar)) -- 3 (False |> sym bc, co4 :: (False |> sym bc) ~ (NoWay |> sym bc)) -- 4 Then we do the process described in Note [simplifyArgsWorker]. 1. Lifting Type (the kind of the first arg) gives us a reflexive coercion, so we don't use it. But we do build a lifting context [k -> co1] (where co1 is a result of flattening an argument, written above). 2. Lifting k gives us co1, so the second argument becomes (Proxy |> co |> sym co1). This is not a dependent argument, so we don't extend the lifting context. Now we need to deal with argument (3). After flattening, should we tack on a homogenizing coercion? The way we normally tell is to lift the kind of the binder. But here, the remainder of the kind of `a` that we're left with after processing two arguments is just `k`. The way forward is look up k in the lifting context, getting co1. If we're at all well-typed, co1 will be a coercion between Π-types, with at least one binder. So, let's decompose co1 with decomposePiCos. This decomposition needs arguments to use to instantiate any kind parameters. Look at the type of co1. If we just decomposed it, we would end up with coercions whose types include j, which is out of scope here. Accordingly, decomposePiCos takes a list of types whose kinds are the *right-hand* types in the decomposed coercion. (See comments on decomposePiCos.) Because the flattened types have unflattened kinds (because flattening is homogeneous), passing the list of flattened types to decomposePiCos just won't do: later arguments' kinds won't be as expected. So we need to get the *unflattened* types to pass to decomposePiCos. We can do this easily enough by taking the kind of the argument coercions, passed in originally. (Alternative 1: We could re-engineer decomposePiCos to deal with this situation. But that function is already gnarly, and taking the right-hand types is correct at its other call sites, which are much more common than this one.) (Alternative 2: We could avoid calling decomposePiCos entirely, integrating its behavior into simplifyArgsWorker. This would work, I think, but then all of the complication of decomposePiCos would end up layered on top of all the complication here. Please, no.) (Alternative 3: We could pass the unflattened arguments into simplifyArgsWorker so that we don't have to recreate them. But that would complicate the interface of this function to handle a very dark, dark corner case. Better to keep our demons to ourselves here instead of exposing them to callers. This decision is easily reversed if there is ever any performance trouble due to the call of coercionKind.) So we now call decomposePiCos co1 (Pair (forall j. j -> Type) (forall (j :: Star). (j |> axStar) -> Star)) [bo |> sym axStar, NoWay |> sym bc] to get co5 :: Star ~ Type co6 :: (j |> axStar) ~ (j |> co5), substituted to (bo |> sym axStar |> axStar) ~ (bo |> sym axStar |> co5) == bo ~ bo res_co :: Type ~ Star We then use these casts on (the flattened) (3) and (4) to get (Bool |> sym axStar |> co5 :: Type) -- (C3) (False |> sym bc |> co6 :: bo) -- (C4) We can simplify to Bool -- (C3) (False |> sym bc :: bo) -- (C4) Of course, we still must do the processing in Note [simplifyArgsWorker] to finish the job. We thus want to recur. Our new function kind is the left-hand type of co1 (gotten, recall, by lifting the variable k that was the return kind of the original function). Why the left-hand type (as opposed to the right-hand type)? Because we have casted all the arguments according to decomposePiCos, which gets us from the right-hand type to the left-hand one. We thus recur with that new function kind, zapping our lifting context, because we have essentially applied it. This recursive call returns ([Bool, False], [...], Refl). The Bool and False are the correct arguments we wish to return. But we must be careful about the result coercion: our new, flattened application will have kind Type, but we want to make sure that the result coercion casts this back to Star. (Why? Because we started with an application of kind Star, and flattening is homogeneous.) So, we have to twiddle the result coercion appropriately. Let's check whether this is well-typed. We know a :: forall (k :: Type). k -> k a (forall j. j -> Type) :: (forall j. j -> Type) -> forall j. j -> Type a (forall j. j -> Type) Proxy :: forall j. j -> Type a (forall j. j -> Type) Proxy Bool :: Bool -> Type a (forall j. j -> Type) Proxy Bool False :: Type a (forall j. j -> Type) Proxy Bool False |> res_co :: Star as desired. Whew. -} -- This is shared between the flattener and the normaliser in FamInstEnv. -- See Note [simplifyArgsWorker] {-# INLINE simplifyArgsWorker #-} simplifyArgsWorker :: [TyCoBinder] -> Kind -- the binders & result kind (not a Π-type) of the function applied to the args -- list of binders can be shorter or longer than the list of args -> TyCoVarSet -- free vars of the args -> [Role] -- list of roles, r -> [(Type, Coercion)] -- flattened type arguments, arg -- each comes with the coercion used to flatten it, -- with co :: flattened_type ~ original_type -> ([Type], [Coercion], CoercionN) -- Returns (xis, cos, res_co), where each co :: xi ~ arg, -- and res_co :: kind (f xis) ~ kind (f tys), where f is the function applied to the args -- Precondition: if f :: forall bndrs. inner_ki (where bndrs and inner_ki are passed in), -- then (f orig_tys) is well kinded. Note that (f flattened_tys) might *not* be well-kinded. -- Massaging the flattened_tys in order to make (f flattened_tys) well-kinded is what this -- function is all about. That is, (f xis), where xis are the returned arguments, *is* -- well kinded. simplifyArgsWorker orig_ki_binders orig_inner_ki orig_fvs orig_roles orig_simplified_args = go [] [] orig_lc orig_ki_binders orig_inner_ki orig_roles orig_simplified_args where orig_lc = emptyLiftingContext $ mkInScopeSet $ orig_fvs go :: [Type] -- Xis accumulator, in reverse order -> [Coercion] -- Coercions accumulator, in reverse order -- These are in 1-to-1 correspondence -> LiftingContext -- mapping from tyvars to flattening coercions -> [TyCoBinder] -- Unsubsted binders of function's kind -> Kind -- Unsubsted result kind of function (not a Pi-type) -> [Role] -- Roles at which to flatten these ... -> [(Type, Coercion)] -- flattened arguments, with their flattening coercions -> ([Type], [Coercion], CoercionN) go acc_xis acc_cos lc binders inner_ki _ [] = (reverse acc_xis, reverse acc_cos, kind_co) where final_kind = mkPiTys binders inner_ki kind_co = liftCoSubst Nominal lc final_kind go acc_xis acc_cos lc (binder:binders) inner_ki (role:roles) ((xi,co):args) = -- By Note [Flattening] in TcFlatten invariant (F2), -- tcTypeKind(xi) = tcTypeKind(ty). But, it's possible that xi will be -- used as an argument to a function whose kind is different, if -- earlier arguments have been flattened to new types. We thus -- need a coercion (kind_co :: old_kind ~ new_kind). -- -- The bangs here have been observed to improve performance -- significantly in optimized builds. let kind_co = mkSymCo $ liftCoSubst Nominal lc (tyCoBinderType binder) !casted_xi = xi `mkCastTy` kind_co casted_co = mkCoherenceLeftCo role xi kind_co co -- now, extend the lifting context with the new binding !new_lc | Just tv <- tyCoBinderVar_maybe binder = extendLiftingContextAndInScope lc tv casted_co | otherwise = lc in go (casted_xi : acc_xis) (casted_co : acc_cos) new_lc binders inner_ki roles args -- See Note [Last case in simplifyArgsWorker] go acc_xis acc_cos lc [] inner_ki roles args | Just k <- getTyVar_maybe inner_ki , Just co1 <- liftCoSubstTyVar lc Nominal k = let co1_kind = coercionKind co1 unflattened_tys = map (pSnd . coercionKind . snd) args (arg_cos, res_co) = decomposePiCos co1 co1_kind unflattened_tys casted_args = ASSERT2( equalLength args arg_cos , ppr args $$ ppr arg_cos ) [ (casted_xi, casted_co) | ((xi, co), arg_co, role) <- zip3 args arg_cos roles , let casted_xi = xi `mkCastTy` arg_co casted_co = mkCoherenceLeftCo role xi arg_co co ] -- In general decomposePiCos can return fewer cos than tys, -- but not here; because we're well typed, there will be enough -- binders. Note that decomposePiCos does substitutions, so even -- if the original substitution results in something ending with -- ... -> k, that k will be substituted to perhaps reveal more -- binders. zapped_lc = zapLiftingContext lc Pair flattened_kind _ = co1_kind (bndrs, new_inner) = splitPiTys flattened_kind (xis_out, cos_out, res_co_out) = go acc_xis acc_cos zapped_lc bndrs new_inner roles casted_args in (xis_out, cos_out, res_co_out `mkTransCo` res_co) go _ _ _ _ _ _ _ = panic "simplifyArgsWorker wandered into deeper water than usual" -- This debug information is commented out because leaving it in -- causes a ~2% increase in allocations in T9872d. -- That's independent of the analagous case in flatten_args_fast -- in TcFlatten: -- each of these causes a 2% increase on its own, so commenting them -- both out gives a 4% decrease in T9872d. {- (vcat [ppr orig_binders, ppr orig_inner_ki, ppr (take 10 orig_roles), -- often infinite! ppr orig_tys]) -}