-- (c) The University of Glasgow 2012 {-# LANGUAGE CPP, DataKinds, DeriveDataTypeable, GADTs, KindSignatures, ScopedTypeVariables, StandaloneDeriving, RoleAnnotations #-} -- | Module for coercion axioms, used to represent type family instances -- and newtypes module CoAxiom ( BranchFlag, Branched, Unbranched, BranchIndex, Branches(..), manyBranches, unbranched, fromBranches, numBranches, mapAccumBranches, CoAxiom(..), CoAxBranch(..), toBranchedAxiom, toUnbranchedAxiom, coAxiomName, coAxiomArity, coAxiomBranches, coAxiomTyCon, isImplicitCoAxiom, coAxiomNumPats, coAxiomNthBranch, coAxiomSingleBranch_maybe, coAxiomRole, coAxiomSingleBranch, coAxBranchTyVars, coAxBranchCoVars, coAxBranchRoles, coAxBranchLHS, coAxBranchRHS, coAxBranchSpan, coAxBranchIncomps, placeHolderIncomps, Role(..), fsFromRole, CoAxiomRule(..), TypeEqn, BuiltInSynFamily(..), trivialBuiltInFamily ) where import GhcPrelude import {-# SOURCE #-} TyCoRep ( Type, pprType ) import {-# SOURCE #-} TyCon ( TyCon ) import Outputable import FastString import Name import Unique import Var import Util import Binary import Pair import BasicTypes import Data.Typeable ( Typeable ) import SrcLoc import qualified Data.Data as Data import Data.Array import Data.List ( mapAccumL ) #include "HsVersions.h" {- Note [Coercion axiom branches] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In order to allow closed type families, an axiom needs to contain an ordered list of alternatives, called branches. The kind of the coercion built from an axiom is determined by which index is used when building the coercion from the axiom. For example, consider the axiom derived from the following declaration: type family F a where F [Int] = Bool F [a] = Double F (a b) = Char This will give rise to this axiom: axF :: { F [Int] ~ Bool ; forall (a :: *). F [a] ~ Double ; forall (k :: *) (a :: k -> *) (b :: k). F (a b) ~ Char } The axiom is used with the AxiomInstCo constructor of Coercion. If we wish to have a coercion showing that F (Maybe Int) ~ Char, it will look like axF[2] <*> <Maybe> <Int> :: F (Maybe Int) ~ Char -- or, written using concrete-ish syntax -- AxiomInstCo axF 2 [Refl *, Refl Maybe, Refl Int] Note that the index is 0-based. For type-checking, it is also necessary to check that no previous pattern can unify with the supplied arguments. After all, it is possible that some of the type arguments are lambda-bound type variables whose instantiation may cause an earlier match among the branches. We wish to prohibit this behavior, so the type checker rules out the choice of a branch where a previous branch can unify. See also [Apartness] in FamInstEnv.hs. For example, the following is malformed, where 'a' is a lambda-bound type variable: axF[2] <*> <a> <Bool> :: F (a Bool) ~ Char Why? Because a might be instantiated with [], meaning that branch 1 should apply, not branch 2. This is a vital consistency check; without it, we could derive Int ~ Bool, and that is a Bad Thing. Note [Branched axioms] ~~~~~~~~~~~~~~~~~~~~~~ Although a CoAxiom has the capacity to store many branches, in certain cases, we want only one. These cases are in data/newtype family instances, newtype coercions, and type family instances. Furthermore, these unbranched axioms are used in a variety of places throughout GHC, and it would difficult to generalize all of that code to deal with branched axioms, especially when the code can be sure of the fact that an axiom is indeed a singleton. At the same time, it seems dangerous to assume singlehood in various places through GHC. The solution to this is to label a CoAxiom with a phantom type variable declaring whether it is known to be a singleton or not. The branches are stored using a special datatype, declared below, that ensures that the type variable is accurate. ************************************************************************ * * Branches * * ************************************************************************ -} type BranchIndex = Int -- The index of the branch in the list of branches -- Counting from zero -- promoted data type data BranchFlag = Branched | Unbranched type Branched = 'Branched type Unbranched = 'Unbranched -- By using type synonyms for the promoted constructors, we avoid needing -- DataKinds and the promotion quote in client modules. This also means that -- we don't need to export the term-level constructors, which should never be used. newtype Branches (br :: BranchFlag) = MkBranches { unMkBranches :: Array BranchIndex CoAxBranch } type role Branches nominal manyBranches :: [CoAxBranch] -> Branches Branched manyBranches brs = ASSERT( snd bnds >= fst bnds ) MkBranches (listArray bnds brs) where bnds = (0, length brs - 1) unbranched :: CoAxBranch -> Branches Unbranched unbranched br = MkBranches (listArray (0, 0) [br]) toBranched :: Branches br -> Branches Branched toBranched = MkBranches . unMkBranches toUnbranched :: Branches br -> Branches Unbranched toUnbranched (MkBranches arr) = ASSERT( bounds arr == (0,0) ) MkBranches arr fromBranches :: Branches br -> [CoAxBranch] fromBranches = elems . unMkBranches branchesNth :: Branches br -> BranchIndex -> CoAxBranch branchesNth (MkBranches arr) n = arr ! n numBranches :: Branches br -> Int numBranches (MkBranches arr) = snd (bounds arr) + 1 -- | The @[CoAxBranch]@ passed into the mapping function is a list of -- all previous branches, reversed mapAccumBranches :: ([CoAxBranch] -> CoAxBranch -> CoAxBranch) -> Branches br -> Branches br mapAccumBranches f (MkBranches arr) = MkBranches (listArray (bounds arr) (snd $ mapAccumL go [] (elems arr))) where go :: [CoAxBranch] -> CoAxBranch -> ([CoAxBranch], CoAxBranch) go prev_branches cur_branch = ( cur_branch : prev_branches , f prev_branches cur_branch ) {- ************************************************************************ * * Coercion axioms * * ************************************************************************ Note [Storing compatibility] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ During axiom application, we need to be aware of which branches are compatible with which others. The full explanation is in Note [Compatibility] in FamInstEnv. (The code is placed there to avoid a dependency from CoAxiom on the unification algorithm.) Although we could theoretically compute compatibility on the fly, this is silly, so we store it in a CoAxiom. Specifically, each branch refers to all other branches with which it is incompatible. This list might well be empty, and it will always be for the first branch of any axiom. CoAxBranches that do not (yet) belong to a CoAxiom should have a panic thunk stored in cab_incomps. The incompatibilities are properly a property of the axiom as a whole, and they are computed only when the final axiom is built. During serialization, the list is converted into a list of the indices of the branches. -} -- | A 'CoAxiom' is a \"coercion constructor\", i.e. a named equality axiom. -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in coreSyn/CoreLint.hs data CoAxiom br = CoAxiom -- Type equality axiom. { co_ax_unique :: Unique -- Unique identifier , co_ax_name :: Name -- Name for pretty-printing , co_ax_role :: Role -- Role of the axiom's equality , co_ax_tc :: TyCon -- The head of the LHS patterns -- e.g. the newtype or family tycon , co_ax_branches :: Branches br -- The branches that form this axiom , co_ax_implicit :: Bool -- True <=> the axiom is "implicit" -- See Note [Implicit axioms] -- INVARIANT: co_ax_implicit == True implies length co_ax_branches == 1. } data CoAxBranch = CoAxBranch { cab_loc :: SrcSpan -- Location of the defining equation -- See Note [CoAxiom locations] , cab_tvs :: [TyVar] -- Bound type variables; not necessarily fresh , cab_eta_tvs :: [TyVar] -- Eta-reduced tyvars -- See Note [CoAxBranch type variables] -- cab_tvs and cab_lhs may be eta-reduded; see -- Note [Eta reduction for data families] , cab_cvs :: [CoVar] -- Bound coercion variables -- Always empty, for now. -- See Note [Constraints in patterns] -- in TcTyClsDecls , cab_roles :: [Role] -- See Note [CoAxBranch roles] , cab_lhs :: [Type] -- Type patterns to match against -- See Note [CoAxiom saturation] , cab_rhs :: Type -- Right-hand side of the equality , cab_incomps :: [CoAxBranch] -- The previous incompatible branches -- See Note [Storing compatibility] } deriving Data.Data toBranchedAxiom :: CoAxiom br -> CoAxiom Branched toBranchedAxiom (CoAxiom unique name role tc branches implicit) = CoAxiom unique name role tc (toBranched branches) implicit toUnbranchedAxiom :: CoAxiom br -> CoAxiom Unbranched toUnbranchedAxiom (CoAxiom unique name role tc branches implicit) = CoAxiom unique name role tc (toUnbranched branches) implicit coAxiomNumPats :: CoAxiom br -> Int coAxiomNumPats = length . coAxBranchLHS . (flip coAxiomNthBranch 0) coAxiomNthBranch :: CoAxiom br -> BranchIndex -> CoAxBranch coAxiomNthBranch (CoAxiom { co_ax_branches = bs }) index = branchesNth bs index coAxiomArity :: CoAxiom br -> BranchIndex -> Arity coAxiomArity ax index = length tvs + length cvs where CoAxBranch { cab_tvs = tvs, cab_cvs = cvs } = coAxiomNthBranch ax index coAxiomName :: CoAxiom br -> Name coAxiomName = co_ax_name coAxiomRole :: CoAxiom br -> Role coAxiomRole = co_ax_role coAxiomBranches :: CoAxiom br -> Branches br coAxiomBranches = co_ax_branches coAxiomSingleBranch_maybe :: CoAxiom br -> Maybe CoAxBranch coAxiomSingleBranch_maybe (CoAxiom { co_ax_branches = MkBranches arr }) | snd (bounds arr) == 0 = Just $ arr ! 0 | otherwise = Nothing coAxiomSingleBranch :: CoAxiom Unbranched -> CoAxBranch coAxiomSingleBranch (CoAxiom { co_ax_branches = MkBranches arr }) = arr ! 0 coAxiomTyCon :: CoAxiom br -> TyCon coAxiomTyCon = co_ax_tc coAxBranchTyVars :: CoAxBranch -> [TyVar] coAxBranchTyVars = cab_tvs coAxBranchCoVars :: CoAxBranch -> [CoVar] coAxBranchCoVars = cab_cvs coAxBranchLHS :: CoAxBranch -> [Type] coAxBranchLHS = cab_lhs coAxBranchRHS :: CoAxBranch -> Type coAxBranchRHS = cab_rhs coAxBranchRoles :: CoAxBranch -> [Role] coAxBranchRoles = cab_roles coAxBranchSpan :: CoAxBranch -> SrcSpan coAxBranchSpan = cab_loc isImplicitCoAxiom :: CoAxiom br -> Bool isImplicitCoAxiom = co_ax_implicit coAxBranchIncomps :: CoAxBranch -> [CoAxBranch] coAxBranchIncomps = cab_incomps -- See Note [Compatibility checking] in FamInstEnv placeHolderIncomps :: [CoAxBranch] placeHolderIncomps = panic "placeHolderIncomps" {- Note [CoAxiom saturation] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * When co Note [CoAxBranch type variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In the case of a CoAxBranch of an associated type-family instance, we use the *same* type variables (where possible) as the enclosing class or instance. Consider instance C Int [z] where type F Int [z] = ... -- Second param must be [z] In the CoAxBranch in the instance decl (F Int [z]) we use the same 'z', so that it's easy to check that that type is the same as that in the instance header. So, unlike FamInsts, there is no expectation that the cab_tvs are fresh wrt each other, or any other CoAxBranch. Note [CoAxBranch roles] ~~~~~~~~~~~~~~~~~~~~~~~ Consider this code: newtype Age = MkAge Int newtype Wrap a = MkWrap a convert :: Wrap Age -> Int convert (MkWrap (MkAge i)) = i We want this to compile to: NTCo:Wrap :: forall a. Wrap a ~R a NTCo:Age :: Age ~R Int convert = \x -> x |> (NTCo:Wrap[0] NTCo:Age[0]) But, note that NTCo:Age is at role R. Thus, we need to be able to pass coercions at role R into axioms. However, we don't *always* want to be able to do this, as it would be disastrous with type families. The solution is to annotate the arguments to the axiom with roles, much like we annotate tycon tyvars. Where do these roles get set? Newtype axioms inherit their roles from the newtype tycon; family axioms are all at role N. Note [CoAxiom locations] ~~~~~~~~~~~~~~~~~~~~~~~~ The source location of a CoAxiom is stored in two places in the datatype tree. * The first is in the location info buried in the Name of the CoAxiom. This span includes all of the branches of a branched CoAxiom. * The second is in the cab_loc fields of the CoAxBranches. In the case of a single branch, we can extract the source location of the branch from the name of the CoAxiom. In other cases, we need an explicit SrcSpan to correctly store the location of the equation giving rise to the FamInstBranch. Note [Implicit axioms] ~~~~~~~~~~~~~~~~~~~~~~ See also Note [Implicit TyThings] in HscTypes * A CoAxiom arising from data/type family instances is not "implicit". That is, it has its own IfaceAxiom declaration in an interface file * The CoAxiom arising from a newtype declaration *is* "implicit". That is, it does not have its own IfaceAxiom declaration in an interface file; instead the CoAxiom is generated by type-checking the newtype declaration Note [Eta reduction for data families] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider this data family T a b :: * newtype instance T Int a = MkT (IO a) deriving( Monad ) We'd like this to work. From the 'newtype instance' you might think we'd get: newtype TInt a = MkT (IO a) axiom ax1 a :: T Int a ~ TInt a -- The newtype-instance part axiom ax2 a :: TInt a ~ IO a -- The newtype part But now what can we do? We have this problem Given: d :: Monad IO Wanted: d' :: Monad (T Int) = d |> ???? What coercion can we use for the ??? Solution: eta-reduce both axioms, thus: axiom ax1 :: T Int ~ TInt axiom ax2 :: TInt ~ IO Now d' = d |> Monad (sym (ax2 ; ax1)) ----- Bottom line ------ For a CoAxBranch for a data family instance with representation TyCon rep_tc: - cab_tvs (of its CoAxiom) may be shorter than tyConTyVars of rep_tc. - cab_lhs may be shorter than tyConArity of the family tycon i.e. LHS is unsaturated - cab_rhs will be (rep_tc cab_tvs) i.e. RHS is un-saturated - This eta reduction happens for data instances as well as newtype instances. Here we want to eta-reduce the data family axiom. - This eta-reduction is done in TcInstDcls.tcDataFamInstDecl. But for a /type/ family - cab_lhs has the exact arity of the family tycon There are certain situations (e.g., pretty-printing) where it is necessary to deal with eta-expanded data family instances. For these situations, the cab_eta_tvs field records the stuff that has been eta-reduced away. So if we have axiom forall a b. F [a->b] = D b a and cab_eta_tvs is [p,q], then the original user-written definition looked like axiom forall a b p q. F [a->b] p q = D b a p q (See #9692, #14179, and #15845 for examples of what can go wrong if we don't eta-expand when showing things to the user.) (See also Note [Newtype eta] in TyCon. This is notionally separate and deals with the axiom connecting a newtype with its representation type; but it too is eta-reduced.) -} instance Eq (CoAxiom br) where a == b = getUnique a == getUnique b a /= b = getUnique a /= getUnique b instance Uniquable (CoAxiom br) where getUnique = co_ax_unique instance Outputable (CoAxiom br) where ppr = ppr . getName instance NamedThing (CoAxiom br) where getName = co_ax_name instance Typeable br => Data.Data (CoAxiom br) where -- don't traverse? toConstr _ = abstractConstr "CoAxiom" gunfold _ _ = error "gunfold" dataTypeOf _ = mkNoRepType "CoAxiom" instance Outputable CoAxBranch where ppr (CoAxBranch { cab_loc = loc , cab_lhs = lhs , cab_rhs = rhs }) = text "CoAxBranch" <+> parens (ppr loc) <> colon <+> brackets (fsep (punctuate comma (map pprType lhs))) <+> text "=>" <+> pprType rhs {- ************************************************************************ * * Roles * * ************************************************************************ Roles are defined here to avoid circular dependencies. -} -- See Note [Roles] in Coercion -- defined here to avoid cyclic dependency with Coercion -- -- Order of constructors matters: the Ord instance coincides with the *super*typing -- relation on roles. data Role = Nominal | Representational | Phantom deriving (Eq, Ord, Data.Data) -- These names are slurped into the parser code. Changing these strings -- will change the **surface syntax** that GHC accepts! If you want to -- change only the pretty-printing, do some replumbing. See -- mkRoleAnnotDecl in RdrHsSyn fsFromRole :: Role -> FastString fsFromRole Nominal = fsLit "nominal" fsFromRole Representational = fsLit "representational" fsFromRole Phantom = fsLit "phantom" instance Outputable Role where ppr = ftext . fsFromRole instance Binary Role where put_ bh Nominal = putByte bh 1 put_ bh Representational = putByte bh 2 put_ bh Phantom = putByte bh 3 get bh = do tag <- getByte bh case tag of 1 -> return Nominal 2 -> return Representational 3 -> return Phantom _ -> panic ("get Role " ++ show tag) {- ************************************************************************ * * CoAxiomRule Rules for building Evidence * * ************************************************************************ Conditional axioms. The general idea is that a `CoAxiomRule` looks like this: forall as. (r1 ~ r2, s1 ~ s2) => t1 ~ t2 My intention is to reuse these for both (~) and (~#). The short-term plan is to use this datatype to represent the type-nat axioms. In the longer run, it may be good to unify this and `CoAxiom`, as `CoAxiom` is the special case when there are no assumptions. -} -- | A more explicit representation for `t1 ~ t2`. type TypeEqn = Pair Type -- | For now, we work only with nominal equality. data CoAxiomRule = CoAxiomRule { coaxrName :: FastString , coaxrAsmpRoles :: [Role] -- roles of parameter equations , coaxrRole :: Role -- role of resulting equation , coaxrProves :: [TypeEqn] -> Maybe TypeEqn -- ^ coaxrProves returns @Nothing@ when it doesn't like -- the supplied arguments. When this happens in a coercion -- that means that the coercion is ill-formed, and Core Lint -- checks for that. } instance Data.Data CoAxiomRule where -- don't traverse? toConstr _ = abstractConstr "CoAxiomRule" gunfold _ _ = error "gunfold" dataTypeOf _ = mkNoRepType "CoAxiomRule" instance Uniquable CoAxiomRule where getUnique = getUnique . coaxrName instance Eq CoAxiomRule where x == y = coaxrName x == coaxrName y instance Ord CoAxiomRule where compare x y = compare (coaxrName x) (coaxrName y) instance Outputable CoAxiomRule where ppr = ppr . coaxrName -- Type checking of built-in families data BuiltInSynFamily = BuiltInSynFamily { sfMatchFam :: [Type] -> Maybe (CoAxiomRule, [Type], Type) , sfInteractTop :: [Type] -> Type -> [TypeEqn] , sfInteractInert :: [Type] -> Type -> [Type] -> Type -> [TypeEqn] } -- Provides default implementations that do nothing. trivialBuiltInFamily :: BuiltInSynFamily trivialBuiltInFamily = BuiltInSynFamily { sfMatchFam = \_ -> Nothing , sfInteractTop = \_ _ -> [] , sfInteractInert = \_ _ _ _ -> [] }