{-| Copyright : (C) 2016 , University of Twente, 2017-2018, QBayLogic B.V., 2017 , Google Inc. License : BSD2 (see the file LICENSE) Maintainer : Christiaan Baaij A type checker plugin for GHC that can derive \"complex\" @KnownNat@ constraints from other simple/variable @KnownNat@ constraints. i.e. without this plugin, you must have both a @KnownNat n@ and a @KnownNat (n+2)@ constraint in the type signature of the following function: @ f :: forall n . (KnownNat n, KnownNat (n+2)) => Proxy n -> Integer f _ = natVal (Proxy :: Proxy n) + natVal (Proxy :: Proxy (n+2)) @ Using the plugin you can omit the @KnownNat (n+2)@ constraint: @ f :: forall n . KnownNat n => Proxy n -> Integer f _ = natVal (Proxy :: Proxy n) + natVal (Proxy :: Proxy (n+2)) @ The plugin can derive @KnownNat@ constraints for types consisting of: * Type variables, when there is a corresponding @KnownNat@ constraint * Type-level naturals * Applications of the arithmetic expression: @{+,-,*,^}@ * Type functions, when there is either: * a matching given @KnownNat@ constraint; or * a corresponding @KnownNat\@ instance for the type function To elaborate the latter points, given the type family @Min@: @ type family Min (a :: Nat) (b :: Nat) :: Nat where Min 0 b = 0 Min a b = If (a <=? b) a b @ the plugin can derive a @KnownNat (Min x y + 1)@ constraint given only a @KnownNat (Min x y)@ constraint: @ g :: forall x y . (KnownNat (Min x y)) => Proxy x -> Proxy y -> Integer g _ _ = natVal (Proxy :: Proxy (Min x y + 1)) @ And, given the type family @Max@: @ type family Max (a :: Nat) (b :: Nat) :: Nat where Max 0 b = b Max a b = If (a <=? b) b a @ and corresponding @KnownNat2@ instance: @ instance (KnownNat a, KnownNat b) => KnownNat2 \"TestFunctions.Max\" a b where natSing2 = let x = natVal (Proxy @a) y = natVal (Proxy @b) z = max x y in SNatKn z \{\-# INLINE natSing2 \#-\} @ the plugin can derive a @KnownNat (Max x y + 1)@ constraint given only a @KnownNat x@ and @KnownNat y@ constraint: @ h :: forall x y . (KnownNat x, KnownNat y) => Proxy x -> Proxy y -> Integer h _ _ = natVal (Proxy :: Proxy (Max x y + 1)) @ To use the plugin, add the @ OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver @ Pragma to the header of your file. -} {-# LANGUAGE CPP #-} {-# LANGUAGE LambdaCase #-} {-# LANGUAGE TupleSections #-} {-# LANGUAGE ViewPatterns #-} {-# LANGUAGE Trustworthy #-} {-# OPTIONS_HADDOCK show-extensions #-} module GHC.TypeLits.KnownNat.Solver ( plugin ) where -- external import Control.Arrow ((&&&), first) import Control.Monad.Trans.Maybe (MaybeT (..)) import Control.Monad.Trans.Writer.Strict import Data.Maybe (catMaybes,mapMaybe) import GHC.TcPluginM.Extra (lookupModule, lookupName, newWanted, tracePlugin) #if MIN_VERSION_ghc(8,4,0) import GHC.TcPluginM.Extra (flattenGivens, mkSubst', substType) #endif import GHC.TypeLits.Normalise.SOP (SOP (..), Product (..), Symbol (..)) import GHC.TypeLits.Normalise.Unify (CType (..),normaliseNat,reifySOP) -- GHC API #if MIN_VERSION_ghc(9,0,0) import GHC.Builtin.Names (knownNatClassName) import GHC.Builtin.Types (boolTy) import GHC.Builtin.Types.Literals (typeNatAddTyCon, typeNatDivTyCon, typeNatSubTyCon) import GHC.Core.Class (Class, classMethods, className, classTyCon) import GHC.Core.Coercion (Role (Representational), mkUnivCo) import GHC.Core.InstEnv (instanceDFunId, lookupUniqueInstEnv) import GHC.Core.Make (mkNaturalExpr) import GHC.Core.Predicate (EqRel (NomEq), Pred (ClassPred,EqPred), classifyPredType) import GHC.Core.TyCo.Rep (Type (..), TyLit (..), UnivCoProvenance (PluginProv)) import GHC.Core.TyCon (tyConName) import GHC.Core.Type (PredType, dropForAlls, eqType, funResultTy, mkNumLitTy, mkStrLitTy, mkTyConApp, piResultTys, splitFunTys, splitTyConApp_maybe, tyConAppTyCon_maybe, typeKind, irrelevantMult) import GHC.Data.FastString (fsLit) import GHC.Driver.Plugins (Plugin (..), defaultPlugin, purePlugin) import GHC.Tc.Instance.Family (tcInstNewTyCon_maybe) import GHC.Tc.Plugin (TcPluginM, tcLookupClass, getInstEnvs) import GHC.Tc.Types (TcPlugin(..), TcPluginResult (..)) import GHC.Tc.Types.Constraint (Ct, ctEvExpr, ctEvidence, ctEvLoc, ctEvPred, ctLoc, ctLocSpan, isWanted, mkNonCanonical, setCtLoc, setCtLocSpan) import GHC.Tc.Types.Evidence (EvTerm (..), EvExpr, evDFunApp, mkEvCast, mkTcSymCo, mkTcTransCo) import GHC.Types.Id (idType) import GHC.Types.Name (nameModule_maybe, nameOccName) import GHC.Types.Name.Occurrence (mkTcOcc, occNameString) import GHC.Types.Var (DFunId) import GHC.Unit.Module (mkModuleName, moduleName, moduleNameString) #else import Class (Class, classMethods, className, classTyCon) #if MIN_VERSION_ghc(8,6,0) import Coercion (Role (Representational), mkUnivCo) #endif import FamInst (tcInstNewTyCon_maybe) import FastString (fsLit) import Id (idType) import InstEnv (instanceDFunId,lookupUniqueInstEnv) #if MIN_VERSION_ghc(8,5,0) import MkCore (mkNaturalExpr) #endif import Module (mkModuleName, moduleName, moduleNameString) import Name (nameModule_maybe, nameOccName) import OccName (mkTcOcc, occNameString) import Plugins (Plugin (..), defaultPlugin) #if MIN_VERSION_ghc(8,6,0) import Plugins (purePlugin) #endif import PrelNames (knownNatClassName) #if MIN_VERSION_ghc(8,5,0) import TcEvidence (EvTerm (..), EvExpr, evDFunApp, mkEvCast, mkTcSymCo, mkTcTransCo) #else import TcEvidence (EvTerm (..), EvLit (EvNum), mkEvCast, mkTcSymCo, mkTcTransCo) #endif #if MIN_VERSION_ghc(8,5,0) import TcPluginM (unsafeTcPluginTcM) #endif #if !MIN_VERSION_ghc(8,4,0) import TcPluginM (zonkCt) #endif import TcPluginM (TcPluginM, tcLookupClass, getInstEnvs) import TcRnTypes (TcPlugin(..), TcPluginResult (..)) import TcTypeNats (typeNatAddTyCon, typeNatSubTyCon) #if MIN_VERSION_ghc(8,4,0) import TcTypeNats (typeNatDivTyCon) #endif import Type (PredType, dropForAlls, eqType, funResultTy, mkNumLitTy, mkStrLitTy, mkTyConApp, piResultTys, splitFunTys, splitTyConApp_maybe, tyConAppTyCon_maybe, typeKind) import TyCon (tyConName) import TyCoRep (Type (..), TyLit (..)) #if MIN_VERSION_ghc(8,6,0) import TyCoRep (UnivCoProvenance (PluginProv)) import TysWiredIn (boolTy) #endif import Var (DFunId) #if MIN_VERSION_ghc(8,10,0) import Constraint (Ct, ctEvExpr, ctEvidence, ctEvLoc, ctEvPred, ctLoc, ctLocSpan, isWanted, mkNonCanonical, setCtLoc, setCtLocSpan) import Predicate (EqRel (NomEq), Pred (ClassPred,EqPred), classifyPredType) #else import TcRnTypes (Ct, ctEvidence, ctEvLoc, ctEvPred, ctLoc, ctLocSpan, isWanted, mkNonCanonical, setCtLoc, setCtLocSpan) import Type (EqRel (NomEq), PredTree (ClassPred,EqPred), classifyPredType) #if MIN_VERSION_ghc(8,5,0) import TcRnTypes (ctEvExpr) #else import TcRnTypes (ctEvTerm) #endif #endif #endif -- | Classes and instances from "GHC.TypeLits.KnownNat" data KnownNatDefs = KnownNatDefs { knownBool :: Class , knownBoolNat2 :: Class , knownNat2Bool :: Class , knownNatN :: Int -> Maybe Class -- ^ KnownNat{N} } -- | Simple newtype wrapper to distinguish the original (flattened) argument of -- knownnat from the un-flattened version that we work with internally. newtype Orig a = Orig { unOrig :: a } -- | KnownNat constraints type KnConstraint = (Ct -- The constraint ,Class -- KnownNat class ,Type -- The argument to KnownNat ,Orig Type -- Original, flattened, argument to KnownNat ) {-| A type checker plugin for GHC that can derive \"complex\" @KnownNat@ constraints from other simple/variable @KnownNat@ constraints. i.e. without this plugin, you must have both a @KnownNat n@ and a @KnownNat (n+2)@ constraint in the type signature of the following function: @ f :: forall n . (KnownNat n, KnownNat (n+2)) => Proxy n -> Integer f _ = natVal (Proxy :: Proxy n) + natVal (Proxy :: Proxy (n+2)) @ Using the plugin you can omit the @KnownNat (n+2)@ constraint: @ f :: forall n . KnownNat n => Proxy n -> Integer f _ = natVal (Proxy :: Proxy n) + natVal (Proxy :: Proxy (n+2)) @ The plugin can derive @KnownNat@ constraints for types consisting of: * Type variables, when there is a corresponding @KnownNat@ constraint * Type-level naturals * Applications of the arithmetic expression: @{+,-,*,^}@ * Type functions, when there is either: * a matching given @KnownNat@ constraint; or * a corresponding @KnownNat\@ instance for the type function To elaborate the latter points, given the type family @Min@: @ type family Min (a :: Nat) (b :: Nat) :: Nat where Min 0 b = 0 Min a b = If (a <=? b) a b @ the plugin can derive a @KnownNat (Min x y + 1)@ constraint given only a @KnownNat (Min x y)@ constraint: @ g :: forall x y . (KnownNat (Min x y)) => Proxy x -> Proxy y -> Integer g _ _ = natVal (Proxy :: Proxy (Min x y + 1)) @ And, given the type family @Max@: @ type family Max (a :: Nat) (b :: Nat) :: Nat where Max 0 b = b Max a b = If (a <=? b) b a $(genDefunSymbols [''Max]) -- creates the 'MaxSym0' symbol @ and corresponding @KnownNat2@ instance: @ instance (KnownNat a, KnownNat b) => KnownNat2 \"TestFunctions.Max\" a b where type KnownNatF2 \"TestFunctions.Max\" = MaxSym0 natSing2 = let x = natVal (Proxy @ a) y = natVal (Proxy @ b) z = max x y in SNatKn z \{\-# INLINE natSing2 \#-\} @ the plugin can derive a @KnownNat (Max x y + 1)@ constraint given only a @KnownNat x@ and @KnownNat y@ constraint: @ h :: forall x y . (KnownNat x, KnownNat y) => Proxy x -> Proxy y -> Integer h _ _ = natVal (Proxy :: Proxy (Max x y + 1)) @ To use the plugin, add the @ OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver @ Pragma to the header of your file. -} plugin :: Plugin plugin = defaultPlugin { tcPlugin = const $ Just normalisePlugin #if MIN_VERSION_ghc(8,6,0) , pluginRecompile = purePlugin #endif } normalisePlugin :: TcPlugin normalisePlugin = tracePlugin "ghc-typelits-knownnat" TcPlugin { tcPluginInit = lookupKnownNatDefs , tcPluginSolve = solveKnownNat , tcPluginStop = const (return ()) } solveKnownNat :: KnownNatDefs -> [Ct] -> [Ct] -> [Ct] -> TcPluginM TcPluginResult solveKnownNat _defs _givens _deriveds [] = return (TcPluginOk [] []) solveKnownNat defs givens _deriveds wanteds = do -- GHC 7.10 puts deriveds with the wanteds, so filter them out let wanteds' = filter (isWanted . ctEvidence) wanteds #if MIN_VERSION_ghc(8,4,0) subst = map fst $ mkSubst' givens kn_wanteds = map (\(x,y,z,orig) -> (x,y,substType subst z,orig)) $ mapMaybe (toKnConstraint defs) wanteds' #else kn_wanteds = mapMaybe (toKnConstraint defs) wanteds' #endif case kn_wanteds of [] -> return (TcPluginOk [] []) _ -> do -- Make a lookup table for all the [G]iven constraints #if MIN_VERSION_ghc(8,4,0) let given_map = map toGivenEntry (flattenGivens givens) #else given_map <- mapM (fmap toGivenEntry . zonkCt) givens #endif -- Try to solve the wanted KnownNat constraints given the [G]iven -- KnownNat constraints (solved,new) <- (unzip . catMaybes) <$> (mapM (constraintToEvTerm defs given_map) kn_wanteds) return (TcPluginOk solved (concat new)) -- | Get the KnownNat constraints toKnConstraint :: KnownNatDefs -> Ct -> Maybe KnConstraint toKnConstraint defs ct = case classifyPredType $ ctEvPred $ ctEvidence ct of ClassPred cls [ty] | className cls == knownNatClassName || className cls == className (knownBool defs) -> Just (ct,cls,ty,Orig ty) _ -> Nothing -- | Create a look-up entry for a [G]iven constraint. #if MIN_VERSION_ghc(8,5,0) toGivenEntry :: Ct -> (CType,EvExpr) #else toGivenEntry :: Ct -> (CType,EvTerm) #endif toGivenEntry ct = let ct_ev = ctEvidence ct c_ty = ctEvPred ct_ev #if MIN_VERSION_ghc(8,5,0) ev = ctEvExpr ct_ev #else ev = ctEvTerm ct_ev #endif in (CType c_ty,ev) -- | Find the \"magic\" classes and instances in "GHC.TypeLits.KnownNat" lookupKnownNatDefs :: TcPluginM KnownNatDefs lookupKnownNatDefs = do md <- lookupModule myModule myPackage kbC <- look md "KnownBool" kbn2C <- look md "KnownBoolNat2" kn2bC <- look md "KnownNat2Bool" kn1C <- look md "KnownNat1" kn2C <- look md "KnownNat2" kn3C <- look md "KnownNat3" return KnownNatDefs { knownBool = kbC , knownBoolNat2 = kbn2C , knownNat2Bool = kn2bC , knownNatN = \case { 1 -> Just kn1C ; 2 -> Just kn2C ; 3 -> Just kn3C ; _ -> Nothing } } where look md s = do nm <- lookupName md (mkTcOcc s) tcLookupClass nm myModule = mkModuleName "GHC.TypeLits.KnownNat" myPackage = fsLit "ghc-typelits-knownnat" -- | Try to create evidence for a wanted constraint constraintToEvTerm :: KnownNatDefs -- ^ The "magic" KnownNatN classes #if MIN_VERSION_ghc(8,5,0) -> [(CType,EvExpr)] #else -> [(CType,EvTerm)] #endif -- All the [G]iven constraints -> KnConstraint -> TcPluginM (Maybe ((EvTerm,Ct),[Ct])) constraintToEvTerm defs givens (ct,cls,op,orig) = do -- 1. Determine if we are an offset apart from a [G]iven constraint offsetM <- offset op evM <- case offsetM of -- 3.a If so, we are done found@Just {} -> return found -- 3.b If not, we check if the outer type-level operation -- has a corresponding KnownNat instance. _ -> go op return ((first (,ct)) <$> evM) where -- Determine whether the outer type-level operation has a corresponding -- KnownNat instance, where /N/ corresponds to the arity of the -- type-level operation go :: Type -> TcPluginM (Maybe (EvTerm,[Ct])) go (go_other -> Just ev) = return (Just (ev,[])) go ty@(TyConApp tc args0) | let tcNm = tyConName tc , Just m <- nameModule_maybe tcNm = do ienv <- getInstEnvs let mS = moduleNameString (moduleName m) tcS = occNameString (nameOccName tcNm) fn0 = mS ++ "." ++ tcS fn1 = mkStrLitTy (fsLit fn0) args1 = fn1:args0 instM = case () of () | Just knN_cls <- knownNatN defs (length args0) , Right (inst, _) <- lookupUniqueInstEnv ienv knN_cls args1 -> Just (inst,knN_cls,args0,args1) | length args0 == 2 , let knN_cls = knownBoolNat2 defs ki = typeKind (head args0) args1N = ki:args1 , Right (inst, _) <- lookupUniqueInstEnv ienv knN_cls args1N -> Just (inst,knN_cls,args0,args1N) | length args0 == 4 , fn0 == "Data.Type.Bool.If" , let args0N = tail args0 args1N = head args0:fn1:tail args0 knN_cls = knownNat2Bool defs , Right (inst, _) <- lookupUniqueInstEnv ienv knN_cls args1N -> Just (inst,knN_cls,args0N,args1N) | otherwise -> Nothing case instM of Just (inst,knN_cls,args0N,args1N) -> do let df_id = instanceDFunId inst df = (knN_cls,df_id) df_args = fst -- [KnownNat x, KnownNat y] . splitFunTys -- ([KnownNat x, KnowNat y], DKnownNat2 "+" x y) . (`piResultTys` args0N) -- (KnowNat x, KnownNat y) => DKnownNat2 "+" x y $ idType df_id -- forall a b . (KnownNat a, KnownNat b) => DKnownNat2 "+" a b #if MIN_VERSION_ghc(9,0,0) (evs,new) <- unzip <$> mapM (go_arg . irrelevantMult) df_args #else (evs,new) <- unzip <$> mapM go_arg df_args #endif if className cls == className (knownBool defs) -- Create evidence using the original, flattened, argument of -- the KnownNat we're trying to solve. Not doing this results in -- GHC panics for: -- https://gist.github.com/christiaanb/0d204fe19f89b28f1f8d24feb63f1e63 -- -- That's because the flattened KnownNat we're asked to solve is -- [W] KnownNat fsk -- given: -- [G] fsk ~ CLog 2 n + 1 -- [G] fsk2 ~ n -- [G] fsk2 ~ n + m -- -- Our flattening picks one of the solution, so we try to solve -- [W] KnownNat (CLog 2 n + 1) -- -- Turns out, GHC wanted us to solve: -- [W] KnownNat (CLog 2 (n + m) + 1) -- -- But we have no way of knowing this! Solving the "wrong" expansion -- of 'fsk' results in: -- -- ghc: panic! (the 'impossible' happened) -- (GHC version 8.6.5 for x86_64-unknown-linux): -- buildKindCoercion -- CLog 2 (n_a681K + m_a681L) -- CLog 2 n_a681K -- n_a681K + m_a681L -- n_a681K -- -- down the line. -- -- So while the "shape" of the KnownNat evidence that we return -- follows 'CLog 2 n + 1', the type of the evidence will be -- 'KnownNat fsk'; the one GHC originally asked us to solve. then return ((,concat new) <$> makeOpDictByFiat df cls args1N args0N (unOrig orig) evs) else return ((,concat new) <$> makeOpDict df cls args1N args0N (unOrig orig) evs) _ -> return ((,[]) <$> go_other ty) go (LitTy (NumTyLit i)) -- Let GHC solve simple Literal constraints | LitTy _ <- op = return Nothing -- This plugin only solves Literal KnownNat's that needed to be normalised -- first | otherwise #if MIN_VERSION_ghc(8,5,0) = (fmap (,[])) <$> makeLitDict cls op i #else = return ((,[]) <$> makeLitDict cls op i) #endif go _ = return Nothing -- Get EvTerm arguments for type-level operations. If they do not exist -- as [G]iven constraints, then generate new [W]anted constraints #if MIN_VERSION_ghc(8,5,0) go_arg :: PredType -> TcPluginM (EvExpr,[Ct]) #else go_arg :: PredType -> TcPluginM (EvTerm,[Ct]) #endif go_arg ty = case lookup (CType ty) givens of Just ev -> return (ev,[]) _ -> do (ev,wanted) <- makeWantedEv ct ty return (ev,[wanted]) -- Fall through case: look up the normalised [W]anted constraint in the list -- of [G]iven constraints. go_other :: Type -> Maybe EvTerm go_other ty = let knClsTc = classTyCon cls kn = mkTyConApp knClsTc [ty] cast = if CType ty == CType op #if MIN_VERSION_ghc(8,6,0) then Just . EvExpr #else then Just #endif else makeKnCoercion cls ty op in cast =<< lookup (CType kn) givens -- Find a known constraint for a wanted, so that (modulo normalization) -- the two are a constant offset apart. offset :: Type -> TcPluginM (Maybe (EvTerm,[Ct])) offset want = runMaybeT $ do let -- Get the knownnat contraints unKn ty' = case classifyPredType ty' of ClassPred cls' [ty''] | className cls' == knownNatClassName -> Just ty'' _ -> Nothing -- Get the rewrites unEq ty' = case classifyPredType ty' of EqPred NomEq ty1 ty2 -> Just (ty1,ty2) _ -> Nothing rewrites = mapMaybe (unEq . unCType . fst) givens -- Rewrite rewriteTy tyK (ty1,ty2) | ty1 `eqType` tyK = Just ty2 | ty2 `eqType` tyK = Just ty1 | otherwise = Nothing -- Get only the [G]iven KnownNat constraints knowns = mapMaybe (unKn . unCType . fst) givens -- Get all the rewritten KNs knownsR = catMaybes $ concatMap (\t -> map (rewriteTy t) rewrites) knowns knownsX = knowns ++ knownsR -- pair up the sum-of-products KnownNat constraints -- with the original Nat operation subWant = mkTyConApp typeNatSubTyCon . (:[want]) exploded = map (fst . runWriter . normaliseNat . subWant &&& id) knownsX -- interesting cases for us are those where -- wanted and given only differ by a constant examineDiff (S [P [I n]]) entire = Just (entire,I n) examineDiff (S [P [V v]]) entire = Just (entire,V v) examineDiff _ _ = Nothing interesting = mapMaybe (uncurry examineDiff) exploded -- convert the first suitable evidence ((h,corr):_) <- pure interesting x <- case corr of I 0 -> pure h I i | i < 0 -> pure (mkTyConApp typeNatAddTyCon [h,mkNumLitTy (negate i)]) | otherwise -> pure (mkTyConApp typeNatSubTyCon [h,mkNumLitTy i]) -- If the offset between a given and a wanted is again the wanted -- then the given is twice the wanted; so we can just divide -- the given by two. Only possible in GHC 8.4+; for 8.2 we simply -- fail because we don't know how to divide. c | CType (reifySOP (S [P [c]])) == CType want -> #if MIN_VERSION_ghc(8,4,0) pure (mkTyConApp typeNatDivTyCon [h,reifySOP (S [P [I 2]])]) #else MaybeT (pure Nothing) #endif -- Only solve with a variable offset if we have [G]iven knownnat for it -- Failing to do this check results in #30 V v | all (not . eqType (TyVarTy v)) knownsX -> MaybeT (pure Nothing) _ -> pure (mkTyConApp typeNatSubTyCon [h,reifySOP (S [P [corr]])]) MaybeT (go x) makeWantedEv :: Ct -> Type #if MIN_VERSION_ghc(8,5,0) -> TcPluginM (EvExpr,Ct) #else -> TcPluginM (EvTerm,Ct) #endif makeWantedEv ct ty = do -- Create a new wanted constraint wantedCtEv <- newWanted (ctLoc ct) ty #if MIN_VERSION_ghc(8,5,0) let ev = ctEvExpr wantedCtEv #else let ev = ctEvTerm wantedCtEv #endif wanted = mkNonCanonical wantedCtEv -- Set the source-location of the new wanted constraint to the source -- location of the [W]anted constraint we are currently trying to solve ct_ls = ctLocSpan (ctLoc ct) ctl = ctEvLoc wantedCtEv wanted' = setCtLoc wanted (setCtLocSpan ctl ct_ls) return (ev,wanted') {- | Given: * A "magic" class, and corresponding instance dictionary function, for a type-level arithmetic operation * Two KnownNat dictionaries makeOpDict instantiates the dictionary function with the KnownNat dictionaries, and coerces it to a KnownNat dictionary. i.e. for KnownNat2, the "magic" dictionary for binary functions, the coercion happens in the following steps: 1. KnownNat2 "+" a b -> SNatKn (KnownNatF2 "+" a b) 2. SNatKn (KnownNatF2 "+" a b) -> Integer 3. Integer -> SNat (a + b) 4. SNat (a + b) -> KnownNat (a + b) this process is mirrored for the dictionary functions of a higher arity -} makeOpDict :: (Class,DFunId) -- ^ "magic" class function and dictionary function id -> Class -- ^ KnownNat class -> [Type] -- ^ Argument types for the Class -> [Type] -- ^ Argument types for the Instance -> Type -- ^ Type of the result #if MIN_VERSION_ghc(8,5,0) -> [EvExpr] #else -> [EvTerm] #endif -- ^ Evidence arguments -> Maybe EvTerm makeOpDict (opCls,dfid) knCls tyArgsC tyArgsI z evArgs | Just (_, kn_co_dict) <- tcInstNewTyCon_maybe (classTyCon knCls) [z] -- KnownNat n ~ SNat n , [ kn_meth ] <- classMethods knCls , Just kn_tcRep <- tyConAppTyCon_maybe -- SNat $ funResultTy -- SNat n $ dropForAlls -- KnownNat n => SNat n $ idType kn_meth -- forall n. KnownNat n => SNat n , Just (_, kn_co_rep) <- tcInstNewTyCon_maybe kn_tcRep [z] -- SNat n ~ Integer , Just (_, op_co_dict) <- tcInstNewTyCon_maybe (classTyCon opCls) tyArgsC -- KnownNatAdd a b ~ SNatKn (a+b) , [ op_meth ] <- classMethods opCls , Just (op_tcRep,op_args) <- splitTyConApp_maybe -- (SNatKn, [KnownNatF2 f x y]) $ funResultTy -- SNatKn (KnownNatF2 f x y) $ (`piResultTys` tyArgsC) -- KnownNatAdd f x y => SNatKn (KnownNatF2 f x y) $ idType op_meth -- forall f a b . KnownNat2 f a b => SNatKn (KnownNatF2 f a b) , Just (_, op_co_rep) <- tcInstNewTyCon_maybe op_tcRep op_args -- SNatKn (a+b) ~ Integer #if MIN_VERSION_ghc(8,5,0) , let EvExpr dfun_inst = evDFunApp dfid tyArgsI evArgs #else , let dfun_inst = EvDFunApp dfid tyArgsI evArgs #endif -- KnownNatAdd a b op_to_kn = mkTcTransCo (mkTcTransCo op_co_dict op_co_rep) (mkTcSymCo (mkTcTransCo kn_co_dict kn_co_rep)) -- KnownNatAdd a b ~ KnownNat (a+b) ev_tm = mkEvCast dfun_inst op_to_kn = Just ev_tm | otherwise = Nothing {- Given: * A KnownNat dictionary evidence over a type x * a desired type z makeKnCoercion assembles a coercion from a KnownNat x dictionary to a KnownNat z dictionary and applies it to the passed-in evidence. The coercion happens in the following steps: 1. KnownNat x -> SNat x 2. SNat x -> Integer 3. Integer -> SNat z 4. SNat z -> KnownNat z -} makeKnCoercion :: Class -- ^ KnownNat class -> Type -- ^ Type of the argument -> Type -- ^ Type of the result #if MIN_VERSION_ghc(8,5,0) -> EvExpr #else -> EvTerm #endif -- ^ KnownNat dictionary for the argument -> Maybe EvTerm makeKnCoercion knCls x z xEv | Just (_, kn_co_dict_z) <- tcInstNewTyCon_maybe (classTyCon knCls) [z] -- KnownNat z ~ SNat z , [ kn_meth ] <- classMethods knCls , Just kn_tcRep <- tyConAppTyCon_maybe -- SNat $ funResultTy -- SNat n $ dropForAlls -- KnownNat n => SNat n $ idType kn_meth -- forall n. KnownNat n => SNat n , Just (_, kn_co_rep_z) <- tcInstNewTyCon_maybe kn_tcRep [z] -- SNat z ~ Integer , Just (_, kn_co_rep_x) <- tcInstNewTyCon_maybe kn_tcRep [x] -- Integer ~ SNat x , Just (_, kn_co_dict_x) <- tcInstNewTyCon_maybe (classTyCon knCls) [x] -- SNat x ~ KnownNat x = Just . mkEvCast xEv $ (kn_co_dict_x `mkTcTransCo` kn_co_rep_x) `mkTcTransCo` mkTcSymCo (kn_co_dict_z `mkTcTransCo` kn_co_rep_z) | otherwise = Nothing -- | THIS CODE IS COPIED FROM: -- https://github.com/ghc/ghc/blob/8035d1a5dc7290e8d3d61446ee4861e0b460214e/compiler/typecheck/TcInteract.hs#L1973 -- -- makeLitDict adds a coercion that will convert the literal into a dictionary -- of the appropriate type. See Note [KnownNat & KnownSymbol and EvLit] -- in TcEvidence. The coercion happens in 2 steps: -- -- Integer -> SNat n -- representation of literal to singleton -- SNat n -> KnownNat n -- singleton to dictionary #if MIN_VERSION_ghc(8,5,0) makeLitDict :: Class -> Type -> Integer -> TcPluginM (Maybe EvTerm) #else makeLitDict :: Class -> Type -> Integer -> Maybe EvTerm #endif makeLitDict clas ty i | Just (_, co_dict) <- tcInstNewTyCon_maybe (classTyCon clas) [ty] -- co_dict :: KnownNat n ~ SNat n , [ meth ] <- classMethods clas , Just tcRep <- tyConAppTyCon_maybe -- SNat $ funResultTy -- SNat n $ dropForAlls -- KnownNat n => SNat n $ idType meth -- forall n. KnownNat n => SNat n , Just (_, co_rep) <- tcInstNewTyCon_maybe tcRep [ty] -- SNat n ~ Integer #if MIN_VERSION_ghc(8,5,0) = do #if MIN_VERSION_ghc(9,0,0) let et = mkNaturalExpr i #else et <- unsafeTcPluginTcM (mkNaturalExpr i) #endif let ev_tm = mkEvCast et (mkTcSymCo (mkTcTransCo co_dict co_rep)) return (Just ev_tm) | otherwise = return Nothing #else , let ev_tm = mkEvCast (EvLit (EvNum i)) (mkTcSymCo (mkTcTransCo co_dict co_rep)) = Just ev_tm | otherwise = Nothing #endif {- | Given: * A "magic" class, and corresponding instance dictionary function, for a type-level boolean operation * Two KnownBool dictionaries makeOpDictByFiat instantiates the dictionary function with the KnownBool dictionaries, and coerces it to a KnownBool dictionary. i.e. for KnownBoolNat2, the "magic" dictionary for binary functions, the coercion happens in the following steps: 1. KnownBoolNat2 "<=?" x y -> SBoolF "<=?" 2. SBoolF "<=?" -> Bool 3. Bool -> SNat (x <=? y) THE BY FIAT PART! 4. SBool (x <=? y) -> KnownBool (x <=? y) this process is mirrored for the dictionary functions of a higher arity -} makeOpDictByFiat :: (Class,DFunId) -- ^ "magic" class function and dictionary function id -> Class -- ^ KnownNat class -> [Type] -- ^ Argument types for the Class -> [Type] -- ^ Argument types for the Instance -> Type -- ^ Type of the result #if MIN_VERSION_ghc(8,6,0) -> [EvExpr] #else -> [EvTerm] #endif -- ^ Evidence arguments -> Maybe EvTerm #if MIN_VERSION_ghc(8,6,0) makeOpDictByFiat (opCls,dfid) knCls tyArgsC tyArgsI z evArgs -- KnownBool b ~ SBool b | Just (_, kn_co_dict) <- tcInstNewTyCon_maybe (classTyCon knCls) [z] , [ kn_meth ] <- classMethods knCls , Just kn_tcRep <- tyConAppTyCon_maybe -- SBool $ funResultTy -- SBool b $ dropForAlls -- KnownBool b => SBool b $ idType kn_meth -- forall b. KnownBool b => SBool b -- SBool b R~ Bool (The "Lie") , let kn_co_rep = mkUnivCo (PluginProv "ghc-typelits-knownnat") Representational (mkTyConApp kn_tcRep [z]) boolTy -- KnownBoolNat2 f a b ~ SBool f , Just (_, op_co_dict) <- tcInstNewTyCon_maybe (classTyCon opCls) tyArgsC , [ op_meth ] <- classMethods opCls , Just (op_tcRep,op_args) <- splitTyConApp_maybe -- (SBool, [f]) $ funResultTy -- SBool f $ (`piResultTys` tyArgsC) -- KnownBoolNat2 f x y => SBool f $ idType op_meth -- forall f x y . KnownBoolNat2 f a b => SBoolf f -- SBoolF f ~ Bool , Just (_, op_co_rep) <- tcInstNewTyCon_maybe op_tcRep op_args , EvExpr dfun_inst <- evDFunApp dfid tyArgsI evArgs -- KnownBoolNat2 f x y ~ KnownBool b , let op_to_kn = mkTcTransCo (mkTcTransCo op_co_dict op_co_rep) (mkTcSymCo (mkTcTransCo kn_co_dict kn_co_rep)) ev_tm = mkEvCast dfun_inst op_to_kn = Just ev_tm | otherwise = Nothing #else makeOpDictByFiat _ _ _ _ _ _ = Nothing #endif