{-| Copyright : (C) 2016 , University of Twente, 2017-2018, QBayLogic B.V., 2017 , Google Inc. License : BSD2 (see the file LICENSE) Maintainer : Christiaan Baaij <christiaan.baaij@gmail.com> 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\<N\>@ 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 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 Data.Maybe (catMaybes,mapMaybe) import GHC.TcPluginM.Extra (lookupModule, lookupName, newWanted, tracePlugin) import GHC.TypeLits.Normalise.SOP (SOP (..), Product (..), Symbol (..)) import GHC.TypeLits.Normalise.Unify (CType (..),normaliseNat,reifySOP) -- GHC API import Class (Class, classMethods, className, classTyCon) import FamInst (tcInstNewTyCon_maybe) import FastString (fsLit) import Id (idType) import InstEnv (instanceDFunId,lookupUniqueInstEnv) import Module (mkModuleName, moduleName, moduleNameString) import Name (nameModule_maybe, nameOccName) import OccName (mkTcOcc, occNameString) import Plugins (Plugin (..), defaultPlugin) import PrelNames (knownNatClassName) import TcEvidence (EvTerm (..), EvLit (EvNum), mkEvCast, mkTcSymCo, mkTcTransCo) import TcPluginM (TcPluginM, tcLookupClass, getInstEnvs, zonkCt) import TcRnTypes (Ct, TcPlugin(..), TcPluginResult (..), ctEvidence, ctEvLoc, ctEvPred, ctEvTerm, ctLoc, ctLocSpan, isWanted, mkNonCanonical, setCtLoc, setCtLocSpan) import TcTypeNats (typeNatAddTyCon, typeNatSubTyCon) import Type (EqRel (NomEq), PredTree (ClassPred,EqPred), PredType, classifyPredType, dropForAlls, eqType, funResultTy, mkNumLitTy, mkStrLitTy, mkTyConApp, piResultTys, splitFunTys, splitTyConApp_maybe, tyConAppTyCon_maybe) import TyCon (tyConName) import TyCoRep (Type (..), TyLit (..)) import Var (DFunId) -- | Classes and instances from "GHC.TypeLits.KnownNat" type KnownNatDefs = Int -> Maybe Class -- ^ KnownNatN class -- | KnownNat constraints type KnConstraint = (Ct -- The constraint ,Class -- KnownNat class ,Type -- The 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\<N\>@ 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 } 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 kn_wanteds = mapMaybe toKnConstraint wanteds' case kn_wanteds of [] -> return (TcPluginOk [] []) _ -> do -- Make a lookup table for all the [G]iven constraints given_map <- mapM (fmap toGivenEntry . zonkCt) givens -- 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 :: Ct -> Maybe KnConstraint toKnConstraint ct = case classifyPredType $ ctEvPred $ ctEvidence ct of ClassPred cls [ty] | className cls == knownNatClassName -> Just (ct,cls,ty) _ -> Nothing -- | Create a look-up entry for a [G]iven constraint. toGivenEntry :: Ct -> (CType,EvTerm) toGivenEntry ct = let ct_ev = ctEvidence ct c_ty = ctEvPred ct_ev ev = ctEvTerm ct_ev in (CType c_ty,ev) -- | Normalise a type to Sum-of-Product type form as defined in the -- `ghc-typelits-natnormalise` package. normaliseSOP :: Type -> Type normaliseSOP = reifySOP . normaliseNat -- | Find the \"magic\" classes and instances in "GHC.TypeLits.KnownNat" lookupKnownNatDefs :: TcPluginM KnownNatDefs lookupKnownNatDefs = do md <- lookupModule myModule myPackage kn1C <- look md "KnownNat1" kn2C <- look md "KnownNat2" kn3C <- look md "KnownNat3" return $ (\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 -> [(CType,EvTerm)] -- All the [G]iven constraints -> KnConstraint -> TcPluginM (Maybe ((EvTerm,Ct),[Ct])) constraintToEvTerm defs givens (ct,cls,op) = do -- 1. Normalise to SOP normal form let ty = normaliseSOP op -- 2. Determine if we are an offset apart from a [G]iven constraint offsetM <- offset ty 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<N> instance. _ -> go ty return (first (,ct) <$> evM) where -- Determine whether the outer type-level operation has a corresponding -- KnownNat<N> 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 args) | let tcNm = tyConName tc , Just m <- nameModule_maybe tcNm , Just knN_cls <- defs (length args) = do let mS = moduleNameString (moduleName m) tcS = occNameString (nameOccName tcNm) fn = mkStrLitTy (fsLit (mS ++ "." ++ tcS)) args' = fn:args ienv <- getInstEnvs case lookupUniqueInstEnv ienv knN_cls args' of Right (inst, _) -> 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` args) -- (KnowNat x, KnownNat y) => DKnownNat2 "+" x y $ idType df_id -- forall a b . (KnownNat a, KnownNat b) => DKnownNat2 "+" a b (evs,new) <- unzip <$> mapM go_arg df_args return ((,concat new) <$> makeOpDict df cls args' op evs) _ -> return ((,[]) <$> go_other ty) go (LitTy (NumTyLit i)) -- Let GHC solve simple Literal constraints | LitTy _ <- op = return Nothing -- This plugin only solves Literal KnownNat's that needed to be normalised -- first | otherwise = return ((,[]) <$> makeLitDict cls op i) 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 go_arg :: PredType -> TcPluginM (EvTerm,[Ct]) go_arg ty = case lookup (CType ty) givens of Just ev -> return (ev,[]) _ -> do -- Create a new wanted constraint wantedCtEv <- newWanted (ctLoc ct) ty let ev = ctEvTerm wantedCtEv 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 let ct_ls = ctLocSpan (ctLoc ct) ctl = ctEvLoc wantedCtEv wanted' = setCtLoc wanted (setCtLocSpan ctl ct_ls) 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 then Just 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 -- pair up the sum-of-products KnownNat constraints -- with the original Nat operation subWant = mkTyConApp typeNatSubTyCon . (:[want]) exploded = map (normaliseNat . subWant &&& id) (knowns ++ knownsR) -- 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 let x = case corr of I 0 -> h I i | i < 0 -> mkTyConApp typeNatAddTyCon [h,mkNumLitTy (negate i)] | otherwise -> mkTyConApp typeNatSubTyCon [h,mkNumLitTy i] _ -> mkTyConApp typeNatSubTyCon [h,reifySOP (S [P [corr]])] MaybeT (go x) {- | 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 -> Type -- ^ Type of the result -> [EvTerm] -- ^ Evidence arguments -> Maybe EvTerm makeOpDict (opCls,dfid) knCls tyArgs 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) tyArgs -- 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` tyArgs) -- 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 , let dfun_inst = EvDFunApp dfid (tail tyArgs) evArgs -- 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 -> EvTerm -- ^ 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 makeLitDict :: Class -> Type -> Integer -> Maybe EvTerm 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 , let ev_tm = mkEvCast (EvLit (EvNum i)) (mkTcSymCo (mkTcTransCo co_dict co_rep)) = Just ev_tm | otherwise = Nothing