{- Data/Singletons/TH/Single/Type.hs (c) Richard Eisenberg 2013 rae@cs.brynmawr.edu Singletonizes types. -} module Data.Singletons.TH.Single.Type where import Language.Haskell.TH.Desugar import Language.Haskell.TH.Syntax import Data.Singletons.TH.Names import Data.Singletons.TH.Options import Data.Singletons.TH.Promote.Type import Data.Singletons.TH.Single.Monad import Data.Singletons.TH.Util import Control.Monad singType :: DType -- the promoted version of the thing classified by... -> DType -- ... this type -> SgM ( DType -- the singletonized type , Int -- the number of arguments , [Name] -- the names of the tyvars used in the sing'd type , DCxt -- the context of the singletonized type , [DKind] -- the kinds of the argument types , DKind ) -- the kind of the result type singType :: DType -> DType -> SgM (DType, Int, [Name], DCxt, DCxt, DType) singType DType prom DType ty = do ([DTyVarBndrSpec] orig_tvbs, DCxt cxt, DCxt args, DType res) <- DType -> SgM ([DTyVarBndrSpec], DCxt, DCxt, DType) forall (m :: * -> *). MonadFail m => DType -> m ([DTyVarBndrSpec], DCxt, DCxt, DType) unravelVanillaDType DType ty let num_args :: Int num_args = DCxt -> Int forall a. [a] -> Int forall (t :: * -> *) a. Foldable t => t a -> Int length DCxt args DCxt cxt' <- (DType -> SgM DType) -> DCxt -> SgM DCxt forall (t :: * -> *) (m :: * -> *) a b. (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b) forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b] mapM DType -> SgM DType singPred_NC DCxt cxt [Name] arg_names <- Int -> SgM Name -> SgM [Name] forall (m :: * -> *) a. Applicative m => Int -> m a -> m [a] replicateM Int num_args (String -> SgM Name forall (m :: * -> *). Quasi m => String -> m Name qNewName String "t") DCxt prom_args <- (DType -> SgM DType) -> DCxt -> SgM DCxt forall (t :: * -> *) (m :: * -> *) a b. (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b) forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b] mapM DType -> SgM DType forall (m :: * -> *). OptionsMonad m => DType -> m DType promoteType_NC DCxt args DType prom_res <- DType -> SgM DType forall (m :: * -> *). OptionsMonad m => DType -> m DType promoteType_NC DType res let args' :: DCxt args' = (Name -> DType) -> [Name] -> DCxt forall a b. (a -> b) -> [a] -> [b] map (\Name n -> DType singFamily DType -> DType -> DType `DAppT` (Name -> DType DVarT Name n)) [Name] arg_names res' :: DType res' = DType singFamily DType -> DType -> DType `DAppT` (DType -> DCxt -> DType foldApply DType prom ((Name -> DType) -> [Name] -> DCxt forall a b. (a -> b) -> [a] -> [b] map Name -> DType DVarT [Name] arg_names) DType -> DType -> DType `DSigT` DType prom_res) -- Make sure to include an explicit `prom_res` kind annotation. -- See Note [Preserve the order of type variables during singling], -- wrinkle 3. arg_tvbs :: [DTyVarBndrSpec] arg_tvbs = (Name -> DType -> DTyVarBndrSpec) -> [Name] -> DCxt -> [DTyVarBndrSpec] forall a b c. (a -> b -> c) -> [a] -> [b] -> [c] zipWith (Name -> Specificity -> DType -> DTyVarBndrSpec forall flag. Name -> flag -> DType -> DTyVarBndr flag `DKindedTV` Specificity SpecifiedSpec) [Name] arg_names DCxt prom_args -- If the original type signature lacks an explicit `forall`, then do not -- give the singled type signature an outermost `forall`. Instead, give it -- a `<singled-ty> :: Type` kind annotation and let GHC implicitly -- quantify any type variables that are free in `<singled-ty>`. -- See Note [Preserve the order of type variables during singling], -- wrinkle 1. ty' :: DType ty' | [DTyVarBndrSpec] -> Bool forall a. [a] -> Bool forall (t :: * -> *) a. Foldable t => t a -> Bool null [DTyVarBndrSpec] orig_tvbs = [DTyVarBndrSpec] -> DCxt -> DCxt -> DType -> DType ravelVanillaDType [DTyVarBndrSpec] arg_tvbs DCxt cxt' DCxt args' DType res' DType -> DType -> DType `DSigT` Name -> DType DConT Name typeKindName | Bool otherwise = [DTyVarBndrSpec] -> DCxt -> DCxt -> DType -> DType ravelVanillaDType ([DTyVarBndrSpec] orig_tvbs [DTyVarBndrSpec] -> [DTyVarBndrSpec] -> [DTyVarBndrSpec] forall a. [a] -> [a] -> [a] ++ [DTyVarBndrSpec] arg_tvbs) DCxt cxt' DCxt args' DType res' (DType, Int, [Name], DCxt, DCxt, DType) -> SgM (DType, Int, [Name], DCxt, DCxt, DType) forall a. a -> SgM a forall (m :: * -> *) a. Monad m => a -> m a return (DType ty', Int num_args, [Name] arg_names, DCxt cxt, DCxt prom_args, DType prom_res) -- Single a DPred, checking that it is a vanilla type in the process. -- See [Vanilla-type validity checking during promotion] -- in Data.Singletons.TH.Promote.Type. singPred :: DPred -> SgM DPred singPred :: DType -> SgM DType singPred DType p = do DType -> SgM () forall (m :: * -> *). MonadFail m => DType -> m () checkVanillaDType DType p DType -> SgM DType singPred_NC DType p -- Single a DPred. Does not check if the argument is a vanilla type. -- See [Vanilla-type validity checking during promotion] -- in Data.Singletons.TH.Promote.Type. singPred_NC :: DPred -> SgM DPred singPred_NC :: DType -> SgM DType singPred_NC = [DTypeArg] -> DType -> SgM DType singPredRec [] -- The workhorse for singPred_NC. singPredRec :: [DTypeArg] -> DPred -> SgM DPred singPredRec :: [DTypeArg] -> DType -> SgM DType singPredRec [DTypeArg] _cxt (DForallT {}) = String -> SgM DType forall a. String -> SgM a forall (m :: * -> *) a. MonadFail m => String -> m a fail String "Singling of quantified constraints not yet supported" singPredRec [DTypeArg] _cxt (DConstrainedT {}) = String -> SgM DType forall a. String -> SgM a forall (m :: * -> *) a. MonadFail m => String -> m a fail String "Singling of quantified constraints not yet supported" singPredRec [DTypeArg] ctx (DAppT DType pr DType ty) = [DTypeArg] -> DType -> SgM DType singPredRec (DType -> DTypeArg DTANormal DType ty DTypeArg -> [DTypeArg] -> [DTypeArg] forall a. a -> [a] -> [a] : [DTypeArg] ctx) DType pr singPredRec [DTypeArg] ctx (DAppKindT DType pr DType ki) = [DTypeArg] -> DType -> SgM DType singPredRec (DType -> DTypeArg DTyArg DType ki DTypeArg -> [DTypeArg] -> [DTypeArg] forall a. a -> [a] -> [a] : [DTypeArg] ctx) DType pr singPredRec [DTypeArg] _ctx (DSigT DType _pr DType _ki) = String -> SgM DType forall a. String -> SgM a forall (m :: * -> *) a. MonadFail m => String -> m a fail String "Singling of constraints with explicit kinds not yet supported" singPredRec [DTypeArg] _ctx (DVarT Name _n) = String -> SgM DType forall a. String -> SgM a forall (m :: * -> *) a. MonadFail m => String -> m a fail String "Singling of contraint variables not yet supported" singPredRec [DTypeArg] ctx (DConT Name n) | Name n Name -> Name -> Bool forall a. Eq a => a -> a -> Bool == Name equalityName = String -> SgM DType forall a. String -> SgM a forall (m :: * -> *) a. MonadFail m => String -> m a fail String "Singling of type equality constraints not yet supported" | Bool otherwise = do Options opts <- SgM Options forall (m :: * -> *). OptionsMonad m => m Options getOptions [DTypeArg] kis <- (DTypeArg -> SgM DTypeArg) -> [DTypeArg] -> SgM [DTypeArg] forall (t :: * -> *) (m :: * -> *) a b. (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b) forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b] mapM DTypeArg -> SgM DTypeArg forall (m :: * -> *). OptionsMonad m => DTypeArg -> m DTypeArg promoteTypeArg_NC [DTypeArg] ctx let sName :: Name sName = Options -> Name -> Name singledClassName Options opts Name n DType -> SgM DType forall a. a -> SgM a forall (m :: * -> *) a. Monad m => a -> m a return (DType -> SgM DType) -> DType -> SgM DType forall a b. (a -> b) -> a -> b $ DType -> [DTypeArg] -> DType applyDType (Name -> DType DConT Name sName) [DTypeArg] kis singPredRec [DTypeArg] _ctx DType DWildCardT = DType -> SgM DType forall a. a -> SgM a forall (m :: * -> *) a. Monad m => a -> m a return DType DWildCardT -- it just might work singPredRec [DTypeArg] _ctx DType DArrowT = String -> SgM DType forall a. String -> SgM a forall (m :: * -> *) a. MonadFail m => String -> m a fail String "(->) spotted at head of a constraint" singPredRec [DTypeArg] _ctx (DLitT {}) = String -> SgM DType forall a. String -> SgM a forall (m :: * -> *) a. MonadFail m => String -> m a fail String "Type-level literal spotted at head of a constraint" {- Note [Preserve the order of type variables during singling] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ singletons-th does its best to preseve the order in which users write type variables in type signatures for functions and data constructors. They are "preserved" in the sense that if one writes `foo @T1 @T2`, one should be able to write out `sFoo @T1 @T2` by hand and have the same order of visible type applications still work. Accomplishing this is surprisingly nontrivial, so this Note documents the various wrinkles one must iron out to get this working. ----- -- Wrinkle 1: Dealing with the presence (and absence) of `forall` ----- If we single a function that has an explicit `forall`, such as this example: const2 :: forall b a. a -> b -> a const2 x _ = x Then our job is easy, as the exact order of type variables has already been spelled out in advance. We single this to: sConst2 :: forall b a (x :: a) (y :: b). Sing x -> Sing y -> Sing (Const2 x y :: a) sConst2 = ... What happens if there is no explicit `forall`, as in this example? data V a absurd :: V a -> b absurd v = case v of {} This time, the order of type variables vis-à-vis TypeApplications is determined by their left-to-right order of appearance in the type signature. This order dictates that `a` is quantified before `b`, so we must mirror this order in the singled type signature. One way to accomplish this would be to compute the order in which the type variables appear and then explicitly quantify them. In the `absurd` example above, this would be tantamount to writing: sAbsurd :: forall a b (v :: V a). Sing v -> Sing (Absurd v :: b) ^^^ ||| Explicitly quantified by singletons-th, not in the original type signature This is possible to do, and indeed, singletons-th used to do this. However, it is a bit tiresome to implement. In order to know which type variables to quantify, you must keep track of which type variables have been brought into scope at all times. For the historical details on how this worked, see this now-removed Note describing the old implementation: https://github.com/goldfirere/singletons/blob/10ef27880d7ecc16241824c504ca83e2bb6ca787/singletons-th/src/Data/Singletons/TH/Promote/Monad.hs#L135-L192 A much more straightforward approach, which singletons-th currently uses, is to let GHC do the hard work of implicitly quantifying the type variables. That is, we will single `absurd` to something like this: sAbsurd :: () => forall (v :: V a). Sing v -> Sing (Absurd v :: b) This works because just like in the original type signature, `a` and `b` are implicitly quantified, and more importantly, they are quantified in exactly the same order as in the original type signature. Why do we need the `() => ...` part? If we had instead written the type signature like this: sAbsurd :: forall (v :: V a). Sing v -> Sing (Absurd v :: b) Then GHC would reject `a` and `b` for being out of scope. This is because of GHC's "forall-or-nothing" rule: if a type signature has an outermost forall, then all type variable occurrences in the type signature must have explicit binding sites. Using `() => forall (v :: V a). ...` prevents the `forall` from being an outermost `forall`, which bypasses the forall-or-nothing rule. Some further complications: * Template Haskell doesn't actually allow you to splice in types of the form `() => ...` in practice. See https://gitlab.haskell.org/ghc/ghc/-/issues/16396. Luckily, this isn't a deal-breaker, as we can also avoid the forall-or-nothing rule by annotating the type signature with an explicit `... :: Type` annotation: sAbsurd :: ((forall (v :: V a). Sing v -> Sing (Absurd v :: b)) :: Type) This is the approach that singletons-th actually uses. Note that there is one spot in the code (in D.S.TH.Single.singInstD) that must be taught to look through these `... :: Type` annotations, but this approach is otherwise fairly non-invasive. * We cannot use this trick when singling the types of data constructors. That is, we cannot single this: data T a where MkT :: a -> T a To this: data ST z where SMkT :: ((forall (x :: a). Sing x -> ST (MkT x)) :: Type) This is because GADT syntax does not currently permit nested `forall`s of this sort. (It might permit them in the future if https://github.com/ghc-proposals/ghc-proposals/blob/master/proposals/0402-gadt-syntax.rst is implemented, but not currently.) As a result, we /always/ explicitly quantify all type variables in a data constructor's type, regardless of whether the original type implicitly quantified them or not. In the example above, that means that the singled version would be: data ST z where SMkT :: forall a (x :: a). Sing x -> ST (MkT x) ----- -- Wrinkle 2: The TH reification swamp ----- There is another issue with type signatures that lack explicit `forall`s, one which the current design of Template Haskell does not make simple to fix. If we single code that is wrapped in TH quotes, such as in the following example: {-# LANGUAGE PolyKinds, ... #-} $(singletons [d| data Proxy a = MkProxy |]) Then our job is made much easier when singling MkProxy, since we know that the only type variable that must be quantified is `a`, as that is the only one specified by the user. This results in the following type signature for MkProxy: MkProxy :: forall a. Proxy a However, this is not the only possible way to single MkProxy. One can alternatively use $(genSingletons [''Proxy]), which uses TH reification to infer the type of MkProxy. There is perilous, however, because this is how TH reifies Proxy: DataD [] ''Proxy [KindedTV a () (VarT k)] Nothing [NormalC 'MkProxy []] [] We must then construct a type signature for MkProxy using nothing but the type variables from the data type header. But notice that `KindedTV a () (VarT k)` gives no indication of whether `k` is specified or inferred! As a result, we conservatively assume that `k` is specified, resulting the following type signature for MkProxy: MkProxy :: forall k (a :: k). Proxy a Contrast this with `MkProxy :: Proxy a`, where `k` is inferred. In other words, if you single MkProxy using genSingletons, then `Proxy @True` will typecheck but `SMkProxy @True` will /not/ typecheck—you'd have to use `SMkProxy @_ @True` instead. Urk! At present, Template Haskell does not have a way to distinguish among the specificities bound by a data type header. Without this knowledge, it is unclear how one could work around this issue. Thankfully, this issue is only likely to surface in very limited circumstances, so the damage is somewhat minimal. ----- -- Wrinkle 3: Where to put explicit kind annotations ----- Type variable binders are only part of the story—we must also determine what the body of the type signature will be singled to. As a general rule, if the original type signature is of the form: f :: forall a_1 ... a_m. (C_1, ..., C_n) => T_1 -> ... -> T_p -> R Then the singled type signature will be: sF :: forall a_1 ... a_m (x_1 :: PT_1) ... (x_p :: PT_p). (SC_1, ..., SC_n) => Sing x1 -> ... -> Sing x_p -> SRes (F x1 ... x_p :: PR) Where: * x_i is a fresh type variable of kind PT_i. * PT_i is the promoted version of the type T_i, and PR is the promoted version of the type R. * SC_i is the singled version of the constraint SC_i. * SRes is either `Sing` if dealing with a function, or a singled data type if dealing with a data constructor. For instance, SRes is `SBool` in `STrue :: SBool (True :: Bool)`. One aspect of this worth pointing out is the explicit `:: PR` kind annotation in the result type `Sing (F x1 ... x_p :: PR)`. As it turns out, this kind annotation is mandatory, as omitting can result in singled type signatures with the wrong semantics. For instance, consider the `Nothing` data constructor: Nothing :: forall a. Maybe a Consider what would happen if it were singled to this type: SNothing :: forall a. SMaybe Nothing This is not what we want at all, since the `a` has no connection to the `Nothing` in the result type. It's as if we had written this: SNothing :: forall {t} a. SMaybe (Nothing :: Maybe t) If we instead generate `forall a. SMaybe (Nothing :: Maybe a)`, then this issue is handily avoided. You might wonder if it would be cleaner to use visible kind applications instead: SNothing :: forall a. SMaybe (Nothing @a) This does work for many cases, but there are also some corner cases where this approach fails. Recall the `MkProxy` example from Wrinkle 2 above: {-# LANGUAGE PolyKinds, ... #-} data Proxy a = MkProxy $(genSingletons [''Proxy]) Due to the design of Template Haskell (discussed in Wrinkle 2), `MkProxy` will be reified with the type of `forall k (a :: k). Proxy a`. This means that if we used visible kind applications in the result type, we would end up with this: SMkProxy :: forall k (a :: k). SProxy (MkProxy @k @a) This will not kind-check because MkProxy only accepts /one/ visible kind argument, whereas this supplies it with two. To avoid this issue, we instead use the type `forall k (a :: k). SProxy (MkProxy :: Proxy a)`. Granted, this type is /still/ technically wrong due to the fact that it explicitly quantifies `k`, but at the very least it typechecks. If Template Haskell gained the ability to distinguish among the specificities of type variables bound by a data type header (perhaps by way of a language feature akin to https://github.com/ghc-proposals/ghc-proposals/pull/326), then we could revisit this design choice. Finally, note that we need only write `Sing x_1 -> ... -> Sing x_p`, and not `Sing (x_1 :: PT_1) -> ... Sing (x_p :: PT_p)`. This is simply because we always use explicit `forall`s in singled type signatures, and therefore always explicitly bind `(x_1 :: PT_1) ... (x_p :: PT_p)`, which fully determine the kinds of `x_1 ... x_p`. It wouldn't be wrong to add extra kind annotations to `Sing x_1 -> ... -> Sing x_p`, just redundant. -}