March 2012 - Glasgow-haskell-users

ADPfusion: Efficient, high-level dynamic programming
by Christian Höner zu Siederdissen 25 Mar '12

25 Mar '12

ADPfusion combines stream-fusion (using the stream interface provided by the vector library) and type-level programming to provide highly efficient dynamic programming (DP) combinators. You can write DP programs in a style similar to Algebraic Dynamic Programming (ADP) (Giegerich et al.), meaning symbolically without explicit indices. The symbolic operators provide a number of advantages: - take care of extracting the correct cell information from data structures (DP matrices) - no more index problems, the grammars are completely free of index calculations by the user - complex operators can be written with "next step" behaviour dependent on other information calculated during runtime - monadic interface - works with pure/monadic, boxed/unboxed, ... data structures - speed close to optimized C (between 1.8x - 3x slower currently -- compared to well-optimized C-code) Hackage: http://hackage.haskell.org/package/ADPfusion 1st example program: http://hackage.haskell.org/package/Nussinov78 Many thanks to Roman Leshchinskiy! Viele Gruesse, Christian Hoener zu Siederdissen ADP: http://bibiserv.techfak.uni-bielefeld.de/adp/adpapp.html

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Stealing ideas from the latest GCC release
by Johan Tibell 24 Mar '12

24 Mar '12

Hi all, While looking at the GCC 4.7 [1] release notes I saw something that's perhaps worth stealing. Taken from the release notes: The inter-procedural constant propagation pass has been rewritten. It now performs generic function specialization. For example when compiling the following: void foo(bool flag) { if (flag) ... do something ... else ... do something else ... } void bar (void) { foo (false); foo (true); foo (false); foo (true); foo (false); foo (true); } GCC will now produce two copies of foo. One with flag being true, while other with flag being false. This leads to performance improvements previously possibly only by inlining all calls. Cloning causes a lot less code size growth. I found myself wanting something like this just today. A common pattern I see in code is this: data Options = Options { ... } defaultOptions :: Options defaultOptions = ... foo :: ... foo = fooWith defaultOptions fooWith :: Options -> ... fooWith = ... It'd be nice if we could get foo to specialize on its input arguments, without having to mark all of fooWith as INLINE. 1. http://gcc.gnu.org/gcc-4.7/changes.html -- Johan

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GHCi and line numbers (with ghc-7.4.1)
by Simon Hengel 23 Mar '12

23 Mar '12

Hi, ghc --interactive now behaves different in regards to line numbers in error messages than previous versions. They are now incremented with each evaluated expression. $ ghc --interactive -ignore-dot-ghci Prelude> foo <interactive>:2:1: Not in scope: `foo' Prelude> bar <interactive>:3:1: Not in scope: `bar' Is there a way to disable this (or alternatively reset the counter for a running session)? Cheers, Simon

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7.4.2 release plans
by Ian Lynagh 23 Mar '12

23 Mar '12

Hi all, Just a quick note to let you know about our release plans: We plan to put out a GHC 7.4.2 release candidate around the end of the March. The final release will probably not happen until around the end of April. Thanks Ian, on behalf of the GHC team

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update to Template Haskell for rich kinds
by Richard Eisenberg 21 Mar '12

21 Mar '12

Hi all, I'm working on bringing Template Haskell up to speed with the new extensions for polymorphic kinds and promoted data kinds. This requires a few small, non-breaking changes to TH datatypes. I've made a (short) wiki page at http://hackage.haskell.org/trac/ghc/wiki/TemplateHaskellRichKinds and the official Trac feature request is hackage.haskell.org/trac/ghc/ticket/5612 Does anyone have any suggestions to what I've written? Any other comments? Thanks! Richard

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How to work around GHC bug
by Volker Wysk 18 Mar '12

18 Mar '12

Hi! The following program demonstrates a (another) GHC bug. The command line isn't properly decoded to Unicode. arg.hs------------------------------ import System main = do [a] <- getArgs putStrLn (show a) -------------------------------------- When called like this: ./arg ä The program will output this: "\195\164" I'll report this as a bug in the GHC Trac. But for now, I need to work around the problem somehow. The encoders in GHC.IO.Encoding all work on buffers. How do I recode the command line, in order to get proper Unicode strings? Bye Volker

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How to declare polymorphic instances for higher-kinded types?
by Herbert Valerio Riedel 16 Mar '12

16 Mar '12

Hello *, For simple-kinded type variables, instances of the type instance NFData a => NFData [a] instance NFData a => NFData (Maybe a) instance (NFData a, NFData b) => NFData (a, b) are common and can be defined effortless; now I wanted do something similiar for a type with a phantom type parameter: {-# LANGUAGE KindSignatures, TypeSynonymInstances #-} import Control.Applicative import Control.Monad data DataBase = DataBase -- specific type not relevant here data Res data Unres -- provides operation to transform an unresolved `Foo_ Unres` to a resolved `Foo_ Res` class Resolvable (e :: * -> *) where resolve :: DataBase -> e Unres -> Either String (e Res) -- trivial /resolvable/ type data Foo_ r = Foo instance Resolvable Foo_ where resolve _ x = return Foo ...it was no problem to define the polymorphic operations outside of an instance: -- Maybe (polymorphic 0 or 1 element container) resolveMaybe :: Resolvable e => DataBase -> Maybe (e Unres) -> Either String (Maybe (e Res)) resolveMaybe db (Just x) = Just <$> resolve db x resolveMaybe db Nothing = pure Nothing -- Pairs resolvePair :: (Resolvable e0, Resolvable e1) => DataBase -> (e0 Unres, e1 Unres) -> Either String (e0 Res, e1 Res) resolvePair db (x,y) = (,) <$> resolve db x <*> resolve db y ...but when I tried to wrap those into polymorphic instances in the style of the instances at the beginning of this mail, I wasn't able to convince GHC: The following attempts wouldn't work: instance Resolvable e => Resolvable (Maybe e) where resolve = resolveMaybe -- GHC fails with: -- Expecting one more argument to `e' -- In the instance declaration for `Resolvable (Maybe e)' Fair enough, but trying to workaround this by defining a type-synonym to get an (*->*)-kinded expression didn't work either, as currying doesn't seem to be supported at the type-level (is there a language-extension for that?): type Maybe_ e r = Maybe (e r) instance Resolvable e => Resolvable (Maybe_ e) where resolve = resolveMaybe -- GHC fails with: -- Type synonym `Maybe_' should have 2 arguments, but has been given 1 -- In the instance declaration for `Resolvable (Maybe_ e)' So, am I really out of luck here, wanting to define polymorphic instances in combination with phantom-types, or is there a trick I haven't thought of yet? PS: while experimenting, I accidentally triggered the following GHC exception: *** Exception: compiler/rename/RnSource.lhs:429:14-81: Irrefutable pattern failed for pattern Data.Maybe.Just (inst_tyvars, _, SrcLoc.L _ cls, _) ...alas I lost the Haskell-code causing this; is this a known issue? Should I try harder to reproduce it again? cheers, hvr --

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profiling and backtracing blues
by Ranjit Jhala 16 Mar '12

16 Mar '12

Hi all, I'm trying to use the nifty backtracing mechanism in GHC 74. AFAICT, this requires everything be built with profiling on), but as a consequence, I hit this: "You can't call hscCompileCoreExpr in a profiled compiler" Any hints on whether there are work-arounds? Thanks! Ranjit.

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Re: How to work around GHC bug
by Volker Wysk 14 Mar '12

14 Mar '12

Am Mittwoch 14 März 2012, 16:04:25 schrieben Sie: > I have $LANG = en_GB.UTF-8 and I am on mac os x, if that helps. Now we have the riddle, of why it works differently on your machine. However, e can leave it at that, I think. Happy hacking, Volker

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Inlining and generic programming
by José Pedro Magalhães 14 Mar '12

14 Mar '12

Hello all, First of all, I'm sorry that this email is so absurdly long. But it's not easy to explain the problem at hand, so I took a step-by-step approach. The executive summary is: GHC can do a *great *job with inlining, but often it doesn't, and I don't understand why. So I have some questions, which are highlighted in the text below. In general, any insights regarding inlining or improving the performance of generics are welcome. My final goal is to be able to state that generic functions (in particular using GHC.Generics) will have no runtime overhead whatsoever when compared to a handwritten type-specific version. The setting Generic programming is based on representing datatypes in a uniform way using a small set of representation types. Functions defined on those representation types can then be applied to all datatypes, because we can convert between datatypes and their representations. However, generic functions tend to be slower than their specialised counterparts, because they have to deal with the conversions. But clever inlining (together with other compiler optimisations) can completely remove this overhead. The problem I'm tackling is how to tell GHC exactly what it should in the particular case of optimisation of generic code. Simplified example I'll focus on the problem of optimising a non-trivial function for generic enumeration of terms. My experience shows that GHC does quite good at optimising simple functions, especially consumers (like generic equality). But producers are trickier. First, we'll need some auxiliary functions: -- | Interleave elements from two lists. Similar to (++), but swap left and > -- right arguments on every recursive application. > -- > -- From Mark Jones' talk at AFP2008 > {-# NOINLINE (|||) #-} > (|||) :: [a] -> [a] -> [a] > [] ||| ys = ys > (x:xs) ||| ys = x : ys ||| xs > > > -- | Diagonalization of nested lists. Ensure that some elements from every > -- sublist will be included. Handles infinite sublists. > -- > -- From Mark Jones' talk at AFP2008 > {-# NOINLINE diag #-} > diag :: [[a]] -> [a] > diag = concat . foldr skew [] . map (map (\x -> [x])) > > skew :: [[a]] -> [[a]] -> [[a]] > skew [] ys = ys > skew (x:xs) ys = x : combine (++) xs ys > > combine :: (a -> a -> a) -> [a] -> [a] -> [a] > combine _ xs [] = xs > combine _ [] ys = ys > combine f (x:xs) (y:ys) = f x y : combine f xs ys > The particular implementation of these functions doesn't really matter. What's important is that we have a way to interleave lists (|||) and a way to diagonalise a matrix into a list (diag). We mark these functions as NOINLINE because inlining them will only make the core code more complicated (and may prevent rules from firing). Suppose we have a type of Peano natural numbers: data Nat = Ze | Su Nat deriving Eq > Implementing enumeration on this type is simple: enumNat :: [Nat] > enumNat = [Ze] ||| map Su enumNat > Now, a generic representation of Nat in terms of sums and products could look something like this: type RepNat = Either () Nat > That is, either a singleton (for the Ze case) or a Nat (for the Su case). Note that I am building a shallow representation, since at the leaves we have Nat, and not RepNat. This mimics the situation with current generic programming libraries (in particular GHC.Generics). We'll need a way to convert between RepNat and Nat: toNat :: RepNat -> Nat > toNat (Left ()) = Ze > toNat (Right n) = Su n > > fromNat :: Nat -> RepNat > fromNat Ze = Left () > fromNat (Su n) = Right n > (In fact, since we're only dealing with a generic producer we won't need the fromNat function.) To get an enumeration for RepNat, we first need to know how to enumerate units and sums: enumU :: [()] > enumU = [()] > > enumEither :: [a] -> [b] -> [Either a b] > enumEither ea eb = map Left ea ||| map Right eb > Now we can define an enumeration for RepNat: enumRepNat :: [RepNat] > enumRepNat = enumEither enumU enumNatFromRep > With the conversion function toNat, we can use enumRepNat to get an enumeration for Nat directly: enumNatFromRep :: [Nat] > enumNatFromRep = map toNat enumRepNat > First, convince yourself that enumNatFromRep and enumNat are equivalent functions: take 100 enumNat == take 100 enumNatFromRep > Now, what I want is that enumNatFromRep generates the same core code as enumNat. That should be possible; here are the necessary steps: map toNat enumRepNat > > == { inline enumRepNat } > > map toNat (enumEither enumU enumNatFromRep) > > == { inline enumEither } > > map toNat (map Left enumU ||| map Right enumNatFromRep) > > == { inline enumU } > > map toNat (map Left [()] ||| map Right enumNatFromRep) > > == { inline map } > > map toNat ([Left ()] ||| map Right enumNatFromRep) > > == { free theorem (|||): forall f a b. map f (a ||| b) = map f a ||| map f > b } > > map toNat [Left ()] ||| map toNat (map Right enumNatFromRep) > > == { inline map } > > [toNat (Left ())] ||| map toNat (map Right enumNatFromRep) > > == { definition of toNat (or inline toNat + case of constant) } > > [Ze] ||| map toNat (map Right enumNatFromRep) > > == { functor composition law: forall f g l. map f (map g l) = map (f . g) > l } > > [Ze] ||| map (toNat . Right) enumNatFromRep > > == { definition of toNat (or inline toNat + case of constant) } > > [Ze] ||| map Su enumNatFromRep > Now let's see what the compiler generates. I'm using GHC-7.4.1. Let's compile with -O1 and use -ddump-simpl to see the final simplifier output (core code) for enumNatFromRep: EnumAlone.enumNatFromRep :: [EnumAlone.Nat] > [GblId, > Str=DmdType, > Unf=Unf{Src=<vanilla>, TopLvl=True, Arity=0, Value=False, > ConLike=False, Cheap=False, Expandable=False, > Guidance=IF_ARGS [] 30 0}] > EnumAlone.enumNatFromRep = > GHC.Base.map > @ EnumAlone.RepNat > @ EnumAlone.Nat > EnumAlone.toNat > EnumAlone.enumRepNat > > EnumAlone.enumRepNat [Occ=LoopBreaker] :: [EnumAlone.RepNat] > [GblId, Str=DmdType] > EnumAlone.enumRepNat = > EnumAlone.||| > @ (Data.Either.Either () EnumAlone.Nat) lvl4_rvV lvl5_rvW > Ah, it didn't even inline enumRepNat because it made it a loop breaker. We certainly want to inline it, so let's add a pragma: {-# INLINE enumRepNat #-} > Recompiling, we get: EnumAlone.enumRepNat [InlPrag=INLINE (sat-args=0)] > :: [EnumAlone.RepNat] > [GblId, > Str=DmdType, > Unf=Unf{Src=InlineStable, TopLvl=True, Arity=0, Value=False, > ConLike=False, Cheap=False, Expandable=False, > Guidance=ALWAYS_IF(unsat_ok=False,boring_ok=False) > Tmpl= EnumAlone.enumEither > @ () @ EnumAlone.Nat EnumAlone.enumU > EnumAlone.enumNatFromRep}] > EnumAlone.enumRepNat = > EnumAlone.||| > @ (Data.Either.Either () EnumAlone.Nat) lvl4_rvV lvl5_rvW > > EnumAlone.enumNatFromRep [Occ=LoopBreaker] :: [EnumAlone.Nat] > [GblId, Str=DmdType] > EnumAlone.enumNatFromRep = > GHC.Base.map > @ EnumAlone.RepNat > @ EnumAlone.Nat > EnumAlone.toNat > EnumAlone.enumRepNat > So no real difference in the generated code, other than the reassignment of loop breakers. For some reason enumRepNat still doesn't get inlined. *Question: why won't GHC inline enumRepNat, even when I tell it to do so with an INLINE pragma?* Well, let's inline it ourselves, then. We redefine enumNatFromRep to: enumNatFromRep = map toNat (enumEither enumU enumNatFromRep) > This however doesn't help much. We get the following core: lvl6_rw5 :: [Data.Either.Either () EnumAlone.Nat] > [GblId] > lvl6_rw5 = > EnumAlone.||| > @ (Data.Either.Either () EnumAlone.Nat) lvl4_rw3 lvl5_rw4 > > EnumAlone.enumNatFromRep [Occ=LoopBreaker] :: [EnumAlone.Nat] > [GblId, Str=DmdType] > EnumAlone.enumNatFromRep = > GHC.Base.map > @ EnumAlone.RepNat @ EnumAlone.Nat EnumAlone.toNat lvl6_rw5 > GHC is really keen on floating that (|||) out. Let's be very explicit about inlining: {-# INLINE toNat #-} > {-# INLINE enumU #-} > {-# INLINE enumEither #-} > Also, maybe it's floating it out because it doesn't have anything else to do to it. Let's add the free theorem of (|||) as a rule: {-# RULES "ft |||" forall f a b. map f (a ||| b) = map f a ||| map f b #-} > We needed this in our manual derivation, so GHC should need it too. Recompiling, we see we've made some progress: lvl5_ryv :: [Data.Either.Either () EnumAlone.Nat] > [GblId] > lvl5_ryv = > GHC.Base.map > @ EnumAlone.Nat > @ (Data.Either.Either () EnumAlone.Nat) > (Data.Either.Right @ () @ EnumAlone.Nat) > EnumAlone.enumNatFromRep > > lvl6_ryw :: [EnumAlone.Nat] > [GblId] > lvl6_ryw = > GHC.Base.map > @ (Data.Either.Either () EnumAlone.Nat) > @ EnumAlone.Nat > EnumAlone.toNat > lvl5_ryv > > EnumAlone.enumNatFromRep [Occ=LoopBreaker] :: [EnumAlone.Nat] > [GblId, Str=DmdType] > EnumAlone.enumNatFromRep = > EnumAlone.||| @ EnumAlone.Nat lvl4_ryu lvl6_ryw > enumNatFromRep finally starts with (|||) directly. But its second argument, lvl6_ryw, is a map of lvl5_ryv, which is itself a map! At this stage I expected GHC to be aware of the fusion law for map, but it seems that it isn't. *Question: why is map fusion not happening automatically?* Let's add it as a rule: {-# RULES "map/map1" forall f g l. map f (map g l) = map (f . g) l #-} > And now we're in a much better situation: lvl3_ryD :: [Data.Either.Either () EnumAlone.Nat] > [GblId, Caf=NoCafRefs] > lvl3_ryD = > GHC.Types.: > @ (Data.Either.Either () EnumAlone.Nat) > EnumAlone.fromNat1 > (GHC.Types.[] @ (Data.Either.Either () EnumAlone.Nat)) > > lvl4_ryE :: [EnumAlone.Nat] > [GblId] > lvl4_ryE = > GHC.Base.map > @ (Data.Either.Either () EnumAlone.Nat) > @ EnumAlone.Nat > EnumAlone.toNat > lvl3_ryD > > lvl5_ryF :: [EnumAlone.Nat] > [GblId] > lvl5_ryF = > GHC.Base.map > @ EnumAlone.Nat > @ EnumAlone.Nat > EnumAlone.Su > EnumAlone.enumNatFromRep > > EnumAlone.enumNatFromRep [Occ=LoopBreaker] :: [EnumAlone.Nat] > [GblId, Str=DmdType] > EnumAlone.enumNatFromRep = > EnumAlone.||| @ EnumAlone.Nat lvl4_ryE lvl5_ryF > Note how toNat is entirely gone from the second part of the enumeration (lvl5_ryF). Strangely enough, the enumerator for Ze (lvl4_ryE) is still very complicated: map toNat ([Left ()]). Why doesn't GHC simplify this to just [Ze]? Apparently because GHC doesn't simplify map over a single element list. *Question: why doesn't GHC optimise map f [x] to [f x]?* Let's tell it to do so: {-# RULES "map/map2" forall f x. map f (x:[]) = (f x):[] #-} > Now we're finally where we wanted: lvl_ryA :: [EnumAlone.Nat] > [GblId, Caf=NoCafRefs] > lvl_ryA = > GHC.Types.: > @ EnumAlone.Nat EnumAlone.Ze (GHC.Types.[] @ EnumAlone.Nat) > > lvl3_ryD :: [EnumAlone.Nat] > [GblId] > lvl3_ryD = > GHC.Base.map > @ EnumAlone.Nat > @ EnumAlone.Nat > EnumAlone.Su > EnumAlone.enumNatFromRep > > EnumAlone.enumNatFromRep [Occ=LoopBreaker] :: [EnumAlone.Nat] > [GblId, Str=DmdType] > EnumAlone.enumNatFromRep = > EnumAlone.||| @ EnumAlone.Nat lvl_ryA lvl3_ryD > This is what I wanted: no more representation types (Either or ()), and the code looks exactly like what is generated for the handwritten enumNat. More realistic generic programming Now let's see if we can transport this to the setting of a generic programming library. I'll use a bare-bones version of GHC.Generics: infixr 5 :+: > infixr 6 :*: > > data U = U deriving (Show, Read) > data a :+: b = L a | R b deriving (Show, Read) > data a :*: b = a :*: b deriving (Show, Read) > newtype Var a = Var a deriving (Show, Read) > newtype Rec a = Rec a deriving (Show, Read) > > class Representable a where > type Rep a > to :: Rep a -> a > from :: a -> Rep a > Let's represent Nat in this library: instance Representable Nat where > type Rep Nat = U :+: (Rec Nat) > from Ze = L U > from (Su n) = R (Rec n) > to (L U) = Ze > to (R (Rec n)) = Su n > (Note, in particular, that we do not need INLINE pragmas on the from/to methods. This might just be because GHC thinks these are small and inlines them anyway, but in general we want to make sure they are inlined, so we typically use pragmas there.) Now we need to implement enumeration generically. We do this by giving an instance for each representation type: class GEnum' a where > genum' :: [a] > > instance GEnum' U where > {-# INLINE genum' #-} > genum' = [U] > > instance (GEnum a) => GEnum' (Rec a) where > {-# INLINE genum' #-} > genum' = map Rec genum > > instance (GEnum a) => GEnum' (Var a) where > {-# INLINE genum' #-} > genum' = map Var genum > > instance (GEnum' f, GEnum' g) => GEnum' (f :+: g) where > {-# INLINE genum' #-} > genum' = map L genum' ||| map R genum' > > instance (GEnum' f, GEnum' g) => GEnum' (f :*: g) where > {-# INLINE genum' #-} > --genum' = diag [ [ x :*: y | y <- genum' ] | x <- genum' ] > genum' = diag (map (\x -> map (\y -> x :*: y) genum') genum') > We explicitly tell GHC to inline each case, as before. Note that for products I'm not using the more natural list comprehension syntax because I don't quite understand how that gets translated into core. In the cases for Var and Rec we use genum from the GEnum class: class GEnum a where > genum :: [a] > {-# INLINE genum #-} > default genum :: (Representable a, GEnum' (Rep a)) => [a] > genum = map to genum' > GEnum' is the class used for instantiating the generic representation types, and GEnum is used for user types. We use a default signature to provide a default method that can be used when we have a Representable instance for the type in question. This makes instantiating Nat very easy: instance GEnum Nat > Unfortunately, the core code generated in this situation (with the same RULES as before) is not nice at all: Main.$fGEnumNat_$cgenum [Occ=LoopBreaker] :: [Base.Nat] > [GblId, Str=DmdType] > Main.$fGEnumNat_$cgenum = > GHC.Base.map > @ (Base.Rep Base.Nat) > @ Base.Nat > Base.$fRepresentableNat_$cto > (lvl37_r79y > `cast` (Sym (GEnum.NTCo:GEnum') <Base.U Base.:+: (Base.Rec Base.Nat)> > ; > (GEnum.GEnum' (Sym > (Base.TFCo:R:RepNat)) ; > GEnum.NTCo:GEnum' <Base.Rep > Base.Nat>) > :: [Base.C Base.Nat_Ze_ Base.U > Base.:+: Base.C Base.Nat_Su_ (Base.Rec Base.Nat)] > ~# > [Base.Rep Base.Nat])) > We see a map of the `to` function, which is definitely not what we want. Oddly enough, if we give an explicit definition of genum for Nat, with the inlined default... instance GEnum Nat where genum = map to genum' > ... then we get the optimised code we want: lvl34_r79p :: [Base.Nat] > [GblId, Caf=NoCafRefs] > lvl34_r79p = > GHC.Types.: @ Base.Nat Base.Ze (GHC.Types.[] @ Base.Nat) > > lvl35_r79q :: [Base.Nat] > [GblId] > lvl35_r79q = > GHC.Base.map @ Base.Nat @ Base.Nat Base.Su Main.$fGEnumNat_$cgenum > > Main.$fGEnumNat_$cgenum [Occ=LoopBreaker] :: [Base.Nat] > [GblId, Str=DmdType] > Main.$fGEnumNat_$cgenum = > GEnum.||| @ Base.Nat lvl34_r79p lvl35_r79q > Again, no representation types, no `to`, just the same code that is generated for enumNat. Perfect. But we had to avoid using the default definition, which is a pity. *Question: why won't GHC inline the default method of a class, even when I have a pragma telling it to do so?* Let's look at one more datatype, because Nat does not use products. So let's consider trees: data Tree a = Leaf | Bin a (Tree a) (Tree a) > > instance Representable (Tree a) where > type Rep (Tree a) = U :+: (Var a :*: Rec (Tree a) :*: Rec (Tree a)) > from (Bin x l r) = R (Var x :*: Rec l :*: Rec r) > from Leaf = L U > to (R (Var x :*: (Rec l) :*: (Rec r))) = Bin x l r > to (L U) = Leaf > We give a GEnum instance using the same trick as before: instance GEnum (Tree Int) where genum = map to genum' > (For simplicity only for trees of integers.) The generated code for trees is unfortunately not as nice: a2_r79M > :: [Base.Rec (Base.Tree GHC.Types.Int) > Base.:*: Base.Rec (Base.Tree GHC.Types.Int) > [GblId, Str=DmdType] > a2_r79M = > GEnum.diag > @ (Base.Rec (Base.Tree GHC.Types.Int) > Base.:*: Base.Rec (Base.Tree GHC.Types.Int)) > lvl8_r79L > > lvl9_r79N :: [Base.Tree GHC.Types.Int] > [GblId] > lvl9_r79N = > GHC.Base.map > @ (Base.Rec (Base.Tree GHC.Types.Int) > Base.:*: Base.Rec (Base.Tree GHC.Types.Int)) > @ (Base.Tree GHC.Types.Int) > lvl5_r79H > a2_r79M > > Main.$fGEnumTree_$cgenum [Occ=LoopBreaker] > :: [Base.Tree GHC.Types.Int] > [GblId, Str=DmdType] > Main.$fGEnumTree_$cgenum = > GEnum.||| @ (Base.Tree GHC.Types.Int) lvl4_r79G lvl9_r79N > Note how lvl9_r79N is a map over a2_r79M, and a2_r79M is a `diag`. Ok, we need the free theorem of `diag` to tell GHC how to commute the `diag` with map: {-# RULES "ft/diag" forall f l. map f (diag l) = diag (map (map f) l) #-} > Unfortunately this doesn't change the generated core code. With some more debugging looking at the generated code at each simplifier iteration, I believe that this is because a2_r79M got lifted out too soon, prevent the rule from applying. With some imagination I decided to try the -fno-full-laziness flag to prevent let-floating. I'm not sure this is a good idea in general, but in this particular case it gives much better results: a1_r72i :: [Base.Rec (Base.Tree GHC.Types.Int) > [GblId, Str=DmdType] > a1_r72i = > GHC.Base.map > @ (Base.Tree GHC.Types.Int) > @ (Base.Rec (Base.Tree GHC.Types.Int)) > ((\ (tpl_B1 :: Base.Tree GHC.Types.Int) -> tpl_B1) > `cast` (<Base.Tree GHC.Types.Int> > -> Sym (Base.NTCo:Rec <Base.Tree GHC.Types.Int>) > :: (Base.Tree GHC.Types.Int -> Base.Tree GHC.Types.Int) > ~# > (Base.Tree GHC.Types.Int -> Base.Rec (Base.Tree > GHC.Types.Int)))) > Main.$fGEnumTree_$cgenum > > Main.$fGEnumTree_$cgenum [Occ=LoopBreaker] > :: [Base.Tree GHC.Types.Int] > [GblId, Str=DmdType] > Main.$fGEnumTree_$cgenum = > GEnum.||| > @ (Base.Tree GHC.Types.Int) > (GHC.Types.: > @ (Base.Tree GHC.Types.Int) > (Base.Leaf @ GHC.Types.Int) > (GHC.Types.[] @ (Base.Tree GHC.Types.Int))) > (GEnum.diag > @ (Base.Tree GHC.Types.Int) > (GHC.Base.map > @ (Base.Rec (Base.Tree GHC.Types.Int)) > @ [Base.Tree GHC.Types.Int] > (\ (x_a1yQ :: Base.Rec (Base.Tree GHC.Types.Int)) -> > GHC.Base.map > @ (Base.Rec (Base.Tree GHC.Types.Int)) > @ (Base.Tree GHC.Types.Int) > (\ (x1_X1zB :: Base.Rec (Base.Tree GHC.Types.Int)) -> > Base.Bin > @ GHC.Types.Int > a_r72h > (x_a1yQ > `cast` (Base.NTCo:Rec <Base.Tree GHC.Types.Int> > :: Base.Rec (Base.Tree GHC.Types.Int) ~# > Base.Tree GHC.Types.Int)) > (x1_X1zB > `cast` (Base.NTCo:Rec <Base.Tree GHC.Types.Int> > :: Base.Rec (Base.Tree GHC.Types.Int) ~# > Base.Tree GHC.Types.Int))) > a1_r72i) > a1_r72i)) > Note how our enum is now of the shape `[Leaf] ||| diag y`, which is good. The only catch is that there are some `Rec`s still laying around, with their associated newtype coercions, and a function a1_r72i that basically wraps the recursive enumeration in a Rec, only to be unwrapped in the body of `$fGEnumTree_$cgenum`. I don't know how to get GHC to simplify this code any further. *Question: why do I need -fno-full-laziness for the ft/diag rule to apply?* *Question: why is GHC not getting rid of the Rec newtype in this case?* I have also played with -O2, in particular because of the SpecConstr optimisation, but found that it does not affect these particular examples (perhaps it only becomes important with larger datatypes). I have also experimented with phase control in the rewrite rules and the inline pragmas, but didn't find it necessary for this example. In general, anyway, my experience with the inliner is that it is extremely fragile, especially across different GHC versions, and it's hard to get any guarantees of optimisation. I have also played with the -funfolding-* options before, with mixed results. [1] It's also a pity that certain flags are not explained in detail in the user's manual [2,3], like -fliberate-case, and -fspec-constr-count and threshold, for instance. Thank you for reading this. Any insights are welcome. In particular, I'm wondering if I might be missing some details regarding strictness. Cheers, Pedro [1] http://dreixel.net/research/pdf/ogie.pdf [2] http://www.haskell.org/ghc/docs/latest/html/users_guide/flag-reference.html [3] http://www.haskell.org/ghc/docs/latest/html/users_guide/options-optimise.ht…

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