[Haskell-cafe] Are type families really this slow, or is this a GHC bug?

[Mike Izbicki]

I'm using the TypeFamilies extension to generate types that are quite
large.  GHC can handle these large types fine when they are created
manually, but when type families get involved, GHC's performance dies.
It's doing in quadratic time what looks to me like it should be linear
time.  I don't know if this is expected behavior, if I'm doing something
wrong, or if this is a GHC bug.

I've attached a code sample below that demonstrates the problem.  Types.hs
generates other haskell files.  The first parameter is the size of the type
(which is type list of that length), and the second specifies which test to
run.  All tests generate the same type in the end, but some use type
families and some don't.

Here's an example of running it:

These tests show quadratic time when using the type family.  I have to
increase the context stack size to be greater than the recursion depth of
the type family.  I don't know if this is a bad sign or to be expected.

$ ghc --version
The Glorious Glasgow Haskell Compilation System, version 7.6.3
$ ghc Types

$ ./Types 200 a > test.hs && time ghc test.hs > /dev/null
-fcontext-stack=250
real    0m2.973s
$ ./Types 300 a > test.hs && time ghc test.hs > /dev/null
-fcontext-stack=350
real    0m6.018s
$ ./Types 400 a > test.hs && time ghc test.hs > /dev/null
-fcontext-stack=450
real    0m9.995s
$ ./Types 500 a > test.hs && time ghc test.hs > /dev/null
-fcontext-stack=550
real    0m15.645s

Without the type family, I get MUCH better performance:

$ ./Types 10000 d > test.hs && time ghc test.hs > /dev/null
real    0m2.271s

------------------------
-- Types.hs below
------------------------

import System.Environment

code :: Int -> String -> String
code i test = concat $ map (++"\n") $
    [ "{-# LANGUAGE TypeOperators,DataKinds,
KindSignatures,TypeFamilies,PolyKinds #-}"
    , "import GHC.TypeLits"

    , "data Nat1 = Zero | Succ Nat1"

    , "type family Replicate1 (n :: Nat1) (x::a) :: [a]"
    , "type instance Replicate1 Zero x = '[]"
    , "type instance Replicate1 (Succ n) x = x ': (Replicate1 n x)"

    , "class Class a where"
    , "    f :: a -> a"

    , "data Data (xs::a) = X | Y"
    , "    deriving (Read,Show)"

    , "main = print test1"
    ]
    ++
    case head test of
        'a' ->
            [ "instance (xs ~ Replicate1 ("++mkNat1 i++") ()) => Class
(Data xs) where"
            , "    f X = Y"
            , "    f Y = X"
            , "test1 = f (X :: Data ( Replicate1 ("++mkNat1 i++") () ))"
            ]
        'b' ->
            [ "instance (xs ~ ("++mkList i++") ) => Class (Data xs) where"
            , "    f X = Y"
            , "    f Y = X"
            , "test1 = f (X :: Data ( Replicate1 ("++mkNat1 i++") () ))"
            ]
        'c' ->
            [ "instance (xs ~ Replicate1 ("++mkNat1 i++") ()) => Class
(Data xs) where"
            , "    f X = Y"
            , "    f Y = X"
            , "test1 = f (X :: Data ( ("++mkList i++") ))"
            ]
        otherwise ->
            [ "instance (xs ~ ("++mkList i++") ) => Class (Data xs) where"
            , "    f X = Y"
            , "    f Y = X"
            , "test1 = f (X :: Data ( ("++mkList i++") ))"
            ]

mkList :: Int -> String
mkList 0 = " '[] "
mkList i = " () ': " ++ mkList (i-1)

mkNat1 :: Int -> String
mkNat1 0 = " Zero "
mkNat1 i = " Succ ( " ++ mkNat1 (i-1) ++ ")"

main = do
    numstr : test : xs <- getArgs
    let num = read numstr :: Int

    putStrLn $ code num test
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