{-# LANGUAGE DataKinds #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE UndecidableInstances #-} {-# OPTIONS_GHC -freduction-depth=0 #-} -- this should terminate! module T9872d where -- Code from Jan Stolarek, labelled "exp-tyfams.hs" on Trac #9872, -- generated by a Template Haskell program -- This file demonstrates exponential compile times with type -- families. Code in this file was extracted from encoding generated -- automatically with Template Haskell by singletons library. import Data.Kind import GHC.TypeLits -- encoding of type-level partially applied functions data TyFun :: Type -> Type -> Type type family Apply (f :: TyFun k1 k2 -> Type) (x :: k1) :: k2 type a @@ b = Apply a b -- some boilerplate type family Error (a :: k) :: k1 type ErrorSym1 a = Error a data ErrorSym0 :: TyFun a b -> Type type instance Apply ErrorSym0 e = Error e data Proxy a = Proxy data KProxy (a :: Type) = KProxy type KindOf (a :: k) = ('KProxy :: KProxy k) -- type-level addition type (:+$$$) (t1 :: Nat) (t2 :: Nat) = t1 + t2 data (:+$$) (l :: Nat) (tf :: TyFun Nat Nat) = forall a. (KindOf (Apply ((:+$$) l) a)) ~ (KindOf ((:+$$$) l a)) => (:+$$###) type instance Apply ((:+$$) l1) l2 = (:+$$$) l1 l2 data (:+$) (l :: TyFun Nat (TyFun Nat Nat -> Type)) = forall a. (KindOf (Apply (:+$) a)) ~ (KindOf ((:+$$) a)) => (:+$###) type instance Apply (:+$) l = (:+$$) l -- type-level lists type NilSym0 = '[] type ConsSym2 (x :: a) (xs :: [a]) = x ': xs data ConsSym1 (x :: a) (l_a3t6 :: TyFun [a] [a]) = forall b. (KindOf (Apply (ConsSym1 x) b)) ~ (KindOf (ConsSym2 x b)) => (:$$###) type instance Apply (ConsSym1 x) xs = ConsSym2 x xs data ConsSym0 (l :: TyFun a (TyFun [a] [a] -> Type)) = forall a. (KindOf (Apply ConsSym0 a)) ~ (KindOf (ConsSym1 a)) => (:$###) type instance Apply ConsSym0 l = ConsSym1 l type Let_1627403919Scrutinee_1627403894Sym4 t1 t2 t3 t4 = Let_1627403919Scrutinee_1627403894 t1 t2 t3 t4 data Let_1627403919Scrutinee_1627403894Sym3 l_a3Dx l_a3Dy l_a3Dz l_a3Dw = forall arg_a3DA. (KindOf (Apply (Let_1627403919Scrutinee_1627403894Sym3 l_a3Dx l_a3Dy l_a3Dz) arg_a3DA)) ~ (KindOf (Let_1627403919Scrutinee_1627403894Sym4 l_a3Dx l_a3Dy l_a3Dz arg_a3DA)) => Let_1627403919Scrutinee_1627403894Sym3KindInference type instance Apply (Let_1627403919Scrutinee_1627403894Sym3 l_a3Dx l_a3Dy l_a3Dz) l_a3Dw = Let_1627403919Scrutinee_1627403894Sym4 l_a3Dx l_a3Dy l_a3Dz l_a3Dw data Let_1627403919Scrutinee_1627403894Sym2 l_a3Dt l_a3Du l_a3Ds = forall arg_a3Dv. (KindOf (Apply (Let_1627403919Scrutinee_1627403894Sym2 l_a3Dt l_a3Du) arg_a3Dv)) ~ (KindOf (Let_1627403919Scrutinee_1627403894Sym3 l_a3Dt l_a3Du arg_a3Dv)) => Let_1627403919Scrutinee_1627403894Sym2KindInference type instance Apply (Let_1627403919Scrutinee_1627403894Sym2 l_a3Dt l_a3Du) l_a3Ds = Let_1627403919Scrutinee_1627403894Sym3 l_a3Dt l_a3Du l_a3Ds data Let_1627403919Scrutinee_1627403894Sym1 l_a3Dq l_a3Dp = forall arg_a3Dr. (KindOf (Apply (Let_1627403919Scrutinee_1627403894Sym1 l_a3Dq) arg_a3Dr)) ~ (KindOf (Let_1627403919Scrutinee_1627403894Sym2 l_a3Dq arg_a3Dr)) => Let_1627403919Scrutinee_1627403894Sym1KindInference type instance Apply (Let_1627403919Scrutinee_1627403894Sym1 l_a3Dq) l_a3Dp = Let_1627403919Scrutinee_1627403894Sym2 l_a3Dq l_a3Dp data Let_1627403919Scrutinee_1627403894Sym0 l_a3Dn = forall arg_a3Do. (KindOf (Apply Let_1627403919Scrutinee_1627403894Sym0 arg_a3Do)) ~ (KindOf (Let_1627403919Scrutinee_1627403894Sym1 arg_a3Do)) => Let_1627403919Scrutinee_1627403894Sym0KindInference type instance Apply Let_1627403919Scrutinee_1627403894Sym0 l_a3Dn = Let_1627403919Scrutinee_1627403894Sym1 l_a3Dn type Let_1627403919Scrutinee_1627403894 f_a3Dd q0_a3De x_a3Df xs_a3Dg = Apply (Apply (Apply ScanrSym0 f_a3Dd) q0_a3De) xs_a3Dg type family Case f q0 x xs t :: [k] where Case f q0 x xs '[] = ErrorSym0 @@ "empty list" Case f q0 x xs (q ': qs) = ConsSym0 @@ (f @@ x @@ q) @@ (ConsSym0 @@ q @@ qs) -- type-level scanr type ScanrSym3 (t1 :: TyFun a (TyFun b b -> Type) -> Type) (t2 :: b) (t3 :: [a]) = Scanr t1 t2 t3 data ScanrSym2 (l1 :: TyFun a (TyFun b b -> Type) -> Type) (l2 :: b) (l3 :: TyFun [a] [b]) = forall a. (KindOf (Apply (ScanrSym2 l1 l2) a)) ~ (KindOf (ScanrSym3 l1 l2 a)) => ScanrSym2KindInference type instance Apply (ScanrSym2 l1 l2) l3 = ScanrSym3 l1 l2 l3 data ScanrSym1 (l_a3D0 :: TyFun a_a3CJ (TyFun b_a3CK b_a3CK -> Type) -> Type) (l_a3CZ :: TyFun b_a3CK (TyFun ([a_a3CJ]) ([b_a3CK]) -> Type)) = forall arg_a3D1. (KindOf (Apply (ScanrSym1 l_a3D0) arg_a3D1)) ~ (KindOf (ScanrSym2 l_a3D0 arg_a3D1)) => ScanrSym1KindInference type instance Apply (ScanrSym1 l_a3D0) l_a3CZ = ScanrSym2 l_a3D0 l_a3CZ data ScanrSym0 (l :: TyFun (TyFun a (TyFun b b -> Type) -> Type) (TyFun b (TyFun [a] [b] -> Type) -> Type)) = forall a. (KindOf (Apply ScanrSym0 a)) ~ (KindOf (ScanrSym1 a)) => ScanrSym0KindInference type instance Apply ScanrSym0 l1 = ScanrSym1 l1 type family Scanr (a_a3D6 :: TyFun a_a3CJ (TyFun b_a3CK b_a3CK -> Type) -> Type) (a_a3D7 :: b_a3CK) (a_a3D8 :: [a_a3CJ]) :: [b_a3CK] where Scanr _z_1627403911_a3Db q0_a3Dc '[] = Apply (Apply ConsSym0 q0_a3Dc) NilSym0 Scanr f_a3Dd q0_a3De (x_a3Df ': xs_a3Dg) = Case f_a3Dd q0_a3De x_a3Df xs_a3Dg (Let_1627403919Scrutinee_1627403894Sym4 f_a3Dd q0_a3De x_a3Df xs_a3Dg) {- foo32 :: Proxy ('[528,527,525,522,518,513,507,500,492,483,473,462,450,437,423, 408,392,375,357,338,318,297,275,252,228,203,177,150,122,93, 63,32,0]) foo32 = Proxy bar32 :: Proxy (ScanrSym0 @@ (:+$) @@ 0 @@ '[1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32]) bar32 = foo32 -} {- foo64 :: Proxy ('[2080,2079,2077,2074,2070,2065,2059,2052,2044,2035,2025,2014, 2002,1989,1975,1960,1944,1927,1909,1890,1870,1849,1827,1804, 1780,1755,1729,1702,1674,1645,1615,1584,1552,1519,1485,1450, 1414,1377,1339,1300,1260,1219,1177,1134,1090,1045,999,952,904, 855,805,754,702,649,595,540,484,427,369,310,250,189,127,64,0]) foo64 = Proxy bar64 :: Proxy (ScanrSym0 @@ (:+$) @@ 0 @@ '[1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33,34,35,36, 37,38,39,40,41,42,43,44,45,46,47, 48,49,50,51,52,53,54,55,56,57,58, 59,60,61,62,63,64]) bar64 = foo64 foo128 :: Proxy ('[8256,8255,8253,8250,8246,8241,8235,8228,8220,8211,8201,8190, 8178,8165,8151,8136,8120,8103,8085,8066,8046,8025,8003,7980, 7956,7931,7905,7878,7850,7821,7791,7760,7728,7695,7661,7626, 7590,7553,7515,7476,7436,7395,7353,7310,7266,7221,7175,7128, 7080,7031,6981,6930,6878,6825,6771,6716,6660,6603,6545,6486, 6426,6365,6303,6240,6176,6111,6045,5978,5910,5841,5771,5700, 5628,5555,5481,5406,5330,5253,5175,5096,5016,4935,4853,4770, 4686,4601,4515,4428,4340,4251,4161,4070,3978,3885,3791,3696, 3600,3503,3405,3306,3206,3105,3003,2900,2796,2691,2585,2478, 2370,2261,2151,2040,1928,1815,1701,1586,1470,1353,1235,1116, 996,875,753,630,506,381,255,128,0]) foo128 = Proxy bar128 :: Proxy (ScanrSym0 @@ (:+$) @@ 0 @@ '[1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33,34,35,36, 37,38,39,40,41,42,43,44,45,46,47, 48,49,50,51,52,53,54,55,56,57,58, 59,60,61,62,63,64,65,66,67,68,69, 70,71,72,73,74,75,76,77,78,79,80, 81,82,83,84,85,86,87,88,89,90,91, 92,93,94,95,96,97,98,99,100,101, 102,103,104,105,106,107,108,109, 110,111,112,113,114,115,116,117, 118,119,120,121,122,123,124,125, 126,127,128]) bar128 = foo128 -} foo256 :: Proxy ('[32896,32895,32893,32890,32886,32881,32875,32868,32860,32851, 32841,32830,32818,32805,32791,32776,32760,32743,32725,32706, 32686,32665,32643,32620,32596,32571,32545,32518,32490,32461, 32431,32400,32368,32335,32301,32266,32230,32193,32155,32116, 32076,32035,31993,31950,31906,31861,31815,31768,31720,31671, 31621,31570,31518,31465,31411,31356,31300,31243,31185,31126, 31066,31005,30943,30880,30816,30751,30685,30618,30550,30481, 30411,30340,30268,30195,30121,30046,29970,29893,29815,29736, 29656,29575,29493,29410,29326,29241,29155,29068,28980,28891, 28801,28710,28618,28525,28431,28336,28240,28143,28045,27946, 27846,27745,27643,27540,27436,27331,27225,27118,27010,26901, 26791,26680,26568,26455,26341,26226,26110,25993,25875,25756, 25636,25515,25393,25270,25146,25021,24895,24768,24640,24511, 24381,24250,24118,23985,23851,23716,23580,23443,23305,23166, 23026,22885,22743,22600,22456,22311,22165,22018,21870,21721, 21571,21420,21268,21115,20961,20806,20650,20493,20335,20176, 20016,19855,19693,19530,19366,19201,19035,18868,18700,18531, 18361,18190,18018,17845,17671,17496,17320,17143,16965,16786, 16606,16425,16243,16060,15876,15691,15505,15318,15130,14941, 14751,14560,14368,14175,13981,13786,13590,13393,13195,12996, 12796,12595,12393,12190,11986,11781,11575,11368,11160,10951, 10741,10530,10318,10105,9891,9676,9460,9243,9025,8806, 8586,8365,8143,7920,7696,7471,7245,7018,6790,6561,6331,6100, 5868,5635,5401,5166,4930,4693,4455,4216,3976,3735,3493,3250, 3006,2761,2515,2268,2020,1771,1521,1270,1018,765,511,256,0]) foo256 = Proxy bar256 :: Proxy (ScanrSym0 @@ (:+$) @@ 0 @@ '[1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33,34,35,36, 37,38,39,40,41,42,43,44,45,46,47, 48,49,50,51,52,53,54,55,56,57,58, 59,60,61,62,63,64,65,66,67,68,69, 70,71,72,73,74,75,76,77,78,79,80, 81,82,83,84,85,86,87,88,89,90,91, 92,93,94,95,96,97,98,99,100,101, 102,103,104,105,106,107,108,109, 110,111,112,113,114,115,116,117, 118,119,120,121,122,123,124,125, 126,127,128,129,130,131,132,133, 134,135,136,137,138,139,140,141, 142,143,144,145,146,147,148,149, 150,151,152,153,154,155,156,157, 158,159,160,161,162,163,164,165, 166,167,168,169,170,171,172,173, 174,175,176,177,178,179,180,181, 182,183,184,185,186,187,188,189, 190,191,192,193,194,195,196,197, 198,199,200,201,202,203,204,205, 206,207,208,209,210,211,212,213, 214,215,216,217,218,219,220,221, 222,223,224,225,226,227,228,229, 230,231,232,233,234,235,236,237, 238,239,240,241,242,243,244,245, 246,247,248,249,250,251,252,253, 254,255,256]) bar256 = foo256