Language/Symantic/Compiling/Foldable.hs

   1 {-# LANGUAGE ConstraintKinds #-}
   2 {-# LANGUAGE UndecidableInstances #-}
   3 {-# OPTIONS_GHC -fno-warn-orphans #-}
   4 -- | Symantic for 'Foldable'.
   5 module Language.Symantic.Compiling.Foldable where
   6
   7 import Data.Foldable (Foldable)
   8 import qualified Data.Foldable as Foldable
   9 import Control.Monad (liftM, liftM2, liftM3)
  10 import Data.Proxy
  11 import Data.Type.Equality ((:~:)(Refl))
  12 import Prelude hiding (Foldable(..)
  13  , all, and, any, concat, concatMap
  14  , mapM_, notElem, or, sequence, sequence_)
  15
  16 import Language.Symantic.Parsing
  17 import Language.Symantic.Parsing.Grammar hiding (any)
  18 import Language.Symantic.Typing
  19 import Language.Symantic.Compiling.Term
  20 import Language.Symantic.Interpreting
  21 import Language.Symantic.Transforming.Trans
  22
  23 -- * Class 'Sym_Foldable'
  24 class Sym_Foldable term where
  25         foldMap    :: (Foldable f, Monoid m) => term (a -> m) -> term (f a) -> term m
  26         foldr      :: Foldable f => term (a -> b -> b) -> term b -> term (f a) -> term b
  27         foldr'     :: Foldable f => term (a -> b -> b) -> term b -> term (f a) -> term b
  28         foldl      :: Foldable f => term (b -> a -> b) -> term b -> term (f a) -> term b
  29         foldl'     :: Foldable f => term (b -> a -> b) -> term b -> term (f a) -> term b
  30         length     :: Foldable f => term (f a) -> term Int
  31         null       :: Foldable f => term (f a) -> term Bool
  32         minimum    :: (Foldable f, Ord a) => term (f a) -> term a
  33         maximum    :: (Foldable f, Ord a) => term (f a) -> term a
  34         elem       :: (Foldable f, Eq  a) => term a -> term (f a) -> term Bool
  35         sum        :: (Foldable f, Num a) => term (f a) -> term a
  36         product    :: (Foldable f, Num a) => term (f a) -> term a
  37         toList     :: Foldable f => term (f a) -> term [a]
  38         all        :: Foldable f => term (a -> Bool) -> term (f a) -> term Bool
  39         and        :: Foldable f => term (f Bool) -> term Bool
  40         any        :: Foldable f => term (a -> Bool) -> term (f a) -> term Bool
  41         concat     :: Foldable f => term (f [a]) -> term [a]
  42         concatMap  :: Foldable f => term (a -> [b]) -> term (f a) -> term [b]
  43         find       :: Foldable f => term (a -> Bool) -> term (f a) -> term (Maybe a)
  44         foldlM     :: (Foldable f, Monad m) => term (b -> a -> m b) -> term b -> term (f a) -> term (m b)
  45         foldrM     :: (Foldable f, Monad m) => term (a -> b -> m b) -> term b -> term (f a) -> term (m b)
  46         forM_      :: (Foldable f, Monad m) => term (f a) -> term (a -> m b) -> term (m ())
  47         for_       :: (Foldable f, Applicative p) => term (f a) -> term (a -> p b) -> term (p ())
  48         mapM_      :: (Foldable f, Monad m) => term (a -> m b) -> term (f a) -> term (m ())
  49         maximumBy  :: Foldable f => term (a -> a -> Ordering) -> term (f a) -> term a
  50         minimumBy  :: Foldable f => term (a -> a -> Ordering) -> term (f a) -> term a
  51         notElem    :: (Foldable f, Eq a) => term a -> term (f a) -> term Bool
  52         or         :: Foldable f => term (f Bool) -> term Bool
  53         sequenceA_ :: (Foldable f, Applicative p) => term (f (p a)) -> term (p ())
  54         sequence_  :: (Foldable f, Monad m) => term (f (m a)) -> term (m ())
  55         traverse_  :: (Foldable f, Applicative p) => term (a -> p b) -> term (f a) -> term (p ())
  56         -- asum :: (Foldable t, GHC.Base.Alternative f) => t (f a) -> f a
  57         -- msum :: (Foldable t, GHC.Base.MonadPlus m) => t (m a) -> m a
  58
  59         default foldMap    :: (Trans t term, Foldable f, Monoid m) => t term (a -> m) -> t term (f a) -> t term m
  60         default foldr      :: (Trans t term, Foldable f) => t term (a -> b -> b) -> t term b -> t term (f a) -> t term b
  61         default foldr'     :: (Trans t term, Foldable f) => t term (a -> b -> b) -> t term b -> t term (f a) -> t term b
  62         default foldl      :: (Trans t term, Foldable f) => t term (b -> a -> b) -> t term b -> t term (f a) -> t term b
  63         default foldl'     :: (Trans t term, Foldable f) => t term (b -> a -> b) -> t term b -> t term (f a) -> t term b
  64         default length     :: (Trans t term, Foldable f) => t term (f a) -> t term Int
  65         default null       :: (Trans t term, Foldable f) => t term (f a) -> t term Bool
  66         default minimum    :: (Trans t term, Foldable f, Ord a) => t term (f a) -> t term a
  67         default maximum    :: (Trans t term, Foldable f, Ord a) => t term (f a) -> t term a
  68         default elem       :: (Trans t term, Foldable f, Eq  a) => t term a -> t term (f a) -> t term Bool
  69         default sum        :: (Trans t term, Foldable f, Num a) => t term (f a) -> t term a
  70         default product    :: (Trans t term, Foldable f, Num a) => t term (f a) -> t term a
  71         default toList     :: (Trans t term, Foldable f) => t term (f a) -> t term [a]
  72         default all        :: (Trans t term, Foldable f) => t term (a -> Bool) -> t term (f a) -> t term Bool
  73         default and        :: (Trans t term, Foldable f) => t term (f Bool) -> t term Bool
  74         default any        :: (Trans t term, Foldable f) => t term (a -> Bool) -> t term (f a) -> t term Bool
  75         default concat     :: (Trans t term, Foldable f) => t term (f [a]) -> t term [a]
  76         default concatMap  :: (Trans t term, Foldable f) => t term (a -> [b]) -> t term (f a) -> t term [b]
  77         default find       :: (Trans t term, Foldable f) => t term (a -> Bool) -> t term (f a) -> t term (Maybe a)
  78         default foldlM     :: (Trans t term, Foldable f, Monad m) => t term (b -> a -> m b) -> t term b -> t term (f a) -> t term (m b)
  79         default foldrM     :: (Trans t term, Foldable f, Monad m) => t term (a -> b -> m b) -> t term b -> t term (f a) -> t term (m b)
  80         default forM_      :: (Trans t term, Foldable f, Monad m) => t term (f a) -> t term (a -> m b) -> t term (m ())
  81         default for_       :: (Trans t term, Foldable f, Applicative p) => t term (f a) -> t term (a -> p b) -> t term (p ())
  82         default mapM_      :: (Trans t term, Foldable f, Monad m) => t term (a -> m b) -> t term (f a) -> t term (m ())
  83         default maximumBy  :: (Trans t term, Foldable f) => t term (a -> a -> Ordering) -> t term (f a) -> t term a
  84         default minimumBy  :: (Trans t term, Foldable f) => t term (a -> a -> Ordering) -> t term (f a) -> t term a
  85         default notElem    :: (Trans t term, Foldable f, Eq a) => t term a -> t term (f a) -> t term Bool
  86         default or         :: (Trans t term, Foldable f) => t term (f Bool) -> t term Bool
  87         default sequenceA_ :: (Trans t term, Foldable f, Applicative p) => t term (f (p a)) -> t term (p ())
  88         default sequence_  :: (Trans t term, Foldable f, Monad m) => t term (f (m a)) -> t term (m ())
  89         default traverse_  :: (Trans t term, Foldable f, Applicative p) => t term (a -> p b) -> t term (f a) -> t term (p ())
  90
  91         foldMap    = trans_map2 foldMap
  92         foldr      = trans_map3 foldr
  93         foldr'     = trans_map3 foldr'
  94         foldl      = trans_map3 foldl
  95         foldl'     = trans_map3 foldl'
  96         length     = trans_map1 length
  97         null       = trans_map1 null
  98         minimum    = trans_map1 minimum
  99         maximum    = trans_map1 maximum
 100         elem       = trans_map2 elem
 101         sum        = trans_map1 sum
 102         product    = trans_map1 product
 103         toList     = trans_map1 toList
 104         all        = trans_map2 all
 105         and        = trans_map1 and
 106         any        = trans_map2 any
 107         concat     = trans_map1 concat
 108         concatMap  = trans_map2 concatMap
 109         find       = trans_map2 find
 110         foldlM     = trans_map3 foldlM
 111         foldrM     = trans_map3 foldrM
 112         forM_      = trans_map2 forM_
 113         for_       = trans_map2 for_
 114         mapM_      = trans_map2 mapM_
 115         maximumBy  = trans_map2 maximumBy
 116         minimumBy  = trans_map2 minimumBy
 117         notElem    = trans_map2 notElem
 118         or         = trans_map1 or
 119         sequenceA_ = trans_map1 sequenceA_
 120         sequence_  = trans_map1 sequence_
 121         traverse_  = trans_map2 traverse_
 122
 123 infix 4 `elem`
 124
 125 type instance Sym_of_Iface (Proxy Foldable) = Sym_Foldable
 126 type instance Consts_of_Iface (Proxy Foldable) = Proxy Foldable ': Consts_imported_by Foldable
 127 type instance Consts_imported_by Foldable = '[]
 128
 129 instance Sym_Foldable HostI where
 130         foldMap    = liftM2 Foldable.foldMap
 131         foldr      = liftM3 Foldable.foldr
 132         foldr'     = liftM3 Foldable.foldr'
 133         foldl      = liftM3 Foldable.foldl
 134         foldl'     = liftM3 Foldable.foldl'
 135         null       = liftM  Foldable.null
 136         length     = liftM  Foldable.length
 137         minimum    = liftM  Foldable.minimum
 138         maximum    = liftM  Foldable.maximum
 139         elem       = liftM2 Foldable.elem
 140         sum        = liftM  Foldable.sum
 141         product    = liftM  Foldable.product
 142         toList     = liftM  Foldable.toList
 143         all        = liftM2 Foldable.all
 144         and        = liftM  Foldable.and
 145         any        = liftM2 Foldable.any
 146         concat     = liftM  Foldable.concat
 147         concatMap  = liftM2 Foldable.concatMap
 148         find       = liftM2 Foldable.find
 149         foldlM     = liftM3 Foldable.foldlM
 150         foldrM     = liftM3 Foldable.foldrM
 151         forM_      = liftM2 Foldable.forM_
 152         for_       = liftM2 Foldable.for_
 153         mapM_      = liftM2 Foldable.mapM_
 154         maximumBy  = liftM2 Foldable.maximumBy
 155         minimumBy  = liftM2 Foldable.minimumBy
 156         notElem    = liftM2 Foldable.notElem
 157         or         = liftM  Foldable.or
 158         sequenceA_ = liftM  Foldable.sequenceA_
 159         sequence_  = liftM  Foldable.sequence_
 160         traverse_  = liftM2 Foldable.traverse_
 161 instance Sym_Foldable TextI where
 162         foldMap    = textI2 "foldMap"
 163         foldr      = textI3 "foldr"
 164         foldr'     = textI3 "foldr'"
 165         foldl      = textI3 "foldl"
 166         foldl'     = textI3 "foldl'"
 167         null       = textI1 "null"
 168         length     = textI1 "length"
 169         minimum    = textI1 "minimum"
 170         maximum    = textI1 "maximum"
 171         elem       = textI2 "elem"
 172         sum        = textI1 "sum"
 173         product    = textI1 "product"
 174         toList     = textI1 "toList"
 175         all        = textI2 "all"
 176         and        = textI1 "and"
 177         any        = textI2 "any"
 178         concat     = textI1 "concat"
 179         concatMap  = textI2 "concatMap"
 180         find       = textI2 "find"
 181         foldlM     = textI3 "foldlM"
 182         foldrM     = textI3 "foldrM"
 183         forM_      = textI2 "forM_"
 184         for_       = textI2 "for_"
 185         mapM_      = textI2 "mapM_"
 186         maximumBy  = textI2 "maximumBy"
 187         minimumBy  = textI2 "minimumBy"
 188         notElem    = textI2 "notElem"
 189         or         = textI1 "or"
 190         sequenceA_ = textI1 "sequenceA_"
 191         sequence_  = textI1 "sequence_"
 192         traverse_  = textI2 "traverse_"
 193 instance (Sym_Foldable r1, Sym_Foldable r2) => Sym_Foldable (DupI r1 r2) where
 194         foldMap    = dupI2 (Proxy @Sym_Foldable) foldMap
 195         foldr      = dupI3 (Proxy @Sym_Foldable) foldr
 196         foldr'     = dupI3 (Proxy @Sym_Foldable) foldr'
 197         foldl      = dupI3 (Proxy @Sym_Foldable) foldl
 198         foldl'     = dupI3 (Proxy @Sym_Foldable) foldl'
 199         null       = dupI1 (Proxy @Sym_Foldable) null
 200         length     = dupI1 (Proxy @Sym_Foldable) length
 201         minimum    = dupI1 (Proxy @Sym_Foldable) minimum
 202         maximum    = dupI1 (Proxy @Sym_Foldable) maximum
 203         elem       = dupI2 (Proxy @Sym_Foldable) elem
 204         sum        = dupI1 (Proxy @Sym_Foldable) sum
 205         product    = dupI1 (Proxy @Sym_Foldable) product
 206         toList     = dupI1 (Proxy @Sym_Foldable) toList
 207         all        = dupI2 (Proxy @Sym_Foldable) all
 208         and        = dupI1 (Proxy @Sym_Foldable) and
 209         any        = dupI2 (Proxy @Sym_Foldable) any
 210         concat     = dupI1 (Proxy @Sym_Foldable) concat
 211         concatMap  = dupI2 (Proxy @Sym_Foldable) concatMap
 212         find       = dupI2 (Proxy @Sym_Foldable) find
 213         foldlM     = dupI3 (Proxy @Sym_Foldable) foldlM
 214         foldrM     = dupI3 (Proxy @Sym_Foldable) foldrM
 215         forM_      = dupI2 (Proxy @Sym_Foldable) forM_
 216         for_       = dupI2 (Proxy @Sym_Foldable) for_
 217         mapM_      = dupI2 (Proxy @Sym_Foldable) mapM_
 218         maximumBy  = dupI2 (Proxy @Sym_Foldable) maximumBy
 219         minimumBy  = dupI2 (Proxy @Sym_Foldable) minimumBy
 220         notElem    = dupI2 (Proxy @Sym_Foldable) notElem
 221         or         = dupI1 (Proxy @Sym_Foldable) or
 222         sequenceA_ = dupI1 (Proxy @Sym_Foldable) sequenceA_
 223         sequence_  = dupI1 (Proxy @Sym_Foldable) sequence_
 224         traverse_  = dupI2 (Proxy @Sym_Foldable) traverse_
 225
 226 instance
 227  ( Read_TypeNameR Type_Name cs rs
 228  , Inj_Const cs Foldable
 229  ) => Read_TypeNameR Type_Name cs (Proxy Foldable ': rs) where
 230         read_typenameR _cs (Type_Name "Foldable") k = k (ty @Foldable)
 231         read_typenameR _rs raw k = read_typenameR (Proxy @rs) raw k
 232 instance Show_Const cs => Show_Const (Proxy Foldable ': cs) where
 233         show_const ConstZ{} = "Foldable"
 234         show_const (ConstS c) = show_const c
 235
 236 instance Proj_ConC cs (Proxy Foldable)
 237 data instance TokenT meta (ts::[*]) (Proxy Foldable)
 238  = Token_Term_Foldable_foldMap (EToken meta ts) (EToken meta ts)
 239  | Token_Term_Foldable_foldr   (EToken meta ts) (EToken meta ts) (EToken meta ts)
 240  | Token_Term_Foldable_foldr'  (EToken meta ts) (EToken meta ts) (EToken meta ts)
 241  | Token_Term_Foldable_foldl   (EToken meta ts) (EToken meta ts) (EToken meta ts)
 242  | Token_Term_Foldable_elem    (EToken meta ts) (EToken meta ts)
 243  | Token_Term_Foldable_null    (EToken meta ts)
 244  | Token_Term_Foldable_length  (EToken meta ts)
 245  | Token_Term_Foldable_minimum (EToken meta ts)
 246  | Token_Term_Foldable_maximum (EToken meta ts)
 247  | Token_Term_Foldable_sum     (EToken meta ts)
 248  | Token_Term_Foldable_product (EToken meta ts)
 249  | Token_Term_Foldable_toList  (EToken meta ts)
 250  | Token_Term_Foldable_all     (EToken meta ts) (EToken meta ts)
 251  | Token_Term_Foldable_any     (EToken meta ts) (EToken meta ts)
 252  | Token_Term_Foldable_and     (EToken meta ts)
 253  | Token_Term_Foldable_or      (EToken meta ts)
 254  | Token_Term_Foldable_concat  (EToken meta ts)
 255 deriving instance Eq_Token meta ts => Eq (TokenT meta ts (Proxy Foldable))
 256 deriving instance Show_Token meta ts => Show (TokenT meta ts (Proxy Foldable))
 257 instance -- CompileI
 258  ( Inj_Const (Consts_of_Ifaces is) Foldable
 259  , Inj_Const (Consts_of_Ifaces is) Monoid
 260  , Inj_Const (Consts_of_Ifaces is) (->)
 261  , Inj_Const (Consts_of_Ifaces is) Int
 262  , Inj_Const (Consts_of_Ifaces is) Bool
 263  , Inj_Const (Consts_of_Ifaces is) Eq
 264  , Inj_Const (Consts_of_Ifaces is) Ord
 265  , Inj_Const (Consts_of_Ifaces is) Num
 266  , Inj_Const (Consts_of_Ifaces is) []
 267  , Proj_Con  (Consts_of_Ifaces is)
 268  , Compile is
 269  ) => CompileI is (Proxy Foldable) where
 270         compileI
 271          :: forall meta ctx ret ls rs.
 272          TokenT meta is (Proxy Foldable)
 273          -> CompileT meta ctx ret is ls (Proxy Foldable ': rs)
 274         compileI tok ctx k =
 275                 case tok of
 276                  Token_Term_Foldable_foldMap tok_a2m tok_ta ->
 277                         -- foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
 278                         compileO tok_a2m ctx $ \ty_a2m (TermO a2m) ->
 279                         compileO tok_ta  ctx $ \ty_ta  (TermO ta) ->
 280                         check_type2 (ty @(->)) (At (Just tok_a2m) ty_a2m) $ \Refl ty_a2m_a ty_a2m_m ->
 281                         check_con (At (Just tok_a2m) (ty @Monoid :$ ty_a2m_m)) $ \Con ->
 282                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t ty_ta_a ->
 283                         check_type
 284                          (At (Just tok_a2m) ty_a2m_a)
 285                          (At (Just tok_ta) ty_ta_a) $ \Refl ->
 286                         k ty_a2m_m $ TermO $
 287                          \c -> foldMap (a2m c) (ta c)
 288                  Token_Term_Foldable_foldr   tok_a2b2b tok_b tok_ta -> foldr_from tok_a2b2b tok_b tok_ta foldr
 289                  Token_Term_Foldable_foldr'  tok_a2b2b tok_b tok_ta -> foldr_from tok_a2b2b tok_b tok_ta foldr'
 290                  Token_Term_Foldable_foldl   tok_b2a2b tok_b tok_ta -> foldl_from tok_b2a2b tok_b tok_ta foldl
 291                  Token_Term_Foldable_elem tok_a tok_ta ->
 292                         -- elem :: (Foldable t, Eq a) => a -> t a -> Bool
 293                         compileO tok_a  ctx $ \ty_a  (TermO a) ->
 294                         compileO tok_ta ctx $ \ty_ta (TermO ta) ->
 295                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t ty_ta_a ->
 296                         check_con (At (Just tok_ta) (ty @Eq :$ ty_ta_a)) $ \Con ->
 297                         check_type
 298                          (At (Just tok_a) ty_a)
 299                          (At (Just tok_ta) ty_ta_a) $ \Refl ->
 300                         k (ty @Bool) $ TermO $
 301                          \c -> a c `elem` ta c
 302                  Token_Term_Foldable_null    tok_ta -> ta2ty_from tok_ta null
 303                  Token_Term_Foldable_length  tok_ta -> ta2ty_from tok_ta length
 304                  Token_Term_Foldable_minimum tok_ta -> ta2a_from tok_ta (ty @Ord) minimum
 305                  Token_Term_Foldable_maximum tok_ta -> ta2a_from tok_ta (ty @Ord) maximum
 306                  Token_Term_Foldable_sum     tok_ta -> ta2a_from tok_ta (ty @Num) sum
 307                  Token_Term_Foldable_product tok_ta -> ta2a_from tok_ta (ty @Num) product
 308                  Token_Term_Foldable_toList  tok_ta ->
 309                         -- toList :: Foldable t => t a -> [a]
 310                         compileO tok_ta ctx $ \ty_ta (TermO ta) ->
 311                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t ty_ta_a ->
 312                         k (ty @[] :$ ty_ta_a) $ TermO $
 313                          \c -> toList (ta c)
 314                  Token_Term_Foldable_all tok_a2Bool tok_ta -> allany_from tok_a2Bool tok_ta all
 315                  Token_Term_Foldable_any tok_a2Bool tok_ta -> allany_from tok_a2Bool tok_ta any
 316                  Token_Term_Foldable_and tok_tBool -> andor_from tok_tBool and
 317                  Token_Term_Foldable_or  tok_tBool -> andor_from tok_tBool or
 318                  Token_Term_Foldable_concat tok_tla ->
 319                         -- concat :: Foldable t => t [a] -> [a]
 320                         compileO tok_tla ctx $ \ty_tla (TermO tla) ->
 321                         check_con1 (ty @Foldable) (At (Just tok_tla) ty_tla) $ \Refl Con _ty_tla_t ty_tla_la ->
 322                         check_type1 (ty @[]) (At (Just tok_tla) ty_tla_la) $ \Refl ty_tla_la_a ->
 323                         k (ty @[] :$ ty_tla_la_a) $ TermO $
 324                          \c -> concat (tla c)
 325                 where
 326                 foldr_from tok_a2b2b tok_b tok_ta
 327                  (fold::forall term f a b.
 328                          (Sym_Foldable term, Foldable f)
 329                          => term (a -> b -> b) -> term b -> term (f a) -> term b) =
 330                  -- foldr  :: Foldable t => (a -> b -> b) -> b -> t a -> b
 331                  -- foldr' :: Foldable t => (a -> b -> b) -> b -> t a -> b
 332                         compileO tok_a2b2b ctx $ \ty_a2b2b (TermO a2b2b) ->
 333                         compileO tok_b     ctx $ \ty_b     (TermO b) ->
 334                         compileO tok_ta    ctx $ \ty_ta    (TermO ta) ->
 335                         check_type2 (ty @(->)) (At (Just tok_a2b2b) ty_a2b2b) $ \Refl ty_a2b2b_a ty_a2b2b_b2b ->
 336                         check_type2 (ty @(->)) (At (Just tok_a2b2b) ty_a2b2b_b2b) $ \Refl ty_a2b2b_b2b_b0 ty_a2b2b_b2b_b1 ->
 337                         check_type
 338                          (At (Just tok_a2b2b) ty_a2b2b_b2b_b0)
 339                          (At (Just tok_a2b2b) ty_a2b2b_b2b_b1) $ \Refl ->
 340                         check_type
 341                          (At (Just tok_a2b2b) ty_a2b2b_b2b_b0)
 342                          (At (Just tok_b) ty_b) $ \Refl ->
 343                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t ty_ta_a ->
 344                         check_type
 345                          (At (Just tok_a2b2b) ty_a2b2b_a)
 346                          (At (Just tok_ta) ty_ta_a) $ \Refl ->
 347                         k ty_b $ TermO $
 348                          \c -> fold (a2b2b c) (b c) (ta c)
 349                 foldl_from tok_b2a2b tok_b tok_ta
 350                  (fold::forall term f a b.
 351                          (Sym_Foldable term, Foldable f)
 352                          => term (b -> a -> b) -> term b -> term (f a) -> term b) =
 353                  -- foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
 354                         compileO tok_b2a2b ctx $ \ty_b2a2b (TermO b2a2b) ->
 355                         compileO tok_b     ctx $ \ty_b     (TermO b) ->
 356                         compileO tok_ta    ctx $ \ty_ta    (TermO ta) ->
 357                         check_type2 (ty @(->)) (At (Just tok_b2a2b) ty_b2a2b) $ \Refl ty_b2a2b_b ty_b2a2b_a2b ->
 358                         check_type2 (ty @(->)) (At (Just tok_b2a2b) ty_b2a2b_a2b) $ \Refl ty_b2a2b_a2b_a ty_b2a2b_a2b_b ->
 359                         check_type
 360                          (At (Just tok_b2a2b) ty_b2a2b_b)
 361                          (At (Just tok_b2a2b) ty_b2a2b_a2b_b) $ \Refl ->
 362                         check_type
 363                          (At (Just tok_b2a2b) ty_b2a2b_b)
 364                          (At (Just tok_b) ty_b) $ \Refl ->
 365                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t ty_ta_a ->
 366                         check_type
 367                          (At (Just tok_b2a2b) ty_b2a2b_a2b_a)
 368                          (At (Just tok_ta) ty_ta_a) $ \Refl ->
 369                         k ty_b $ TermO $
 370                          \c -> fold (b2a2b c) (b c) (ta c)
 371                 ta2ty_from
 372                  :: forall typ. Inj_Const (Consts_of_Ifaces is) typ
 373                  => EToken meta is
 374                  -> (forall term t a. (Sym_Foldable term, Foldable t) => term (t a) -> term typ)
 375                  -> Either (Error_Term meta is) ret
 376                 ta2ty_from tok_ta f =
 377                  -- length :: Foldable t => t a -> Int
 378                  -- null   :: Foldable t => t a -> Bool
 379                         compileO tok_ta ctx $ \ty_ta (TermO ta) ->
 380                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t _ty_ta_a ->
 381                         k (TyConst inj_const::Type (Consts_of_Ifaces is) typ) $ TermO $
 382                          \c -> f (ta c)
 383                 ta2a_from
 384                  :: forall con.
 385                     EToken meta is
 386                  -> Type (Consts_of_Ifaces is) con
 387                  -> (forall term t a. (Sym_Foldable term, Foldable t, con a) => term (t a) -> term a)
 388                  -> Either (Error_Term meta is) ret
 389                 ta2a_from tok_ta q f =
 390                  -- minimum :: (Foldable t, Ord a) => t a -> a
 391                  -- maximum :: (Foldable t, Ord a) => t a -> a
 392                  -- sum     :: (Foldable t, Num a) => t a -> a
 393                  -- product :: (Foldable t, Num a) => t a -> a
 394                         compileO tok_ta ctx $ \ty_ta (TermO ta) ->
 395                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t ty_ta_a ->
 396                         check_con (At (Just tok_ta) (q :$ ty_ta_a)) $ \Con ->
 397                         k ty_ta_a $ TermO $
 398                          \c -> f (ta c)
 399                 allany_from tok_a2Bool tok_ta
 400                  (g::forall term f a.
 401                          (Sym_Foldable term, Foldable f)
 402                          => term (a -> Bool) -> term (f a) -> term Bool) =
 403                  -- all :: Foldable t => (a -> Bool) -> t a -> Bool
 404                  -- any :: Foldable t => (a -> Bool) -> t a -> Bool
 405                         compileO tok_a2Bool ctx $ \ty_a2Bool (TermO a2Bool) ->
 406                         compileO tok_ta ctx $ \ty_ta (TermO ta) ->
 407                         check_type2 (ty @(->)) (At (Just tok_a2Bool) ty_a2Bool) $ \Refl ty_a2Bool_a ty_a2Bool_Bool ->
 408                         check_con1 (ty @Foldable) (At (Just tok_ta) ty_ta) $ \Refl Con _ty_ta_t ty_ta_a ->
 409                         check_type
 410                          (At (Just tok_a2Bool) ty_a2Bool_a)
 411                          (At (Just tok_ta) ty_ta_a) $ \Refl ->
 412                         check_type
 413                          (At Nothing (ty @Bool))
 414                          (At (Just tok_a2Bool) ty_a2Bool_Bool) $ \Refl ->
 415                         k (ty @Bool) $ TermO $
 416                          \c -> g (a2Bool c) (ta c)
 417                 andor_from tok_tBool
 418                  (g::forall term f.
 419                          (Sym_Foldable term, Foldable f)
 420                          => term (f Bool) -> term Bool) =
 421                  -- and :: Foldable t => t Bool -> Bool
 422                  -- or  :: Foldable t => t Bool -> Bool
 423                         compileO tok_tBool ctx $ \ty_tBool (TermO tBool) ->
 424                         check_con1 (ty @Foldable) (At (Just tok_tBool) ty_tBool) $ \Refl Con _ty_tBool_t ty_tBool_Bool ->
 425                         check_type
 426                          (At Nothing (ty @Bool))
 427                          (At (Just tok_tBool) ty_tBool_Bool) $ \Refl ->
 428                         k (ty @Bool) $ TermO $
 429                          \c -> g (tBool c)
 430 instance -- TokenizeT
 431  Inj_Token meta ts Foldable =>
 432  TokenizeT meta ts (Proxy Foldable) where
 433         tokenizeT _t = mempty
 434          { tokenizers_infix = tokenizeTMod []
 435                  [ tokenize2 "foldMap" infixN5 Token_Term_Foldable_foldMap
 436                  , tokenize3 "foldr"   infixN5 Token_Term_Foldable_foldr
 437                  , tokenize3 "foldr'"  infixN5 Token_Term_Foldable_foldr'
 438                  , tokenize3 "foldl"   infixN5 Token_Term_Foldable_foldl
 439                  , tokenize2 "elem"    (infixN 4) Token_Term_Foldable_elem
 440                  , tokenize1 "sum"     infixN5 Token_Term_Foldable_sum
 441                  , tokenize1 "product" infixN5 Token_Term_Foldable_product
 442                  , tokenize1 "toList"  infixN5 Token_Term_Foldable_toList
 443                  , tokenize2 "all"     infixN5 Token_Term_Foldable_all
 444                  , tokenize2 "any"     infixN5 Token_Term_Foldable_any
 445                  , tokenize1 "and"     infixN5 Token_Term_Foldable_and
 446                  , tokenize1 "or"      infixN5 Token_Term_Foldable_or
 447                  , tokenize1 "concat"  infixN5 Token_Term_Foldable_concat
 448                  ]
 449          }
 450 instance Gram_Term_AtomsT meta ts (Proxy Foldable) g