symantic/Language/Symantic/Transforming/Trans.hs

   1 module Language.Symantic.Transforming.Trans where
   2
   3 -- |
   4 -- * 'trans' is generally not /surjective/
   5 -- * 'unTrans' is not /injective/
   6 -- * 'unTrans' . 'trans' == 'id'
   7 -- * 'trans' . 'unTrans' /= 'id'
   8 --
   9 -- NOTE: @DefaultSignatures@ can be used
  10 -- when declaring a symantic type class
  11 -- to provide default definition of the methods:
  12 -- implementing their identity transformation
  13 -- in order to avoid boilerplate code
  14 -- when writting 'Trans' instances which
  15 -- do not need to alterate those methods.
  16 class Trans tr where
  17         -- | Return the underlying @tr@ of the transformer.
  18         type UnT tr :: * -> *
  19
  20         -- | Lift a tr to the transformer's.
  21         trans :: UnT tr a -> tr a
  22         -- | Unlift a tr from the transformer's.
  23         unTrans :: tr a -> UnT tr a
  24
  25         -- | Identity transformation for a unary symantic method.
  26         trans1 :: (UnT tr a -> UnT tr b) -> (tr a -> tr b)
  27         trans1 f = trans . f . unTrans
  28
  29         -- | Identity transformation for a binary symantic method.
  30         trans2
  31          :: (UnT tr a -> UnT tr b -> UnT tr c)
  32          -> (tr a -> tr b -> tr c)
  33         trans2 f t1 t2 = trans $ f (unTrans t1) (unTrans t2)
  34
  35         -- | Identity transformation for a ternary symantic method.
  36         trans3
  37          :: (UnT tr a -> UnT tr b -> UnT tr c -> UnT tr d)
  38          -> (tr a -> tr b -> tr c -> tr d)
  39         trans3 f t1 t2 t3 = trans $ f (unTrans t1) (unTrans t2) (unTrans t3)